Question

Consider a bond with a par value of $1,000, a coupon rate of 8%, and 10 years until maturity. What is the most you should pay for this asset if your required rate of return for assets like this is 5% and the coupon payments are paid annually? How does your answer change if the bond is semi-annual? Does the semi-annual bond sell at a premium or a discount?

Answer 1

(a)-Price of the Bond if the required rate of return is 5% and the coupon payments are annual

Face Value of the bond = $1,000

Annual Coupon Amount = $80 [$1,000 x 8%]

Annual Yield to Maturity = 5%

Maturity Period = 10 Years

Price of the Bond = Present Value of the Coupon Payments + Present Value of the face Value

= $80[PVIFA 5%, 10 Years] + $1,000[PVIF 5%, 10 Years]

= [$80 x 7.72173] + [$1,000 x 0.61391]

= $617.74 + $613.91

= $1,231.65

(a)-Price of the Bond if the coupon payments are made semi-annually

Face Value of the bond = $1,000

Semi-annual Coupon Amount = $40 [$1,000 x 8% x ½]

Semi-annual Yield to Maturity = 2.50% [5% x ½]

Maturity Period = 20 Years [10 Years x 2]

Price of the Bond = Present Value of the Coupon Payments + Present Value of the face Value

= $40[PVIFA 2.50%, 20 Years] + $1,000[PVIF 2.50%, 20 Years]

= [$40 x 15.58916] + [$1,000 x 0.61027]

= $623.57 + $610.27

= $1,233.84

(c)- The semi-annual bond is selling at premium, since the price of the Bond ($1,233.84) is greater than the Par Value of the Bond ($1,000).