Question

# &nb

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?

NPV = PV of Cash Inflows - PV of Cash Outflows

a). NPV(A) = [\$75,000 / 1.14] + [\$65,000 / 1.142] - \$100,000

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

NPV(B) = [\$40,000 / 1.14] + [\$42,000 / 1.142] + [\$44,000 / 1.143] + [\$46,000 / 1.144] - \$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) / 1.142] + [\$75,000 / 1.143] + [\$65,000 / 1.144] - \$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

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