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Corporate Finance – (Real) Option Pricing
Prof. Dr. Christoph Kaserer
Chair for Financial Management
and Capital Markets
Technische Universität München
Arcisstr. 21
D-80290 München
Tel.:
+49 89 / 289 - 25489
Fax:
+49 89 / 289 - 25488
Mail:
christoph.kaserer@tum.de
URL:
www.fm.wi.tum.de
1
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Agenda “Real option pricing"
Repetition of basic option pricing models to options
Application 1: Equity as call option (Merton 1974)
Application 2: Real option analysis
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | (Real) Option Pricing
2
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
What is a Financial Option?
Option = Right to buy/sell an asset in the future at some predetermined price
Call / Put option
Underlying
Strike or exercise price X
Expiration date
Option to buy / sell
Asset which can be bought or sold
Price at which underlying can be bought or sold
Date the option matures
Some important distinctions
Option price
Price of underling S
Exercise value
Market price of the option contract
Market price of underlying asset in contract
Option value if exercised today = Max(0, Current S - X)
American option
European option
Exercise possible any time until expiration
Exercise possible at expiration only
In-the-money call
Out-of-the-money call
At-the-money call
Call where currently strike X < S
Call where currently strike X > S
Call where currently strike X ≈ S
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | (Real) Option Pricing
3
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
How do options work in principle?
Graphical representation of option pay-offs
Profit
Profit
X
Calls
Buy a call
ST
X
Profit
ST
Sell a call
Profit
Sell a put
Puts
X
ST
X
ST
Buy a put
Note: X = strike price, ST = Stock price,
= long in leveraged stock,
= short in deleveraged stock
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | (Real) Option Pricing
4
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Put-Call-Parity
Consider a portfolio consisting of
• One stock S
• One put P with strike X
• One sold/written call C with strike X
Portfolio value today is S0 + P0 - C0
Portfolio value at maturity (T) is
Stock
Put
Call
Portfolio
if S < X
if S > X
S
X-S
0
S + (X-S) – 0 = X
S
0
(S - X)
S + 0 – (S – X) = X
Therefore, in order to exclude arbitrage opportunities it must hold:
S + P −C =
X
(1+ rf )T
with risk-free zero-bond
B of value PV(X)
S-B=C-P
C-P corresponds to leveraged stock position
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | (Real) Option Pricing
5
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Binomial model assumes stock price can move up or down
One-step Binomial Model: Set-up (I/II)
Specific assumptions of the binomial model
• Stock price S follows multiplicative binomial process
- Two possible states of the world in each time step
• Trading occurs only at discrete times
Consider the following examplve
• S = $20
= Stock Price
• X = $21
= Exercise Price
• q = 0.9
= Objective probability, that stock will move upward
• u = 1.2
= multiplicative upward movement in the stock price
• d = 0.67
= multiplicative downward movement in the stock price
• rf = 10%
= risk -free rate p.a.
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | (Real) Option Pricing
6
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Stock price and call payoff can be determined in a simple way
One-step Binomial Model: Set-up (II/II)
A one-period binomial process for S:
uS = $24.00
q
$20=S
1-q
dS = $13.40
Payoffs for a one-period call option:
c u = MAX [0, us - X ] = $3
q
c
1-q
c d = MAX [0, ds - X ] = $0
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | (Real) Option Pricing
7
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Pricing method constructs risk-free arbitrage portfolio
One-step binomial model: Pricing (I/II)
Basic idea: Construct risk-free hedge portfolio, composed of
• one share of stock S
• m shares of call option on the stock S
The payoffs for this hedge portfolio are
constructs risk-free arbitrage portfolio q
uS - mc u
S-mc
1-q
dS - mc d
For portfolio to be risk-free, end-of-period payoffs must be equal in each state
uS - mc u = dS - mc d
m is number of options needed for hedge (hedging ratio)
m=
uS - dS
cu - cd
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | (Real) Option Pricing
8
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Call pricing equation can be determined
One-Step Binomial Model: Pricing (II/II)
Because hedge portfolio is constructed to be risk-less it must hold
(1 + r )(S - mc ) = uS - mc
f
Ûc=
u
S[(1 + rf ) - u ] + mc u
m(1 + rf )
Substituting the hedge ratio m into this pricing equation yields
é æ (1 + rf ) - d ö
æ u - (1 + rf ) öù
c = êc u ç
÷ + cd ç
÷ ÷ (1 + rf )
è u - d øúû
ë è u -d ø
Defining
=p
=(1 - p) as risk-neutral probabilities,
gives a simplified formula for the value of the call c
c=
pcu + (1 - p )cd
1 + rf
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | (Real) Option Pricing
9
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Pricing equation is simplified by introducing risk-neutral probabilities
One-Step Binomial Model: Example
Solving for the hedge ratio m gives the number of call options to be written against the stock
m=
S (u - d ) $20(1.2 - .67)
=
= 3.53
cu - cd
$3 - $0
And a value of the put p and call c
p=
c=
(1 + r f ) - d
u-d
=
(1 + 0.1) - 0.67
= 0.81
1.2 - 0.67
pcu + (1 - p )cd
0.81 ´ 3 + (1 - 0.81) ´ 0
=
= 2.21
1 + rf
1 + 0.1
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | (Real) Option Pricing
10
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
One-step binomial model can be easily extended to several periods
Two-Step Binomial Model: Setting (I/II)
Stock prices with a two-period binomial
process
• Recombining binomial tree
• S=$20, u=1.2, d=0.67 as before
q
uS=$24.00
q²
u²S=$28.80
q(1-q)
udS=$16.08
S=$20
1-q
dS=$13.40
q(1-q)
(1-q)²
d²S=$8.98
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | (Real) Option Pricing
11
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Call payoffs determined in analogue to one-step model
Two-Step Binomial Model: Setting (II/II)
• Assume option is European
• Two-period binomial European call payoffs are
- Strike X=$21
q²
q
cu
cuu=MAX[0,u²S-X]=$7.80
q(1-q)
c
cud =cdu =MAX[0,udS-X]=$0
1-q
cd
q(1-q)
(1-q)²
cdd =MAX[0,d²S-X]=$0
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | (Real) Option Pricing
12
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Price of the call is determined recursively
Two-step binomial model: Pricing (I/II)
Solving for the option values in period 1 cu and cd
c u = [pc uu + (1 - p )c ud ] ÷ (1 + rf )
c d = [pc du + (1 - p )c dd ] ÷ (1 + rf )
The present value of the call c is given by
c = [pc u + (1 - p )c d ] ÷ (1 + rf )
2
(
c = [ p 2c uu + 2 p(1 − p)c ud + (1 − p) c dd ] ÷ 1+ rf
)
2
€
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | (Real) Option Pricing
13
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Call price formula by substituting second step result in first step
Two-Step Binomial Model: Pricing (II/II)
Substituting the values of cu and cd
2
(
c = [ p 2c uu + 2 p(1 − p)c ud + (1 − p) pc dd ] ÷ 1+ rf
Where
€
€
)
2
c uu = MAX [0,u 2 S − X ]
c ud = c du = MAX [0,udS − X ]
c dd = MAX [0,d 2 S − X ]
For the numerical example given above we get
€
€
2
(
c = [ p 2c uu + 2 p(1 − p)c ud + (1 − p) c dd ] ÷ 1+ rf
2
2
)
2
= [(.8113) $7.80 + 2(.8113)(.1887)$0 + (.1887) $0] ÷1.12 = $4.2430
€
€
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | (Real) Option Pricing
14
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Black-Scholes Option Pricing Formula as generalization in cont. time
Black-Scholes Option Pricing Model
Assumptions
• Stock price moves randomly in continuous time
- Stock price modeled as geometric Brownian motion
(return normally distributed, constant volatility)
• No dividends
• No market frictions: No arbitrage opportunities, no transaction costs,
constant interest rate, no short-sale restrictions
Then: Continuous-time option pricing formula for a European call
Fischer Black
1938-1995
Myron Scholes
Nobel prize '97
(with R. Merton),
Founder of LTCM
c = S × N (d1 ) - X × e - rf T × N (d 2 )
ln(S / X ) + rrT 1
d 2 = d1 - s T
+ s T
2
s T
Note, BSM is equivalent to Binomial model, if a large number of steps is used and the
following holds: u = es DT
where
d1 =
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | (Real) Option Pricing
15
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Black-Scholes Option Pricing Model
Example (I/II)
What is the value of the following Call Option according to the BlackScholes Model?
-
S = $50 = Stock Price
X = $45 = Exercise Price
rf = 0.06 = annual risk-free rate
T = 0.25 = Time to maturity (in years)
σ2 = 0.2 = Return Variance (per year)
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | (Real) Option Pricing
16
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
The Black-Scholes Option Pricing Model
Example (II/II)
Substituting the values of the parameters into d1 we get
d1 =
ln(50 / 45) + 0.06 × 0.25 1
+ × 0.2 × 0.25 = 0.65
2
0.2 × 0.25
Using this result we can solve for d2
d 2 = 0.65 - 0.2 × 0.25 = 0.4264
The values N(.) from a normal distribution table are1
N (d1 ) = N (0.65) = 0.5 + 0.242 = 0.742
N (d 2 ) = N (0.4264) = 0.5 + 0.1652 = 0.6651
Using these result the value of the call option turns out to be:
c = 50 × 0.742 - 45 × e -0.06×0.25 × 0.6651 = 37.10 - 29.48 = $7.62
1) Attention: Two types of normal distribution tables exist. One provides one-sided values ("+0.5"), one provides two-sided values.
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | (Real) Option Pricing
17
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Agenda “Real option pricing"
Repetition of basic option pricing models to options
Application 1: Equity as call option (Merton 1974)
Application 2: Real option analysis
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | (Real) Option Pricing
18
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Equity is call option on market value of firm with debt value as strike
Merton (1974): Equity can be seen as a Call Option on firm value (I/II)
Setting
• Firm with firm value V
- Consisting of risky equity S and debt
• Debt is zero coupon bond
- With face value D and maturity in T years from now
• Debt is secured by assets of firm
• Firm pays no dividends
Value of equity S at maturity T is given by
S = MAX [0, V - D ]
• At maturity T, equity holders get value of the firm V in excess of debt value D
• If V < D, the firm will default
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | (Real) Option Pricing
19
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Equity payoff diagram same as call option diagram
Merton (1974): Equity can be seen as a Call Option (II/II)
Price
Firm Value
Debt value at
maturity
30
25
20
15
10
5
Equity value at
debt maturity
5
10
15
20
25
30
35
Default
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | (Real) Option Pricing
40
45
50
Firm Value
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Example: Equity and debt value calculated in option pricing framework
Assumptions
Firm value V is € 5 m
Firm has zero-bond D with principle € 4 m with maturity 10 years
Continuous risk free interest rate r = 2%
Firms asset variance is 25%
Firm pays no dividends
What is the value of the firm's equity and firm’s debt?
S = V × N ( d1 ) - D × e
d1 =
- rf T
× N (d 2 )
ln(V / D ) + rrT 1
+ s T
s T
2
d 2 = d1 - s T
!" = 0.9305; !* = 0.1400;
- !" = 0.8240; - !* = 0.5557;
1 = 2.300; 2 = 2.700;
345 =
67
4
− 1 = 4.01%;
2.700
4 : 0.5557 + 4 : <<= 1 − 0.5557 = 2.7 : > ?.?*:"? ;
→ <<= = 60.49%
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | (Real) Option Pricing
21
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Agenda “Real option pricing"
Repetition of basic option pricing models to options
Application 1: Equity as call option (Merton 1974)
Application 2: Real option analysis
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | (Real) Option Pricing
22
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Reminder NPV-Method
The net present value (NPV) rule states: Project should be accepted if it
increases shareholders wealth
E ( FCFt )
>0
t
t =1 (1 + WACC )
N
NPV = - I 0 + å
where
I0 = initial investment
FCFt = Free cash flow in period t
WACC = Weighted average cost of capital
N = Number of years of the project
Implicit assumption: Pre-commitment to a deterministic course of action
• NPV-method not suitable for flexible, multi-period decision making under uncertainty
• Real option explicitly model this flexibility
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | (Real) Option Pricing
23
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
First Example: The Gas Turbine Power Station
Operating
Mode
Stand-by
Mode
Abandon
The flexibility in this project is reflected in three
options (two switching options plus an abandonment
option). Note that the value of these options depends
on the switching strategy pursued.
Example: assume the average electricity price to
be €30/MWh and the operating cost of the
GTPS to be €27/MWh. With 400MW capacity
and 8,766 operating hours per year, you would
have earned a net profit of 400MW · €3/MWh ·
8,766h = €10.5 mn.
Taking into account that the GTPS can change
into stand-by modus (Flexibility) makes this
calculation widely incorrect. To simplify assume
that you can only shut down once a week and
without cost. Assume over 30 weeks the
electricity price is above €27/MWh. The average
price in these weeks is €34/MWh. If you had
operated only during these weeks, total
operating hours would be 30 · 24 · 7 = 5,040
hours. Hence, you would have earned 400MW ·
€7/MWh · 5,040h = €14.1 mn.
Ignoring the real option to shut down and reopen
would not have been a forgivable valuation
mistake!
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | (Real) Option Pricing
24
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Many corporate decisions alternatives can be modeled as real options
Types of Real Options
Expansion option: Growth option on an underlying asset that assumes precommitment
of a series of investments to growing demand over time
• American call with 'cost of expandable investment' as exercise price and 'multiple of the
value of the underlying risky asset' as option value
Contraction option: Option to receive cash for partially giving up the use of asset
• American put with present value of cash as exercise price and fraction of the value of
operations given up as value of the underlying
Abandonment option: Right to sell an asset for given price, which can change through
time rather than continuing to hold it (American put)
Extension option: Allows manager to pay a cost for the ability to extend the life of a
project (European call with cost of extension as exercise price)
Deferral option: Right to defer the start of a project (American call)
Switching option: Right to turn a project on and off
Compound options: Options on options
• Many corporate investment decisions, as equity can be regarded as an option on firm
value
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | (Real) Option Pricing
25
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Second Example: Decision-Tree Analysis (I)
• Assume United Studios holds the movie rights for a national best-seller and
an option to produce a sequel based on the same book.
• It believes that shooting both movies simultaneously (in t=0) could be
produced for a total budget of $500 million.
• If instead the movies are produced sequentially, the total expected cost will
be $575 million, where the production of the first movie costs $350 million.
• The present value of expected earnings for the first movie in t=1 are $450
million, the cost of capital applied to stand-alone movie projects is 15%.
• The present value of expected earnings in t=1 are $628.7 million, if both
movies are produced.
• In a regular NPV analysis the company would choose simultaneous
production as this maximizes the NPV.
628.7
− 500 = $46.701
1.15
• Note, that producing only the first movie would lead to an NPV of $41.3
million.
NPV =
Chair for Financial Management and Capital Markets– Prof. Dr. Christoph Kaserer
(Slides based on Berk/deMarzo, Corporate Finance)
26
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Example: Decision-Tree Analysis (II)
• United Studios, however, knows that the probability for a sequel to become a
blockbuster strongly depends on whether the first movie was one.
• Specifically, the company believes that there is a 50% probability for the first
movie to be a blockbuster. In this case the PV of earnings in t=1 is 600.
Otherwise the earnings would only be 300.
• In case the first movie is a blockbuster, there is a 75% probability that the
sequel will also be one. In this case the PV of earnings in t=1 (relative to the
sequel) is 400, otherwise earnings would only be 11. In case the first movie
is a flop, the probability that the sequel will also be a flop is 75%.
• The stand alone production of the first movie in t=0 has a cost of $350
million; continuing with the production of the sequel in t=1 has a cost of
$258.75 million.
• How would the decision of United Studios look like?
Chair for Financial Management and Capital Markets– Prof. Dr. Christoph Kaserer
(Slides based on Berk/deMarzo, Corporate Finance)
27
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Example: Decision-Tree Analysis (III)
50
%
S
BB
N
600258,75
600
%
400
%
11
75
25
-350
N
50
%
Flop
S
300
300278,75
25
75
%
%
400
11
S = United decides to produce the sequel
N = United decides not to produce the sequel
Chair for Financial Management and Capital Markets– Prof. Dr. Christoph Kaserer
(Slides based on Berk/deMarzo, Corporate Finance)
28
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Example: Decision-Tree Analysis (IV)
• Based on the resolution of uncertainty shown in the tree on the slide
before, United can define four different conditional strategies.
