The company you work for is considering a new product line projected to have the net cash flows (NCF) shown. The values are in future dollars, which have been inflated by 5% per year. Because the plant manager is unsure how the present worth is calculated, he asked you to do it in two ways over the 4-year planning horizon: (1) using the compa­ny’s market rate of 20% per year, and (2) converting all of the estimates into CV dollars and using the company’s real rate. You said both ways will pro­vide the same answer, but he asked you to show him the calculations. What is the present worth by method (1) and method (2)? Solve by hand and spreadsheet.

Question

Answer 1

By hand:



Method 1: PW = -10,000 + 2000(P/F,20%,1) + 5000(P/A,20%,3)(P/F,20%,1)

= -10,000 + 2000(0.8333) + 5000(2.1065)(0.8333)

= $443.33



Method 2: Must convert all NCF to CV dollars and the inflated rate if to a real rate i

Real i: 0.20 = i + 0.05 + (i)(0.05)

1.05i = 0.15

i = 0.1429 (14.29%)

PW = -10,000 + [2000/(1.05)1](P/F,14.29%,1) +

+ [5000/(1.05)2](P/F,14.29%,2) + [5000/(1.05)3](P/F,14.29%,3)

+ [5000/(1.05)4](P/F,14.29%,4)

= -10,000 + 1666.60 + 3471.96 + 2893.19 + 2410.90

= $442.65 (rounding error)

By spreadsheet: Convert to CV; sample function for year 2: = $B7/(1 + $B$2)^$A7