Question

Copa Corporation is considering the purchase of a new machine costing $150,000. The machine would generate net cash inflows of $43,690 per year for 5 years. At the end of 5 years, the machine would have no salvage value. Copa’s cost of capital is 12 percent. Copa uses straight-line depreciation. The present value factors of annuity of $1.00 for different rates of return are as follows:

Period	12%	14%	16%	18%
4	3.03735	2.91371	2.79818	2.69006
5	3.60478	3.43308	3.27429	3.12717
6	4.1141	3.88867	3.68474	3.49760

The proposal's internal rate of return (rounded to the nearest percent) is

Select one:

A. 14 percent.

B. 16 percent.

C. 18 percent.

D. 12 percent.

Answer 1

Payback period = Initial investment / Annual cash inflow

Payback period = $ 150,000/ $ 43,690 = 3.43328 year.

From PVIFA table we have to see in 5 years 3.43328 lies in which discount rate. PVIFA ( t = 5, i = 14) is 3.43308 and PVIFA ( t = 5, i = 12) is 3.60478. So, roughly IRR is inbetween 12% to 14%.

Present value of cash inflows at 12% discounting factor = $ 43,690 X 3.60478 = $ 157,493

Present value of cash inflows at 14% discounting factor = $ 43,690 X 3.43308 = $ 149,991

IRR = lower discounting rate + [ present value at lower discounting rate - initial investment ] / [ present value at lower discounting rate - present value at higher discounting rate ] X [ Higher discounting rate - lower discounting rate]

IRR = 12% + [ 157,493 - 150,000] / [ 157,493 - 149,991] X [ 14 - 12]

IRR = 12% + [ 7,493 / 7,502] X2

IRR = 12% + 1.9976%

IRR = 13.9976% or 14%