Solution 12/7/2012
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%
Cost of debt:
B-T rd × (1 – T) = A-T rd
10% 65% 6.50%
Cost of preferred stock (including flotation costs):
$3.30 $30.00 11.00%
Cost of common equity, DCF (ignoring flotation costs):
$2.25 $50.00 7% 11.49%
Cost of common equity, CAPM:
D0 × (1 + g) / P0 × (1 – F) + g = re
$2.25 $45.00 7% 11.99%
b. Calculate the cost of new stock using the DCF model.
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.
IMPORTANT NOTE: HERE THE CAPM AND THE DCF 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 DCF method and add that differential to the CAPM value for rs.)
Market risk premium, RPM6.0%
Risk free rate, rRF 6.5%
5%
rs+ Differential = re
11.48% + 0.50% = 11.98%
Again, we would not normally find that the CAPM and DCF methods yield identical results.
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%.
d. Assuming that Gao will not issue new equity and will continue to use the same capital structure, what is the
company’s WACC?
Project C’s WACC exceeds its expected rate of return, so it should be rejected.