Question

Consider three bonds with 6.1% coupon rates, all selling at face value. The short-term bond has a maturity of 4 years, the intermediate-term bond has maturity 8 years, and the long-term bond has maturity 30 years. a. What will be the price of each bond if their yields increase to 71%? (Do not round intermediate calculations. Round your answers to 2 decimal places.) Bond price 4 Years $ 30 Years $ b. What will be the price of each bond if their yields decrease to 5.1%? (Do not round intermediate calculations. Round your answers to 2 decimal places.) 8 Years Bond price 4 Years $0 $0 30 Years $0

Answer 1

Assuming the Face Value of Bond = $1000

(a) Maturity = 4 years

Number of periods to maturity = n = 4 years

Yield to Maturity = r = 7.1% = 0.071

Face Value FV = $1000

Annual Coupon Payment P = 6.1% of $1000 = 0.061*1000 = $61

Hence, Price of Bond = PV = P/(1+r) + P/(1+r)2 + .... + P/(1+r)n + FV/(1+r)n

= P[1 - (1+r)-n]/r + FV/(1+r)n = 61[1-(1+0.071)-4]/0.071 + 1000/(1+0.071)4 = $966.2

Maturity = 8 years

Number of periods to maturity = n = 8 years

Yield to Maturity = r = 7.1% = 0.071

Face Value FV = $1000

Annual Coupon Payment P = 6.1% of $1000 = 0.061*1000 = $61

Hence, Price of Bond = PV = P/(1+r) + P/(1+r)2 + .... + P/(1+r)n + FV/(1+r)n

= P[1 - (1+r)-n]/r + FV/(1+r)n = 61[1-(1+0.071)-8]/0.071 + 1000/(1+0.071)8 = $940.52

Maturity = 30 years

Number of periods to maturity = n = 30 years

Yield to Maturity = r = 7.1% = 0.071

Face Value FV = $1000

Annual Coupon Payment P = 6.1% of $1000 = 0.061*1000 = $61

Hence, Price of Bond = PV = P/(1+r) + P/(1+r)2 + .... + P/(1+r)n + FV/(1+r)n

= P[1 - (1+r)-n]/r + FV/(1+r)n = 61[1-(1+0.071)-30]/0.071 + 1000/(1+0.071)30 = $877.15

(b) Maturity = 4 years

Number of periods to maturity = n = 4 years

Yield to Maturity = r = 5.1% = 0.051

Face Value FV = $1000

Annual Coupon Payment P = 6.1% of $1000 = 0.061*1000 = $61

Hence, Price of Bond = PV = P/(1+r) + P/(1+r)2 + .... + P/(1+r)n + FV/(1+r)n

= P[1 - (1+r)-n]/r + FV/(1+r)n = 61[1-(1+0.051)-4]/0.051 + 1000/(1+0.051)4 = $1035.38

Maturity = 8 years

Number of periods to maturity = n = 8 years

Yield to Maturity = r = 5.1% = 0.051

Face Value FV = $1000

Annual Coupon Payment P = 6.1% of $1000 = 0.061*1000 = $61

Hence, Price of Bond = PV = P/(1+r) + P/(1+r)2 + .... + P/(1+r)n + FV/(1+r)n

= P[1 - (1+r)-n]/r + FV/(1+r)n = 61[1-(1+0.051)-8]/0.051 + 1000/(1+0.051)8 = $1064.37

Maturity = 30 years

Number of periods to maturity = n = 30 years

Yield to Maturity = r = 5.1% = 0.051

Face Value FV = $1000

Annual Coupon Payment P = 6.1% of $1000 = 0.061*1000 = $61

Hence, Price of Bond = PV = P/(1+r) + P/(1+r)2 + .... + P/(1+r)n + FV/(1+r)n

= P[1 - (1+r)-n]/r + FV/(1+r)n = 61[1-(1+0.051)-30]/0.051 + 1000/(1+0.051)30 = $1151.99