Question

1. ) You are the bond buyer on the corporate bond desk for the brokerage firm, Dewey Scruem and Howe, and there are three bonds that you want to add to your portfolio. The current yield to maturity in the market on similar issues with similar ratings is 5.67% and you are looking for bonds that pay semi-annual coupon interest payments with $1,000 maturity. What price will you pay for each bond?

Bond	Coupon	Years to Maturity	Price
1	4.35%	6
2	6.11%	9
3	8.72%	11

Answer 1

1.

Number of periods = n = 6*2 = 12 semiannual periods

Yield r = 5.67%/2 = 0.0567/2 = 0.02835

Semiannual Payment P = 4.35%*1000/2 = $21.75

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 = 21.75(1 - 1.02835^-12)/0.02835 + 1000/1.02835¹² = $933.65

2.

Number of periods = n = 9*2 = 18 semiannual periods

Yield r = 5.67%/2 = 0.0567/2 = 0.02835

Semiannual Payment P = 6.11%*1000/2 = $30.55

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 = 30.55(1 - 1.02835^-18)/0.02835 + 1000/1.02835¹⁸ = $1030.68

3.

Number of periods = n = 11*2 = 22 semiannual periods

Yield r = 5.67%/2 = 0.0567/2 = 0.02835

Semiannual Payment P = 8.72%*1000/2 = $43.6

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 = 43.6(1 - 1.02835^-22)/0.02835 + 1000/1.02835²² = $1247.10