Question

4. A coupon bond that pays interest semi-annually has a par value of $1,000, matures in 5 years, and has a yield to maturity of 10%. The value of the bond today will be rate is 8% a. $1,075.80 b.$924.16 if the coupon c. $922.78 d. $1,077.20 e. none of the above 5. A zero-coupon bond has a yield to maturity of 9% and a par value of$1,000. Ifthe bond matu in 8 years, the bond should sell for a price of today. a. $501.87 b. 422.41 c.$513.16

Answer 1

4.

Number of periods to maturity = n = 5*2 = 10 semiannual years

Yield to Maturity = r = 10%/2 = 5%

Semiannual Coupon Payment P = 8%*1000/2 = $40

Face Value FV = $1000

Hence, 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 = 40(1 - 1.05^-10)/0.05 + 1000/1.05¹⁰ = $922.78

5.

Number of periods to maturity = n = 8 years

Yield to Maturity = r = 9%

Face Value FV = $1000

Hence, PV = FV/(1+r)ⁿ = 1000/1.09⁸ = $501.87