1.If the first movie is a BB, produce the sequel, and if it is a flop, do not produce the
sequel
2.Produce the sequel in any case
3.Produce the sequel under no circumstance
4.If the first movie is a BB, do not produce the sequel, and if it is a flop, produce the
sequel
• The NPVs of these four strategies can be calculated as follows:
,--./01.203-.2045--3-./0466
7-+ 0.5
= $9:;<
6.60
6.60
,--./01.203-.2045--3-./0466
7--./01.203-./045--3-.20466
0.5
+ 0.5
6.60
6.60
1. #$% = −350 + 0.5
2. #$% = −350 +
− $5=>
,-7-3. #$% = −350 + 0.5
+ 0.5
= $41=>
4. #$% = −350 +
6.60
,-0.5
+
6.60
6.60
7--./01.203-./045--3-.20466
0.5
6.60
=
= −$24=>
Chair for Financial Management and Capital Markets– Prof. Dr. Christoph Kaserer
(Slides based on Berk/deMarzo, Corporate Finance)
29
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Decision-Tree Analysis (DTA)
•
•
•
•
•
•
•
The example shows that the pre commitment implicitly assumed in
the NPV-method ignores the value of flexibility.
In this case, the value of flexibility is 60-46.7=$13.3 million.
Effectively, the company had an extension as well as an
abandonment option, which was ignored in the NPV calculation in
the first place.
Companies can increase their value by flexibly adjusting to new
information revealed on the market.
This is especially important in the context of innovations as
uncertainty is much larger than on mature markets.
Moreover, intangible assets (like IP-rights) often have a build-in
optionality.
Typical examples: R&D-intensive projects (pharmaceuticals,
biotech, etc.), where the investment decision depends on the
achievement of specific milestones.
Chair for Financial Management and Capital Markets– Prof. Dr. Christoph Kaserer
(Slides based on Berk/deMarzo, Corporate Finance)
30
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Decision-Tree Analysis vs. Real Options
• In the example before we used objective probabilities and the
company’s WACC for calculating the conditional NPVs.
• This is, however, wrong, as the exploitation of flexibility
changes the risk profile of a firm. Therefore, branchdependent WACCs have to be used. However, it is often very
hard (impossible?) to estimate them.
• Alternatively, risk-neutral valuation methods could be applied.
If risk-neutral probabilities are used, discounting could be
done with the risk-free rate and, hence, WACC estimation is
not a problem anymore.
• This risk-neutral approach is called the Real Option Approach
(ROA). The value of flexibility is then calculated with option
pricing models.
Chair for Financial Management and Capital Markets– Prof. Dr. Christoph Kaserer
(Slides based on Berk/deMarzo, Corporate Finance)
31
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Example: Real Option Analysis (I)
• EXOIL is an oil company considering a greenfield investment in a new
oilfield. The following information is given.
• The oilfield is assumed to have total reserves of 2 million barrel.
• The current price for comparable crude oil is $62.5/bbl.
• The necessary investment for starting oil drilling is $90 million. The cost for
buying the drilling rights from the competent authorities is $15 million (onetime payment). These right expire without any compensation, if the EXOIL
does not start with drilling after two years, at the latest.
• To simplify, we assume that stock markets are valuing oil drilling companies
at 80 percent of the market value of its in-ground reserves.
• The oil price is assumed to follow a binomial distribution with u=1.2 and
d=0.8. The risk-free rate is 0%. The physical probability of the oil price to
increase is assumed to be q=0.75.
ü Would the company buy the drilling right on the basis of a pure mNPVanalysis?
ü What if the company does a real option analysis? In this case use a binomial
model with one year corresponding to one binomial step.
Chair for Financial Management and Capital Markets– Prof. Dr. Christoph Kaserer
(Slides based on Berk/deMarzo, Corporate Finance)
32
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Example: Real Option Analysis (II)
Binomial tree for the market value of the drilling company
• Recombining binomial tree
• Oil drilling right is like a call option
with an exercise price of $90 million
• Risk-neutral probability: p=0.5
q
S=$100mn
C=$16.5mn
1-q
uS=$120mn
Cu=$30mn
dS=$80mn
Cd=$3mn
q²
u²S=$144mn
Cuu=$54mn
q(1-q)
q(1-q)
(1-q)²
udS=$96mn
Cud=$6mn
d²S=$64mn
Cdd=0
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | (Real) Option Pricing
33
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Example: Real Option Analysis (III)
ü The NPV of the project is negative as the price of the drilling right plus the
investment cost is larger than the market value of the asset (NPV=100-105=$5 million).
ü However, taking into account the flexibility of the drilling right (i.e. investment
decision can be postponed for two years) things change. The value of the oil
drilling company including the drilling right expiring in two years is $116.5
million. Hence, taking flexibility into account it follows NPV=116.5-105=$11.5
million.
• What if the drilling right would have a cost of $30 million?
ü In this case the NPV of the projects remains negative, even if flexibility is
taken into account: NPV=116.5-120=-$3.5 million.
Chair for Financial Management and Capital Markets– Prof. Dr. Christoph Kaserer
(Slides based on Berk/deMarzo, Corporate Finance)
34
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Analysing the EXOIL decision using DTA (I)
ü In a DTA the value of the drilling right would be derived by using the physical
probability of an upward movement of the oil price and discounting the future
asset values with the WACC of EXOIL.
ü Note that the following relationship must hold on an efficient market for the
asset values of any firm:
$!% + (1 − $)!+
!" =
1 + ,-..
ü This relationship can be re-written as
1 + ,-.. = $ / 0 + (1 − $) / 1
or
$=
1 + ,-.. − 1
0−1
Chair for Financial Management and Capital Markets– Prof. Dr. Christoph Kaserer
(Slides based on Berk/deMarzo, Corporate Finance)
35
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Analysing the EXOIL decision using DTA (II)
ü Assuming WACC=10% it follows q=0.75.
ü Doing now a DTA the value of the drilling right turns out to be $26.96 million.
ü Hence, the value of the oil drilling company including the drilling right
expiring in two years according to DTA is $126.96 million, which is
significantly more than the $116.5 million derived under ROA.
ü One can easily see that this might change the decision. In case the price of
the drilling right is $30 million, the company would not do the investment, if it
is basing the decision on ROA, but it would do the decision, if it uses DTA.
ü Economically spoken DTA is wrong, because it uses the same WACC for
valuing a company with and without flexibility. But flexibility changes the risk
profile, therefore the WACC has to be adjusted.
ü In our example the company with the drilling right is a portfolio of an
underlying asset (oil reserves) and a call option (decision to drill). The
expected return of such a portfolio by definition is different than the expected
return of the underlying asset only.
Chair for Financial Management and Capital Markets– Prof. Dr. Christoph Kaserer
(Slides based on Berk/deMarzo, Corporate Finance)
36
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Difference to decision tree is branch-dependent discount rate
Comparison real options with decision trees
•
Note, decision tree approach (DTA) adjusts discount rate for risk (by using the WACC)
and uses physical probabilities
•
Real options approach (ROA) discounts with risk-free discount rate and adjusts
probabilities for risk by using the risk-neutral probability
•
Note, call value formula can be modified to
pCu (1 - p )Cd
qCu
(1 - q )Cd
qCu
(1 - q )Cd
+
=
+
=
+
1 + rf
1 + rf
(1 + rf ) q (1 + rf ) (1 - q ) (1 + ru ) (1 + rd )
(1 - p )
p
Decision tree method uses single discount rate for both branches
real option approach implicitly uses branch-dependent discount rates (ru and rd)
C=
•
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | (Real) Option Pricing
37
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Comparing NPV with decision trees and real options
+
NPV method
Decision tree method
Simple to
implement
+
Incorporates
flexibility
-
+
+
NP
V
-
Real option method
+
No flexibility after
investment decision
Underestimates the
value of a project
-
Incorporates
flexiblity
Arbitrage-free
valuation
Valuation is not based
on physical probability
Does not obey to
the law of one price
A constant WACC is
assumed
Physical probabilities?
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | (Real) Option Pricing
38
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
DTA or ROA?
1. In principle ROA is always the better choice as it is the only consistent(arbitrage
free) approach to value flexibility.
2. Problem: there must be an observable market price for the project without
flexibility. This is often not the case (think about innovations, which are not yet
traded by definition).
3. In such case the only solution is to use DTA, even though one has to be aware
of all the problems associated with this method. But most likely it is better to
accept this problem rather to ignore flexibility at all.
4. In practice, must approaches labelled as real options, in reality, are a DTA.
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | (Real) Option Pricing
39
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Staging Investments is a Real Option
• Companies often have to stage investment tranches, because of
technological or capacity reasons. This is a typical problem in R&D
investments.
• By doing so real options are realized (deferral, abandonment, expansion,
etc.).
• Of course, there is also a downside, for instance because there is a loss in
the time value of money of future cash flows. Moreover, it could also be that
future investments become more expensive or that a competitive advantage
is lost.
• However, staging give additional flexibility leading to a potential additional
value.
• The company has to find a way to maximize this value.
Chair for Financial Management and Capital Markets– Prof. Dr. Christoph Kaserer
(Slides based on Berk/deMarzo, Corporate Finance)
40
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Example: Staging Investments (I)
• Eclectic motors is developing a new electric car.
• To be successful they have to overcome three technological hurdles:
ü Developing lighter material in order to reduce the weight of the car
ü Developing a rapidly recharging battery
ü Increase the storage capacity of the battery without increasing weight
• The project will only be successful, if all three hurdles are passed. If
development is successful, the NPV (excluding the development costs) of
the project is $4.4 billion.
• The development costs and time frames for each stage as well as its
success probabilities are given in the following table. Note, that success
probabilities in each stage are independent from the outcome of the other
stages.
• The WACC of the company is 6%
ü In which order should the company stage the investments?
ü What is the maximum NPV the company can achieve by optimally staging
the investments?
Chair for Financial Management and Capital Markets– Prof. Dr. Christoph Kaserer
(Slides based on Berk/deMarzo, Corporate Finance)
41
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Example: Staging Investments (II)
Technology
Cost
Time
Probability of success
Materials (M)
$100 million
1 year
50%
Recharger (R)
$400 million
1 year
50%
Battery (B)
$100 million
4 years
25%
• The NPV of doing the stages simultaneously would be
!"# = −100 − 500 ) 1.06,- + 0.5 ) 0.5 ) 0.25 ) 4.400 ) 1.06,1 = −302
• However, this is not an optimal way to proceed, as the company could
postpone the investment in a new development stage until it knows whether
the preceding development investment was successful.
• The question is then, how the company should optimally stage the
investments.
Chair for Financial Management and Capital Markets– Prof. Dr. Christoph Kaserer
(Slides based on Berk/deMarzo, Corporate Finance)
42
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Example: Staging Investments (III)
• In this example the problem could be solved by brute force. There are 3!=6
ways to order the three investment stages.
• Lets start with the ordering BMR. The NPV can then be calculated as
follows:
!"#(%&') = −100 + 0.25 1 1.0634 −100 + 0.50 1 1.0635 −400 + 0.50 1 4,400 1 1.0635
= 37
• BMR is the optimal ordering as the NPVs for the other alternatives are:
!"#(%'&) = −100 + 0.25 1 1.0634 −400 + 0.50 1 1.0635 −100 + 0.50 1 4,400 1 1.0635
=5
!"# &'% = −100 + 0.50 1 1.0635 −400 + 0.50 1 1.0635 −100 + 0.25 1 4,400 1 1.0634
= −117
!"# &%' = −100 + 0.50 1 1.0635 −100 + 0.25 1 1.0634 −400 + 0.50 1 4,400 1 1.0635
=9
!"# '&% = −400 + 0.50 1 1.0635 −100 + 0.50 1 1.0635 −100 + 0.25 1 4,400 1 1.0634
= −276
!"# '%& = −400 + 0.50 1 1.0635 −100 + 0.25 1 1.0634 −100 + 0.50 1 4,400 1 1.0635
= −262
Chair for Financial Management and Capital Markets– Prof. Dr. Christoph Kaserer
(Slides based on Berk/deMarzo, Corporate Finance)
43
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
A General Rule for Staging Investments (I)
• Intuitively we have seen in the example before that it is not a good
idea to start with the most expensive stage.
• Intuitively we can also infer that it is better to start with the most risky
(least successful) investment stage, as the outcome of this stage is
most informative regarding the overall viability of the project.
• Finally, starting with the most lengthy project tends to be an
advantage as the PV of the investments for the succeeding stages is
smaller (provided that there is no cost of postponing, which is not so
clear, for instance because of inflation).
• In general, it seems to be beneficial to invest in less capital intensive,
riskier and lengthier projects first.
Chair for Financial Management and Capital Markets– Prof. Dr. Christoph Kaserer
(Slides based on Berk/deMarzo, Corporate Finance)
44
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
A General Rule for Staging Investments (II)
• Typically it will be impossible to monotonically order the projects according
to the three criteria mentioned before.
• Therefore, we are looking for an ordering taking all three dimensions into
account. This is fulfilled by the following failure cost criteria:
1 − #$(&'(()&&)
#$(+,-)&./),.)
• PV(success) is the expected marginal present value contribution of $1
revenue (which will only be generated, if the overall project is successful).
• PV(investment) is the present value of the necessary investment for the
specific stage.
• Note that this rule is similar to the profitability index, which was defined as
NPV/Investment.
• The approach can be used in a ROA or DTA setting.
Chair for Financial Management and Capital Markets– Prof. Dr. Christoph Kaserer
(Slides based on Berk/deMarzo, Corporate Finance)
45
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Example: Staging Investments (IV)
• Using the failure cost index the ordering is exactly as we have determined it
according to our brute force approach, i.e. BMR:
• This can be checked by calculating the failure cost index for all three stages:
#.%
Materials:
!"&.#'
!((
Recharger:
Battery:
!"
!"
#.%
&.#'
.((
#.1%
&.#'2
!((
= 0.00528
= 0.00132
= 0.00802
• By starting with the stage with the highest failure cost index and finishing
with the project with the lowest one the ordering BMR results.
• Of course, in reality it might be difficult to get all the relevant parameters, so
that companies are often using more simple rules of thumb.
Chair for Financial Management and Capital Markets– Prof. Dr. Christoph Kaserer
(Slides based on Berk/deMarzo, Corporate Finance)
46
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
To recognize real options look for flexibility and future rights
Aristoteles accounts in 'Politica' of Thales of Miletos
"He was reproached for his poverty, which was supposed to show that
philosophy was of no use. [...] He knew by his skill in the stars while it was yet
winter that there would be a great harvest of olives in the coming year; so,
having a little money, he gave deposits for the use of all the olive-presses in
Chios and Miletus, which he hired at a low price because no one bid against
him. When the harvest-time came, and many were wanted all at once and of a
sudden, he let them out at any rate which he pleased, and made a quantity of
money. Thus he showed the world that philosophers can easily be rich if they
like, but that their ambition is of another sort."
Thales von Miletos
(624-546 B.C.)
Usual structure of real options (here: European call)
• Exercise price = investment required (here: normal rental)
• Maturity = duration of right (here: time to harvest)
• Underlying = PV of project without flexibility (here: rental rate)
Source: Aristoteles (350 B.C.) Politica
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | (Real) Option Pricing
47
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Lessons learned "Real options"
• Binomial option pricing model
• Closed-form pricing with Black-Scholes formula
• Assumptions: continuous time, stock price as geometric Brownian motion,
no frictions
• Application of formula
• Equity can be modeled as a call option on the asset value of a firm
• Real options can be found in many corporate decisions
• Capture flexibility of decision in response to arrival of new information
- Flexibility contrasts with precommittment in NPV-model
- Difference to decision tree is branch-dependent discount rate
• Types: expansion, contraction, abandonment, extension, deferral,
compound
• Real options can be priced using option pricing techniques
• Real option analysis does not depend on subjective probabilities, as decision
tree analysis does, but model assumptions (incl. MAD) must be obeyed.
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | (Real) Option Pricing
48
Corporate Finance – Capital Structure
Prof. Dr. Christoph Kaserer
Chair for Financial Management
and Capital Markets
Technische Universität München
Arcisstr. 21
D-80290 München
Tel.:
+49 89 / 289 - 25489
Fax:
+49 89 / 289 - 25488
Mail:
christoph.kaserer@tum.de
URL:
www.fm.wi.tum.de
1
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Schedule Capital Structure
Introduction
Modigliani, Miller (1961): Perfect capital markets
Trade-off theory: Taxes and bankruptcy cost
Pecking-order theory: Signaling
Free cash flow theory: Agency cost
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Capital Structure
2
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
What makes debt and equity different?
