A project requires an initial investment of $1,000 and yields cash inflows of $400 at the end of years 1–3. The internal rate of return is approximately ____%?

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Multiple Choice

A project requires an initial investment of $1,000 and yields cash inflows of $400 at the end of years 1–3. The internal rate of return is approximately ____%?

Explanation:
Internal rate of return is the discount rate that makes the project’s net present value equal to zero. For this project, the equation is -1000 + 400/(1+r) + 400/(1+r)^2 + 400/(1+r)^3 = 0. A quick check near 10% helps pinpoint the rate. At r = 10%, the present value of the three inflows is about 994.9, so the NPV is roughly -5.1. This means the IRR is a bit below 10%. Checking a touch lower, say around 9.6%, the PV of inflows is about 1001, giving a small positive NPV. Since the NPV crosses zero between 9.6% and 10%, the IRR is approximately 9.7%. Overall, the rate that makes the inflows just equal the initial investment is about 9.7%.

Internal rate of return is the discount rate that makes the project’s net present value equal to zero. For this project, the equation is -1000 + 400/(1+r) + 400/(1+r)^2 + 400/(1+r)^3 = 0.

A quick check near 10% helps pinpoint the rate. At r = 10%, the present value of the three inflows is about 994.9, so the NPV is roughly -5.1. This means the IRR is a bit below 10%. Checking a touch lower, say around 9.6%, the PV of inflows is about 1001, giving a small positive NPV. Since the NPV crosses zero between 9.6% and 10%, the IRR is approximately 9.7%.

Overall, the rate that makes the inflows just equal the initial investment is about 9.7%.

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