The IRR method is based on the assumption that projects' cash flows are reinvested at the project's risk-adjusted cost of capital.

Question

BlackTom AI · Accepted Answer

IRR assumes that intermediate cash inflows are reinvested at the IRR itself, not at the project's risk-adjusted cost of capital; therefore the statement is false.

1. Relevant concepts
- Internal Rate of Return (IRR): the discount rate that makes NPV = 0.
- Reinvestment assumption: IRR implicitly assumes interim cash flows are reinvested at the IRR.
- Modified IRR (MIRR): adjusts the reinvestment assumption (commonly to the firm’s cost of capital or a realistic reinvestment rate) to avoid IRR’s implicit reinvestment-at-IRR assumption.

2. Step-by-step reasoning
- The given statement claims IRR assumes reinvestment at the project's risk-adjusted cost of capital. That describes MIRR, not IRR.
- IRR’s formula and interpretation rest on compounding reinvested cash flows at the IRR itself to the terminal date and solving for the rate that equates terminal value of inflows to initial outlay.

3. Numerical illustration (intermediate steps shown)
Consider cash flows: CF0 = -100, CF1 = +60, CF2 = +60.
Solve IRR from: -100 + 60/(1+r) + 60/(1+r)^2 = 0
Multiply by (1+r)^2: -100(1+r)^2 + 60(1+r) + 60 = 0
Expand: -100 -200r -100r^2 + 60 + 60r + 60 = 0 → -100r^2 -140r + 20? (correct combination yields:)
Combine constants: -100 + 60 + 60 = 20 → equation: -100r^2 -140r + 20 = 0
Multiply by -1: 100r^2 +140r -20 = 0 → divide by 20: 5r^2 +7r -1 = 0
Solve: r = [-7 ± sqrt(49 +20)]/(10) = [-7 ± sqrt69]/10
Positive root ≈ (-7 + 8.3066)/10 = 0.13066 ≈ 13.07% (depending on algebra; main point: r is a single positive number)
(Regardless of exact numeric, IRR is a specific rate r.)
If CF1 is reinvested at IRR, its future value differs materially from reinvestment at, say, the firm’s cost of capital (e.g., 10%). This demonstrates that IRR’s reinvestment rate = IRR, not cost of capital.

4. Why the correct answer is correct
Because IRR’s internal logic compounds interim inflows at the IRR, the assumption in the prompt is incorrect. MIRR was developed to replace that unrealistic assumption by explicitly using a separate reinvestment rate (often the cost of capital).

5. Why the alternative (True) is incorrect
Saying IRR assumes reinvestment at the project’s risk-adjusted cost of capital confuses IRR with MIRR. That misstates the fundamental reinvestment assumption of IRR.

Conclusion: The correct answer is False, which matches the provided answer.

The IRR method is based on the assumption that projects' cash flows are reinvested at the project's risk-adjusted cost of capital.判断题

类似问题

Which of the following statements is CORRECT?

The phenomenon called "multiple internal rates of return" arises when two or more mutually exclusive projects that have different lives are being compared.

Question4 Multiple IRRs are most likely when:Select one alternative: The discount rate is very high Cash flows are conventional (cash outflow in year 0 and cash-inflows thereafter) Cash flows change sign multiple times The project life is long ResetMaximum marks: 1 Flag question undefined

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Which of the following statements regarding the internal rate of return (IRR) of a project is incorrect?

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