Financing types
Mechanics/Waterfalls
Liabilities
Equity
Common stock
Preferred stock
Debt
Subordinated debt
Ordinary debt
Secured debt
high
Mezzanine
financing
Control
rights
low
low
Priority
of being
served
(seniority)
high
high
Risk
and
return
low
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Capital Structure
3
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
How is capital structure correctly measured?
Market and
Book
debt ratios
Debt/
EBITDA
ratios
As a similar
measure the
ICR=EBIT/Int.Exp.
is often used.
Source: Damodaran’s Homepage
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Capital Structure
4
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Capital structure varies between countries and over time
Equity Ratios of Non-Financial Listed Companies
[1992-2013]
Equity Ratios of EU15 Companies
[2000-2012]
Belgium
Germany
+9%
USA
Europe
Germany
France
+44%
44
40
43
2000-02
2005-07
+21%
34
31
24
Italy
+19%
32
34
2005-07
2010-12
28
20
19
2000-02
2005-07
24
+4%
53
+13%
55
40
+39%
45
44
2010-12
31
2000-02
2005-07
2010-12
Austria
Portugal
+29%
1992-2002
2003-2013
1992-2002
2003-2013
1992-2002
26
30
2000-02
2005-07
2000-02
Spain
+37%
34
32
37
2010-12
+16%
43
39
39
2000-02
2005-07
45
2003-2013
2010-12
2000-02
2005-07
2010-12
2010-12
Source: Thomson/Reuters, BACH, own calculations
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Capital Structure
5
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Business risk is a major driver for the capital structure
R&D expenditures and equity ratios
of German listed manufacturing
companies (2008)
Debt ratios in %
Business risk and equity ratios of
German listed manufacturing
companies (2006)
Source: CEFS, Thomson Financial
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Capital Structure
6
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Large scale empirical analysis
Frank, Goyal (1999): Capital Structure Decisions: Which Factors are Reliably
Important?
This study analyses US non-financial firms over the period 1950 to 2003. It includes
more than 180,000 firm-year-observations.
The following six core factors explain 27% of variation in (market) leverage, while all
other factors add only a further 2%:
• Industry median leverage (+)
• Tangibility (ratio of tangible assets) (+)
• Profitability (+)
• Firm size (+)
• Market-to-book assets ratio (-)
• Expected inflation (+)
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Capital Structure
7
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
What determines capital structure decisions?
E.ON will Aktienrückkauf bis Ende 2008 abschließen - Kein neues Programm
DÜSSELDORF (AWP International) - Der Energieversorger E.ON hält an seinen
bisherigen Plänen zum Aktienrückkauf fest. Bis Anfang November oder spätestens bis
zum Ende des Jahres würden Aktien in Höhe von bis zu 7 Milliarden Euro gekauft
und eingezogen, sagte Finanzvorstand Marcus Schenck am Donnerstag in Düsseldorf
und bestätigte damit frühere Aussagen. Bis Anfang August hätte der Konzern Papiere im
Wert von 5,2 Milliarden Euro zurückgekauft. Nun sei bis 2010 bisher kein neues
Programm absehbar, sagte Schenck.
Mit dem aktuellen Programm habe E.ON die Kapitalstruktur in Richtung eines
höheren Verschuldungsgrades umgestalten wollen, und das sei gelungen. Die
Nettoverschuldung gemessen am bereinigten Ergebnis vor Zinsen, Steuern und
Abschreibungen werde bis zum Ende des Jahres den Faktor drei erreichen. Dies sei
nötig für ein Single A Rating bei den Ratingagenturen./sc/sk
Source: Handelszeitung vom 07.08.2008
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Capital Structure
8
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Value maximization: How companies think about capital structure (I)
Source: EON
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Capital Structure
9
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Value maximization: How companies think about capital structure (II)
Source: Bayer (2016)
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Capital Structure
10
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Schedule Capital Structure
Introduction
Modigliani, Miller (1961): Perfect capital markets
Trade-off theory: Taxes and bankruptcy cost
Pecking-order theory: Signaling
Free cash flow theory: Agency cost
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Capital Structure
11
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
MM: Capital structure is irrelevant in perfect capital markets
Modigliani, Miller (1961): Overview and assumptions
Main question: What is the effect of leverage on firm value in a perfect capital market?
Main assumption: Perfect capital markets
1. No taxes
2. No cost of bankruptcy
–
Debt can be risky, but no extra cost of bankruptcy
besides non-repayment of debt
3. Perfect information
4. No transaction costs for issuing debt and equity
5. Investment decision not affected by capital structure
–
F. Modigliani
1918-2003
Nobel price
1985
M. H. Miller
1923-2000
Nobel price
1990
"Separation of financing and investment decision"
Main result: Firm value is independent of its capital structure1)
• Any value from leverage must results from violations of above assumptions
1) "The value of the pie is independent of how it is sliced"
Source: Modigliani, Miller (1961) "The Cost of Capital, Corporation Finance and the Theory of Investment", American Economic Review
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Capital Structure
12
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Expected ROE increases with
leverage...
Exp. return on assets ru equals
the WACC
VD
VE
rU = rD + rE
V
V
... however, risk increases, too
Beta of the firm is weighted
average beta
• Asset beta βU measures
variability of cash flows against
market portfolio
Therefore, expected ROE is
VD
rE = rU + ( rU − rD )
VE
Return on equity increases in
proportion to leverage (MM
proposition II)
βU =
VD
V
βD + E βE
V
V
• βU equals beta of unlevered firm
€
β E = βU + (βU − β D )
VD
VE
• Equity betas βE must be larger
than debt beta βD, because
equity holders bear extra risk
In perfect capital markets the increase in expected return exactly
compensates for the increase in risk
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Capital Structure
13
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
The Cost of Risky Debt – Using the Option Pricing Model
• Even though risky debt without bankruptcy costs does not alter the basic
Modigliani- Miller results, it is still interesting how the cost of risky debt is affected
by changes in the capital structure
• One way to solve this problem is to apply a structural model (e.g. Merton model),
where equity is modeled as a call option on the firm value, i.e. S = MAX [0, V - D ]
• Assumptions
- Firm issues zero-coupon bonds that prohibit any capital distribution (such as
dividend payments) until the bonds mature T time periods later
- Firm value follows a geometric Brownian motion
- No transaction costs or taxes
- Thus, the value of the firm is unaffected by its capital structure
- Risk-free interest rate is non-stochastic and known
- Homogeneous expectations about the stochastic process of value of the
firm‘s assets
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Capital Structure
14
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Using the CAPM to solve the problem
The continuous-time version of the CAPM developed by Merton [1973] is compatible with
the option pricing model.
The continuous-time CAPM states
RE = R f +[RM − R f ]β E
Where:
RE= the instantaneous expected rate of return on risky equity
βs= the instantaneous equity beta,
RM= the expected instantaneous rate of return on the market portfolio
Rf= the nonstochastic instantaneous annualized rate of return on the
risk-free asset
Note the market determines the cost of capital as the expected rate of
return of an asset; hence we can write rU≈RU, rE≈RE and rD≈RD (as
the discrete return is not exactly equal to the instantaneous return)
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Capital Structure
15
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
cont.
From the CAPM we know that the beta of the unlevered firm is:
RU − R f
βU =
RM − R f
Substituting this into the CAPM equation for the stock yields
RE = R f + (RU − R f )
βE
βU
• Note, if M is the value of the market portfolio the following transformation applies:
βE ≡
∂VE M ∂VE ∂V V M
V
=
= N ( d1 ) βU
∂M VE ∂V ∂M VE V
VE
• Substituting this result into the former equation yields
RE = R f + N (d1 )(RU − R f )
V
VE
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Capital Structure
16
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
cont.
The same transformation can be applied to the expected return on the bonds.
Because of the Put-Call-Parity it must hold:
∂VD
= N (−d1 ) = 1− N (d1 )
∂V
Using this relationship and proceeding a before yields the following equation for
the cost of debt:
RD = R f + (RU − R f )N (−d1 )
V
VD
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Capital Structure
17
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Example
• A numerical example can be used to illustrate how the cost of debt, in the
absence of bankruptcy costs, increases with the firm‘s utilization of debt
• Example
• Suppose the current value of a firm, V, is $3 million; the face value of
debt is $1.5 million; and the debt will mature in T = 8 years. The
variance of returns on the firm‘s assets, s2, is 0.09; its required return on
assets is RU = 12%; and for the riskless rate Rf = 5% holds.
• From the Black-Scholes option pricing model, we know:
d1 =
=
ln(V / D ) + R f T
s T
1
+ s T
2
ln(3 / 1.5) + .05(8)
+ .5(.3) 8 = 1.7125
.3 8
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Capital Structure
18
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Example (cont.)
For the normal cumulative density function N(x), the value of N(-1.7125) is approximately
0.0434. Substituting this into the cost of debt, we get
RD = .05 + (.12 −.05)(.0434)
3
= .05 +.0097 = .0597
0, 9408
The following figure shows the relationship of the cost of debt and the ratio of the face value of
debt to the current market value of the firm.
%
.08
.07
.06
R f = .05
.04
0.5
1.0
VD
V
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Capital Structure
19
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Of course, the MM-theorem holds also in the OPM context
To arrive at a weighted average cost of capital, the cost of debt, is multiplied by the
percentage of debt in the capital structure, VD/V,
Then this result is added to the cost of equity, multiplied by VE/V, the percentage of equity
in the capital structure.
The result is:
RD
VD
V "
V %V "
V %V
+ RE E = $ R f + (RU − R f )N (−d1 ) ' D + $ R f + N (d1 )(RU − R f ) ' E
V
V #
VD & V #
VE & V
! V + VE $
= Rf + # D
& + (RU − R f )[N (−d1 ) + N (d1 )]
" V %
= R f + (RU − R f )[1− N (d1 ) + N (d1 )] = RU = WACC
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Capital Structure
20
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Cost of capital in case of risky debt and no taxes in the OPM
No taxes
RE = RU + ( RU − RD )
RU
Rf
VD
VE
WACC = RU
RD = R f + ( RU − R f ) N (−d1 )
V
VD
1.0
VD
V
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Capital Structure
21
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
What is value-impact of relaxing the MM assumptions?
Violations of MM-assumptions
Subsequent discussion
1
Taxes
Tax shield
2
Cost of bankruptcy
Trade-off-theory
3
Asymmetric information
Pecking-order theory
4
Transaction costs
5
Moral hazard
Free cash-flow theory
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Capital Structure
22
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Schedule Capital Structure
Introduction
Modigliani, Miller (1961): Perfect capital markets
Trade-off theory: Taxes and bankruptcy cost
• Tax shield
• Empirical evidence
• Bankruptcy cost
• Trade-off theory
• Excursus: Ratings
Pecking-order theory: Signaling
Free cash flow theory: Agency cost
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Capital Structure
23
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
What is value-impact of relaxing the MM assumptions?
Violations of MM-assumptions
Subsequent discussion
1
Taxes
Tax shield
2
Cost of bankruptcy
Trade-off-theory
3
Asymmetric information
Pecking-order theory
4
Transaction costs
5
Moral hazard
Free cash-flow theory
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Capital Structure
24
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
How the tax shield affects the WACC
In general, the following relationship holds:
!" = !$ + !& = !' + (!)*
Where VL and VU are the enterprise values of the levered and unlevered firm. PVTS is the
present value of the tax shield.
Note, however, that deriving the unlevered cost of capital rU in general is not obvious, as for an
investor holding all the outstanding claims of a firm the following relationship applies (rT is the
expected return associated with the tax shield):
+$ !$ + +& !& = +' !' + +, (!)*
Assume a constant leverage ratio (case I)
In this case rT=rU, as debt is proportional to firm value and tax shields. Therefore, debt has
the same risk as free cash flows.
1
(!)* = ./0
+& !&,. )
!$
!&
!&
;
+
=
+
+
+
;
5677
=
+
−
+
)
;
'
$
&
'
&
1 + +' .
!"
!"
!"
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Capital Structure
9' = 9$
!$
!&
+ 9& ;
!"
!"
25
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Assume a constant debt level (case II)
In this case rT=rD, as debt is constant and the tax shield has the same risk as debt.
Combining this result with the well-know WACC-formula yields:
4
-.,/ = 0
123
5* .* ,
;
1 + 5* 1
5$ = 5"
."
.* 1 − ,
+ 5*
." + .* 1 − ,
." + .* 1 − ,
Combining this with the WACC-formula yields:
7899 = 5$ 1 − ,
.*
." + .*
Finally, taking into account that expected returns can be expressed in terms of the CAPM&
equation, this result can also be expressed in the following way: !" = !$ + &' !$ − !* 1 − ,
(
&
This is known as the Hamada equation. If debt is riskless, this yields: !" = !$ 1 + &' 1 − ,
(
Note, the results presented above are just two special solutions to the following general
relationship
.*
7899 = 5$ −
, 5* + : 5$ − 5*
." + .*
where k measures the permanence of the debt level, i.e. k=0 in case I and k=1 in case II
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Capital Structure
26
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Example I: constant leverage ratio
Assume a firm with rE=10%, rD=6% and T=35%. The debt-to-equity-ratio is fixed at 1. Moreover,
rf=2% and MRP=6%. What is the firm’s WACC, what is the unlevered cost of capital? What do
Betas look like?
0.5
0.5
!"## = 6% 1 − 0.35
+ 10%
= 6.95%
1.0
1.0
0.5
0.5
/0 = 6%
+ 10%
= 8% 20 = 1 23 = 1 4 26 = 7
1.0
1.0
5
5
Now, assume that the company changes to a permanent debt-to-equity-ratio of 1/3. By doing so,
the debt-beta decrease to 1/3. What happens to the WACC and the equity beta?
1
/6 = 2% + 6% = 4%
3
;
20 − 26 ;6 1 − 1 1
2
1
34 = 12
<
23 =
=
/3 = 2% + 1 6% = 9 %
;3
3
9
9
3
;<
4
1
1 3
!"## = 4% 1 − 0.35 + 9 % = 7.65%
4
3 4
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Capital Structure
27
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Example II: constant debt level
Assume a firm with rE=10%, rD=6% and T=35%. The firm has a constant debt level which
currently leads to a debt-to-equity-ratio of 1. Moreover, rf=2% and MRP=6%. What is the firm’s
WACC, what is the unlevered cost of capital? How do Betas look like?
0.5
!"## = 8.42% 1 − 0.35
= 6.95%
1.0
0.5 1 − 0.35
0.5
12 = 6%
+ 10%
= 8.42%
0.5 + 0.5 1 − 0.35
0.5 + 0.5 1 − 0.35
9
1 2
75 + 78 8 1 − :
1
+ 3 1 1 − 0.35
95
3
72 =
=
= 1.07
98
1
+
1
1
−
0.35
1+9 1−:
5
Now, assume that the company changes to a new permanent debt level which leads to a current
debt-to-equity-ratio of 1/3. By doing so, the debt-beta decrease to 1/3. What happens to the
WACC and the equity beta?
75 = 1.07 +
1
1
1.07 −
3
3
1 − 0.35 = 1.23
15 = 2% + 1.23 6 6% = 9.38%
1
3
!"## = 4% 1 − 0.35 + 9.38% = 7.68%
4
4
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Capital Structure
28
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Leverage also increases probability of financial distress
• As cash-flows are volatile, increasing debt will also increase the probability of
failure in debt interest payments
• Failure in debt interest payments result in financial distress
• Result of limited liability
• Ultimate result is firm bankruptcy
• Financial distress incurs additional cost on top of non-payment of debt interest
•
•
Direct costs: Administrative costs; fees for layers, accountants, consultants; revenue loss,
because customers walk away; additional working capital, because suppliers lower or cut
payment periods; lost management time
Indirect costs: Lost business; additional working capital, because suppliers lower or cut
payment periods; lost investment opportunities,...
