Build a Model Solution
Chapter: 10
Problem: 23
Expected Net Cash Flows
Time Project A Project B
0($375) ($575)
1($300) $190
@ 12% cost of capital @ 18% cost of capital
WACC = 12% WACC = 18%
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.
Project A Project B
$226.96 $206.17
0% $951.00 $565.00
2% $790.31 $489.27
4% $648.61 $421.01
6% $523.41 $359.29
8% $412.58 $303.35
c. What is each project’s IRR?
We find the internal rate of return with Excel’s IRR function:
11/26/2018
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.
Gardial Fisheries is considering two mutually exclusive investments. The projects’ expected net cash flows are as follows:
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?
Use Excel’s NPV function as explained in
this chapter’s Tool Kit. Note that the
-$400
$800
$1,000
NPV
NPV Profiles
2($200) $190
3($100) $190
7($200) $0
d. What is the crossover rate, and what is its significance?
Cash flow
Time differential
0$200
1 ($490)
3 ($290)
4$410
5$410
6$736 $182
7 ($200)
@ 12% cost of capital @ 18% cost of capital
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 (375) (300) (200) (100) 600 $600 $926 ($200)
Project B
Time period 0 1 2 3 4 5 6 7
Cash flow -$575 $190 $190 $190 $190 $190 $190 $0
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 -$375 -$300 -$200 -$100 $600 $600 $926 -$200
Project B
Time period 0 1 2 3 4 5 6 7
Cash flow -$575 $190 $190 $190 $190 $190 $190 $0
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.
h. What is the profitability index for each project if the cost of capital is 12%?
PV of future cash flows for A: $601.96
PI of A: 1.61
PV of future cash flows for B: $781.17
PI of B: 1.36