Fundamentals of Corporate Finance

1
Capital budgeting and the capital asset pricing
model
Less is more. Mies can der Rohe, Architect
2
Cost of Capital Applications

• The company cost of capital is the correct
  discount rate for projects that have the same
  risk as the companys existing business but not
  for those projects that are safer or riskier than
  the companys average.
• The company cost of capital equals the company
  cost of equity for companies that are financed
  with 100 equity (i.e. companies without any
  debt).
• CAPM is only one model to estimate company cost
  of equity to arrive at the cost of capital. Other
  models (like APT) can be employed to do similar
  analysis.

3
Using the CAPM to Estimate the Equity Cost of
Capital
Four steps Step 1 Measure the risk-free
rate rf Step 2 Estimate the expected
market risk premium rm -
rf Step 3 Estimate beta b Note
Estimation errors tend to cancel out when you
estimate betas for portfolios. Step 4
Calculate r rf b (rm - rf )
4
Step 1Measure the risk-free rate rf

• Use for risk free project.
• Use the T-bill rate?
• Use the T-bond rate?
• Use average future T-bill rate expected during
  life of the project?
• Expected average T-bill rate T-bond yield -
  premium of bonds
• over bills
• Use historical (or forecasted) premium of bonds
  with maturity close to expected project life.

5
Step 2Estimating the Expected Market Risk Premium

• Arithmetic versus Geometric mean return
• Suppose stock rises 33 and then falls 25
• Arithmetic mean return (33 - 25)/2 4
• Geometric mean return 1.33 x .75 - 1
  0
• (compound return)
• Note If returns are lognormally distributed,
• geometric mean arithmetic mean - variance/2

6
Step 2 - continuedFor cost of capital estimation
use thearithmetic mean

• Suppose stock price is 100 and it could rise to
  133 or fall to 75
• with equal probability
• Expected payoff (.5 x 133) (.5 x 75)
  104
• Expected return 104/100 - 1 4
• PV Expected payoff/1.04 104/1.04 100
• If we look at this stock over many years, its
  arithmetic mean return
• should be 4, but its geometric mean return is
  0.
• Investors would not invest in a project that
  offered an expected return
• of 0.

7
Step 2 - continuedUse a large number of years to
estimatethe expected risk premium

• The standard error of the mean is s / N
• Even with a large number of years the standard
  error
• of the mean is high
• Example
• In the UK standard deviation of market
  return
• is about 20. Therefore with 64 years (N
  64)
• standard error 20/ 64 20/8 2.5

8
Step 3 - Estimating Beta. Example Microsoft's
beta
Microsoft return
30
25
20
Beta 1.2
15
10

• 10

• 5

10
Mkt return

• 5

• 15

• 20

9
Note on the Stability of betas
IN SAME
WITHIN ONE RISK CLASS 5
CLASS 5 CLASS YEARS LATER
YEARS LATER 10 (High betas) 35
69 9
18 54 8
16 45 7 13
41 6 14
39 5
14 42 4
13 40 3
16 45 2
21 61 1 (Low
betas) 40 62
Source Sharpe and Cooper (1972)
10
Step 4Estimating equity cost of capital with CAPM
BOSTON EDISON Estimated equity beta
.49 Cost of (equity) capital interest rate
beta x expected market risk premium
interest rate .49 x 8.6 interest rate
4.2 MICROSOFT Estimated equity beta
1.20 Cost of (equity) capital interest
rate 1.20 x 8.6 interest rate 10.3
11
Capital Structure and the Company Cost of Capital

• Stockholders are exposed to
• - Business Risk
• - Financial Risk
• Financial risk does not affect the expected
  return on a firms assets, but it does increase
  the risk to common stockholders and hence also
  the return they demand.

12
Company Cost of Capital

• Use Company Cost of Capital (not the expected
  return on common stock which is just company cost
  of equity) in capital budgeting decisions.
• The company cost of capital can be found
• 1. Using the firms asset beta, (not the beta of
  common stock).
• or
• 2. Using a weighted average of the returns
  investors expect from securities issued by the
  firm.

13
The firms asset Beta

• The firms asset beta is equal to the beta of a
  portfolio made up of all the securities a firm
  has issued.
• Asset Beta (D/(DE) Debt Beta) ( E/(DE)
  Equity Beta)
• Once you have calculated the asset Beta you can
  use CAPM to calculate the company cost of
  capital.
• company cost of capital rf basset
  (r m - r f )

14
Company cost of capital is averageof cost of
equity cost of debt
WEIGHTED AVERAGE COST OF CAPITAL (WACC)
x
x NOTE Taxes are ignored
here - we will consider taxes in later chapters.
EQUITY
DEBT
COST OF
COST OF
EQUITY
DEBT
DEBT
DEBT
EQUITY
EQUITY
15
Avoiding fudge factors example - part 1
Don't add fudge factor to discount rate to cover
things that could go wrong. Adjust cash flow
forecasts instead. Cash flow in
millions
Chance of
Probable disaster? Project Most
likely range (cash flow 0) A
1.0 .8 - 1.2 No
B 1.0 .8 - 1.2
Yes If r .10, PVA 1.0/(1 .1) .909
or 909,000 PVB should be less - but how much
less?
Note We assume disaster doesn't change beta
16
Avoiding fudge factors example - part 2
Unbiased forecast probability-weighted
average
outcome Suppose for project B probability of
disaster is .2 Then B's unbiased forecast could
be (.2 x 0) (.8 x 1) .8
17
Avoiding fudge factors example - part 3
B's present value is .8 PV
.727 or 727,000 1.1 You
could get right answer with a 37.5 discount rate
(fudge factor) 1.0 PV
.727 1.375 But you
don't know right fudge factor until
you can adjust forecast once you
adjust forecast you don't need
fudge factor
18
Cost of capital and project lives
Using the same cost of capital for each
year's cash flow assumes risk increases
steadily with time. Therefore do NOT use a
higher cost of capital simply because a
project has a long life.
19
Risk,DCF and CEQ