Answer:
Project A:
initial outlay -$40 million
cash flows $6.39 million for 20 years
PV of cash flows = $6,390,000 x 9.1285 (PV annuity factor, 9%, 20 periods) = $58,331,115
NPV = -$40,000,000 + $58,331,115 = $18,331,115 ≈ $18.33 million
IRR = 15%
Project B:
initial outlay -$13 million
cash flows $2.91 million for 20 years
PV of cash flows = $2,910,000 x 9.1285 (PV annuity factor, 9%, 20 periods) = $26,563,935
NPV = -$13,000,000 + $26,563,935 = $13,563,935 ≈ $13.56 million
IRR = 22%
Crossover rate = 11.4%
I solved the cross over rate the following way:
project A project B difference
-40 -13 -27
6,39 2,91 3,48
6,39 2,91 3,48
6,39 2,91 3,48
6,39 2,91 3,48
6,39 2,91 3,48
6,39 2,91 3,48
6,39 2,91 3,48
6,39 2,91 3,48
6,39 2,91 3,48
6,39 2,91 3,48
6,39 2,91 3,48
6,39 2,91 3,48
6,39 2,91 3,48
6,39 2,91 3,48
6,39 2,91 3,48
6,39 2,91 3,48
6,39 2,91 3,48
6,39 2,91 3,48
6,39 2,91 3,48
6,39 2,91 3,48
Using a financial calculator or excel spreadsheet, find the IRR of the difference and that is the crossover rate (discount rate at which both projects have the same NPV).
