7. Problem 6.11 (Default Risk Premium) K eBook A company's 5-year bonds are yielding 10% per year. Treasury bonds with the same maturity are yielding 4.5% per year, and the real risk-free rate (r) is 2.25%. The average inflation premium is 1.85%, and the maturity risk premium is estin (t-1) %, where t number of years to maturity. If the liquidity premium is 1.2%, what is the default risk premium on the corporate bonds? Round your answer to two decimal places.

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## Problem 6.11 (Default Risk Premium)

### Problem Statement:

A company's 5-year bonds are yielding 10% per year. Treasury bonds with the same maturity are yielding 4.5% per year, and the real risk-free rate (r*) is 2.25%. The average inflation premium is 1.85%, and the maturity risk premium is estimated to be 0.1 × (t - 1)%, where t = number of years to maturity. If the liquidity premium is 1.2%, what is the default risk premium on the corporate bonds? Round your answer to two decimal places.

### Input Field:

- Enter your answer: _______ %

### Explanation:

This question involves calculating the default risk premium on corporate bonds. To solve this problem, you need to understand the different components that contribute to the yield of a bond:

1. **Real Risk-Free Rate (r*):** The theoretical return on an investment with zero risk, not accounting for inflation.

2. **Inflation Premium:** The additional yield required by investors to compensate for inflation.

3. **Maturity Risk Premium:** The additional yield on a long-term bond to compensate for risks associated with time until maturity. In this case described by the formula \(0.1 \times (t - 1)\%\).

4. **Liquidity Premium:** The additional yield required by investors for holding a less liquid asset.

5. **Treasury Bonds Yield:** Considered free of default risk; used as a benchmark.

6. **Company's Bond Yield:** The total yield which includes all the aforementioned premiums plus the default risk premium.

### Equation:

The yield on the corporate bond can be expressed as the sum of these components:

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

Substituting the given values into the equation and solving for the Default Risk Premium will yield the answer. 

### Calculations:

To find the default risk premium, use:

\[ \text{Default Risk Premium} = \text{Company's Bond Yield} - (\text{Treasury Bond Yield} + \text{Liquidity Premium}) \]

Substitute the given yields and premiums into this formula to determine the Default Risk Premium.
Transcribed Image Text:## Problem 6.11 (Default Risk Premium) ### Problem Statement: A company's 5-year bonds are yielding 10% per year. Treasury bonds with the same maturity are yielding 4.5% per year, and the real risk-free rate (r*) is 2.25%. The average inflation premium is 1.85%, and the maturity risk premium is estimated to be 0.1 × (t - 1)%, where t = number of years to maturity. If the liquidity premium is 1.2%, what is the default risk premium on the corporate bonds? Round your answer to two decimal places. ### Input Field: - Enter your answer: _______ % ### Explanation: This question involves calculating the default risk premium on corporate bonds. To solve this problem, you need to understand the different components that contribute to the yield of a bond: 1. **Real Risk-Free Rate (r*):** The theoretical return on an investment with zero risk, not accounting for inflation. 2. **Inflation Premium:** The additional yield required by investors to compensate for inflation. 3. **Maturity Risk Premium:** The additional yield on a long-term bond to compensate for risks associated with time until maturity. In this case described by the formula \(0.1 \times (t - 1)\%\). 4. **Liquidity Premium:** The additional yield required by investors for holding a less liquid asset. 5. **Treasury Bonds Yield:** Considered free of default risk; used as a benchmark. 6. **Company's Bond Yield:** The total yield which includes all the aforementioned premiums plus the default risk premium. ### Equation: The yield on the corporate bond can be expressed as the sum of these components: \[ \text{Company's Bond Yield} = \text{Real Risk-Free Rate} + \text{Inflation Premium} + \text{Maturity Risk Premium} + \text{Liquidity Premium} + \text{Default Risk Premium} \] Substituting the given values into the equation and solving for the Default Risk Premium will yield the answer. ### Calculations: To find the default risk premium, use: \[ \text{Default Risk Premium} = \text{Company's Bond Yield} - (\text{Treasury Bond Yield} + \text{Liquidity Premium}) \] Substitute the given yields and premiums into this formula to determine the Default Risk Premium.
**Problem 6.17 (Interest Rate Premiums)**

A 5-year Treasury bond has a 4.2% yield. A 10-year Treasury bond yields 6.7%, and a 10-year corporate bond yields 8.1%. The market expects that inflation will average 2.8% over the next 10 years (\(IP_{10} = 2.8%\)). Assume that there is no maturity risk premium (\(MRP = 0\)) and that the annual real risk-free rate, \(r^*\), will remain constant over the next 10 years. 

*(Hint: Remember that the default risk premium and the liquidity premium are zero for Treasury securities: DRP = LP = 0.)* 

A 5-year corporate bond has the same default risk premium and liquidity premium as the 10-year corporate bond described. What is the yield on this 5-year corporate bond? Round your answer to one decimal place.

[Input box for answer]

---

There are no graphs or diagrams in this problem.
Transcribed Image Text:**Problem 6.17 (Interest Rate Premiums)** A 5-year Treasury bond has a 4.2% yield. A 10-year Treasury bond yields 6.7%, and a 10-year corporate bond yields 8.1%. The market expects that inflation will average 2.8% over the next 10 years (\(IP_{10} = 2.8%\)). Assume that there is no maturity risk premium (\(MRP = 0\)) and that the annual real risk-free rate, \(r^*\), will remain constant over the next 10 years. *(Hint: Remember that the default risk premium and the liquidity premium are zero for Treasury securities: DRP = LP = 0.)* A 5-year corporate bond has the same default risk premium and liquidity premium as the 10-year corporate bond described. What is the yield on this 5-year corporate bond? Round your answer to one decimal place. [Input box for answer] --- There are no graphs or diagrams in this problem.
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