Question

NPV and IRR: Equal Annual Net Cash Inflows
Winter Fun Company is evaluating a capital expenditure proposal that requires an initial investment of $66,338, has predicted cash inflows of $15,000 per year for seven years, and has no salvage value.

a. Using a discounted rate of 14 percent, determine the net present value of the investment proposal.

Use a negative sign with your answer, if appropriate.
$Answer

b. Determine the proposal's internal rate of return. (Refer to Appendix 25B if you use the table approach.)

Round to the nearest percent. (Example: 0.1568 = 15%)
Answer

%

c. What discount rate would produce a net present value of zero?
Answer

%

Answer 1

Solution Initial Investment Salvage value Yearly Cash inflows Life span of the project Discount rate $66,338 $0 $15,000 7 Years 14% Required (a): NPV of the project Period Amount PV factor Present Value ($66,338.00) ($66,338) 1 Cash outflows: - Initial Investment Cash inflows: - Yearly cash inflows 1-7 $15,000 4.28830 $64,324.50 Net present Value ($2,013.50) Net present value ($2,013.50) Note: Present value annuity factor is rounded off upto 5 decimal points. Present value annuity factor is calculated as under: Present value annuity factor (Excel formula) = PV(14%,7,-1,,0) = 4.28830 Required (b): Computation of Internal rate of return (IRR) Internal rate of return (IRR) is the rate at which the NPV of the proposal shall be zero. In above requirement 1, it may be noted that at 14% discount rate, the NPV for the proposal is negative, hence the IRR is below 14%. To calculate the IRR for the proposal, we shall apply the trial and error method. We shall calculate the NPV at multiple discount rate to find out the IRR of the proposal. 1096 Yearly cash inflows Present value annuity factor Present value of cash inflows Less: Initial investment Net present Value 13% $15,000 4.42261 $66,339 ($66,338) Discount Rate 12% 11% $15,000 $15,000 4.56376 4.71220 $68,456 $70,683 ($66,338) ($66,338) $2,118) $4,345 $15,000 4.86842 $73,026 ($66,338) $6,688 $1_ From, the above table, it may be noted that at discount rate 13%, the NPV of the project is approximtely zero. Hence, the internal rate of return is 13%. Internal rate of return (IRR) 13% Required (c): At internal rate of return, the net present value becomes zero. The internal rate of return is 13%, hence discount rate 13% would produce a net present value of zero. 13%