Solution
Chapter: 10
Problem: 23
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
@ 12% cost of capital @ 18% cost of capital
WACC = 12% WACC = 18%
NPV A = $226.96 NPV A = $18.24
NPV B = $206.17 NPV B = $89.54
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
10% $314.28 $252.50
12% $226.96 $206.17
14% $149.27 $163.85
16% $80.03 $125.10
18% $18.24 $89.54
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.
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 range
does not include the costs, which are
added separately.
$200
$400
$600
$800
$1,000
NPV NPV Profiles
Project A
Project B
22% ($86.39) $26.71
24% ($130.65) ($1.11)
26% ($170.34) ($26.85)
28% ($205.97) ($50.72)
30% ($237.98) ($72.88)
c. What is each project’s IRR?
We find the internal rate of return with Excel’s IRR function:
IRR A = 18.64%
IRR B = 23.92%
d. What is the crossover rate, and what is its significance?
Cash flow
Time differential
0$200
1 ($490)
2 ($390) Crossover rate = 13.14%
3 ($290)
4$410
5$410
6$736 $182
7 ($200)
@ 12% cost of capital @ 18% cost of capital
MIRR A = 15.43% MIRR A = 18.34%
MIRR B = 17.87% MIRR B = 20.88%
f. What is the regular payback period for these two projects?
Project A
Time period 0 1 2 3 4 5
Cash flow (375) (300) (200) (100) 600 $600
Cumulative cash flow -$375 -$675 –$875 -$975 -$375 $225
— — — — 4.625
4.625
Project B
Time period 0 1 2 3 4 5
Cash flow -$575 $190 $190 $190 $190 $190
Cumulative cash flow -$575 -$385 –$195 –$5 $185 $375
— — — 3.026 —
3.026
Intermediate calculation for payback
Payback using intermediate calculations
Intermediate calculation for payback
Payback using intermediate calculations
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.
Note in the graph above that the X-axis intercepts are equal to the two
The crossover rate represents the cost of
capital at which the two projects value, at
a cost of capital of 13.14% is:
-$400
-$200
$0 0% 5% 10% 15% 20%
Cost of Capital
Payback using PERCENTRANK 3.026 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
Cash flow -$375 -$300 -$200 -$100 $600 $600
Disc. cash flow -$375 -$268 -$159 –$71 $381 $340
Disc. cum. cash flow -$375 -$643 -$802 -$873 -$492 -$152
— — — — —
5.323
Project B
Time period 0 1 2 3 4 5
Cash flow -$575 $190 $190 $190 $190 $190
Disc. cash flow -$575 $170 $151 $135 $121 $108
Disc. cum. cash flow -$575 -$405 -$254 -$119 $2 $110
— — — 3.983 —
3.983
Discounted Payback using PERCENTRANK 3.983 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: $601.96
PI of A: 1.61
PV of future cash flows for B: $781.17
PI of B: 1.36
Payback using intermediate calculations
Payback using intermediate calculations
Intermediate calculation for payback
Intermediate calculation for payback
3/18/2015
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.
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 range
does not include the costs, which are
added separately.
Project B
6 7
$926 ($200)
$1,151 $951
— —
6 7
$190 $0
$565 $565
— —
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.
Note in the graph above that the X–axis intercepts are equal to the two
25% 30%
Cost of Capital
6 7
$926 -$200
$469 -$90
$317 $227
5.323 —
6 7
$190 $0
$96 $0
$206 $206
— —