A $1,000 fave value bond has a remaining maturity of 10 years and a required return of 9%. The bond's coupon rate is 7.4%. What is the fair value of this bond?
To calculate the fair value of a bond, we need to use the present value formula. The formula for the fair value of a bond can be calculated as follows:
Fair Value = [(Coupon Payment × (1 - (1/(1 + required return)^(remaining years)))) / required return] + [Face Value / (1 + required return)^(remaining years)]
Let's breakdown the components of the formula using the given information:
Coupon Payment: This is the annual interest payment that the bondholder receives. It is calculated by multiplying the bond's coupon rate (7.4%) by its face value ($1,000). So, Coupon Payment = 0.074 × $1,000 = $74.
Required Return: This is the minimum rate of return that an investor demands for this bond. In this case, it is given as 9% or 0.09.
Remaining Years: This represents the number of years remaining until the bond matures. In this case, it is 10 years.
Face Value: The face value is the amount that the bondholder will receive at maturity. In this case, the face value is $1,000.
Now, let's substitute these values into the formula:
Fair Value = [(Coupon Payment × (1 - (1/(1 + required return)^(remaining years)))) / required return] + [Face Value / (1 + required return)^(remaining years)]
= [( $74 × (1 - (1/(1 + 0.09)^(10)))) / 0.09] + [$1,000 / (1 + 0.09)^(10)]
To get the accurate value, you can now use a calculator or spreadsheet software to perform the calculations:
Fair Value = $751.69 + $385.54
= $1,137.23
Therefore, the fair value of the bond is approximately $1,137.23.