1. Cost of Capital and Leverage.
WACC
Chapter 4

2. Outline
Project selection for a levered firm
Beta and cost of equity of a levered firm
Hamada equation
WACC
Project selection in a diversified firm
Mensac case
2

3. What types of capital do firms use?
Debt
Preferred stock
Common equity
Existing shareholders
New stock
3

4. Do different investors ask for the same
return?
Example: A company has the following EBIT
every year (see the table next page). kRF=4%,
the market risk premium is 6%. If the company
is all-equity financed, its beta is 1
• What is the cost of equity in this case? What is
the company value? If there are 1,000 shares
outstanding, what is the share price?
• If company wants to issue 40,000 of debt to
buy back some shares, what is the cost of debt
and the new cost of equity assuming no taxes?
4

5. Example (2)
Economy
Bad Avg. Good
Prob. 0.25 0.50 0.25
EBIT 5,000 10,000 15,000
Cost of equity is
• 4%+6%x1=10%
The company value is
• (0.25x5,000 + 0.5x10,000 + 0.25x15,000)/.1 =100,000
The share price is 100
5

6. Example (3)
Probability 0.25 0.5 0.25
EBIT $ 5,000.00 $ 10,000.00 $ 15,000.00
Interest $ - $ - $ -
EBT $ 5,000.00 $ 10,000.00 $ 15,000.00
Taxes $ - $ - $ -
NI $ 5,000.00 $ 10,000.00 $ 15,000.00
EPS $ 5.00 $ 10.00 $ 15.00
Average NI $ 10,000
Average EPS $ 10
Standard deviation 3.54
Value of equity $ 100,000
Share price $ 100.00
6

7. Example (4)
For the levered firm let us assume that the
debt is risk-free and check, whether this is
the case or not:
Debt $ 40,000
Interest rate 4%
Number of shares 600
Probability 0.25 0.5 0.25
EBIT $ 5,000.00 $ 10,000.00 $ 15,000.00
Interest $ 1,600.00 $ 1,600.00 $ 1,600.00
EBT $ 3,400.00 $ 8,400.00 $ 13,400.00
Taxes $ - $ - $ -
NI $ 3,400.00 $ 8,400.00 $ 13,400.00
EPS $ 5.67 $ 14.00 $ 22.33
Average NI $ 8,400
Average EPS $ 14.00
Standard deviation 5.89
7

8. Example (5)
The cost of equity of the levered firm
becomes
cost of equity kLS = EPS/Share price = 14/100
= 14%
Why?
Return to shareholders is riskier now (look
at EPS volatility)
It should be higher
8

9. Beta and cost of equity of a levered firm:
Hamada equation (risk-free debt)
Because the increased use of debt causes both
the costs of debt and equity to increase, we need
to estimate the new cost of equity
The Hamada equation attempts to quantify the
increased cost of equity due to financial leverage
It uses the unlevered beta of a firm, which
represents the risk of a firm as if it had no debt
Hamada equation assumes that the debt is risk-
free
9

10. Hamada equation (cont’d)
βL = βU [1 + (1 – T)(D/E)]
where T is the tax rate; D/E is the debt-equity
ratio and βU is the beta of equity of an unlevered
firm with the same operating cash flow
In our example βU = 1, D/E = 400/600 = 2/3
βL = 1(1+0.67)=1.67
kLS = 4% + 1.67 x 6% = 14 %
Notice that
kLS = kUS [1 + (1 – T)(D/E)]-kRF (1 – T)(D/E)
10

11. Beta and cost of equity of a levered firm:
risky debt
If debt is risky, the cost of equity of a
levered firm is found using the following
equation:
L
S
U
S
D U
k = k + (1 − T ) k S − k D
E
( )
where kD is the cost of risky debt. Similarly,
for beta we can write
D D
β = β 1 + (1 − T )
L
S
U
S − (1 − T ) β D
E E
11

12. Example
The risk-free rate is 6%, as is the market
risk premium. The unlevered beta of the
firm is 1.0. The total assets are 2,000,000
• Find the cost of equity of a levered firm if it
has 250,000 of a risk-free debt
• The same if the beta of debt is 0.2
12

13. Example (2)
For riskless debt we have
βL = βU[1 + (1 – T)(D/E)]
β
kL = kRF + (kM – kRF)βL
13

14. Example (3)
For riskless debt we have
βL = βU[1 + (1 – T)(D/E)]
βL = 1.0[1 + (1 – 0.4)( 250/ 1,750)]
β
kL = kRF + (kM – kRF)βL
kL = 6.0% + (6.0%)1.0857
14

15. Example (4)
For riskless debt we have
βL = βU[1 + (1 – T)(D/E)]
βL = 1.0[1 + (0.6)(0.1429)]= 1.0857
β
kL = kRF + (kM – kRF)βL
kL = 6.0% + (6.0%)1.0857 = 12.51%
15

