What role does the risk-adjusted discount rate play in project evaluation?

Question

BlackTom AI · Accepted Answer

A risk-adjusted discount rate raises the required rate of return when future cash flows are more uncertain, so riskier projects are discounted more heavily.

1) Relevant concepts and definitions:
- Discount rate: the rate used to convert future cash flows into present value.
- Risk-adjusted discount rate: the discount rate increased (or decreased) to reflect project-specific risk; often estimated by adding a risk premium to a base cost of capital (e.g., using CAPM or a subjective premium).
- NPV formula: NPV = Σ (CF_t / (1 + r)^t) − Initial Investment.

2) Step-by-step reasoning:
- Higher perceived risk → investors require higher expected return → use a larger discount rate r.
- A larger r reduces the present value of future cash flows, lowering NPV, which compensates investors for bearing extra risk.

3) Calculation example (all intermediate steps shown):
- Suppose a one-year payoff CF1 = $100 and initial investment = $80.
- If r = 5% (low risk): PV = 100 / 1.05 = 95.238; NPV = 95.238 − 80 = 15.238.
- If r = 15% (higher risk): PV = 100 / 1.15 = 86.957; NPV = 86.957 − 80 = 6.957.
- Raising r for riskier projects reduced PV and NPV, reflecting required compensation for uncertainty.

4) Why the correct answer is correct:
- The purpose of risk-adjusting the discount rate is to compensate investors for additional uncertainty by increasing the required return. This is exactly described by “It increases for riskier projects to compensate for uncertainty.”

5) Why other options are incorrect:
- “It decreases the project’s cost to improve its NPV”: Incorrect — increasing the rate reduces NPV, it does not decrease cost.
- “It eliminates the need for scenario analysis”: Incorrect — scenario/sensitivity analysis remain valuable; rate adjustment does not replace them.
- “It ensures that all projects have the same risk level”: Incorrect — it does the opposite by reflecting differing risk levels via different rates.

6) Conclusion:
Therefore, the correct choice is “It increases for riskier projects to compensate for uncertainty,” which matches the provided answer.

What role does the risk-adjusted discount rate play in project evaluation?单项选择题

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