Question

Suppose Ice Cubes Inc. has a liability of $100 million due in five years and the company is going to buy 5 year bonds today in order to meet this future liability.

At the current YTM of 8 percent, what is the face (market) value of the bonds the company has to purchase today in order to meet its future obligations? Assume the desired bonds carry a coupon rate of 5.5% and how many bonds could be purchased given the standard par value of $1000?

Answer 1

Face Value of Bond = $1,000

Annual Coupon Rate = 5.50%
Annual Coupon = 5.50% * $1,000
Annual Coupon = $55

Annual YTM = 8%
Time to Maturity = 5 years

Market Value of Bond = $55 * PVIFA(8%, 5) + $1,000 * PVIF(8%, 5)
Market Value of Bond = $55 * (1 - (1/1.08)^5) / 0.08 + $1,000 / 1.08^5
Market Value of Bond = $900.18

Number of bonds purchased = Liability Amount / Market Value of Bond
Number of bonds purchased = $100,000,000 / $900.18
Number of bonds purchased = 111,089