Question

Consider three bonds with 6.40% coupon rates, all making annual coupon payments and all selling at face value. The short-term bond has a maturity of 4 years, the intermediate-term bond has a maturity of 8 years, and the long-term bond has a maturity of 30 years.

a. What will be the price of the 4-year bond if its yield increases to 7.40%? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

b. What will be the price of the 8-year bond if its yield increases to 7.40%? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

c. What will be the price of the 30-year bond if its yield increases to 7.40%? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

d. What will be the price of the 4-year bond if its yield decreases to 5.40%? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

e. What will be the price of the 8-year bond if its yield decreases to 5.40%? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

f. What will be the price of the 30-year bond if its yield decreases to 5.40%? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

g. Comparing your answers to parts (a), (b), and (c), are long-term bonds more or less affected than short-term bonds by a rise in interest rates?

More affected

Less affected

h. Comparing your answers to parts (d), (e), and (f), are long-term bonds more or less affected than short-term bonds by a decline in interest rates?

More affected

Less affected

Answer 1

Answer a.

Face Value = $1,000
Annual Coupon = 6.40%*$1,000 = $64
Time to Maturity = 4 years
Interest Rate = 7.40%

Price of Bond = $64 * PVIFA(7.40%, 4) + $1,000 * PVIF(7.40%, 4)
Price of Bond = $64 * (1 - (1/1.074)^4) / 0.074 + $1,000 / 1.074^4
Price of Bond = $966.43

Answer b.

Face Value = $1,000
Annual Coupon = 6.40%*$1,000 = $64
Time to Maturity = 8 years
Interest Rate = 7.40%

Price of Bond = $64 * PVIFA(7.40%, 8) + $1,000 * PVIF(7.40%, 8)
Price of Bond = $64 * (1 - (1/1.074)^8) / 0.074 + $1,000 / 1.074^8
Price of Bond = $941.20

Answer c.

Face Value = $1,000
Annual Coupon = 6.40%*$1,000 = $64
Time to Maturity = 30 years
Interest Rate = 7.40%

Price of Bond = $64 * PVIFA(7.40%, 30) + $1,000 * PVIF(7.40%, 30)
Price of Bond = $64 * (1 - (1/1.074)^30) / 0.074 + $1,000 / 1.074^30
Price of Bond = $880.74

Answer d.

Face Value = $1,000
Annual Coupon = 6.40%*$1,000 = $64
Time to Maturity = 4 years
Interest Rate = 5.40%

Price of Bond = $64 * PVIFA(5.40%, 4) + $1,000 * PVIF(5.40%, 4)
Price of Bond = $64 * (1 - (1/1.054)^4) / 0.054 + $1,000 / 1.054^4
Price of Bond = $1,035.13

Answer e.

Face Value = $1,000
Annual Coupon = 6.40%*$1,000 = $64
Time to Maturity = 8 years
Interest Rate = 5.40%

Price of Bond = $64 * PVIFA(5.40%, 8) + $1,000 * PVIF(5.40%, 8)
Price of Bond = $64 * (1 - (1/1.054)^8) / 0.054 + $1,000 / 1.054^8
Price of Bond = $1,063.60

Answer f.

Face Value = $1,000
Annual Coupon = 6.40%*$1,000 = $64
Time to Maturity = 30 years
Interest Rate = 5.40%

Price of Bond = $64 * PVIFA(5.40%, 30) + $1,000 * PVIF(5.40%, 30)
Price of Bond = $64 * (1 - (1/1.054)^30) / 0.054 + $1,000 / 1.054^30
Price of Bond = $1,146.96

Answer g.

Long-term bonds are more affected than short-term bonds by a rise in interest rates.

Answer h.

Long-term bonds are more affected than short-term bonds by a decline in interest rates.