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project_.xlsx
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Portfolio Diversification Project
Instructions: Complete the models of Problem 1 and 2 and upload your excel file on
Blackboard before 6 PM of November 28 (Tuesday).
Problem 1:
INPUTS USED IN THE MODEL:
P0
$50.00
Net Ppf
$30.00
Dpf
$3.30
D0
g
B-T rd
Skye’s beta
Market risk premium, RPM
$2.10
7%
10%
0.83
6.0%
Risk free rate, rRF
Target capital structure from debt
Target capital structure from preferred stock
Target capital structure from common stock
Tax rate
Flotation cost for common
6.5%
45%
5%
50%
35%
10%
a. Calculate the cost of each capital component, that is, the after-tax cost of debt, the cost of preferred stock
(including flotation costs), and the cost of equity (ignoring flotation costs). Use both the DCF method and the
CAPM method to find the cost of equity.
Cost of debt:
B-T rd
(1 – T)
×
=
A-T rd
Cost of preferred stock (including flotation costs):
Dpf
/
Net Ppf
=
rpf
Cost of common equity, DCF (ignoring flotation costs):
D1
/
P0
+
g
=
rs
Cost of common equity, CAPM:
rRF
+
b × RPM
=
b. Calculate the cost of new stock using the DCF model.
rs
D0 × (1 + g)
/
P0 × (1 – F)
+
g
=
re
c. What is the cost of new common stock based on the CAPM?
d. Assuming that Gao will not issue new equity and will continue to use the same capital structure, what is the
company’s WACC?
wd
45.0%
wpf
5.0%
ws
50.0%
100.0%
wd × A-T rd +
wpf × rpf
+
ws × rs
=
WACC
e. Suppose Gao is evaluating three projects with the following characteristics:
(1) Each project has a cost of $1 million. They will all be financed using the target mix of long-term debt,
preferred stock, and common equity. The cost of the common equity for each project should be based
on the beta estimated for the project. All equity will come from reinvested earnings.
(2) Equity invested in Project A would have a beta of 0.5. The project has an expected return of 9.0%.
(3) Equity invested in Project B would have a beta of 1.0. The project has an expected return of 10.0%.
(4) Equity invested in Project C would have a beta of 2.0. The project has an expected return of 11.0%.
Analyze the company’s situation and explain why each project should be accepted or rejected.
Project A
Project B
Project C
Beta
0.5
1.0
2.0
rs
rps
rd(1 – T)
WACC
Problem 2:
Following is information for the required returns and standard deviations of returns for A, B, and C.
Here are the expected returns and standard deviations for stocks A, B, and C:
Stock
ri
si
A
7.0%
33.11%
B
10.0%
53.85%
C
20.0%
89.44%
Expected
return on
project
Here is the correlation matrix:
A
B
C
A
1.0000
0.1571
0.1891
B
0.1571
1.0000
0.1661
C
0.1891
0.1661
1.0000
a. Suppose a portfolio has 30 percent invested in A, 50 percent in B, and 20 percent in C. What are the
expected return and standard deviation of the portfolio?
wA =
wB =
wC =
30%
50%
20%
rp =
Portfolio variance =
sp =
b. The partial model lists 66 different combinations of portfolio weights. For each combination of
weights, find the required return and standard deviation. If you would like a return of 10.50 percent,
what is the smallest standard deviation that you must accept? Why?
Portoflio #
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
wA
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.2
0.2
0.2
0.2
0.2
0.2
wB
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0.0
0.1
0.2
0.3
0.4
0.5
wC
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.8
0.7
0.6
0.5
0.4
0.3
Variance
sp
rp
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
0.2
0.2
0.2
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.5
0.5
0.5
0.5
0.5
0.5
0.6
0.6
0.6
0.6
0.6
0.7
0.7
0.7
0.7
0.8
0.8
0.8
0.9
0.9
1.0
0.6
0.7
0.8
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.0
0.1
0.2
0.3
0.4
0.5
0.0
0.1
0.2
0.3
0.4
0.0
0.1
0.2
0.3
0.0
0.1
0.2
0.0
0.1
0.0
0.2
0.1
0.0
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.5
0.4
0.3
0.2
0.1
0.0
0.4
0.3
0.2
0.1
0.0
0.3
0.2
0.1
0.0
0.2
0.1
0.0
0.1
0.0
0.0
…
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