NPV profiles: scale differencesA company is considering two mutually e

QUESTION

NPV profiles: scale differencesA 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 bui
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%) =

2)(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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