Question

# Apple Inc has a bond with \$1000 face value and a coupon rate of 8%, and...

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?

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.

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