Which of the following statements about NPV and IRR is TRUE?

Question

BlackTom AI · Accepted Answer

NPV is preferred when evaluating mutually exclusive projects because it directly measures the dollar increase in firm value and therefore aligns with shareholder wealth maximization.

1. Relevant knowledge points and concepts
- Net Present Value (NPV): NPV = sum_t (CF_t / (1 + r)^t) − initial investment. It gives the absolute present-value gain (in currency) from a project using the firm's required return (cost of capital) r.
- Internal Rate of Return (IRR): the discount rate that sets NPV = 0. IRR is a percentage return measure.
- Key differences: NPV measures value added in dollars; IRR measures rate of return and implicitly assumes reinvestment of intermediate cash flows at the IRR. IRR can give multiple values for nonconventional cash flows and can rank projects differently from NPV when projects differ in scale or timing.

2. Step-by-step reasoning
- For mutually exclusive projects you must choose the project that maximizes firm value (dollars), not the one with the highest percentage return.
- Because NPV uses the firm's cost of capital, it correctly accounts for the scale of cash flows and realistic reinvestment, avoiding ranking anomalies.

3. Numerical illustration (all intermediate steps)
Consider two one-period, mutually exclusive projects at a 10% cost of capital:
Project A: initial −1000, cash inflow +1500 in one year.
IRR_A = (1500 / 1000) − 1 = 0.50 = 50%.
NPV_A = −1000 + 1500 / 1.10 = −1000 + 1363.64 = 363.64.

Project B: initial −5000, cash inflow +6000 in one year.
IRR_B = (6000 / 5000) − 1 = 0.20 = 20%.
NPV_B = −5000 + 6000 / 1.10 = −5000 + 5454.55 = 454.55.

IRR ranks A higher (50% vs 20%), but NPV ranks B higher (454.55 > 363.64). Since B adds more dollar value, it is the correct choice for mutually exclusive projects.

4. Why the correct answer is correct
NPV is preferred because it selects the project that increases shareholder wealth the most in absolute terms and uses a consistent reinvestment assumption (the cost of capital). IRR’s percent measure can mislead when projects differ in scale or timing.

5. Why other common statements are incorrect
- “IRR is always preferred”: incorrect because IRR can give misleading rankings for mutually exclusive projects and can produce multiple IRRs for nonconventional cash flows.
- “NPV and IRR always agree”: incorrect; they can conflict when projects differ in scale or timing (as shown).
- “Higher IRR always means better project”: incorrect if a lower-IRR project yields a higher NPV (greater dollar benefit).

6. Conclusion
The correct choice—NPV is preferred when evaluating mutually exclusive projects—matches the provided answer.

Which of the following statements about NPV and IRR is TRUE?单项选择题

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