• The levered firm value then becomes
VL = VU + PVTS - PV(costs of financial distress)
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Capital Structure
29
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Total cost of bankruptcy are empirically substantial, esp. indirect costs
Warner (1977): Direct costs are too low to be significant
• Sample: Direct costs (lawyers, accountants, managerial time,...) in 11 railroad bankruptcies
between 1933 and 1955
• Result: Direct costs are 1% of firm value 7 years prior and 5% immediately prior to bankruptcy
Altman (1984): Indirect costs are substantial, but economies of scale
• Method: Indirect costs calculated from comparing expected with actual profits in a time-series
regression
• Results: Average indirect costs are 8.1% of firm value 3 years prior and 11% in year of
bankruptcy; relative costs are lower for large firms
Lawrence and Weiss (1990): Direct costs are too low to be significant
• Sample: 31 bankruptcies in 1980-86
• Result: Direct costs are 3% of firm value in year prior to bankruptcy
Andrade and Kaplan (1998): Total costs are substantial
• Sample of troubled and highly leveraged firms
• Costs are 10-20% of pre-distressed market value
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Capital Structure
30
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Enterprise value
According to Trade-off Theory the optimal debt level is
achieved where the marginal benefit (tax shield) equals
the marginal cost (financial distress)
PV cost of financial
distress
PVTS
Value of the unlevered firm
D*
Debt
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Capital Structure
I&F
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Does the trade-off theory of debt explain capital structure in reality?
Pros
• Predicts moderate leverage
– Avoids extreme predictions
• Successfully explains industry
differences in capital structure
– Example: High tech companies
with high risk and high intangible
assets with low salvage value
have little debt
– Example: Airlines with tangible
assets borrow heavily
• Corresponds to management
behavior
– Surveys indicate, that managers
follow a target capital structure,
which is in accordance with tradeoff theory
Cons
• Some successful companies have
little debt
– Some of these companies even
have negative debt
• Relation between tax-shield and
value is not empirically evident
– Fama, French (1998)
• There is an ongoing empirical
debate how tax sensitive capital
structure really is
ded
e
e
is n
y
r
theo
l
a
ion
t
i
d
Ad
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Capital Structure
32
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Schedule Capital Structure
Introduction
Modigliani, Miller (1961): Perfect capital markets
Trade-off theory: Taxes and bankruptcy cost
• Tax shield
• Empirical evidence
• Bankruptcy cost
• Trade-off theory
• Excursus: Ratings and bankruptcy
Pecking-order theory: Signaling
Free cash flow theory: Agency cost
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Capital Structure
33
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Subinvestment
grade
Investment
grade
Moody’s: Long Term Ratings Definitions
5yr
10yr
0,08
0,36
0,15
0,34
0,41
0,87
1,60
2,87
7,86
11,40
20,66
24,59
39,32
41,18
Cumulative default rates
(in %); sample period:
1970-2005. Source:
Moody’s
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Capital Structure
34
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Ratings of Moody's, S&P and Fitch
Investment grade
Sub-investment grade
("junk bond")
Fitch
ratin
g
S&P
ratin
g
Moody's
rating
AAA
AAA
Aaa
Highest credit quality
AA
AA
Aa
Very high credit quality
A
A
a
High credit quality
BBB
BBB
Baa
Good credit quality
BB
BB
Ba
Speculative
B
B
B
Highly speculative
CCC
CCC
Caa
Real default probability
CC
CC
Ca
Probable default
C
C
C
Imminent default
RD
CI
C
Partial default
D
D
C
Bankruptcy
Description
Additional common assumption is 50 % loss given default
Note: Fitch and S&P ratings are differentiated with + and -, Moody's with 1 to 3
Source: Rating websites
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Capital Structure
35
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
The Rating Methodology
Source: Standard & Poor’s (2015)
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Capital Structure
36
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Source: Standard & Poor’s (2015)
The Rating Methodology: Important Financial Ratios
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Capital Structure
37
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Practically, the ICR is a central determinant for the ratings
Source: Damodaran’s website; Data as of January 2019; only firms with a market cap larger than $ 5 bn
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Capital Structure
38
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Empirically, ratings work somehow well
Source: Standard & Poor’s (2015)
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Capital Structure
39
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Ratings are a critical determinant for the cost of debt
Spread (in %) of BBB-rated US corporate
bonds
Spread (in %) of sub-investment grade US
corporate bonds
Source: FRED (2010)
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Capital Structure
40
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Schedule Capital Structure
Introduction
Modigliani, Miller (1961): Perfect capital markets
Trade-off theory: Taxes and bankruptcy cost
Pecking-order theory: Signaling
• Background
• Intuitive explanation
• Formal model
Free cash flow theory: Agency cost
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Capital Structure
41
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
What is value-impact of relaxing the MM assumptions?
Violations of MM-assumptions
Subsequent discussion
1
Taxes
Tax shield
2
Cost of bankruptcy
Trade-off-theory
3
Asymmetric information
Pecking-order theory
4
Transaction costs
5
Moral hazard
Free cash-flow theory
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Capital Structure
42
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
The Lemon Problem: How to signal the true value of an asset?
Akerlof (1970) examined market for cars
• Four types available: New, old and good, bad
• Information asymmetry: Only owner knows true value of the car
Result
• Market pays same price for good and bad cars
• Good cars get not priced at true value
• Good cars will not be traded, only "lemons" are on the market
(adverse selection)
Georg A. Akerlof
Nobel price 2001
(together with
Michael Spence
and Joseph Stiglitz)
=
What is the effect of asymmetric information and signaling on capital structure?
Reference: George Akerlof: The Market for 'Lemons': Quality Uncertainty and the Market Mechanism, The Quarterly Journal of Economics, Vol. 84 No. 3 (Aug. 1970)
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Capital Structure
43
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Example: Mayers/Maijluf (1984)
Two possible states of the world
•
•
Outcome can be either good (i=G) or bad (i=B)
Each state has equal probability (=50%)
Stewart
Myers
MIT Sloan
Asymmetric information
•
•
Only management knows true state of the world
Management acts in the best interest of shareholders (= no agency problems)
Nicolas
Majluf
U de Chile
Management has two alternative strategies: 'Issue equity' worth 100 or 'do nothing'
True firm values are given by
Do nothing
Issue equity
Good state
V1 = 250
V1 = 250 + 100 =
350
Bad state
V1 = 150
V1 = 150 + 100 =
250
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Capital Structure
44
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Optimal strategy is to issue equity if stock is overvalued (bad state)
If firm does nothing, market determines current firm value as the expected value
• Equals unconditional firm value
(
!" = $ )% !% = 200
%&'
If total firm is valued at 200, then payout to old shareholders is
Do nothing
Issue equity
Good
250
233.33
Bad
150
166.67
!,-. |0 =
!"
200
|
! 0+2 =
350 = 233.33
!" + 2 '
300
!,-. |6 =
!"
200
!' |6 + 2 =
250 = 166.67
!" + 2
300
Rational expectation equilibrium result
• Management chooses best strategy in each state (=
)
• Management issues equity if market value is higher than true value, i.e. if the firm is overvalued
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Capital Structure
45
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Adverse selection cost of equity financing
However, market now uses issue as signal of bad state
• Market knows, that management will only issue equity if equity
overvalued
!" |$%%&' = 150
Payout to old shareholders then is
Do nothing
Issue equity
Good
250
210
Bad
150
150
!,-. |/ =
!"
150
!2 |/ + 1 =
350 = 210
!" + 1
250
!,-. |5 =
!"
150
!2 |5 + 1 =
250 = 150
!" + 1
250
True firm value is revealed and rational expectation equilibrium results
Note, this mechanism may prevent company from financing new positive NPV
projects => Underinvestment problem due dot adverse selection costs of
equity financing
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Capital Structure
46
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Pecking-order theory of debt suggests preferences in
financing sources
• Positive NPV projects are carried out if financed by retained earnings
Thus, firms might carry excess liquid assets for future growth
• Positive NPV projects will be carried out if financed by debt
Debt financing has payoffs less correlated with future states of nature,
therefor adverse selection cost is a minor problem
• Result: Pecking order theory suggests preference in financing sources
1. Retained earnings (internal equity)
2. Debt financing
3. External equity financing
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Capital Structure
47
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Further implications of pecking-order theory
• Capital structure dynamically depends on firm history
• Explains, why successful companies have little debt
Because they don't need external financing
• There is no defined optimal debt-equity mix
• Because equity ratio depends on the availability of retained earnings
• Tax-shield effects are assumed to be of second order
• Note: debt financing cannot always solve the adverse selection problem of
equity financing because of the debt overhang problem.
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Capital Structure
48
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Transaction costs of financing reinforce pecking-order
Transaction cost of financing choice in % of financing volume (indicative)
6 - 20%
2 - 5%
0%
Retained
earnings
~0,5 %
Debt
Equity reraise
(SEO)
New equity issue
Cost depend on financing volume and exchange,
for details see chapter „Initial Public Offerings (IPO)“
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Capital Structure
49
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Survey empirical evidence is mixed
Source: Graham/Harvey (2002)
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Capital Structure
50
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Empirical evidence favors pecking order theory over trade-off theory …
Shyam-Sunder and Myers (1999)
Trade-off theory
Pecking order theory
Type
• Static theory
• Dynamic theory
Main
prediction
• Changes in debt will revert
towards the firm‘s target
• Change in debt depends on the
fund flow deficit that year
(
)
DDi ,t = a + bi Di*,t - Di ,t -1 + e i ,t
Regressio
n equation
– ∆D = change in debt each year
– D* = target capital structure
– D = current debt
DDi ,t = a + bi DEFi ,t + e i ,t
– ∆D = change in debt each year
– DEF = firm‘s cash flow deficit
Expected
results
• Speed of adjustment b is high and
>0
• Debt issue if deficit (b=1) and
nothing unexplained (a=0)
Results
• Low speed of adjustment (b =
0.33)
• Low explanatory power (R2 = 21%)
• High slope (b = 0.75)
• Higher explanatory power (R2 =
68%)
Sample: 157 industrial firms for year endings of 1971, 1981, and 1989
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Capital Structure
51
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
… or vice versa
Frank, Goyal (2003): Testing the Pecking Order Theory of Capital Structure
This study analyses US
industrial firms over the
period 1971 to 1998. It
includes more than 140,000
firm-year-observations.
Interestingly, net equity
issuances track financing
deficits much closer than
net debt issuances
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Capital Structure
52
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Is the evidence in favor of the Pecking Order Theory an artefact?
Frank, Goyal (2003): Testing the Pecking Order Theory of Capital Structure
Here, the same period as in Shyam-Sunder and Myers (1999) is used; however, the number of firms is much
larger (768 firms over 19 years).
While Shyam-Sunder and Myers (1999) use only firms with continuously reported variables, here also firms with
data gaps are considered as a robustness test.
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Capital Structure
53
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Is the evidence in favor of the Pecking Order Theory an artefact?
Frank, Goyal (2003): Testing the Pecking Order Theory of Capital Structure
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Capital Structure
54
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Schedule Capital Structure
Introduction
Modigliani, Miller (1961): Perfect capital markets
Trade-off theory: Taxes and bankruptcy cost
Pecking-order theory: Signaling
Free cash flow theory: Agency cost
• Intuitive explanation
• Agency cost of debt and equity
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Capital Structure
55
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
What is value-impact of relaxing the MM assumptions?
Violations of MM-assumptions
Subsequent discussion
1
Taxes
Tax shield
2
Cost of bankruptcy
Trade-off-theory
3
Asymmetric information
Pecking-order theory
4
Transaction costs
5
Moral hazard
Free cash-flow theory
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Capital Structure
56
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Investment decision when firm actions are non-observable
Jensen and Meckling (1976) argue optimal leverage minimizes total agency cost
• Agency cost arise from debt and equity
• Agency costs influence probability distribution of cash flows
Risk shifting: an example of agency costs of debt
• Firm’s investment decisions are non-observable
• Firm has two possible investment projects
- Investment of $8,000 for each
- Same systematic risk but different variances
- Project payoffs and expected returns are
State
Probability
CF project 1
CF project 2
1
0.5
9,000
2,000
2
0.5
11,000
18,000
10,000
10,000
Expected return
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Capital Structure
57
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Agency cost of debt because of risk-shifting
Firm shows project 1 to lenders and asks to borrow $7,000
• Lenders accept, because project 1 can always pay back loan
Investment project payoffs with debt of $7,000 for shareholders are
State
Probability
CF project
1
CF project
2
1
0.5
2,000
0
2
0.5
4,000
11,000
3,000
5,500
Expected return
• Project 2 with higher expected shareholder return
• If possible, owners switch to project 2
• Wealth transfer from bond-holders to shareholders
Therefore, bondholders will install protective covenants and monitoring devices
• Cost of writing and enforcing such covenants may be nontrivial
• Debtholders must charge higher ex ante yields to compensate them
(=agency costs of debt)
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Capital Structure
58
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Agency cost of equity: excess cash leads to inefficiencies
Jensen (1986): How to motivate managers?
–
Enough cash avoids underinvestment
(pecking order theory)
–
Excess cash leads to inefficiencies
Michael C. Jensen
• Overinvestment (below cost of capital), Prof. Emeritus, HBS
e.g., empire building,
or organizational slack, e.g. perks
• Solution: Proper incentives (e.g. stock options) or
more debt, as debt exerts financial pressure on
managers
Main assumptions
• Separation of ownership and control (= management)
• Asymmetric information between management and investors
• Managers can maximize their wealth at expense of shareholders
Source: Jensen (1986) "Agency Costs of Free Cash Flow, Corporate Finance and Takeovers", American Economic Review 26
Downloadable at http://papers.ssrn.com/sol3/papers.cfm?abstract_id=99580
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Capital Structure
59
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Optimal capital structure minimizes total agency costs
Firm Value
Total agency costs
Agency cost of debt
Agency cost of equity
Optimal 100%
capital structure
Debt Ratio
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Capital Structure
60
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Google Founders’ Ultimate Perk: A NASA Runway
Free cash flow theory – An example?
SAN FRANCISCO, In the annals of perks enjoyed by America’s corporate executives,
the founders of Google may have set a new standard: an uncrowded, federally
managed runway for their private jet that is only a few minutes’ drive from their offices.
For $1.3 million a year, Larry Page and Sergey Brin get to park their customized
wide-body Boeing 767-200, as well as two other jets used by top Google executives, on
Moffett Field, an airport run by NASA that is generally closed to private aircraft. [...] It is a
perk that is likely to turn other Silicon Valley tycoons green with envy, as no other private
jets have landing rights there. [...]
The Google founders’ jet has been the talk of Silicon Valley since 2005, when the pair
purchased the plane [...] the contractor described requests for modifying the plane to
include California king-size beds for the founders. At one point,
the founders asked whether hammocks could be
hung from the ceiling. The contractor said that Mr.
Schmidt had described the jet as “party airplane.”
Source:
online, Sept 13th 2007, www.nytimes.com/2007/09/13/technology/13google.html
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Capital Structure
61
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Bringing Theory to Practice – An Minicase
Problem: You have been appointed as new CFO of
Smart Thinking Inc. You first job is to check
whether the capital structure of the company is
value maximizing. It takes you just a few hours to
collect the following information:
The company has a net debt of 10bn € and a
market cap of 40bn €. EBIT is 3.8bn € and
assumed to stay rather constant; tax rate is 30%.
The company has a AA-rating.
Moreover, you figure out that the current beta of
the firm 0.7, the market risk premium is 4% and
the risk free rate is 3%. Spread on corporate
bonds are determined by an illiquidity spread of
1% plus the default risk spread according to the
rating of the bond. From a research study you
learn that ratings are mostly determined by the
Interest Coverage Ratio (EBIT/Net interest
payments) and that as of the year 2011 there is an
empirical relationship according to the table given
here:
Source: Damodaran’s Website
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Capital Structure
62
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Minicase cont.
Q#1: What is the current WACC of the firm?
A#1: According to the table give above rD=3%+1%+0.65%=4.65%. Interest payments are 465mn
€, ICR=First, note that ICR=8.17; rE=3%+0.7x4%=5.8%. Hence it follows:
WACC=0.2x0.7x4.65%+0.8x5.8%=5.29%
Q#2: Could the firm reduce the WACC by changing the leverage? Check this question by looking
at the following two alternatives. First, what happens with the WAAC, if the company aims at
getting a AAA-rating by eliminating all the debt through a share issue. Second, the company
considers a debt financed share repurchase in a way that the resulting rating is BBB (ICR=2.53).
A#2a: Unlevered beta is given by 0.7/(1+0.7x10/40)=0.5957. Therefore, in case of a 100%-equity
financing the cost of equity would be rE=3%+0.5957x4%=5.38%=WACC.
