A one-year U.S. Treasury bond and a one-year corporation bond both promise to pay $11,934 next year. The corporation bond carries a risk premium of 15 percent over Treasury bond. The price of the Treasury bond today is $11,700. What is the price of the corporation bond?
Question
A one-year U.S. Treasury bond and a one-year corporation bond both promise to pay 11,700. What is the price of the corporation bond?
Solution
To find the price of the corporation bond, we first need to calculate the yield of the Treasury bond, then add the risk premium to get the yield of the corporation bond, and finally use that yield to find the price of the corporation bond.
Step 1: Calculate the yield of the Treasury bond The yield of a bond is the annual return an investor would receive if the bond is held until maturity. It can be calculated using the formula:
Yield = (Future Value - Present Value) / Present Value
For the Treasury bond, the future value is 11,700 (the price of the bond today). So the yield of the Treasury bond is:
Yield = (11,700) / $11,700 = 0.02 or 2%
Step 2: Calculate the yield of the corporation bond The corporation bond carries a risk premium of 15 percent over the Treasury bond. This means the yield of the corporation bond is 15 percent higher than the yield of the Treasury bond. So the yield of the corporation bond is:
Corporation bond yield = Treasury bond yield + risk premium = 2% + 15% = 17%
Step 3: Calculate the price of the corporation bond Now that we have the yield of the corporation bond, we can use it to find the price of the corporation bond. The price of a bond is the future value divided by one plus the yield. So the price of the corporation bond is:
Price = Future Value / (1 + Yield) = 10,200.85
Therefore, the price of the corporation bond is $10,200.85.
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