Question

BOND VALUATION Bond X is noncallable and has 20 years to maturity, a 10% annual coupon, and a $1,000 par value. Your required return on Bond X is 9%; if you buy it, you plan to hold it for 5 years. You (and the market) have expectations that in 5 years, the yield to maturity on a 15-year bond with similar risk will be 10%. How much should you be willing to pay for Bond X today? (Hint: You will need to know how much the bond will be worth at the end of 5 years.) Do not round intermediate calculations. Round your answer to the nearest cent. $

Answer 1

Firstly, the value of the bond at the end of 5 years will be equal to face value of the bond because, if the annual coupon of the bond equals yeild to maturity, then the bond will be trading at face value.

Therefore, the bond will be worth $1,000 at the end of 5 years.

Now, given that the bond will be worth $1,000 at the end of 5 years and the bond holder will receive $100 per annum for 5 years (assuming the investor purchases the bond today and sells 5 years later), we will need to discount the cash inflow with the required rate of return (9%) to arrive at the value of the bond that the investor will be willing to pay today.

Value of the bond investor is willing to pay today based on above:

=($100 / (1.09)^1) + ($100 / (1.09)^2) + ($100 / (1.09)^3) + ($100 / (1.09)^4) + ($100 / (1.09)^5) + ($1,000 / (1.09)^5)

=$1,038.9