Question at position 10 (6 marks, difficulty level: Medium) The Dunley Corp. plans to issue one-year zero-coupon bonds. It believes the bonds will have a BBB rating, and the average debt beta for BBB rating is 0.12. Suppose AAA bonds with the same maturity have a 2.5% yield. If the market risk premium is 5%, use the annual default rates by debt rating here and calculate the yield to maturity of Dunley's one-year bond, assuming an expected 70% loss rate in the event of default during average economic times. [table]
Rating: | AAA | AA | A | BBB | BB | B | CCC | CC-C Default Rate: | | | | | | | | Average | 0.0% | 0.1% | 0.2% | 0.5% | 2.2% | 5.5% | 12.2% | 14.1% In Recessions | 0.0% | 1.0% | 3.0% | 3.0% | 8.0% | 16.0% | 48.0% | 79.0%
[/table] 5.070%2.900%3.450%4.065%

Question

Question at position 10 (6 marks, difficulty level: Medium) The Dunley Corp. plans to issue​ one-year zero-coupon bonds. It believes the bonds will have a BBB rating, and the average debt beta for BBB rating is 0.12. Suppose AAA bonds with the same maturity have a 2.5% yield. If the market risk premium is 5%​, use the annual default rates by debt rating​ here and calculate the yield to maturity of Dunley's one-year bond, assuming an expected 70% loss rate in the event of default during average economic times. [table]
Rating: | AAA | AA | A | BBB | BB | B | CCC | CC-C Default Rate: |  |  |  |  |  |  |  |  Average | 0.0% | 0.1% | 0.2% | 0.5% | 2.2% | 5.5% | 12.2% | 14.1% In Recessions | 0.0% | 1.0% | 3.0% | 3.0% | 8.0% | 16.0% | 48.0% | 79.0%
[/table] 5.070%2.900%3.450%4.065%

BlackTom AI · Accepted Answer

To tackle this one-year zero-coupon bond problem, I’ll break down the components that contribute to the one-year yield for Dunley’s BBB-rated issue.
First, identify the baseline risk-free or AAA benchmark: the AAA yield is given as 2.5%. This serves as the starting point for the required return.
Next, incorporate the systematic risk component for the bond using the debt beta and the market risk premium. The debt beta for BBB is 0.12, and the market risk premium is 5%. A simple way to adjust for this systematic risk is to add beta × market risk premium: 0.12 × 5% = 0.60%.
Now, account for expected credit losses due to the possibility of default. The problem provides the average default rate for BBB as 0.5%. The expected loss given default is 70% of the bond’s value (loss rate in default). The expected annual loss from default is therefore 0.5% × 70% = 0.35%.
Combine these components to estimate the one-year yield: starting from the AAA baseline (2.50%), add the systematic risk premium (0.60%), and add the expected default loss (0.35%), yielding 2.50% + 0.60% + 0.35% = 3.45%.
Now examine the other options to see why they don’t fit this calculation:
- 5.070% would require a much larger adjustment than provided by the given beta and default data; it would imply either a much higher beta or a much higher default expectation than given.
- 2.900% is too low because it omits either the systematic risk premium or the expected default loss; at minimum you should include the 0.60% beta adjustment and the 0.35% expected loss, which already push the yield above 2.50%.
- 4.065% might arise if one double-counted components or used a different, nonstandard method; however, with the stated inputs (AAA baseline, BBB beta, default rate, and loss given default), 3.45% is the consistent outcome.
Overall, the most coherent synthesis of the provided data yields a one-year yield of 3.45% for Dunley’s BBB-rated, one-year zero-coupon bond. The calculation aligns with applying the beta-adjusted market risk premium and the expected default loss to the AAA benchmark.

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