Consider three bonds with 6.70% coupon rates, all making annual coupon payments
ID: 1172427 • Letter: C
Question
Consider three bonds with 6.70% 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 7.70%? (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 7.70%? (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 7.70%? (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 5.70%? (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 5.70%? (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 5.70%? (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
Explanation / Answer
Answer a.
Face Value = $1,000
Annual Coupon = 6.70%*$1,000 = $67
Time to Maturity = 4 years
Yield to Maturity = 7.70%
Price of Bond = $67 * PVIFA(7.70%, 4) + $1,000 * PVIF(7.70%, 4)
Price of Bond = $67 * (1 - (1/1.077)^4) / 0.077 + $1,000 / 1.077^4
Price of Bond = $966.66
Answer b.
Face Value = $1,000
Annual Coupon = 6.70%*$1,000 = $67
Time to Maturity = 8 years
Yield to Maturity = 7.70%
Price of Bond = $67 * PVIFA(7.70%, 8) + $1,000 * PVIF(7.70%, 8)
Price of Bond = $67 * (1 - (1/1.077)^8) / 0.077 + $1,000 / 1.077^8
Price of Bond = $941.87
Answer c.
Face Value = $1,000
Annual Coupon = 6.70%*$1,000 = $67
Time to Maturity = 30 years
Yield to Maturity = 7.70%
Price of Bond = $67 * PVIFA(7.70%, 30) + $1,000 * PVIF(7.70%, 30)
Price of Bond = $67 * (1 - (1/1.077)^30) / 0.077 + $1,000 / 1.077^30
Price of Bond = $884.16
Answer d.
Face Value = $1,000
Annual Coupon = 6.70%*$1,000 = $67
Time to Maturity = 4 years
Yield to Maturity = 5.70%
Price of Bond = $67 * PVIFA(5.70%, 4) + $1,000 * PVIF(5.70%, 4)
Price of Bond = $67 * (1 - (1/1.057)^4) / 0.057 + $1,000 / 1.057^4
Price of Bond = $1,034.89
Answer e.
Face Value = $1,000
Annual Coupon = 6.70%*$1,000 = $67
Time to Maturity = 8 years
Yield to Maturity = 5.70%
Price of Bond = $67 * PVIFA(5.70%, 8) + $1,000 * PVIF(5.70%, 8)
Price of Bond = $67 * (1 - (1/1.057)^8) / 0.057 + $1,000 / 1.057^8
Price of Bond = $1,062.84
Answer f.
Face Value = $1,000
Annual Coupon = 6.70%*$1,000 = $67
Time to Maturity = 30 years
Yield to Maturity = 5.70%
Price of Bond = $67 * PVIFA(5.70%, 30) + $1,000 * PVIF(5.70%, 30)
Price of Bond = $67 * (1 - (1/1.057)^30) / 0.057 + $1,000 / 1.057^30
Price of Bond = $1,142.18
Answer g.
More affected
Answer h.
More affected