Question

5.A 15-year corporate bond has a par value of $100,000 and a 4.5% annual coupon rate. Assume that your required rate of return is 8% and that you plan to hold onto this bond for 10 years. You and the market have expectations that in 10 years the yield-to-maturity for this bond (or another bond with similar risk and maturity) will be 10%. How much are you willing to pay for this bond today

Answer 1

$66,857.55

Step-by-step explanation:

The price of the bond in 10 years will be:

PV of face value = $100,000 / (1 + 10%)⁵ = $62,092.13

PV of coupon payments = $4,500 x 3.7908 (PV annuity factor, 10%, 5 periods) = $17,058.60

market value in 10 years = $79,150.73

In order to determine the price that you are willing to pay for the bond:

PV of market value in 10 years = $79,150.73 / (1 + 8%)¹⁰ = $36,662.10

PV of coupon payments = $4,500 x 6.7101 (PV annuity factor, 8%, 20 periods) = $30,195.45

Price you should be willing to pay = $66,857.55