Question

Expected Net Cash Flows

Year Project A Project B

0 ($100,000) ($100,000)

1 75,000 40,000

2 65,000 42,000

3 — 44,000

4 — 46,000

The projects provide a necessary service, so whichever one is selected is expected to be repeated into the foreseeable future. Both projects have a 14% cost of capital.

a. What is each project’s initial NPV without replication?

b. What is each project’s equivalent annual annuity?

c. Suppose you replicate Project A so that it has the same life as Project B. Which project would you choose?

Answer #1

NPV = PV of Cash Inflows - PV of Cash Outflows

a). NPV(A) = [$75,000 / 1.14] + [$65,000 / 1.14^{2}] -
$100,000

= $65,789.47 + $50,015.39 - $100,000 = $15,804.86

NPV(B) = [$40,000 / 1.14] + [$42,000 / 1.14^{2}] +
[$44,000 / 1.14^{3}] + [$46,000 / 1.14^{4}] -
$100,000

= $35,087.72 + $32,317.64 + $29,698.75 + $27,235.69 - $100,000 = $24,339.79

b). EAA = NPV / [{1 - (1 + r)^{n}} / r]

EAA(A) = $15,804.86 / [{1 - 1.14^{-5}} / 0.14] =
$15,804.86 / 3.4331 = $4,603.70

EAA(B) = $24,339.79 / [{1 - 1.14^{-5}} / 0.14] =
$24,339.79 / 3.4331 = $7,089.78

c). NPV(A) = [$75,000 / 1.14] + [($65,000 - 100,000) /
1.14^{2}] + [$75,000 / 1.14^{3}] + [$65,000 /
1.14^{4}] - $100,000

= $65,789.47 - $26,931.36 + $50,622.86 + $38,485.22 - $100,000 = $27,966.19

If replicating the project A is possible, then Project A should be selected as it has a higher NPV

Expected Net Cash Flows
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F
0
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($100,000)
1
75,000
40,000
2
65,000
42,000
3
—
44,000
4
—
46,000
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selected is expected to be repeated into the foreseeable future.
Both projects have a 12% cost of capital.
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replication?
b. What is each project’s equivalent annual
annuity?
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Expected Net Cash Flows
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0
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75,000
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2
65,000
42,000
3
—
44,000
4
—
46,000
The projects provide a necessary service, so whichever one is
selected is expected to be repeated into the foreseeable future.
Both projects have a 12% cost of capital.
c. Suppose you replicate Project T so that it has
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