Decreasing the debt ratio from 20% down to zero would increase the WACC by about 9 bp. In
case of a non-growing firm this would imply a change in market value of about -1.7%=5.29/5.38-1.
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Capital Structure
63
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Minicase cont.
A#2b: ICR=2.53 implies interest payment of 3.8/2.53=1.5bn €; according to the rating table now
kD=5.6% holds. Additional debt capacity is (1500-465)/0.056=18.5bn €, hence net debt raises to
28.5bn €, market cap falls to 21.5bn €.
Unlevered beta is given by 0.7/(1+0.7x10/40)=0.5957. Therefore, debt increase would make stock
beta equal to 0.5957(1+0.7x28.5/21.5)=1.15. It follows: kE=3%+1.15x4%=7.6%. Therefore:
WACC=28.5/50x0.7x5.6%+21.5/50x7.6%=5.5%.
Increasing the debt ratio from 20% to 57% would not be optimal either, as the WACC would
increase by 21 bp.
Q#3: Why does an optimal capital structure exist? What are the economic determinants? Discuss!
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Capital Structure
64
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Capital Structure: Lessons learned
1. Trade-off theory: Optimal capital structure trades-off bankruptcy cost and tax shield
Tax shield is the higher the higher the debt ratio
Direct and indirect bankruptcy cost have to be considered
2. Pecking-order theory
Understand model of Myers and Majluf (1984): Information asymmetry, rational
expectation equilibrium, signaling
Information asymmetry causes adverse selection costs of equity financing as an equity
issued is considered as a signal for overvaluation
It might cause an underinvestment problem
Firms have a pecking-order of financing sources
1. Retained earnings (internal equity)
2. Debt
3. External equity
As consequence, capital structure depends on firm history
3. Free cash flow theory: Optimal capital structure minimizes total agency costs
Agency cost resulting from monitoring to prevent bondholder expropriation
Agency cost of external equity resulting from monitoring managerial slack
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Capital Structure
65
Corporate Finance – Payout Policy
Prof. Dr. Christoph Kaserer
Chair for Financial Management
and Capital Markets
Technische Universität München
Arcisstr. 21
D-80290 München
Tel.:
+49 89 / 289 - 25489
Fax:
+49 89 / 289 - 25488
Mail:
christoph.kaserer@tum.de
URL:
www.fm.wi.tum.de
1
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Agenda
Distributions to Shareholders
Irrelevance of Payout Policy
Payout Policy and the Clientele Effect
Payout Policy and Signaling
Payout Policy and Agency Costs
2
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Source: Staista
Dividend Payments of DAX companies since 2003 (€bn)
Note that the current (April 2019) DAX market cap is about 1.2 €trn; therefore, the value
weighted average dividend yield is about 3.3%.
3
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
How to pay out Earnings
Dividends vs. share repurchases
Payout*
Share repurchase ( 71 AktG)
-
Decision by the ASM
Max. retained earnings plus
free reserves
Max. 10% of equity
Equality principle must be
obeyed
Repurchased shares typically
are used to reduce share
capital
The company does not have
any rights out of its own
shares
Dividend
-
Decision by the ASM
Max. retained earnings plus
free reserves
*Note: stock dividends (stock splits) are not a mean
of payout policy but just an instrument to deflate
stock prices
While dividends are expected to stay constant or steadily increase over
time, share repurchases are considered to be a one-time pay-out. This
is important when considering the signalling impact of a pay-out
announcement.
4
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
The Changing Composition of Shareholder Payouts in the US
Source: Berk/de Marzo (2017), Compustat data for U.S. firms, excluding financial firms and utilities.
5
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Agenda
Distributions to Shareholders
Irrelevance of Payout Policy
Payout Policy and the Clientele Effect
Payout Policy and Signaling
Payout Policy and Agency Costs
6
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Dividends Deliver and do not Generate Value
Modigliani and Miller (1961) proved irrelevance of dividend policy in perfect capital
markets
- No taxes or transaction costs
- Perfect information: Everyone fully informed about the distribution of the
firm‘s future cash flows
- Investment decision is independent of dividend policy (all positive NPV
projects will be executed)
Dividends are way to deliver, not to generate value. There is no optimal dividend.
The same reasoning applies to share repurchases
But markets react to dividend changes and share repurchases,
so what are possible explanations?
Reference: Miller and Modigliani (1961) Dividend Policy, Growth and the Valuation of Shares, Journal of Business
7
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Example: Pay Dividend with Excess Cash
The company decided to pay a $2 dividend.
Black
Cum-Dividend
Balance Sheet
Ex-Dividend
Balance Sheet
Cash
20
0
Other assets
400
400
Total market value
420
400
Shares(millions)
10
10
share price
$42
$40
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Example: Repurchase Stocks with Excess Cash
The company decided to use the cash to repurchase
20mn/42=476,190 stocks.
Black
Before Repurchase
Balance Sheet
After Repurchase
Balance Sheet
Cash
20
0
Other assets
400
400
Total market value
420
400
Shares(millions)
10
9.524
share price
$42
$42
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Irrelevance of Payout Policy
•
In perfect capital markets, an open market share repurchase has no
effect on the stock price, and the stock price is the same as the cumdividend price if a dividend were paid instead.
•
In perfect capital markets, investors are indifferent between the firm
distributing funds via dividends or share repurchases. By reinvesting
dividends or selling shares, they can replicate either payout method on
their own (homemade dividend).
10
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Three Alternative Explanations for Relevance of Payout Policy
Violations of MM-assumptions
Subsequent discussion
1
Taxes
Clientele effect
2
Asymmetric information
Signaling theory
3
Agency cost
Agency theory
11
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Agenda
Distributions to Shareholders
Irrelevance of Payout Policy
Payout Policy and the Clientele Effect
Payout Policy and Signaling
Payout Policy and Agency Costs
12
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Three Alternative Explanations for Relevance of Payout Policy
Violations of MM-assumptions
Subsequent discussion
1
Taxes
Clientele effect
2
Asymmetric information
Signaling theory
3
Agency cost
Agency theory
13
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
The Tax Disadvantage of Dividends
Taxes on Dividends and Capital Gains
- In many countries dividends are taxed at a higher rate than capital gains.
- There is an economic reason: stock prices already reflect the future tax
burden due to dividend taxation. If an investor sells the stock before
dividend payment, he implicitly pays the dividend tax as the stock price is
reduced by the present value of this tax. Hence, a capital gains tax leads
to a double taxation of dividends.
- However, by reducing the capital gains tax stock repurchases are
becoming more attractive leading to a change in the firm’s payout policy.
- Its hard to say anything about a tax structure making payout policy
irrelevant from a tax perspective.
14
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Tax Rate depends on Type of Investor
Excursus: Capital income taxation in Germany
All capital income taxed equally at 25+% ('Abgeltungssteuer')
• = 25% + 'Solidaritätszuschlag' (5.5%)
• Includes interest, dividends and other capital income
– Removes tax exemption of long-term investment gain (until 2008)
• Deducted at source (i.e. banks)
• No tax progression beyond allowable deduction
Differs to taxation regime in many countries
• In many countries dividends are taxed higher than capital gains
• Taxation of foreign capital gain depends on individual double taxation agreements
For qualified corporate investors 95% of dividend income is tax free. Capital gains
are threated similarly.
Under the current German system choice between dividends and share
repurchases seems to be irrelevant at best (at least over a one year investment
horizon).
15
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Altana Pays High Special Dividend
Lessons from a Real Live Case
"Altana – Sonderdividende lohnt sich nicht für jeden"
Aktionärsschützer raten sogar zu Verkauf der Aktie
Nach der Ankündigung der Altana AG, eine Sonderdividende von 33 Euro auszuschütten, hat die Deutsche
Schutzvereinigung für Wertpapierbesitz (DSW) zu einer differenzierten Strategie geraten. Es sei
vorhersehbar, dass der Aktienkurs [...] um diese 33 Euro nachgeben werde [...]. Darum sei es nicht
unbedingt ratsam, vor der Hauptversammlung am 3. Mai Altana-Papiere zu kaufen, um die hohe Dividende
mitzunehmen. Aktionäre müssten nicht nur Abschläge hinnehmen, sondern die Dividende auch versteuern
[...].
Altana hatte [...] angekündigt, dass der Gewinn aus dem Verkauf der Pharmasparte – 4,5 Mrd € – in Form einer
Sonderdividende […] vollständig an die Aktionäre weitergereicht werde. […] Fast die Hälfte davon fällt an
Mehrheitsaktionärin Susanne Klatten. Für Altana-Aktionäre, die seit mindestens einem Jahr Aktien des
Chemieunternehmens hielten, könne es sich angesichts des hohen Aktienkurses lohnen, vor der
Ausschüttung steuerfrei zu verkaufen […]. Nach der Ausschüttung und dem erwarteten Kursabschlag
könnten die Aktionäre die Aktie dann deutlich billiger zurück erwerben, sagte er [, das sogenannte] „DividendenStripping".
Tagesspiegel vom 15.03.2007
„AltanaAktionäre sauer
wegen Sonderdividende
Da Altana einen Großteil
seiner Kriegskasse ausschüttet, geht allerdings
auch Kursfantasie verloren.
Capital vom 17.11.2007
Susanne Klatten "Volksaktionär"
Fokus online
16
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
High Price Decline and High Volume at Ex-Dividend Date
Altana stock price (01.01.2007 - 14.11.2007)
Ex-dividend date *
S1 = S0 - 33 € - 1.8
€
19,69
* Special dividend of € 33 and regular dividend of € 1.80
Note: at that time a
retail investor could
have avoided
taxation on
dividends by simply
selling the stock
right before the
dividend payment.
This is because
capital gains, in
principle, were tax
exempted at that
time.
=> Tax Arbitrage
17
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Clientele Effect
• Ignoring transaction costs investors could sell the shares on the cumdate to those investors that have the lowest marginal tax rate on
dividends, provided that capital gains tax-wise are treated more
favorably than dividends.
• Taking transaction costs and risk considerations into account,
aggregated tax burden can also be minimized by a dividend policy
that reflects the tax preference of its investor clientele
- Investors in the highest tax brackets select into those companies
that pay no or low dividends.
- Investors in the lowest tax brackets select into those companies that
pay high dividends.
• Firms should follow a constant dividend policy.
18
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Empirical Approach with an Event Study on Ex-Dividend Date
Elton and Gruber (1970) tried to measure clientele effect
• Method: Observe average price decline on ex-dividend date
- Sample: 4,148 observations in 01.04.1966 - 31.03.1967
• To prevent arbitrage profits, it must hold
PB - t g (PB - PC ) = PA - t g (PA - PC ) + div(1 - t0 )
Where:
PC = Original stock purchase price
PB = Stock price before it goes ex-dividend
PA = Ex-dividend price
t g = Capital gains tax rate
t0 = Ordinary tax rate
div = Dividend per share
• Therefore, tax rate of marginal investor can be estimated
PB − PA 1− t0
=
≈ 78%
div
1− t g
• Implies marginal tax bracket for dividends of average investor of 36.4%, because at
that time capital gains tax was half of the ordinary tax.
19
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Empirical Evidence is in Favor of Clientele Effect
Elton and Gruber (1970): Results ' Dividend Yield Statistics Ranked by Decile'
High dividend yield (div/P) corresponds to
high relative price decline, i.e. low tax-brackets
20
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
The US Dividend Tax Cut in 2003
Consider an individual investor in the highest U.S. tax bracket who plans to hold a
stock for more than one year. What was the effective dividend tax rate for this
investor in 2002? How did the effective dividend tax rate change in 2003? (Ignore
state taxes.)
From Berk/de Marzo (2017), Table 17.2, in 2002: td = 39% and tg = 20%. Thus
td* =
0.39 - 0.20
= 23.75%
1 - 0.20
This indicates a significant tax disadvantage of dividends; each $1 of dividends
is worth only $0.7625 in capital gains. However, after the 2003 tax cut,
td = 15% and tg = 15%, and
0.15 - 0.15
t =
= 0%
1 - 0.15
*
d
Therefore, the 2003 tax cut eliminated the tax disadvantage of dividends for a
one-year investor.
21
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Taxes and Cash Retention
Source: Berk/de Marzo (2017)
Cash is equivalent to negative leverage, so the tax advantage of leverage
implies a tax disadvantage to holding cash.
22
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Agenda
Distributions to Shareholders
Irrelevance of Payout Policy
Payout Policy and the Clientele Effect
Payout Policy and Signaling
Payout Policy and Agency Costs
23
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Three Alternative Explanations for Relevance of Payout Policy
Violations of MM-assumptions
Subsequent discussion
1
Taxes
Clientele effect
2
Asymmetric information
Signaling theory
3
Agency cost
Agency theory
24
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Signaling Assumes Asymmetric Information and Proper Incentives
Ross (1977) assumptions
1. Managers as insiders have privileged access to information about the firm
• Assumption of asymmetric information
2. Managers will choose unambiguous signals about firm's future,
• If proper incentives in place
3. Managers are reluctant to decrease dividends (because of the clientele effect, for
instance)
4. Under assumptions 1. to 3. dividend announcements help to better predict future
returns, i.e. they should have an impact on share prices
ÞDividend Signaling Hypothesis
ÞEmpirical evidence supports this hypothesis. However, the effect is economically rather
weak
25
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
GMʼs Earnings and Dividends per Share, 1985–2008
Source: Berk/de Marzo (2017), Compustat and CapitalIQ.
26
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Stock Splits and Stock Dividends
According to the Dividend Signaling Hypothesis stock dividends and splits
should have a positive impact on share prices.
The number of shares increase, i.e. under the assumption of a constant
dividend per share the payout volume is expected to increase.
Under this perspective the effect is the same as for a dividend increase.
27
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Source: Berk/de Marzo (2014)
Share repurchases are a credible signal that
the shares are underpriced, because if they
are overpriced a share repurchase is costly
for current shareholders
28
Source: Berk/de Marzo (2017)
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
29
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Agenda
Distributions to Shareholders
Irrelevance of Payout Policy
Payout Policy and the Clientele Effect
Payout Policy and Signaling
Payout Policy and Agency Costs
30
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Three Alternative Explanations for Relevance of Payout Policy
Violations of MM-assumptions
Subsequent discussion
1
Taxes
Clientele effect
2
Asymmetric information
Signaling theory
3
Agency cost
Agency theory
31
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Optimal dividend balances reduced agency costs with higher
transaction costs
Rozeff (1982): Optimal dividend policy trades off between the transaction costs of
raising external capital and the benefit of reduced agency costs
• Increasing dividend reduces agency costs
- More dividend increases need for external capital
- External capital provides additional monitoring of management
- Relates to Jensen’s Free Cash Flow Theory
Michael Rozeff
U of Buffalo
• Increasing dividend increases transaction costs
- More dividend increases need for external capital
- Raising external capital is costly
• Trade-off: Value optimizing dividend balances reduced agency cost against
higher transaction costs
- Similar to free cash-flow theory of debt
Reference: Rozeff (1982) Growth, Beta and Agency Costs as Determinants of Dividend Payout Ratios, Journal of Financial Research
32
Corporate Finance – Raising Capital
Prof. Dr. Christoph Kaserer
Chair for Financial Management
and Capital Markets
Technische Universität München
Arcisstr. 21
D-80290 München
Tel.:
+49 89 / 289 - 25489
Fax:
+49 89 / 289 - 25488
Mail:
christoph.kaserer@tum.de
URL:
www.fm.wi.tum.de
1
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Agenda
Raising Debt: Corporate Bonds and their Structure
Raising Equity by Private Firms: Venture Capital
Raising Equity by Public Firms: IPOs
The IPO-Process
IPO Puzzles
SEOs
2
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Bond Markets are a significant Source of Financing
- Corporate debt outstanding in the Eurozone was estimated to be about €4.5 trn in 2016
(compared to more than $6 trn in the US).
- Unfortunately, European corporate debt markets are very illiquid. On average, 6 days after
issuance bonds trade less than twice a day.
- European bond markets are still fragmented (lack of standardization, lack of harmonization
in insolvency rules, etc.)
