Question

Whipple Corp. just issued 340,000 bonds with a coupon rate of 6.38 percent paid semiannually that mature in 25 years. The bonds have a YTM of 6.82 percent and have a par value of $2,000. How much money was raised from the sale of the bonds? (Round your intermediate calculations to two decimal places and final answer to the nearest whole dollar amount.)

Answer 1

No of periods = 25 years * 2 = 50 semi-annual periods

Coupon per period = (Coupon rate / No of coupon payments per year) * Face value

Coupon per period = (6.38% / 2) * $2000

Coupon per period = $63.8

Bond Price = Coupon / (1 + YTM / 2)^period + Face value / (1 + YTM / 2)^period

Bond Price = $63.8 / (1 + 6.82% / 2)¹ + $63.8 / (1 + 6.82% / 2)² + ...+ $63.8 / (1 + 6.82% / 2)⁵⁰ + $2000 / (1 + 6.82% / 2)⁵⁰

Using PVIFA = ((1 - (1 + Interest rate)^{- no of periods}) / interest rate) to value coupons

Bond Price = $63.8 * (1 - (1 + 6.82% / 2)^-50) / (6.82% / 2) + $2000 / (1 + 6.82% / 2)⁵⁰

Bond Price = $1521.07 + $374.03

Bond Price = $1895.10

Amount raised through Bond issue = Bond price * No of bonds issued

Amount raised through Bond issue = $1895.10 * 340,000

Amount raised through Bond issue = $644,334,000