Part 1

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Part 1

INPUTS USED IN THE MODEL
P0 $50.00
Net Ppf $30.00
Dpf $3.30
D0 $2.10
g 7%
B-T rd 10%
Skye’s beta 0.83
Market risk premium, RPM 6.0%
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%
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.
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, dividend growth approach (ignoring flotation costs):
D1 / P0 + g = rs
Cost of common equity, CAPM:
rRF + b × RPM = rs
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.
b. Calculate the cost of new stock using the dividend growth approach.
D0 × (1 + g) / P0 × (1 – F) + g = re
$2.25 $45.00
DII Labs: F is flotation cost.		 7% 11.99%
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.)
rs + Differential = re
Again, we would not normally find that the CAPM and dividend growth methods yield identical results.
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.
Beta rs rps rd(1 – T) WACC Expected return on project
Project A 0.5
Project B 1.0
Project C 2.0
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.

Part 2

Gardial Fisheries is considering two mutually exclusive investments. The projects’ expected net cash flows are as follows:
Expected Net Cash Flows
Time Project A Project B
0 ($375) ($575)
1 ($300) $190
2 ($200) $190
3 ($100) $190
4 $600 $190
5 $600 $190
6 $926 $190
7 ($200) $0
a. If each project’s cost of capital is 12%, which project should be selected? If the cost of capital is 18%, what project is the proper choice?
@ 12% cost of capital @ 18% cost of capital
Use Excel’s NPV function as explained in this chapter’s Tool Kit. Note that the range does not include the costs, which are added separately.
WACC = 12% WACC = 18%
NPV A = DII Labs: Net Present Value of “A” discounted at a WACC of 12% NPV A =
DII Labs: Net Present Value of “A” discounted at a WACC of 18% NPV B = NPV B =
At a cost of capital of 12%, Project A should be selected. However, if the cost of capital rises to 18%, then the choice is reversed, and Project B should be accepted.
b. Construct NPV profiles for Projects A and B.
Before we can graph the NPV profiles for these projects, we must create a data table of project NPVs relative to differing costs of capital.
Project A Project B
0%
2%
4%
6%
8%
10%
12%
14%
16%
18%
20%
22%
24%
26%
28%
30%
c. What is each project’s IRR?
We find the internal rate of return with Excel’s IRR function:
IRR A = Note in the graph above that the X-axis intercepts are equal to the two projects’ IRRs.
IRR B =
d. What is the crossover rate, and what is its significance?
Cash flow
Time differential
0
DII Labs: The difference in cash flows between Project “A” and Project “B”. 1
2 Crossover rate =
DII Labs: The IRR for the Cash Flow Differential 3
4 The crossover rate represents the cost of capital at which the two projects value, at a cost of capital of 13.14% is: have the same net present value. In this scenario, that common net present
5
6
7
e. What is each project’s MIRR at a cost of capital of 12%? At r = 18%? Hint: note that B is a 6-year project.
@ 12% cost of capital @ 18% cost of capital
MIRR A = DII Labs: Use Excel’s MIRR function MIRR A =
MIRR B = MIRR B =
f. What is the regular payback period for these two projects?
Project A
Time period 0 1 2 3 4 5 6 7
Cash flow (100) 600 600 926 (200) $0 $0 $0
Cumulative cash flow
Intermediate calculation for payback
Payback using intermediate calculations
Project B
Time period 0 1 2 3 4 5 6 7
Cash flow
Cumulative cash flow
Intermediate calculation for payback
Payback using intermediate calculations
Payback using PERCENTRANK Ok because cash flows follow normal pattern.
g. At a cost of capital of 12%, what is the discounted payback period for these two projects?
WACC = 12%
Project A
Time period 0 1 2 3 4 5 6 7
Cash flow
Disc. cash flow
Disc. cum. cash flow
Intermediate calculation for payback
Payback using intermediate calculations
Project B
Time period 0 1 2 3 4 5 6 7
Cash flow
Disc. cash flow
Disc. cum. cash flow
Intermediate calculation for payback
Payback using intermediate calculations
Discounted Payback using PERCENTRANK Ok because cash flows follow normal pattern.
h. What is the profitability index for each project if the cost of capital is 12%?
PV of future cash flows for A:
PI of A:
PV of future cash flows for B:
PI of B:
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