The State Pension System wants to sell a 20-year original maturity General Industries’ bond that it purchased 10 years ago. The bond pays interest twice each year. The par value of the bond is $100 million. The coupon rate is 8.6 percent. If the current market interest rate is 4.5 percent and there are exactly 10 years left until maturity, how much will the pension plan be paid for the bond? (Be sure to show all your work, including the factors you used to determine the value of the bond.)

$132,725,610

Explanation:

current price of the bond = PV of its maturity value + PV of the remaining coupons

10 years left to maturity, semi annual coupons (8.6%, coupon = $4,300,000) with a current market interest rate of 4.5%

PV of maturity = $100,000,000 / (1 + 2.25%)²⁰ = $64,081,647

PV of coupons = coupon x [ 1 - (1 + r)⁻ⁿ] / r = $4,300,000 x [ 1 - (1 + 2.25%)⁻²⁰] / 2.25% = $68,643,963

current bond price = $64,081,647 + $68,643,963 = $132,725,610

since the bond's coupon rate is higher than the current market rate, then the bond will be sold at a premium.

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