Question

A 20-year maturity bond with par value of $1,000 makes annual coupon payments at a coupon rate of 8%. Find the bond equivalent and effective annual yield to maturity of the bond for the following bond prices.

a. What is the bond’s yield to maturity if the bond is selling for $970?
b. What is the bond’s yield to maturity if the bond is selling for $1,000?
c. What is the bond’s yield to maturity if the bond is selling for $1,170?

Answer 1

since you are required to calculate the effective yield to maturity, you cannot use the approximate YTM formula since it is not exact. You will need to use a financial calculator, online calculator or excel spreadsheet. I prefer to use an excel spreadsheet and use the IRR function:

a) initial outlay = -$970

cash flows 1 - 19 = $80

cash flow 20 = $1,080

IRR = 8.31%

Since the bond is sold at a discount, the effective yield will be higher than the coupon rate.

b) if hte bond is sodl at par, the effective yield to maturity is the coupon rate = 8%

c) initial outlay = -$1,170

cash flows 1 - 19 = $80

cash flow 20 = $1,080

IRR = 6.49%

Since the bond is sold at a premium, the effective yield will be lower than the coupon rate.