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Features of Public Debt
• Prospectus
- Legal document accompanying any public debt issue
- Technically it works similar to a stock issue
• Bearer vs. registered bonds
• Bond characteristics
- Volume, face value, coupon, payment frequency, maturity
• Special features
- Secured (e.g. mortgage bonds, ABS
- Unsecured
- Senior vs. junior
- Zero bonds
- Call provisions
- Convertibility/Warrant
- Covenants (e.g. Debt/EBITDA-ratio is restricted)
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Top 10 Underwriters in International Bond Markets
Source: Global Capital, April 2019, Year to Date
5
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Top 10 Underwriters of Syndicated Loans
Source: Global Capital, April 2019, Year to Date
6
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Features of Private Debt
• Bank loans
• Syndicated bank loans
• Private placements/Schuldscheine
- Sold to a small group of investors
- Rules for public debt issues do not apply
- Less liquid than public debt
• Loans by debt funds (a new market player emerged since the
financial crisis)
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Call Provision (I/II)
•
A call feature allows the issuer of the bond the right (but not the
obligation) to retire all outstanding bonds on (or after) a specific date
(the call date), for the call price.
- The call price is generally set at or above the face value, and expressed
as a percentage of, the bond’s face value.
•
A firm may choose to call a bond issue if interest rates have fallen.
- The issuer can lower its borrowing costs by exercising the call on the
callable bond and then immediately refinancing the issue at a lower
rate.
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Call Provision (II/II)
• Holders of callable bonds understand that the issuer will
exercise the call option only when the coupon rate of the bond
exceeds the prevailing market rate.
- If a bond is called, investors must reinvest the proceeds
when market rates are lower than the coupon rate they are currently
receiving.
- This makes callable bonds relatively less attractive to bondholders than
identical non-callable bonds.
- A callable bond will trade at a lower price (and therefore a higher yield)
than an otherwise equivalent non-callable bond.
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Prices of Callable (at par) and Non-Callable Bonds
on the Call Date
Source: Berk/de Marzo (2017), Figure 24.2
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Prices of Callable and Non-Callable Bonds Prior to the
Call Date
Source: Berk/de Marzo (2017), Figure 24.3
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Convertible Provisions
•
Convertible bond
•
Conversion ratio.
- A corporate bond with a provision that gives the bondholder an option to
convert each bond owned into a fixed number of shares.
- The number of shares received upon conversion of a convertible bond
per a given face value.
•
Conversion price
•
Conversion period
- The conversion ratio determines a conversion price, which is equal to
the face value divided by the number of shares received upon
conversion
- The period over which the conversion option can be exercised. Often,
this period is equal to the lifetime of the bond.
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Convertible Provisions: Example
Assume you have a convertible bond with a $1000 face
value and a conversion ratio of 15.
•
•
If you convert the bond into stock, you will receive 15 shares.
If you do not convert, you will receive $1000.
- By converting you essentially “pay” $1000 for 15 shares, implying a
price per share of $66.67.
- If the price of the stock exceeds $66.67, you will choose to convert;
otherwise, you will take the cash.
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Convertible Bond Value
Source: Berk/de Marzo (2017), Figure 24.4
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Convertible Provisions: Warrants
• A call option written by the company itself on new
stock
- When a holder of a warrant exercises it and thereby
purchases stock, the company delivers this stock by
issuing new stock.
- Convertible debt carries a lower interest rate because it has
an embedded warrant.
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Agenda
Raising Debt: Corporate Bonds and their Structure
Raising Equity by Private Firms: Venture Capital
Raising Equity by Public Firms: IPOs
The IPO-Process
IPO Puzzles
SEOs
16
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Introduction – The Financial Lifecycle
Public Equity
Private Equity
Venture Capital
Entpreneurs,
Public Subsidizes,
Business Angels,
Family&Friends
Venture Capital Firms
(incl. CVC)
Private Equity Firms
Institutional and
Private Investors
(incl. Hedge Funds)
low
Seed
Early Stage Expansion Late Stage
Development
IPO
Buyout
Revenues
Investor s Risk
high
high
low
Firm
stage
17
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Some Important Terms in Private Equity
•
•
•
•
•
•
•
•
VC firm
PE firm
general partner (GP)
VC fund
Fund of Funds (FOF)
limited partner (LP)
raised, closed
vintage year
•
•
•
•
•
•
•
•
private placement memorandum
(PPM)
fees
carried interest=carry
hurdle returns
capital call = drawdown =
takedown
distributions=dividends
committed capital
contributed capital
18
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Structure of a PE/VC Limited Partnership
19
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Top 10 Private Equity Funds in 2017
Rank
Firm name
Headquarters
Five-Year Fundraising
Total (in $ billion)
1
Blackstone
New York
58.3
2
Kohlberg Kravis Roberts
New York
41.6
3
The Carlyle Group
Washington D.C.
40.7
4
TPG Capital
Fort Worth
36.1
5
Warburg Pincus
New York
30.8
6
Advent International
Boston
27.0
7
Apollo Global Management
New York
24.0
8
EnCap Investments
Houston
21.2
9
Neuberger Berman Group
New York
20.4
10
CVC Capital Partners
London
19.9
Source: Private Equity International, www.peimedia.com
Note: there is not a single German based PE firm in this ranking. The first two
Continental European firms are Ardian (Paris, 24, $11.3 bn) and EQT (Stockholm, 31,
$10 bn).
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Some Important Terms in Venture Capital Financing
•
•
•
•
•
•
•
•
•
Closing date
Pre-money-/Post-money-valuation
(Financing) Rounds
Fully diluted share count
Proposed ownership percentage
Tranch
Milestones
•
•
•
•
•
•
•
Deemed liquidation event
(Participating) Liquidation preference
(2X, 3X, etc.)
Dividend preference
Cumulative vs. non-cumulative
dividends
Stock dividends = Payment-in-kind
(PIK) dividends
Step vesting, cliff vesting
Right of first refusal, Right of first
offer
Drag-along rights
Take-me-along = tag-along rights
21
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Top 10 Venture Capital Firms in 2017
Rank
Firm name
Headquarters
Ten-Year Fundraising
Total (in $ billion)
1
Tiger Global Management
New York
12.0
2
New Enterprise Associates
Menlo Park
8.2
3
Sequoia Capital
Menlo Park
7.9
4
DST Global
Hong Kong
7.2
5
Kleiner Perkins Caufield &
Bayers
Menlo Park
7.1
6
Andreessen Horowitz
Menlo Park
5.5
7
Accel Partners
Palo Alto
5.5
8
IDG Capital
Bejing
5.0
9
Index Ventures
London
4.7
10
Lightspeed Venture
Partners
Menlo Park
4.6
Source: Preqin Special Report 2017
Note: the first German based VC firm in this ranking is Rocket Internet with a fundraising
volume of $1 bn.
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Agenda
Raising Debt: Corporate Bonds and their Structure
Raising Equity by Private Firms: Venture Capital
Raising Equity by Public Firms: IPOs
The IPO-Process
IPO Puzzles
SEOs
23
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Most active IPO markets in 2018 by proceeds
Source: E&Y
24
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Top 10 IPOs world-wide and in Germany
World-wide
Year Company
2014
Alibaba
2018
Germany
Exchange
Value
$bn
Year Company
Value
€bn
NYSE
21.8
1996 Deutsche Telekom
Softbank
TYO
21.3
2000 Deutsche Post
5,8
1998
NTT DoCoMo Inc.
TYO
18,1
2000 Infineon
5,4
2008
VISA
NYSE
17,9
2016 innogy
4,6
2010
AIA
HK
17,8
1999
Enel
Euronext
16,5
2018 Healthineers
4,2
2012
Facebook
Nasdaq
16,0
2018 Knorr Bremse
3,8
2010
GM
NYSE
15,8
2000 T-Online
2,5
2006
ICBC
HK
14,0
2013 Evonik*
2,2
1996
Deutsche Telekom
FSE/NYSE
14,0
2007 Tognum
2,0
2004 Deutsche Postbank
1,6
Source: Renaissance Capital
10,4
* This, effectively, was a private placement
Source: Deutsche Börse, own calculations
25
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Some Important Terms in IPO Financing
•
•
•
•
•
•
•
•
•
•
new issue
placing
introduction
dual listing
global IPO
prospectus / offering document
primary offering
secondary offering
underpricing
lock-up
•
•
•
•
•
•
•
•
•
•
•
beauty contest
(lead) underwriter
syndicate
best effort / firm commitment
greenshoe (over-allotment)
road show
equity story
bookbuilding / fixed offering /
auctioning
offer price
gross spread
total flotation costs
26
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Agenda
Raising Debt: Corporate Bonds and their Structure
Raising Equity by Private Firms: Venture Capital
Raising Equity by Public Firms: IPOs
The IPO-Process
IPO Puzzles
SEOs
27
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
What reasons are generally most important?
IPO Motivation – Empirical survey among 335 CFOs in the US
Pros
Cons
Maintain control
M&A
Establish market price
Avoid ownership dilution
Image
Bad market conditions
Loss of confidentiality
Minimize cost of capital
Reporting requirements
Broaden ownership base
Have enough capital
Allow principles to diversify
Costs/fees
Attract analyst attention
Officer liabilities
Allow VCs to cash-out
Low stock price
Requires new equity
Prefer to be acquired
New debt too expensive
Avoid EPS dillution
1
2
3
4
5
1
2
3
4
5
Note: 1 = not important, 5 = very important
Source: Brau, Fawcett (2006) "Initial Public Offerings: An Analysis of Theory and Practice", Journal of Finance
28
-
Regulated
markets
The European regulatory capital market landscape
Prime Standard (DBAG):
- Bilingual investor
communication
- Quarterly reports
- Yearly analyst meetings
- Interim reports
- IFRS Financial
Statements
- Prospectus
-
Ad-hoc
disclosure
Insider rules
Market abuse
ban
Disclosure of
directors‘
dealings
Disclosure of
ownership
percentages
Takeover rules
Exchangeregulated markets
Listing
- Offering
document
- Financial
Statements
according to local
GAAP (e.g. HGB)
Entry Standard (DBAG):
- Interim reports
- Company calendar and
portrait on website
-
Ad-hoc
disclosure
Insider rules
Market abuse
ban
Disclosure of
directors‘
dealings
MiFID II, MiFIR, Prospectus Directive, Market
Abuse Directive, Transparency Directive,
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
29
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Preparation period for an IPO is around 4-5 months
Typical time schedule: IPO at Prime or General Standard of Deutsche Börse
1
2
3
Kick-off
Selection of advisors
Selection of investment bank
Due Diligence (2-4 Weeks)
Determination of Prospectus
English Translation (3 Weeks)
Preparation analyst presentation
4
5
6
Premarketing
Preparation Research (2-3 Weeks)
Publication Research
Approval of Prospectus by BaFin (min. 20 days)
Publication of
Print Prospectus
preliminary
Bookbilding
Prospectus
Allocation//Pricing
First day of trading
1. Month
2. Month
3. Month
4. Month
5. Month
30
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Bookbuilding mechanics are determined by discretionary allocation
Investment bank manages the process
• Sets indicative price range
• Solicits indication of interest from institutional investors
– Not legally binding from investor, but rare deviations
• Constructs demand curve
• Sets price to generate oversubscription (demand > supply)
• Allocates shares to bidders at discretion
Example of curves
for a real issue
Demand
Allocation is used by IB to reward investors
• ... for providing better information
– Indication of interest provides information to IB from investors
Supply
– Limit price indication favored over quantity indication
• ... for being regular investor
– Providing insurance to IBs by also bying bad-received issues
• ... for submitting bids directly to the bookrunner
– Favored over bids to other syndicate members
– Maximizes internal bookrunner fees
Source: Cornelli (2001) "Bookbuilding and Strategic Allocation", Journal of Finance
31
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Top 10 underwriters in global equity markets
Source: Global Capital, April 2019
32
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Listing / post-IPO: Price stabilization for long-term shareholders
Lock-up period
• Defines no-sale period for old shareholders
• Usually 6-12 months
• Important for signalling of existing shareholders
Greenshoe option
• Stabilizes post-IPO price
• Also called over-allotment option
• Named after company "Greenshoe Manufacturing" where first applied in 1963
• Underwriter issues a maximum of 15% more stocks than initially available
(short position)
- If price falls, underwriter buys back shares
- If price rises, underwriter can increase issue to fulfil demand
• Strictly regulated
Quiet period
• Press and brokers can start covering stock after 25th day
33
The Facebook IPO – A Brief Case Study
• On May 18th, 2012, Facebook‘s stocks were traded for the first time on the Nasdaq
trading system.
• Within the IPO 421 mn shares were offered, of wich180 mn were primary shares. After
the IPO the company had a total of 2,138 mn shares outstanding.
• In the bookbuilding process preceding the IPO shares were offered within a
bookbuilding range of 32 to 38 $. At the end of the bookbuilding process the company
together with the lead underwriter (J.P. Morgan) decided to allocate the shares at 38 $.
• After the end of the black-out period (end of June) J.P. Morgan issued a research
report stating that the target price of the Facebook stock should be 45 $. However,
other more independent analysts at the same time came up with a lower target price
(Macquarie: 34 $; RBC Capital Market: 40 $; Wells Fargo: 37-40 $; Morgan Stanley:
38 $). All these analysts used different valuation approaches including a DCF as well
as a multiple approach.
• J.P. Morgan had a greenshoe-option on an additional 15% of shares.
• The company determined a lock-up period timetable allowing incumbent shareholders
to start selling their shares in the following steps: on August 15th 2012 10% of
outstanding shares, on October 14th 2012 9%, on November 13th 2012 49%, on
December 13th 2012 5% and on May 17th 2013 2%.
34
Prof. Dr. Christoph Kaserer, Department of Financial Markets and Capital Markets
18
.0
5.
1
25 2#
.0
5.
1
01 2#
.0
6.
1
08 2#
.0
6.
1
15 2#
.0
6.
1
22 2#
.0
6.
1
29 2#
.0
6.
1
06 2#
.0
7.
1
13 2#
.0
7.
1
20 2#
.0
7.
1
27 2#
.0
7.
1
03 2#
.0
8.
1
10 2#
.0
8.
1
17 2#
.0
8.
1
24 2#
.0
8.
1
31 2#
.0
8.
1
07 2#
.0
9.
1
14 2#
.0
9.
1
21 2#
.0
9.
1
28 2#
.0
9.
1
05 2#
.1
0.
1
12 2#
.1
0.
1
19 2#
.1
0.
1
26 2#
.1
0.
1
02 2#
.1
1.
1
09 2#
.1
1.
1
16 2#
.1
1.
1
23 2#
.1
1.
12
#
Stock Prices and Trading
Facebook's*Stock*Price*(IPO*to*11/27/12)*
40#
160%#
140%#
36#
120%#
32#
100%#
28#
80%#
24#
60%#
40%#
20#
20%#
16#
0%#
Volume#(%#of#stocks#offered)#
Closing#Price#
Offering#Price#
35
Prof. Dr. Christoph Kaserer, Department of Financial Markets and Capital Markets
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Agenda
Raising Debt: Corporate Bonds and their Structure
Raising Equity by Private Firms: Venture Capital
Raising Equity by Public Firms: IPOs
The IPO-Process
IPO Puzzles
SEOs
36
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Four IPO characteristics are puzzling to financial economist
1. Underpricing
• Positive return on first day – why?
2. Number of issues is cyclical
• Swings are larger than the magnitude of growth opportunities – why?
3. Costs of IPOs are very high
• Costs are substantially larger than for other securities – why?
• See section on issue costs
4. Poor long-run post-IPO performance
• 3-5 year returns post return are (debatably) negatively abnormal – why?
• See also chapter on efficient markets
37
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
International Comparison of Flotation Costs
Median (first) and average (second) total
flotation costs 1999 – March 2011
Small Cap Market Segments
Large Cap Market Segments
Source: Kaserer/Schiereck
(2011)
38
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
What explains the difference in the distribution of US vs.
European IPO gross spreads? (1998-2007)
Source: Abrahamson et al. (2011)
39
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Underpricing is a time-varying phenomenon in all capital markets
Empirical studies worldwide of underpricing (=positive first-day return)
Underpricing represents money "left on the
table"
Source: Berk/de Marzo (2017)
40
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
However, underpricing is yet unexplained (I/II)
Possible explanations: UP positively related to degree of asymmetric information
Asymmetric information
Possible explanation
Description
Source
• Signaling
• Lemmon market problem and
underpricing profit as signal
• Mixed evidence
• Allen, Faulhaber (1989),
Grinblatt, Hwang (1989),
Welch (1989)
• Ex-ante Uncertainty
• Unknown demand for stock
• Beatty/Ritter (1986)
• Winner's curse
• Protection against getting issue exactly
when being overoptimistic
• Rock (1986)
• Negative cascade
• Investors buy if others buy
• UP induces positive cascade
• Welch (1992
• Institutional aspects of
allotment
• Revealing demand at bookbuilding will
increase final issue price lowering ret.
