A company's 5-year bonds are yielding 8% per year. Treasury bonds with the same maturity are yielding 5% per year, and the real risk-free rate (r*) is 3.05%. The average inflation premium is 1.55%, 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 0.9%, what is the default risk premium on the corporate bonds? Round your answer to two decimal places.
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To calculate the default risk premium on the corporate bonds, we need to add the default risk premium to the other risk premiums.
The default risk premium is the additional return investors require to compensate for the risk of default on the corporate bonds.
To find the default risk premium, we first need to calculate the total risk premium.
Total risk premium = Inflation premium + Maturity risk premium + Liquidity premium
Inflation premium = 1.55%
Maturity risk premium = 0.1 × (5 - 1)% = 0.4%
Liquidity premium = 0.9%
Total risk premium = 1.55% + 0.4% + 0.9% = 2.85%
Next, we need to subtract the risk-free rate from the total risk premium to get the default risk premium.
Default risk premium = Total risk premium - Risk-free rate
Risk-free rate = r* + Inflation premium = 3.05% + 1.55% = 4.60%
Default risk premium = 2.85% - 4.60% = -1.75%
The default risk premium on the corporate bonds is -1.75%.
To calculate the default risk premium on the corporate bonds, we need to determine the difference between the yield on the corporate bonds and the risk-free rate adjusted for inflation.
The default risk premium is the additional yield investors demand to compensate for the risk of default on the corporate bonds. It represents the compensation for taking on the risk that the issuing company may default on its bond payments.
To calculate the default risk premium, we can use the following formula:
Default Risk Premium = Yield on Corporate Bonds - Risk-Free Rate Adjusted for Inflation
First, let's determine the risk-free rate adjusted for inflation. The risk-free rate is the sum of the real risk-free rate (r*) and the average inflation premium:
Risk-Free Rate = Real Risk-Free Rate (r*) + Average Inflation Premium
Risk-Free Rate = 3.05% + 1.55% = 4.60%
Next, let's calculate the yield on the corporate bonds. The yield on the corporate bonds consists of the risk-free rate, the maturity risk premium, and the liquidity premium:
Yield on Corporate Bonds = Risk-Free Rate + Maturity Risk Premium + Liquidity Premium
The maturity risk premium is given as 0.1 × (t - 1)%, where t is the number of years to maturity. In this case, the bonds have a 5-year maturity, so t = 5.
Maturity Risk Premium = 0.1 × (5 - 1)% = 0.1 × 4% = 0.4%
The liquidity premium is given as 0.9%.
Yield on Corporate Bonds = 4.60% + 0.4% + 0.9% = 5.90%
Now, we can calculate the default risk premium:
Default Risk Premium = 5.90% - 4.60% = 1.30%
Therefore, the default risk premium on the corporate bonds is 1.30%, rounded to two decimal places.