Question

Acme Oscillators is considering an investment project that has the following rather unusual cash flow pattern.

Year 0, Cash Flow $101
Year 1, Cash Flow -460
Year 2, Cash Flow 790
Year 3, Cash Flow -602.9
Year 4, Cash Flow 171.6
a. Calculate the​ project's NPV at each of the following discount​ rates: 00​%, 5​%, 10​%, 20​%, 30%​, 40​%, 50​%.
b. What do the calculations tell you about this​ project's IRR? The IRR rule tells managers to invest if a​ project's IRR is greater than the cost of capital. If Acme​ Oscillators' cost of capital is 88​%, should the company accept or reject this​investment?
c. Notice that this​ project's greatest NPVs come at very high discount rates. Can you provide an intuitive explanation for that​pattern?

Answer 1

a. NPV at different rates: $101, $295.24, $308.99, $236.06, $169.69, $107.60, $57.43.

b. Project's IRR is around 30-40%. With a cost of capital at 88%, reject the investment.

c. Unusual cash flow pattern leads to higher NPVs at lower discount rates, emphasizing the project's sensitivity to timing and magnitude of cash flows.

Step-by-step explanation:

The Net Present Value (NPV) of a project is calculated by discounting its cash flows at a specific rate. In this case, the NPVs are highest at lower discount rates because the negative cash flows in the initial years are less heavily discounted, allowing the positive cash flows in later years to have a more substantial impact. The unconventional cash flow pattern, with significant negative cash flows followed by positive ones, contributes to this behavior.

The Internal Rate of Return (IRR) is the discount rate that makes the NPV of a project zero. The calculations suggest that the IRR for this project is between 30% and 40%. Since Acme Oscillators' cost of capital is 88%, which is higher than the IRR, following the IRR rule would advise against accepting the investment.

The project's sensitivity to discounting, with NPVs peaking at high discount rates, underscores the importance of considering the timing and magnitude of cash flows. The unique cash flow profile of this project makes it less favorable at higher discount rates, emphasizing the need for a thorough analysis that goes beyond conventional NPV and IRR assessments.