Question

A year ago, you purchased two bonds issued by the same company, ABC Co. : (1) a 20- year $1,000 par value, annual coupon bond with a 7 percent coupon rate, and (2) a 5-year $1,000 par value, annual coupon bond also with a 7 percent coupon rate. Both bonds had a yield to maturity (required rate of return) of 9 percent when you bought them.

a. What price did you pay for each bond a year ago?

b. Today, assume the yield to maturity on both bonds is 11 percent. What is total rate of return on each bond if you sell these bonds today?

c. Now, imagine today's yield to maturity is 13 percent for each bond. Unfortunately, you need cash from selling these bonds for your winter vacation trip to Aspen and Jamaica. What is total rate of return on each bond if you sell these bonds today?

d. Examine your answers for each bond from questions b and c. Which bond had the best return in each question and why? What bond risk concept does this problem illustrate?

Answer 1

a)

20 year bond price

Price = $817.43

5 year bond price

Price = $922.21

b)

one year elapses so number of year to maturity will reduce by 1 year.

when YTM is 11% lets calculate price of each bond

20 year bond:

Total rate of return = (sale price + coupon - purchase price) / purchase price

= (686.43 + 70 - 817.43) / 817.43

= -7.46%

5 - year bond:

total rate of return = (875.90 + 70 - 922.21)/922.21

= 2.57%

c)

when YTM - 13%

20 - year bond:

Price when YTM 13% = 583.72 (formula =-PV(13%,19,70,1000) ]

total rate of return = (583.72 + 70 -817.43 ) / 817.43

= -20.03%

5 - year bond:

Price when YTM 13% = $821.53 (formula =-PV(13%,4,70,1000) ]

Total rate of return = (821.53 + 70 - 922.21) / 922.21

= -3.33%

d)

5 - year bond had the best return because it has shorter maturity period when compare to other bond.

the risk concept this problem illustrates is interest rate risk.