Exercise 19.9 NPV and IRR Each of the following scenarios is independent. All ca
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Question
Exercise 19.9 NPV and IRR Each of the following scenarios is independent. All cash flows are after-tax cash flows. Required: 1. Patz Corporation is considering the purchase of a computer-aided manufacturing system. OBJECTIVE The cash benefits will be $800,000 per year. The system costs $4,000,000 and will last eight years. Compute the NPV assuming a discount rate of 10 percent. Should the company buy the new system? Sterling Wetzel has just invested $270,000 in a restaurant specializing in German food. He expects to receive $43,470 per year for the next eight years. His cost of capital is 5.5 percent. Compute the internal rate of return. Did Sterling make a good decision? 2.Explanation / Answer
Computation of NPV assuming discount rate of 10%:
Annual cash benefits = $800,000
Initial investment = $4,000,000
Life = 8 years
NPV = present value of cash inflows – present value of cash outflows
Present value of cash inflows = annual cash inflows x (P/A, 10%, 8)
= $800,000 x 5.335 = $4,268,000
Present value of cash outflows = initial investment x (P/F, 10%, 0) [initial investment is made immediately, hence year 0 and factor =1]
Present value of cash outflows = $4,000,000 x 1 = $4,000,000
NPV = $4,268,000 - $4,000,000 = $268,000
NPV of investment in computer aided manufacturing system at 10% discount rate is $268,000.
Since the project generates a positive NPV, the company should buy the system.
Initial Investment = $270,000
Annual cash inflows = $43,470
Expected period = 8 years
Cost of capital = 5.5%
To make the investment a profitable one, Sterling Wetzel’s return on investment should be above the cost of capital of 5.5%.
Internal rate of return is that rate at which the present value of cash outflows equals to present value of cash inflows.
At the internal rate of return, the Net Present Value (NPV) is zero.
So, using trial and error approach,
We calculate the NPV at a discount rate higher than the 5.5%.
Assuming a discount rate of 6%
The NPV = present value of cash inflows – present value of cash outflows
Present value of cash inflows = $43,470 x (P/A, 6%, 8)
= 43,470 x 6.210 = $269,949
Present value of cash outflows = $270,000 x 1 = $270,000
NPV = $269,949- $270,000 = ($51)
Though the NPV is negative at 6% rate, the value shows a slight difference of -$51.
Assuming discount rate of 5%,
Present value of cash inflows = $43,470 x (P/A, 5%, 8)
= 43,470 x 6.463 = $280,947
Present value of cash outflows = $270,000 x 1 = $270,000
NPV = $280,947 - $270,000 = $10,947
Considering the above NPVs at 5% and 6%, the internal rate of return is almost equal to 6%.
Since, the cost of capital is 5.5%, and the investment earns almost 6% internal rate of return, the investment is profitable.
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