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 / 1.14²] - $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