SOLUTIONS TO ENDOFCHAPTER PROBLEMS
101
NPV = $40,000 + $9,000[(1/I) – (1/(I × (1 + I)N)]
= $40,000 + $9,000[(1/0.11) – (1/(0.11 × (1 + 0.11)7)]
= $2,409.77.
Financial calculator solution: Input CF0 = 40000, CF17 = 9000, I/YR = 11, and then
solve for NPV = $2,409.77.
102
Financial calculator solution: Input CF0 = 40000, CF18 = 9000, and then solve for IRR =
12.84%.
103
MIRR: PV Costs = $40000.
FV Inflows:
PV
0

40,000
1

9,000
2

9,000
3

9,000
4

9,000
MIRR= 11.93%
5

9,000
6

9,000
FV
7

9,000
9,900
11,089
12,309
13,663
15,166
16,834
88,049
Financial calculator: Obtain the FVA by inputting N = 7, I/YR = 11, PV = 0, PMT =
9000, and then solve for FV = $87,049. The MIRR can be obtained by inputting N = 7,
PV = 40000, PMT = 0, FV = 88049, and then solving for I/YR = 11.93%.
104
PV = $9,000[(1/I) – (1/(I × (1 + I)N)]
= $9,000[(1/0.11) – (1/(0.11 × (1 + 0.11)7)]
= $42,410.
Financial calculator: Find present value of future cash flows by inputting N = 7, I/YR =
11, PMT = 9000, FV = 0, then solve for PV = $42,409.
PI = PV of future cash flows/Initial cost
= $42,409/$40,000 = 1.06.
105
Since the cash flows are a constant $9,000, calculate the payback period as:
$40,000/$9,000 = 4.44, so the payback is about 4 years.
106
The project’s discounted payback period is calculated as follows:
Discounted CF
Cumulative
Year
Annual CF
(@11%)
Discounted CF
0
40,000
40,000.00
1
9,000
8,108.11
(31,891.89)
2
9,000
7,304.60
(24,587.29)
3
9,000
6,580.72
(18,006.57)
4
9,000
5,928.58
(12,077.99)
5
9,000
5,341.06
(6,736.93)
6
9,000
4,811.77
(1,925.16)
7
9,000
4,334.93
2,409.77
The discounted payback period is 6 + years, or 6.44 years.
107
a. Project A: Using a financial calculator, enter the following:
CF0 = 15000000
CF1 = 5000000
CF2 = 10000000
CF3 = 20000000
I/YR = 10; NPV = $12,836,213.
Change I/YR = 10 to I/YR = 5; NPV = $16,108,952.
Change I/YR = 5 to I/YR = 15; NPV = $10,059,587.
Project B: Using a financial calculator, enter the following:
CF0 = 15000000
CF1 = 20000000
CF2 = 10000000
CF3 = 6000000
I/YR = 10; NPV = $15,954,170.
Change I/YR = 10 to I/YR = 5; NPV = $18,300,939.
Change I/YR = 5 to I/YR = 15; NPV = $13,897,838.
b. Using the data for Project A, enter the cash flows into a financial calculator and solve
for IRRA = 43.97%. The IRR is independent of the WACC, so IRR doesn’t change
when the WACC changes.
Using the data for Project B, enter the cash flows into a financial calculator and solve
for IRRB = 82.03%. Again, the IRR is independent of the WACC, so IRR doesn’t
change when the WACC changes.
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