Question

How to calculate NPV?

You are considering constructing a new plant to manufacture a new product. You anticipate that the plant will take a year to build and cost $100.0 million upfront. Once built, it will generate cash flows of $15.0 million at the end of every year over the life of the plant. The plant will wear out 20 years after its completion At that point you expect to get 510.0 million in salvage value for the plant. Using a cost of capital of 12.0%, calculate the NPV. Assume the IRR is 13%. Do the NPV and IRR rules agree in this case? Using a cost of capital of 12.0%, calculate the NPV. The NPV is $ 0.96 million (Round to two decimal places) Assume the IRR is 13%. Do the NPV and IRR rules agree in this case? Select from the following choices YES, the two rules agree

Answer 1

NPV = sum of present values of all cash flows

Present value of each cash flow = cash flow / (1 + cost of capital)ⁿ

where n = number of years after which the cash flow occurs.

NPV = $13.08 million

Yes, the two rules agree. As per NPV rule, a project should be accepted if NPV is positive. As per IRR rule, a project should be accepted if IRR > cost of capital.

2 А B с 1 Year CF PV of CF 0 ($100.00) ($100.00) 3 1 $15.00 $13.39 4 2 $15.00 $11.96 5 3 $15.00 $10.68 6 4 $15.00 $9.53 7 5 $15.00 $8.51 8 6 $15.00 $7.60 9 7 $15.00 $6.79 10 8 $15.00 $6.06 11 9 $15.00 $5.41 12 10 $15.00 $4.83 13 11 $15.00 $4.31 14 12 $15.00 $3.85 15 13 $15.00 $3.44 16 $15.00 $3.07 17 15 $15.00 $2.74 18 16 $15.00 $2.45 19 17 $15.00 $2.18 20 18 $15.00 $1.95 21 19 $15.00 $1.74 22 20 $25.00 $2.59 23 NPV $13.08 14

A B с 1 Year CF PV of CF 20 -100 =B2/(1+12%)^A2 3 1 15 =B3/(1+12%)^A3 4 2 15 =B4/(1+12%)^A4 5 3 15 =B5/(1+12%)^A5 6 4 15 =B6/(1+12%)^A6 7 5 15 =B7/(1+12%)^AZ 8 6 15 =B8/(1+12%)^A8 9 7 15 =B9/(1+12%)^A9 10 8 15 =B10/(1+12%)^A10 11 9 15 =B11/(1+12%)^A11 12 10 15 =B12/(1+12%)^A12 13 11 15 =B13/(1+12%)^A13 14 12 15 =B14/(1+12%)^A14 15 13 15 =B15/(1+12%)^A15 16 14 15 =B16/(1+12%)^A16 17 15 15 =B17/(1+12%)^A17 18 16 15 =B18/(1+12%)^A18 19 17 15 =B19/(1+12%)^A19 20 18 15 =B20/(1+12%)^A20 21 19 15 =B21/(1+12%)^A21 22 20 =15+10 =B22/(1+12%)^A22 23 NPV =SUM(C2:C22)