A firm's bonds trade with a promised YTM of 10%, but the firm has meaningful default risk. For WACC purposes, the relevant cost of debt is:

Question

BlackTom AI · Accepted Answer

YTM is the promised yield on the bond’s contractual cash flows; the expected return to investors must account for the probability of default and any recovery, so it will generally be lower than the promised YTM when default risk exists.

1) Relevant knowledge points and concepts
- Yield to maturity (YTM) is the internal rate of return that equates promised cash flows to price; it assumes all promised payments are made.  
- Expected return accounts for the chance of default and the recovery value received in default.  
- WACC should use the firm’s expected cost of debt (after-tax in the WACC formula), not the promised YTM when default risk is meaningful.

2) Step-by-step reasoning
- If a bond promises 10% (YTM) but has nonzero default probability p and recovery fraction R of par in default, actual investor payoffs differ from the promised ones.  
- Compute expected payoff and convert to expected return; this is the rate investors actually expect to earn, which is lower than the promised 10% because some proportion of scenarios produce losses.

3) Calculation with intermediate steps (illustrative numerical example)
- Assume par = $100, promised coupon+principal in one period = $110, default probability p = 5% (0.05), recovery R = 40% → recovery payoff = $40.  
- Expected cash received = (1 − p) × $110 + p × $40 = 0.95×110 + 0.05×40 = 104.5 + 2 = $106.50.  
- Expected return = (Expected cash − Price)/Price = (106.50 − 100)/100 = 6.5%, which is below the 10% promised YTM.

4) Why the correct answer is correct
- The expected return reflects default losses and is therefore lower than the promised YTM; WACC should use the expected cost of debt because it measures the firm’s actual average financing cost, not the overstated promised yield.

5) Why other options are incorrect
- “The firm’s cost of equity …” is not appropriate: equity cost is higher and unrelated as the debt component in WACC should reflect debt cost.  
- “The 10% YTM …” is incorrect because YTM ignores default losses (it prices promised cash flows, not expected cash flows).  
- “Above 10% …” is wrong: investors do not expect a return above the promised yield; they expect less once default risk and recoveries are accounted for.

6) Conclusion
- Therefore the relevant cost of debt for WACC is below 10%, matching the provided correct answer.

A firm's bonds trade with a promised YTM of 10%, but the firm has meaningful default risk. For WACC purposes, the relevant cost of debt is:单项选择题

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