NPV profiles: scale differences A company is considering two mutually exclusive

Question

NPV profiles: scale differences

A company is considering two mutually exclusive expansion plans. Plan A requires a $39 million expenditure on a large-scale integrated plant that would provide expected cash flows of $6.23 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 10%.

1. Calculate each project's NPV. Round your answer to two decimal places.

Plan A $_______million
Plan B $_______million

Calculate each project's IRR. Round your answer to two decimal places.

Plan A 15.0%
Plan B 21.96%

Graph the NPV profiles for Plan A and Plan B and approximate the crossover rate to the nearest percent.

_____%

2. Calculate the crossover rate where the two projects' NPVs are equal. Round your answer to the nearest hundredth.
11.26%

Explanation / Answer

1) Calculating NPV: NPV A = -39M + 6.23M (P/A,10%,20) NPV A = -39M + 6.23M (4.8696) = -8.66M NPV B = -13M + 2.91M (P/A,10%,20) NPV B = -13M + 2.91M (4.8696) = 1.17M IRR ALTERNATIVE A: P = A(P/A,i,20) 39M/6.23M = (P/A,i,20) 6.2600 = (P/A,i,20) Now using tables we will find the values of two i (whose P/A at year 20 are more and less than ours) For i = 15% -> P/A = 6.2593 (6.2593 is very close to 6.2600, so we can assume that our i is 15%) IRR ALTERNATIVE B: P = A(P/A,i,20) 13M/2.91M = (P/A,i,20) 4.4674 = (P/A,i,20) Now using tables we will find the values of two i (whose P/A at year 20 are more and less than ours) For i = 20% -> P/A = 4.8696 For i = ? -> P/A = 4.4674 For i = 25% -> P/A = 3.9539 Now interpolating you get: (? - 20%) / (25% - 20%) = (4.8696 - 4.4674) / (4.8696-3.9539) (? - 20%) = (0.4022)(5%)/0.9157 ? = 20% + 2.196% = 22.2% 2) -39M + 6.23M (P/A,i,20) = -13M + 2.91M (P/A,i,20) 6.23M(P/A,i,20) - 2.91M (P/A,i,20) = 39M - 13M (6.23M-2.91M)(P/A,i,20) = 26M 3.32M(P/A,i,20) = 26M (P/A,i,20) = 7.8313 Now using tables we will find the values of two i (whose P/A at year 20 are more and less than ours) For i = 10% -> P/A = 8.5136 For i = ? -> P/A = 7.8313 For i = 12% -> P/A = 7.4694 Now interpolating you get: (? - 10%) / (12% - 10%) = (8.5136 - 7.8313) / (8.5136-7.4694) (? - 10%) = (0.6823)(2%)/1.0442 ? = 10% + 1.3068% = 11.31%

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