• UP is compensation for info revelation
• Only partial explanation for magnitude
• Benveniste, Spindt
(1989), Benveniste,
Wilhelm (1990), Spatt,
Srivastava (1991)
• Substitute for marketing
expense
• UP as marketing method
• Only partial explanation for magnitude
• Habib and Ljungqvist
(2001)
Source: Ritter, Welch (2002) "A Review of IPO Activity, Pricing, and Allocations", Journal of Finance
41
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
However, underpricing is yet unexplained (II/II)
Possible explanations: Asymmetric info. and allocation process determinants
Allocation process
Symmetric info.
Possible explanation
• Insurance against legal
liability
Description
• UP reduces probability of issuer being
sued
• Disputed, because UP also outside US
• After market support
• Conflict of interest betw.
underwriter and issuer
• Strategic ownership
control
• Underwriter reputation
• UP & oversubscription increases aftermarket trading
• Underwriter benefits from market making
fee, issuer if increased liquidity
persistent
Source
• Tinic (1988), Hughes,
Thakor (1992)
• Boehmer, Fishe (2001),
Ruud (1993), Aggarwal
(2000), Zhang (2001)
• Loughran and Ritter
(2002)
• Underwriters favor buy-side clients
• Issuers tolerate if firm is worth more than
thought before (prospect theory)
• Several
• UP creates oversubscription allowing
strategic allotment to specific
shareholders
• Institutionals provide monitoring, small
investors provide liquidity
• Carter, Manaster (1990)
• UP is compensation for reputation
Source: Ritter, Welch (2002) "A Review of IPO Activity, Pricing, and Allocations", Journal of Finance
42
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
The Winner’s Curse: Example (1 of 4)*
Problem
Thompson Brothers, a large underwriter, is offering its customers the following
opportunity: Thompson will guarantee a piece of every IPO it is involved in.
Suppose you are a customer. On each deal you must commit to buying 2000
shares. If the shares are available, you get them. If the deal is oversubscribed,
your allocation of shares is rationed in proportion to the oversubscription. Your
market research shows that typically 80% of the time Thompson’s deals are
oversubscribed 16 to 1 (there are 16 orders for every 1 order that can be filled),
and this excess demand leads to a price increase on the first day of 20%.
However, 20% of the time Thompson’s deals are not oversubscribed, and while
Thompson supports the price in the market (by not exercising the green shoe
provision and instead buying back shares), on average the price tends to
decline by 5% on the first day. Based on these statistics, what is the average
under pricing of a Thompson IPO? What is your average return as an investor?
* Example is taken from Berk/de Marzo (2017), Example 23.5
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
The Winner’s Curse: Example (2 of 4)
Solution
First, note that the average first-day return for Thompson Brothers
deals is large: 0.8(20%) + 0.2(−5%) = 15%. If Thompson had one IPO
per month, after a year you would earn an annual return of
1.1512 - 1 = 435%!
In reality, you cannot earn this return. For successful IPOs you will earn
a 20% return, but you will only receive
2000
= 125 shares.
16
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
The Winner’s Curse: Example (3 of 4)
Assuming an average IPO price of $15 per share, your profit is
$15 per share × (125 shares) × (20% return) = $375
For unsuccessful IPOs you will receive your full allocation of 2000
shares. Because these stocks tend to fall by 5%, your profit is
$15 per share × (2000 shares) × (−5% return) = −$1500
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
The Winner’s Curse: Example (4 of 4)
Because 80% of Thompson’s IPOs are successful, your average
profit is therefore
0.80($375) + 0.20(−$1500) = $0
That is, on average you are just breaking even! As this example
shows, even though the average IPO may be profitable, because
you receive a higher allocation of the less successful IPOs, your
average return may be much lower. Also, if Thompson’s average
under pricing were less than 15%, uninformed investors would lose
money and be unwilling to participate in its IPOs.
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Agenda
Raising Debt: Corporate Bonds and their Structure
Raising Equity by Private Firms: Venture Capital
Raising Equity by Public Firms: IPOs
The IPO-Process
IPO Puzzles
SEOs
47
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Seasoned Equity Offerings (SEOs)
• When a public company offers new shares (primary shares) for
sale
- Public firms use SEOs to raise additional equity.
- When a firm issues stock using an SEO, it follows some of the
same steps as for an IPO.
- The main difference is that a market price for the stock
already exists, so the price-setting process is not
necessary.
- As a consequence SEOs are much cheaper than IPOs
- Two main ways to offer the shares:
ü Rights offering (still common in Europe, especially
Germany)
ü Cash offering or Bookbuilding (common in the US)
48
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
The mechanics of SEOs
• Primary Shares
New shares issued by a company in an equity offering
• Secondary Shares
Shares sold by existing shareholders in an equity offering
• Tombstones
A newspaper advertisement in which an underwriter advertises a
security issuance
49
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Short term announcement effects (+/- 1d) of SEOs
Source: Eckbo et al. (2007)
50
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Long term announcement effects of SEOs relative to a
Source: Eckbo et al. (2007)
risk-adjusted portfolio
51
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Post-SEO Performance
Source: Berk/de Marzo (2017), Figure 23.7, adapted from A. Brav, C. Geczy, and P. Gompers, “Is the
Abnormal Return Following Equity Issuances Anomalous,” Journal of Financial Economics 56
(2000): 209–249, Figure 3.
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Flotation costs are significantly lower as for IPOs
Source: Bühner/Kaserer
(2002)
53
Corporate Finance – Practical Valuation
Prof. Dr. Christoph Kaserer
Chair for Financial Management
and Capital Markets
Technische Universität München
Arcisstr. 21
D-80290 München
Tel.:
+49 89 / 289 - 25489
Fax:
+49 89 / 289 - 25488
Mail:
christoph.kaserer@tum.de
URL:
www.fm.wi.tum.de
1
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Agenda
§
DCF Valuation
§
Practical Example
§
The APV Method
§
Multiple Valuation
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Practical Valuation
2
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
The fundamentals of corporate valuation
In a complete and arbitrage free capital market the market value of any asset (V)
can be expressed as the expected present value of its future cash flows (FCF)
using the risk-free rate (rf) as the discount factor and the risk-neutral probability
measure E* (Fundamental Asset Pricing Theorem – FAPT)
'
!=#
$%&
( ∗ *+*$
1 + ./
$
For company valuation, under the assumption that a constant stochastic discount
factor exists, this is equivalent to the DCF entity approach:
'
!=#
$%&
( *+*$
1 + 01++
$
Ø E() denotes the objective probability measure
Ø WACC denotes the firm’s cost of capital on a complete and arbitrage free capital market
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Practical Valuation
3
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Corporate valuation – A synthesis
Corporate
Valuation
DCF
WACC
APV
Multiples
Equity
Approach
Entity
Multiples
Equity
Multiples
Asset
Stripping
Liquidation
Asset
Values
Entity Approach
Going Concern Values
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Practical Valuation
4
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
DCF – Entity vs. equity approach
Free Cash Flow to the Firm
6,0
Value
of
debt*
7,0
6,5
5,0
0,2
t=1
t=2
0,2
t=3
0,2
0,2
0,2
0,3
t=4
t=5
t=6
t=7
Cost of the firm’s debt capital
Entity
value
2,0
1,0
t=2
0,2
Free Cash Flows to Equityholders
3,0
t=1
Cash Flows to Debtholders
t=3
t=4
t=5
t=6
Cost of equity6,7
Value
of
equity**
t=7
Weighted cost of capital (WACC)
5,8
6,3
4,8
2,8
1,8
0,8
t=1
V0 =
€
E [ FCFF1 ]
1 +
(1+ WACC)
E [ FCFF2 ]
(1+ WACC)
Entity Approach
2
+
E [ FCFF3 ]
(1+ WACC)
3
+ ...
t=2
t=3
t=4
t=5
t=6
t=7
* often approximated by the book
E [ FCFE1 ] E [ FCFE2 ] E [ FCFE3 ]
value of debt
VE =
+
+
+...
1
2
3
(1+ rE )
(1+ rE )
(1+ rE )
** value of equity = # shares
multiplied by the share price
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Practical Valuation
Equity Approach
5
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
How to derive the FCFF
Earnings before Interest and Taxes (EBIT)
-
- Taxes are determined based on EBIT
à Taxes = Tax Rate * EBIT
Taxes
= Net Operating Profit after Taxes (NOPAT)
+ Depreciation
- Investment (fixed assets)
- Increase in Net Operating Working Capital
(NOWC=receivables + inventory – payables –
operational provisions)
This is a virtual “FREE CASH
FLOW” which you
generally cannot observe
in practice!!!
= Free Cash Flow to the Firm (FCFF - Entity Approach)
Essentially, free cash flow to the firm (FCFF) is the amount of
money that can be distributed to all suppliers of capital
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Practical Valuation
6
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
How to derive the FCFE
Earnings before Taxes (EBT)
-
Taxes
= Net Income (NI)
= Free Cash Flow to Equity (FCFE - Equity Approach)
Essentially, free
cash flow to
equity (FCFE)
is the amount of
money that can
be distributed to
equityholders
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Practical Valuation
7
+ Depreciation
- Investments (fixed operating assets)
- Increase in Net Operating Working Capital
(NOWC=receivables + inventory – payables –
operational provisions)
- Cash flow to debt (Repayment of debt – new debt issued)
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Entity Value (Firm Value) vs. Enterprise Value
Entity Value =
Enterprise Value (=Value of operations)
∞
VOp = ∑
t =1
FCFFt
(1+WACC)
t
+
Value of non-operating assets
§
Marketable securities
§
Ownership of non-controlling interest in
another company
§
Firm value or entity value are used interchangeably; they indicate the value of all operating and non-operating
assets, i.e. VOp+VNOA=VD+VE
§
Enterprise value reflects the value of operating assets only, i.e.
!"# = !% + !' − !)"* = !% + +,- .,/§
Debt reduced by the market value of non-operating assets (mostly cash) is called net debt, i.e
Net Debt = VD-VNOA. Therefore, when calculating the DCF enterprise value the capital structure has to
be measured on the basis of the net debt.
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Practical Valuation
8
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Cash flow projection as a two step procedure
Phase I: detailed planning
Phase II: (Constant) growth
6,5
7,0
6,0
5,0
3,0
2,0
1,0
2012
2013
TV17 =
2014
2015
2016
2017
FCFF18
FCFF18
1
⇒ TV12 =
⋅
WACC − g
WACC − g (1+ WACC )5
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Practical Valuation
2018
Q: How to calculate the
terminal value?
A: By using the GordonGrowth Formula
9
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Issues in cash flow projection
Detailed forecast of next three years CFs with three alternative methods
• Historical estimates
– Sensitive to choice of method and time period
– Possibly no good proxy for future (esp. if CFs negative)
• Expert estimates: Analysts forecasts
– Better for larger, better covered firms
– Not necessarily accurate, possibly positively biased
• Fundamental business modeling
– Delivers most accurate, subjective value estimate
– Takes time, skill and insight
Terminal value (TV) determined by long-term future CF and long-term growth
• Growth rate g assumption essential
– Usually inflation plus long-term growth of economy
• Different terminal value methods possible
– Perpetuity growth model: TV = CF / (k – g)
– Exit multiple approach
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Practical Valuation
10
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
How to estimate the cost of equity
Cost of equity estimation is (mostly) based on CAPM
Issues in implementing this model
Rational investors tend to diversify their risks
-
Market risk premiums are highly disputued
… thus only the market risk component is
compensated by the market.
-
IDW currently recommends 5.5 to 7% (pre-tax)
-
Beta estimation is not very robust and subject
to discretion
CAPM pricing formula
rE = rriskfree + β stock ⋅ ( rmarket return − rriskfree )
From the CAPM pricing formula it follows that
… securities are not priced with respect to their
stand-alone risk but their with respect to their
market risk only!
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Practical Valuation
-
Sampling frequency (daily, monthly, etc.)
-
Estimation window (250 days, 60 months,
etc.)
-
Market geography (national, world-wide)
-
Market index
-
Alternative market models (CAPM, FF3FM,
etc.)
-
Individual vs. industry betas
-
Problem of de- and releveraging
11
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Betas are not very robust
Rolling 60 months beta of Lanxess based on mid of month and end of month prices (2005 to 2015)
Lanxess$
1,9$
1,8$
1,7$
1,6$
≈0,4
1,5$
1,4$
1,3$
2010.01$
2010.07$
2011.01$
2011.07$
2012.01$
2012.07$
End$of$month$
2013.01$
2013.07$
2014.01$
2014.07$
2015.01$
Mid$of$month$
Source: ThomsonReuters, own calculations
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Practical Valuation
12
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
How to de-/re-leverage beta
§Betas of different companies need to be re-leveraged to make them comparable
ØBecause company-specific leverage has large influence
ØBeta with leverage of target company has to be calculated
ØAlternatively, adjustment can be done via the WACC-formula
§For firms with constant risk-free debt de-leveraged equity (asset) beta can be
calculated according to the Hamada-Equation
" VD
%
β E = βU $1+ (1− T ) '
# VE
&
Example
Firm
Daimler
Volkswagen
Renault
FCA
BMW
Avg.%Beta
Beta
1,14
0,98
1,54
1,46
1,31
1,29
Tax+Rate
30%
30%
35%
40%
30%
Debt/to/
Equity+Ratio
0,77
0,79
1,39
1,25
1,05
Asset+
Beta
0,74
0,63
0,81
0,83
0,76
0,75
Notes: Example is based on information as of July 2015
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Practical Valuation
13
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Industry asset betas
Source: Berk/deMarzo, Figure 12.4
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Practical Valuation
14
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Calculating the WACC
If a firm is financed by debt and equity simultaneously, then the discount rate in the entity approach
must reflect this fact
è weighted average cost of capital (WACC)
VD
VE
WACC = rD (1− T )
+ rE
V
V
where
- rD is the cost of debt,
§
è WACC provides a tool to determine V and VE but both
parameters are needed as inputs to determine WACC
è may use rollback methods to solve the problem
§
Problem 2: Debt regime
§
è The left hand side WACC assumes a constant leverage
(based on market values)
§
Alternative method: APV Approach
- T is the corporate tax rate,
- rE is the cost of equity,
Problem 1: circularity problem
- VD the market value of outstanding net debt,
è APV splits the entity value of a debt finance firm into the
value as if it would be fully equity financed and the tax
shield of debt
- VE the market value of outstanding equity
è may use rollback methods to solve the problem
Note that V=VD+VE holds by definition
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Practical Valuation
15
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Risk-free rate and term structure
Estimating the term structure
• Ideally the term structure should be reflected in the discount rate
– This can be done by looking at the empirical term structure of forward rates
– Alternatively, the Svensson-method can be applied
0
0
1 − -./ − 1
1 − -./ − 1
0
+
+
!"# $ 100 = () + (+
+
(
−
-./
−
2
0
0
1+
1+
1+
+ (3
0
1 − -./ − 1
0
2
−
-./
−
0
12
12
– This gives the continuously compounded risk-free rate for maturity t; all
parameters are daily reported by the Bundesbank or the FED
Practitioners, however, often operate with a single discount rate
• This discount rate k is derived by solving (numerically, t≈250) the equation
∞
∑
t =1
(1+ g)
t
(1+ kt )
t
1+ g
=
k −g
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Practical Valuation
16
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Problems with the Svensson-method
• Note, however, that applying the Svensson-Method beyond the observable 30year maturity can lead to strange patterns in the term structure:
3.5"
3.5"
3"
3"
2.5"
2.5"
R 2"
a
t
e% 1.5"
R 2"
a
t
e% 1.5"
1"
1"
0.5"
0.5"
0"
0"
5"
10"
15"
20"
0"
0"
Maturity(in(years(
50"
100"
150"
200"
250"
Maturity(in(years(
• One solution is to estimate an ultimate forward rate (UFR).
• Alternatively, it is often assumed that beyond the year 30 the term structure is flat.
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Practical Valuation
17
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Valuation and personal taxes
- Hitherto we have looked at corporate taxes only, personal taxes were ignored
Taking into account personal taxes
• According to IDW S1, cif. 28, personal taxes on any distribution made by the
company has to be taken into account (after tax valuation).
