XYZ Corp. made a coupon payment on their 6.25% bonds yesterday that mature in 11.5 years. What is the market price
of these bonds if the required return is 9.2% APR?
To calculate the market price of the bonds, we can use the present value formula for bond pricing. The formula is:
Market Price = (Coupon Payment / Required Return) * (1 - (1 / (1 + Required Return)^n)) + (Face Value / (1 + Required Return)^n)
Where:
- Coupon Payment: The annual interest payment made by the bond.
- Required Return: The rate of return that investors require for taking on the risk of buying the bond.
- n: The number of periods until the bond matures.
- Face Value: The amount of money the bondholder will receive when the bond matures.
In this case, the coupon payment is the same as the annual interest payment, which is 6.25% of the face value. The required return is 9.2% APR, which needs to be converted to a decimal and divided by the number of periods in a year. The number of periods until maturity is 11.5 years.
Let's plug the values into the formula:
Coupon Payment = 6.25% of Face Value = 0.0625 * Face Value
Required Return = 9.2% APR = 0.092 / 1 = 0.092
n = 11.5 years
Face Value = ?
Substituting these values into the formula:
Market Price = (0.0625 * Face Value / 0.092) * (1 - (1 / (1 + 0.092)^11.5)) + (Face Value / (1 + 0.092)^11.5)
To find the market price, we need to solve for Face Value. We can rearrange the formula:
Market Price - (0.0625 * Face Value / 0.092) * (1 - (1 / (1 + 0.092)^11.5)) = (Face Value / (1 + 0.092)^11.5)
Multiply both sides of the equation by (1 + 0.092)^11.5 to eliminate the denominators:
(1 + 0.092)^11.5 * Market Price - (0.0625 * Face Value / 0.092) * (1 + 0.092)^11.5 * (1 - (1 / (1 + 0.092)^11.5)) = Face Value
Now, we can plug in the values and solve for Face Value:
Market Price = (1 + 0.092)^11.5 * Market Price - (0.0625 * Face Value / 0.092) * (1 + 0.092)^11.5 * (1 - (1 / (1 + 0.092)^11.5)) - Face Value
Simplifying the equation will give us the market price of the bonds.