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Solution 7/16/2015
Chapter: 9
Problem: 18
INPUTS USED IN THE MODEL
P0$50.00
Net Ppf $30.00
Dpf $3.30
D0$2.10
g
7%
B-T rd10%
Skye's beta
0.83
Market risk premium, RPM6.0%
Risk free rate, rRF 6.5%
Target capital structure from debt
45%
Target capital structure from preferred stock
5%
Target capital structure from common stock
50%
Tax rate
35%
Flotation cost for common
10%
Cost of debt:
B-T rd × (1 – T) = A-T rd
10% 65% 6.50%
Cost of preferred stock (including flotation costs):
Dpf / Net Ppf = rpf
$3.30 $30.00 11.00%
Cost of common equity, dividend growth approach (ignoring flotation costs):
D1 / P0 + g = rs
$2.25 $50.00 7% 11.49%
Cost of common equity, CAPM:
rRF + b × RPM =rs
6.5% 4.98% =11.48%
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 the CAPM method
and the dividend growth approach to find the cost of equity.
IMPORTANT NOTE: HERE THE CAPM AND THE DIVIDEND GROWTH METHODS PRODUCE APPROXIMATELY
THE SAME COST OF EQUITY. THAT OCCURRED BECAUSE WE USED A BETA IN THE PROBLEM THAT
FORCED THE SAME RESULT. ORDINARILY, THE TWO METHODS WILL PRODUCE SOMEWHAT DIFFERENT
RESULTS.
D0 × (1 + g) / P0 × (1 – F) + g = re
$2.25 $45.00 7% 11.99%
rs+ Differential = re
11.48% +0.50% = 11.98%
Again, we would not normally find that the CAPM and dividend growth methods yield identical results.
wd45.0%
wpf 5.0%
ws50.0%
100.0%
wd × A-T rd + wpf × rpf + ws × rs = WACC
2.93% 0.55% 5.75% =9.22%
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.
Beta
rsrps rd(1 – T) WACC
Expected
return on
project
Project A 0.5 9.50% 11.00% 6.50%
8.23% 9%
Project B 1.0 12.50% 11.00% 6.50%
9.73% 10%
Project C 2.0 18.50% 11.00% 6.50%
12.73% 11%
d. Assuming that Gao will not issue new equity and will continue to use the same capital structure, what is
the company's WACC?
The expected returns on Projects A and B both exceed their risk-adjusted WACCs, so they should be accepted.
However, Project C's WACC exceeds its expected rate of return, so it should be rejected.
b. Calculate the cost of new stock using the dividend growth approach.
IMPORTANT NOTE: HERE THE CAPM AND THE DIVIDEND GROWTH METHODS PRODUCE APPROXIMATELY
THE SAME COST OF EQUITY. THAT OCCURRED BECAUSE WE USED A BETA IN THE PROBLEM THAT
FORCED THE SAME RESULT. ORDINARILY, THE TWO METHODS WILL PRODUCE SOMEWHAT DIFFERENT
RESULTS.
c. What is the cost of new common stock based on the CAPM? (Hint: Find the difference between re and rs
as determined by the dividend growth approach and add that differential to the CAPM value for rs.)
(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
