Question

A company is considering two mutually exclusive expansion plans. Plan A requires a $40 million expenditure on a large-scale integrated plant that would provide expected cash flows of $6.39 million per year for 20 years. Plan B requires a $13 million expenditure to build a somewhat less efficient, more labor-intensive plant with an expected cash flow of $2.91 million per year for 20 years. The firm's WACC is 9%.Calculate each project's NPV. Round your answers to two decimal places. Enter your answers in millions. For example, an answer of $10,550,000 should be entered as 10.55.Plan A $ millionPlan B $ millionCalculate each project's IRR. Round your answer to two decimal places.Plan A %Plan B %Graph the NPV profiles for Plan A and Plan B and approximate the crossover rate to the nearest percent.Calculate the crossover rate where the two projects' NPVs are equal. Round your answer to the nearest hundredth.%

Answer 1

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).