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Answer: 2.19%
The average credit spread of the company's bonds is calculated by taking the difference between the yield of the debt (RD) and the risk-free rate (Rf). The formula provided in the file content is: \[ \text{Credit spread} = RD - Rf = -\left(\frac{1}{T}\right) \ln\left(\frac{D}{F}\right) - Rf \] Where: - \( D \) is the market value of the debt (CAD 100 million). - \( F \) is the face value of the debt (CAD 115 million). - \( T \) is the time to maturity (2 years). - \( Rf \) is the risk-free rate, which is the yield on Canada government bonds with a 2-year maturity, given as 4.8% per year. Plugging in the values: \[ \text{Credit spread} = -\left(\frac{1}{2}\right) \ln\left(\frac{100}{115}\right) - 0.048 \] Calculating the natural logarithm and then the credit spread: \[ \text{Credit spread} = -\left(\frac{1}{2}\right) \ln(0.86956) - 0.048 \approx 0.0219 \text{ or } 2.19\% \] This calculation shows that the average credit spread is 2.19%, which corresponds to option C. This spread represents the additional yield that investors demand to compensate for the higher risk associated with the company's bonds compared to the risk-free government bonds. The other options provided (A, B, and D) are incorrect due to various reasons such as using the wrong yield calculation or not applying continuous compounding correctly.
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To better understand the financial health and relative risk of the company's bonds, we need to determine the credit spread, which reflects the additional yield that investors demand to hold the company's bonds over risk-free government bonds. The company's bonds in question have a face value of CAD 115 million and a current market value of CAD 100 million. These bonds are scheduled to mature in 2 years. For comparison, we will use Canada's government bonds of the same maturity, which have a continuously compounded yield of 4.8% per annum. What is the mean credit spread for the company's bonds?
A
1.09%
B
2.44%
C
2.19%
D
3.43%