Chapter 12: Risk, Return, and Capital Budgeting
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Transcript Chapter 12: Risk, Return, and Capital Budgeting
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
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Calculating the Equity Beta
Calculating average returns:
rU Air ( S ) 0.040.340.420.34 27.5%
rTSE 300 0.00180.145340.28350.1498 14.42%
Calculating the covariance:
sˆU Air ( S ), TSE 300
0.040.275 0.00180.1442 0.30.275 0.14530.1442410.420.275 0.28350.1442 0.340.275 0.1498 0.1442
0.0183
Calculating the market variance:
2
sˆ TSE
300
0.0018 0.1442 2 0.14530.1442 2 0.2835 0.1442 2 0.1498 0.1442 2
4 1
0.0136
Calculating beta:
bˆU Air ( S )
sˆU Air ( S ), TSE300
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 rf 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 = $3.65, by the dividend growth model:
rs = (D1/P0) + g
=
For the remainder of the case, we will assume that the Cost of Equity is
that obtained by the CAPM, i.e. 16.6%
Jacoby, Stangeland and Wajeeh, 2000
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Case – Part 2 – Q2
The Investment Decision
Suppose that U-Air is an all equity firm. Recall that the new
Bahamas project generates the following CFs ($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
Jacoby, Stangeland and Wajeeh, 2000
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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 X 1b1 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
Jacoby, Stangeland and Wajeeh, 2000
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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
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