Question

Apple Inc has a bond with $1000 face value and a coupon rate of 8%, and Apple Inc has another bond with $1000 face value and a coupon rate of 12%. Both bonds pay coupon payment on January 1st in each year. Both bonds have 10-year maturities from today (January 2, 2010) and both sell at a yield to maturity of 10%. Suppose their yields to maturity next year are still 10%.

Now, suppose you purchase two bonds today (January 2, 2010) and hold both bonds for 1 year (until January 1, 2011).

(i) What is the rate of return on each bond? [Rate or Return (RoR) = (Coupon income + Bond price changes)/initial investment in the bond.]

(ii) Does the higher coupon bond provide a higher rate of return?

Answer 1

i) Bond 1:

Using a financial calculator:

Year 1: PMT = 80, FV = 1,000, i= 10%, n= 10; compute PV0= $877.11

Year 2: PMT = 80, FV = 1,000, i= 10%, n= 9; compute PV1= $884.82

Rate of Return = (Coupon + PV1 - PV0) / PV0

= ($80 + $884.82 - $877.11) / $877.11 = $87.71/$877.11 = 10%

Bond 1:

Using a financial calculator:

Year 1: PMT = 120, FV = 1,000, i= 10%, n= 10; compute PV0= $1,122.89

Year 2: PMT = 120, FV = 1,000, i= 10%, n= 9; compute PV1= $1,115.18

Rate of Return = (Coupon + PV1 - PV0) / PV0

= ($120 + $1,115.18 - $1,122.89) / $1,122.89 = $112.29/$1,122.89 = 10%

ii). No, Both bonds provide the same rate of return.