Chapter 12
Case – Part 2 - Q1
The Cost of Equity
 The Cost of Equity (CAPM):
E(rS) = rf + bs [E(rm) - rf]
 Equity Beta:
bS = sSm / sm2
Example:
The following are U-Air stocks and TSE300 index returns for
the 1994-1997 period:
YearU-Air
1994
1995
1996
1997
4.00%
30.00
42.00
34.00
TSE300
-0.18%
14.53
28.35
14.98
Jacoby, Stangeland and Wajeeh, 2000
1
Calculating the Equity Beta
 Calculating average returns:
rU  Air ( S )  0.040.340.420.34  27.5%
rTSE300  0.0018 0.145340.2835 0.1498  14.42%
 Calculating the covariance:
sˆU  Air ( S ), TSE300
 0.04 0.275 0.0018 0.1442 0.30.275 0.14530.1442410.42 0.275 0.2835 0.1442 0.34 0.275 0.1498 0.1442 
 0.0183
 Calculating the market variance:
2
sˆ TSE
300

 0.0018 0.1442 2  0.1453 0.1442 2  0.2835 0.1442 2  0.1498 0.1442 2
4 1
 0.0136
 Calculating beta:
bˆU  Air ( S ) 
sˆU  Air ( S ), TSE 300
2
sˆTSE
300

2
Case – Part 2 – Q2
Calculating the Cost of Equity
 U-Air’s Cost of Equity (CAPM):
Given a 5.09% average T-bill rate, the average historical
market risk-premium for the 1994-1997 period is
rTSE300  r f  14.42% - 5.09%  9.33%
By the CAPM, if the current T-bill rate is 4%, then the
cost of U-Air’s equity is given by:
E(rs) = rf + bs [E(rm) - rf]
=
=
3
An alternative Method for Calculating the Cost of Equity
 For U-Air it is given that:
Year Dividend
0
$0.39
-1
$0.37
-2
$0.36
-3
$0.34
-4
$0.33
(1+g)4 D-4 = D0
(1+g)4 0.33 = 0.39
=> g =
Also: D1 = Do(1+g) = 0.39%1.0427 = 0.41
Since P0 = $3.65, by the dividend growth model:
rs = (D1/P0) + g
=
 For the remainder of the case, we will assume that the Cost of Equity is
that obtained by the CAPM, i.e. 16.6%
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Case – Part 2 – Q2
The Investment Decision
 Suppose that U-Air is an all equity firm. Recall that the new
Bahamas project generates the following CFs ($Ks):
YearCF
0
(41,600)
1
4,740
IRR = 10.95%
2
11,180
NPV  41600  4,740  11,1802  15,1853  25,954.375
1.166
1.166
1.166
1.166 4
3
15,185
 $5,690.98 K  0  reject
4
25,954.375
Assume:
 U-Air is an all equity firm
 The Bahamas project beta is the same as U-Air’s beta (1.35)
Decision:
 NPV = -$5,690.98 < 0 => reject the project. Or:
 Since by the CAPM (SML) the required return for beta of 1.35 is
16.6%, and IRR=10.95%<16.6% => reject the Bahamas project
5
The SML and the Investment Decision
Expected
Return (%)
SML
*
16.6
U-Air
*
IRR = 10.95
Bahamas
Project
4
1.35
Jacoby, Stangeland and Wajeeh, 2000
Beta
6
Determinants of Beta
 Factors affecting Equity Beta:

Business Risk
Cyclicity of Revenues
Operating Leverage

Financial Risk
Financial Leverage
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Financial Leverage
 When the firm is not “All Equity”
 Recall: the beta of a portfolio (p) with N assets is given by:
N
b p  X1b1  X 2 b 2    X N b N   X i b i
i 1
 The Firm’s Assets are financed by Equity and Debt
Assets
Equity (S)
Debt (B)
 Firm’s Assets = Portfolio with Equity and Debt:
bASSETS = bEQUITY [S/(S+B)] + bDEBT [B/(S+B)]
Jacoby, Stangeland and Wajeeh, 2000
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The Cost of Capital of a Levered Firm
 Recall: the return of a portfolio (p) with N assets is given by:
N
rp  X 1r1  X 2 r2    X N rN   X i ri
i 1
 The Weighted Average Cost of Capital(WACC):
WACC = rASSETS = rS [S/(S+B)] + rB (1 – Tc) [B/(S+B)]
after-tax
cost of debt
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Case – Part 2 – Q3
Assuming that a project has the same beta and financial
leverage as the whole firm:

calculate the NPV of the project based on the firm’s WACC

compare the IRR of the project to its WACC
It is given that: Equity/Assets = 0.53, and
Debt/Assets = 0.47
Recall: by the CAPM: rS = 16.6%
U-Air’s Long-Term bonds are traded with YTM = 6.04%
Recall that Tc = 0.4
Then, U-Air’s Weighted Average Cost of Capital(WACC) is:
WACC = rS [S/(S+B)] + rB (1 – Tc) [B/(S+B)]
=
10
Case – Part 2 – Q4
WACC of the Bahamas Project
 If the Bahamas project has the same beta and financial leverage,
then
NPV  41600 
4 , 740
1.105
 $508 .88 K  0
 11,1802  15,1853  25,954.375
4
1.105
1.105
1.105
 accept
 Also: IRR=10.95%>10.5% => accept the Bahamas project
Jacoby, Stangeland and Wajeeh, 2000
11
Case – Part 2 – Q5 & Q6
When the Firm’s beta Differs from the Project’s Beta
 The project and the firm may have different betas


when the project and the firm are not from the same line of business
- use industry beta (not always available, e.g. Amazon.com)
when the project’s risk is inherently different (even if same industry)
 Suppose that the beta of the Bahamas line is 1.8 (higher than U-Air). By the
CAPM:
rBAHAMAS = rf + bs [E(rm) - rf] =
 Then, the WACC of the Bahamas project is:
WACCBAHAMAS = rBAHAMAS [S/(S+B)] + rB (1 – Tc) [B/(S+B)]
=
, 740
 11,1802  15,1853  25,954.375
 $1,916 .11K  reject
 NPV  41600  1.41272
1.1272
1.1272
1.1272 4
 Or: IRR=10.95%<12.72% => reject the Bahamas project
12