Question

Answer the following question regarding the price of a five percent coupon bond with the face value of $1000, which matures in three years from today. Coupon is paid annually at the end of the year. Your investment plan is to purchase the coupon bond today and hold it to the maturity.

1. a) Assuming the market price of bond is $1000, what would be the yield to maturity?

2. b) Suppose that you can reinvest your coupon at the annual rate of return of 3%. What is your effective

   annual rate of return on the bond investment. Why is your effective rate of return different from the yield to maturity, if it is different? Under what circumstance, effective rate of return is equal to yield to maturity?

3. c) Now suppose the market price of bond drops to $900 right after the purchase. Would you expect higher or lower effective rate of return on the bond investment than the yield to maturity you compute in a? Explain why.

Answer 1

a) Assuming the market price of bond is $1000, what would be the yield to maturity?

If the price of the bond = par value, then yield = coupon rate. Hence, the yield to maturity = 5%

b) Suppose that you can reinvest your coupon at the annual rate of return of 3%. What is your effective annual rate of return on the bond investment. Why is your effective rate of return different from the yield to maturity, if it is different? Under what circumstance, effective rate of return is equal to yield to maturity?

FV of coupons = FV (Rate, Period, PMT, PV) = FV (3%, 3, -5% x 1000, 0) = $ 154.545

Plus you will also get the par value on redemption = $ 1000

Hence, total proceeds at the time of maturity = 154.545 + 1,000 = $ 1,154.545

Hence, effective rate of return = (1,154.545 / 1000)^1/3 - 1 = 4.91%

It's different because YTM calculation assumes that all intermediate coupon payments are reinvested at the same rate as yield (YTM). Since this is not the case here, our effective rate of return has turned out to be different from YTM.

If coupons are reinvested at the same rate as YTM i.e. 5%, then the effective rate of return will be equal to yield to maturity.

c) Now suppose the market price of bond drops to $900 right after the purchase. Would you expect higher or lower effective rate of return on the bond investment than the yield to maturity you compute in a? Explain why.

Since, we are going to hold the bond till maturity and not sell it any time in between, the market price of the bond after purchase, doesn't matter. Hence, our rate of return will still remain the same as the YTM we computed in part (a)