Questions: A company's 5-year bonds yield 7% per year. Treasury bonds with the same maturity yield of 4.8% per year, and the average 5-year inflation premium is 2.05%. Suppose maturity and liquidity risk premiums are zero. What is the default risk premium on the company's bond?

A company's 5-year bonds yield 7% per year. Treasury bonds with the same maturity yield of 4.8% per year, and the average 5-year inflation premium is 2.05%. Suppose maturity and liquidity risk premiums are zero. What is the default risk premium on the company's bond?
Transcript text: A company's 5 -year bonds yield $7 \%$ per year. Treasury bonds with the same maturity yield of $4.8 \%$ per year, and the average 5 -year inflation premium is $2.05 \%$. Suppose maturity and liquidity risk premiums are zero. What is the default risk premium on the company's bond?
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Solution

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To determine the default risk premium on the company's bond, we can use the following formula:

\[ \text{Company's Bond Yield} = \text{Risk-Free Rate} + \text{Inflation Premium} + \text{Default Risk Premium} + \text{Maturity Risk Premium} + \text{Liquidity Risk Premium} \]

Given:

  • Company's bond yield = 7%
  • Treasury bond yield (Risk-Free Rate) = 4.8%
  • Inflation premium = 2.05%
  • Maturity and liquidity risk premiums = 0

We need to find the default risk premium. Rearranging the formula to solve for the default risk premium:

\[ \text{Default Risk Premium} = \text{Company's Bond Yield} - (\text{Risk-Free Rate} + \text{Inflation Premium}) \]

Substitute the given values:

\[ \text{Default Risk Premium} = 7\% - (4.8\% + 2.05\%) \]

\[ \text{Default Risk Premium} = 7\% - 6.85\% \]

\[ \text{Default Risk Premium} = 0.15\% \]

However, this result does not match any of the provided options. Let's re-evaluate the options:

  1. It is not possible to answer the question without the real interest rates: This is incorrect because we have enough information to calculate the default risk premium using the given yields and premiums.

  2. $4.95\%$: This is incorrect because it does not match the calculated default risk premium.

  3. $2.75\%$: This is incorrect because it does not match the calculated default risk premium.

  4. $2.2\%$: This is incorrect because it does not match the calculated default risk premium.

Upon reviewing the calculation, it seems there might be a misunderstanding in the options provided. Based on the calculation, the default risk premium should be 0.15%, but this is not listed as an option. Therefore, none of the provided options accurately reflect the calculated default risk premium.

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