A project has an initial cost of $41,125, expected net cash inflows of $12,000 p
ID: 2640019 • Letter: A
Question
A project has an initial cost of $41,125, expected net cash inflows of $12,000 per year for 9 years, and a cost of capital of 14%. What is the project's NPV? (Hint: Begin by constructing a time line.) Do not round your intermediate calculations. Round your answer to the nearest cent.
A project has an initial cost of $52,125, expected net cash inflows of $12,000 per year for 8 years, and a cost of capital of 12%. What is the project's IRR? Round your answer to two decimal places.
A project has an initial cost of $64,250, expected net cash inflows of $15,000 per year for 12 years, and a cost of capital of 8%. What is the project's MIRR? Round your answer to two decimal places.
Explanation / Answer
NPV = -$52,125 + $12,000[(1/i)-(1/(i*(1+i)n)]
= -$52,125 + $12,000[(1/0.12)-(1/(0.12*(1+0.12)8)]
= -$52,125 + $12,000(4.9676) = $7,486.20.
Payback Period:
$52,125/$12,000 = 4.3438, so the payback is about 4 years
Full Solution
a. $52,125/$12,000 = 4.3438, so the payback is about 4 years.
b. Project K's discounted payback period is calculated as follows:
Annual Discounted @12%
Period Cash Flows Cash Flows Cumulative
0 ($52,125) ($52,125.00) ($52,125.00)
1 12,000 10,714.80 (41,410.20)
2 12,000 9,566.40 (31,843.80)
3 12,000 8,541.60 (23,302.20)
4 12,000 7,626.00 (15,676.20)
5 12,000 6,808.80 (8,867.40)
6 12,000 6,079.20 (2,788.20)
7 12,000 5,427.60 2,639.40
8 12,000 4,846.80 7,486.20
The discounted payback period is 6 + years, or 6.51 years.
Alternatively, since the annual cash flows are the same, one can divide $12,000 by 1.12 (the discount rate = 12%) to arrive at CF1 and then continue to divide by 1.12 seven more times to obtain the discounted cash flows (Column 3 values). The remainder of the analysis would be the same.
c. NPV = -$52,125 + $12,000[(1/i)-(1/(i*(1+i)n)]
= -$52,125 + $12,000[(1/0.12)-(1/(0.12*(1+0.12)8)]
= -$52,125 + $12,000(4.9676) = $7,486.20.
Financial calculator: Input the appropriate cash flows into the cash flow register, input I = 12, and then solve for NPV = $7,486.68.
d. Financial calculator: Input the appropriate cash flows into the cash flow register and then solve for IRR = 16%.
e. MIRR: PV Costs = $52,125.
FV Inflows:
PV FV
12%
0 1 2 3 4 5 6 7 8
| | | | | | | | |
12,000 12,000 12,000 12,000 12,000 12,000 12,000 12,000
13,440
15,053
16,859
18,882
21,148
23,686
26,528
52,125 MIRR = 13.89% 147,596
Financial calculator: Obtain the FVA by inputting N = 8, I = 12, PV = 0, PMT = 12000, and then solve for FV = $147,596. The MIRR can be obtained by inputting N = 8,
PV = -52125, PMT = 0, FV = 147596, and then solving for I = 13.89%.
12%
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