16. Example (5)
For risky debt we have
β
kD = kRF + (kM – kRF)βD=6%+(6%)0.2 =7.2%
βL = βU[1 + (1 – T)(D/E)]-(1 – T)(D/E)βD
β
βL = 1.0[1 + (0.6)(0.1429)]- (0.6)(0.1429)0.2
= 1.0857-0.0171 = 1.0686
kL = kU + (1 – T)(D/E)(kU - kD)
kL = 12% + (0.6)(0.1429)(4.8%) = 12.411%
16

17. How to determine the cost of equity for a
new company?
Identify the peer companies
For each peer, find its unlevered β and cost
of equity using their cost of debt and D/E
ratio
• Try using market values of debt and equity
Find the average unlevered β and kSU
Find β and kSL for your company, using its
cost of debt and D/E ratio
17

18. Determining levered cost of equity, kLs
Find kU directly
D
k + (1 − t c )
L
S kD
kS =
U E
D
1 + (1 − t c )
Find average kUs E
Find kLs
L
S
U
S
D U
E
(
k = k + (1 − tC ) k S − k D )
18

19. WACC
E L D
WACC = k S + (1 − tc )k D
V V
E D
if k D = k f , WACC = k U
S + (1 − tc )
V V
19

20. Example: Find WACC, given these inputs:
Target D/E ratio = 66.7 %
kD = 10%
kRF = 7%
Tax rate = 40%
Market risk premium = 6%
Industry Beta = 0.95
20

21. Example: Find WACC
2
βL = 0.95× 1+ (1− 0.4) = 1.33
3
k = .07 +1.33×.06 = 0.15 = 15%
L
S
1 .67
WACC= ×.15 + (1− .4)× ×.10
1+ .67 1+ .67
WACC= 11.4%
21

22. WACC Estimates for Some Large
U. S. Corporations, Nov. 1999
Company WACC
Intel 12.9%
General Electric 11.9
Motorola 11.3
Coca-Cola 11.2
Walt Disney 10.0
AT&T 9.8
Wal-Mart 9.8
Exxon 8.8
H. J. Heinz 8.5
BellSouth 8.2
22

23. Should the company use the composite
(company average) WACC as the hurdle
rate for each of its projects?
NO! The composite WACC reflects the risk
of an average project undertaken by the
firm. Therefore, the WACC only represents
the “hurdle rate” for a typical project with
average risk.
Different projects have different risks. The
project’s WACC should be adjusted to
reflect the project’s risk.
23

24. Risk and the Cost of Capital
Rate of Return
(%) Acceptance Region
W ACC
12.0 H
10.5 A Rejection Region
10.0
9.5 B
8.0 L
Risk
0 Risk L Risk A Risk H
24

25. Divisional Cost of Capital
Rate of Return
(%)
WACC
13.0
Division H’s WACC
Composite WACC
11.0 for Firm A
Project H
10.0
9.0 Project L
7.0
Division L’s WACC
Risk
0 RiskL Risk H
RiskAverage
25

26. What are the types of project risk?
Stand-alone risk
Corporate risk
Market risk
26

27. How is each type of risk used?
Market risk is theoretically best in most
situations.
However, creditors, customers, suppliers,
and employees are more affected by
corporate risk
Therefore, corporate risk is also relevant
27

28. How to determine the risk-adjusted cost of
capital for a particular project or division?
By making subjective adjustments to the
firm’s composite WACC
Not very scientific!
By attempting to estimate what the cost of
capital would be if the project/division were
a stand-alone firm with the same capital
structure. This requires estimating the
project’s beta
28

29. Methods for Estimating a Project’s Beta
Pure play:
Find several publicly traded companies
exclusively in project’s business
Use average of their betas as proxy for
project’s beta
Difficulties: Sometimes it is hard to find
such companies
29

30. Methods for Estimating a Project’s Beta
Using Accounting beta (won’t use in the
class)
• Estimate the project’s beta by running
regression between project’s ROA and
market ROA (S&P index)
Problems:
• Accounting betas are not perfectly
correlated with market betas (correlation is
about 0.5–0.6)
• Normally can’t get data on new projects’
ROAs before the capital budgeting decision
has been made
30

31. Example
Find the division’s market risk and cost of
capital based on the CAPM, given these
inputs
Target debt/value ratio = 40% (D/E = 66.7%)
kD = 10%
kRF = 7%
Tax rate = 40%
betaDivision = 1.7
Market risk premium = 6%.
31

32. Example (contd.)
Levered beta = 1.7, so division has more
market risk than the company on average
(1.33).
Division’s required return on equity:
ks = kRF + (kM – kRF)βDiv.
= 7% + (6%)1.7 = 17.2%
WACCDiv. = wdkd(1 – T) + wcks
= 0.4(10%)(0.6) + 0.6(17.2%)
= 12.72% 32

33. Mensac case
33