• The after tax cost of equity is calculated according to the tax CAPM. Under the
current tax regime (Abgeltungssteuer) it follows:
AT
rEAT = (1− π ) rriskfree + β stock ⋅ ( rmarket
return − (1− π ) rriskfree )
where p is the personal tax rate (26.4%) and AT stands for after tax
• According to IDW the after tax market risk premium should be around 5 to 6%
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Practical Valuation
18
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Agenda
§
DCF Valuation
§
Practical Example
§
The APV Method
§
Multiple Valuation
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Practical Valuation
19
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Practical example: DCF Valuation of Facebook
• The valuation is done by the beginning of the year 2012 in order to prepare for the
IPO consumed on May 18th, 2012
• For conducting a DCF valuation (entity approach) the estimates provided by the lead
investment bank (J.P. Morgan) are used. These estimates are summarized on the
following page.
• Moreover, use and discuss the following assumptions:
a) Risk-free rate: 2%
b) Beta (unlevered): 1,2
c) Market risk premium: 7%
d) Tax rate: 41%
e) Terminal growth rate: 2%
f) #shares: 2,138 mn
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Practical Valuation
20
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Balance Sheet
All numbers are in $ million unless mentioned otherwise
Assets
Current Assets:
Cash & Cash Equivalents
Marketable Securities
Accounts Receivable
Prepaid Expenses & Other Current Assets
Total Current Assets
FY 10
FY 11
FY 12
FY 13
FY 14
FY 15
FY 16
1.785
373
88
2.246
1.512
2.396
547
149
4.604
1.199
2.396
1.264
252
5.111
2.534
2.396
1.281
427
6.638
3.685
2.396
2.924
723
9.728
7.936
2.396
3.399
1.225
14.956
14.481
2.396
6.377
2.074
25.328
574
59
37
74
2.990
1.475
80
82
90
6.331
1.992
3.365
149
215
82
82
179
250
7.513 10.549,435
5.066
350
82
414
15.640
7.979
529
82
622
24.168
12.054
816
82
962
39.242
Liabilities and Stockholders’ Equity
Current Liabilities:
AccountsPayable
PlatformPartners Payable
Accrued Expenses & Other Current Liabilities
Deferred Revenue & Deposits
Current Portion of Capital Lease Obligations
Total Current Liabilities
29
75
137
42
106
389
63
171
296
90
279
899
104
267
640
90
279
1.379
141
382
1.382
90
279
2.274
244
633
2.985
90
279
4.231
358
958
6.450
90
279
8.135
553
1.449
13.936
90
279
16.308
Non-Current Liabilities:
Capital Lease Obligations, Less Current Portion
Long-Term Debt
Other Liabilities
Total Liabilities
117
250
72
828
398
135
1.432
322
135
1.836
228
135
2.637
109
135
4.475
17
135
8.287
11
135
16.454
615
947
(6)
606
2.162
615
2.684
(6)
1.606
4.899
2.684
(6)
2.999
5.677
2.684
(6)
5.235
7.913
2.684
(6)
8.487
11.165
2.684
(6)
13.203
15.881
2.684
(6)
20.111
22.789
2.990
6.331
7.513 10.549,435
15.640
24.168
39.242
Source: www.edupristine.com
Non-Current Assets:
Property & Equipment, net
Intangible Assets, net
Goodwill
Other Assets
Total Assets
Stockholders’ Equity
Convertible Preferred Stock
Common Stock
Additional Paid-in Capital
Accumulated Other Comprehensive Loss
Retained Earnings
Total Stockholders’ Equity
Total Liabilities and Stockholders’ Equity
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Practical Valuation
21
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Income Statement
All numbers are in $ million unless mentioned otherwise
FY 09
Revenue
Advertising Revenue
764
Payments & Other Fees Revenue
13
Total Revenue
777
FY 10
FY 11
FY 12
FY 13
FY 14
FY 15
FY 16
1.868
106
1.974
3.154
557
3.711
5.231
557
5.788
8.518
557
9.075
13.615
557
14.172
21.355
557
21.912
32.853
557
33.410
223
115
87
90
262
493
184
144
121
1.032
860
427
388
280
1.756
1.483
687
695
487
2.436
2.231
989
1.270
668
3.915
3.467
1.620
2.268
1.102
5.717
5.453
2.498
3.944
1.721
8.295
8.234
3.756
6.682
2.561
12.177
Interest Expense
Other Income (Expense), net
EBT
(10)
2
254
(22)
(2)
1.008
(42)
(19)
1.695
(68)
(7)
2.361
(104)
(22)
3.790
(163)
(41)
5.512
(253)
(48)
7.994
(384)
(84)
11.709
Provision for Income Taxes
Net Income
25
229
402
606
695
1.000
968
1.393
1.554
2.236
2.260
3.252
3.278
4.716
4.801
6.908
* Cost of Services include depreciation and Amortizaton Expenses
Depreciation & Amortization
78
139
323
497
736
1.200
1.839
2.782
Cost & Expenses
Cost of Revenue*
Marketing and Sales
Research and Development
General andAdministrative
Income from Operations (EBIT)
Source: www.edupristine.com
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Practical Valuation
22
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
All numbers are in $ million unless mentioned otherwise
Cash Flow from Operating
Net Income
Accounts Receivable
Prepaid Expenses & Other Current Assets
Accounts Payable
Platform Partners Payable
Accrued Expenses & Other Current Liabilities
Deferred Revenue & Deposits
Cash Flow From Operation
Cash Flow Statement
FY 10
Cash Flow from Investment
Property and Equipment
Intangible Assets
Goodwill
Marketable Securities
Other Assets
Cash from Investing Activities
Cash Flow from Financing
Capital Lease Obligations
Long-Term Debt
Other Liabilities
Convertible Preferred Stock
Common Stock
Additional Paid-in Capital
Accumulated Other Comprehensive Loss
Retained Earnings
Cash from Financing Activities
Net Change in Cash
Cash Balance
Opening Balance
Net Change in Cash
Closing Balance
1.785
FY 11
FY 12
FY 13
FY 14
FY 15
FY 16
1.000
(174)
(61)
34
96
159
48
1.102
1.393
(717)
(103)
41
96
344
0
1.052
2.236
(17)
(175)
38
115
742
0
2.939
3.252
(1.643)
(296)
102
252
1.604
0
3.271
4.716
(475)
(501)
114
324
3.465
0
7.643
6.908
(2.978)
(849)
195
492
7.486
0
11.253
(901)
(21)
(45)
(2.396)
(16)
(3.379)
(517)
(69)
(89)
(674)
(1.373)
(66)
(71)
(1.510)
(1.701)
(135)
(164)
(2.000)
(2.913)
(180)
(208)
(3.300)
(4.075)
(287)
(340)
(4.702)
454
(250)
63
1.737
2.004
(76)
(615)
(691)
(94)
(94)
(119)
(119)
(92)
(92)
(6)
(6)
(273)
(313)
1.335
1.151
4.251
6.545
1.785
(273)
1.512
1.512
(313)
1.199
1.199
1.335
2.534
2.534
1.151
3.685
3.685
4.251
7.936
7.936
6.545
14.481
Source: www.edupristine.com
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Practical Valuation
23
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
DCF-Valuation of Facebook
Valuation (Entity Approach)
Risk free rate
Beta
Expected return from market
WACC
Tax Rate
Terminal Growth Rate
No. of Equity Shares
2%
1,20
9%
10,4%
41%
2%
2.138
All numbers are in $ million, except per share data
FY 12
FY 13
FY 14
FY 15
FY 16
DCF Valuation using FCFE
EBIT
Less: Taxes
Add: Depreciation
Less: Capex
Less: Increase in Working Capital
Free Cashflow to the Firm (FCFF)
2.436
(999)
497
(586)
(341)
1.008
3.915
(1.605)
736
(1.439)
704
2.311
5.717
(2.344)
1.200
(1.836)
18
2.755
8.295
(3.401)
1.839
(3.092)
2.927
6.568
12.177
(4.992)
2.782
(4.362)
4.345
9.949
4
4.421
120.813
5
79.733,1
Terminal Value
No. of Years
Total Present Value of cash flow
1
913
Enterprise Value (Operating assets)
89.012
Net Debt
(3.465)
Stock Price
2
1.896
3
2.048
43,25
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Practical Valuation
24
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Calculating the WACC for Orange plc
The mobile telecommunication company Orange plc shall be listed on the LSE. For preparing
their valuation reports financial analysts are wondering what the appropriate WACC might be in
the DCF valuation models. For assessing Orange’s WACC the following information is
available:
The company has a target debt-to-equity ratio of 0.35. Net debt is equal to GBP 400 mn. The
pre-tax cost of debt is 7%.
Tax rate is 33%, the risk-free rate is 4.6% and the market risk premium is 4%.
Vodafone is listed and widely comparable company. For this company we know:
The stock beta is 1.24, the tax rate is 28%, net debt is equal to GBP 1.4 bn and the market
value of equity is GBP 7.1 bn.
üWhat is the WACC of Orange financial analysts’ should use in the DCF valuation models?
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Practical Valuation
25
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Agenda
§
DCF Valuation
§
Practical Example
§
The APV Method
§
Multiple Valuation
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Practical Valuation
26
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
WACC- and APV-method
E [ FCFF1 ]
E [ FCFF2 ]
E [ FCFF3 ]
Enterprise Value (WACC):
V0 =
Enterprise Value (APV):
E [ FCFF1 ] E [ FCFF2 ] E [ FCFF3 ]
V0 =
+
+
+... + PVTS
1
2
3
(1+ rU )
(1+ rU )
(1+ rU )
€
1
(1+ WACC)
+
(1+ WACC)
2
+
(1+ WACC)
3
+ ...
The Adjusted Present Value Method (APV) is a general approach for valuing firms that do not
have constant debt ratios. The enterprise value is split-up into a value of the unlevered firm VU
and present value of the tax shield PVTS. Note, however, that deriving the unlevered cost of
capital rU in general is not obvious, as for an investor holding all the outstanding claims of a firm
the following relationship applies (rT is the expected return associated with the tax shield):
!" = !$ + !& = !' + (!)*
+$ !$ + +& !& = +' !' + +, (!)*
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Practical Valuation
27
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
The APV-method leads to simple solutions only in specific cases
Assume a constant leverage ratio (case I)
In this case rT=rU, as debt is proportional to firm value and tax shields. Therefore, debt has the
same risk as free cash flows.
*
+, ",,' #
"2
",
",
!"#$ = &
;
+
=
+
+
+
;
3455
=
+
−
+
#
;
0
2
,
0
,
1 + +0 '
"
"
"
'()
Assume a constant debt level (case II)
In this case rT=rD, as debt is constant and the tax shield has the same risk as debt.
*
+, ", #
"2
", 1 − #
!"#$ = &
;
+
=
+
+
+
0
2
,
1 + +, '
"
+
"
1
−
#
"2 + ", 1 − #
2
,
'()
Combining this result with the well-know WACC-formula yields: 3455 = +0
",
1−#
"2 + ",
These are two special solutions to the following general relationship
",
3455 = +0 −
# +, + 7 +0 − +,
"2 + ",
where k measures the permanence of the debt level, i.e. k=0 in case I and k=1 in case II
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Practical Valuation
28
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Example I: constant leverage ratio
Assume a firm with FCFF1=4.25mn€ and g=4%, rE=10%, rD=6% and T=35%. The debt-toequity-ratio is fixed at 50%. Calculate the enterprise value according to the WACC- and the
APV-method.
Using the WACC-method
!"## = 6% 1 − 0.35
0=
0.5
1
+ 10%
= 7.97%
1.5
1.5
4.25
= 10734€
0.0797 − 0.04
Using the APV-method
0.5
1
67 = 6%
+ 10%
= 8.67%
1.5
1.5
07 =
90:; =
4.25
= 9134€
0.0867 − 0.04
1
107 < 3 < 0.06 < 0.35
0.0867 − 0.04
= 1634€
0 = 91 + 16 = 10734€
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Practical Valuation
29
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Example II: constant debt level
Assume a firm with FCFF1=4.25mn€ and g=0%, rE=10%, rD=6% and T=35%. The debt level is
fixed at 17.775mn€, which equals one third of the current firm value. Calculate the enterprise
value according to the WACC- and the APV-method.
Using the WACC-method
!"## = 6% 1 − 0.35
0=
0.5
1
+ 10%
= 7.97%
1.5
1.5
4.25
= 53.3434€
0.0797
Using the APV-method
67 =
7.97%
= 9.02%
1
1 − 0.35 8 3
4.25
07 =
= 47.1234€
0.0902
90:; = 17.775 8 0.35 = 6.2234€
0 = 47.12 + 6.22 = 53.3434€
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Practical Valuation
30
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Agenda
§
DCF Valuation
§
Practical Example
§
The APV Method
§
Multiple Valuation
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Practical Valuation
31
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Multiples as an outcome of the DCF-approach
If two firms have the same WACC and growth rate, the ratio of the enterprise value to the FCFF
is the same for both. This ratio can be labelled as a multiple.
EV = FCFF1 × M
∞
t
EV = ∑ FCFFt ⋅ (1+ g) ⋅ (1+ WACC )
t=1
⇒
−t
FFCF1
=
WACC − g
1
M=
WACC − g
For a non-growing firm, FCFF=EBIT(1-T) holds; hence, for firms with the same WACC and
growth rate the ratio EV/EBITDA should be the same.
Similarly, For firms with equal risk, growth rates and capital structure the cost of equity is the
same; hence, they should have the same price/earnings ratio.
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Practical Valuation
32
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Most important multiples used in practice
EV / Sales
EV / EBITDA
EV / EBIT
P/E
§
Applicable to young companies with negative
Annual Net Profit
§
Good availability of data
+
+
+
§
Reflects operating profitability
§
Influence of accounting because of depreciation
eliminated
§
Reflects operating profitability
§
Independent from capital structure decision à
high international comparability
§
Easy to communicate
§
High degree of aggregation
§
Suitable if capital structure is similar
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Practical Valuation
§
Sales is a bad indicator of profit situation
§
Problems with ccounting effects (e.g. non-cash sales)
§
EV reflects the tax shield of comparables à multiple
relates pre-tax earnings figure to after tax market
value
§
Problems due to differences in CAPEX and change in
NWC
§
EV reflects the tax shield of comparables à multiple
relates pre-tax earnings figure to after tax market
value
§
Influence of depreciation policy
§
EV reflects the tax shield of comparables à multiple
relates pre-tax earnings figure to after tax market
value
§
Annual Net Profit distorted due to depreciation, taxes,
capital structure
-
33
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Enterprise vs. Equity multiples
Value of a firm
Value
of
net debt
Enterprise
value
Enterprise multiples based on
measures of overall performance
(e.g. EBIT, EBITDA, Sales,
Customers, etc)
Often approximated by the book value of
debt
Value
of
equity
market value of equity = # shares
multiplied by the price per share
Share price multiples based on
measures of equity return
(e.g. Price per share /Earnings
(P/E-multiple))
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Practical Valuation
34
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Finding peer group firms is the fundamental problem in multiple valuation
Trading multiples
§ Multiples are derived from share prices of companies listed on stock exchange
§ „Peer Group“ usually based on firms of same industry (same size, etc)
§ Implies „correct“ valuation of comparable companies by the market
§ For valuation of acquisitions: share prices usually do not contain a control premium; thus it
has to be taken into account separately as a premium
Transaction multiples
§ Multiples are derived from observed acquisitions prices of recent comparable transactions / from
observed IPOs from recent IPOs
§ Acquisition prices usually contain control or strategic premia: thus no need to be taken into
account separately!
Problems
§ It is often hard to find comparable firms.
§ The average ratio for the sample of comparable firms often has a wide range.
§ For example, the average P/E ratio might be 20, but the range could be from 10 to 50. How
do you know whether your firm should be compared to the low, average, or high performers?
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Practical Valuation
35
Chair of Financial Management and Capital Markets
TUM School of Management
Technische Universität München
Adjusting multiples is another important problem in multiple valuation
Various key figures can be used for calculating multiples
(e.g.: Sales Revenue, EBITDA, EBIT, NOPLAT, Net Profit,...)
Unique events and discretionary accounting policy may distort key data
and thus company values calculated
Key figures should be standardized and/or adjusted.
Adjustments
• Extraordinary expenses/earnings
• Disposition-contingent expenses/earnings (e.g. stock options, R&D expenses,
non cash -revenues, pension reserves)
Prof. Dr. Christoph Kaserer (TUM) | Corporate Finance | Practical Valuation
36