Imagination Dragons Corporation needs to raise funds to finance a plant expansion, and it has decided to issue 25-year zero coupon bonds with a par value of $1,000 each to raise the money. The required return on the bonds will be 9 percent. Assume semiannual compounding periods.

What will these bonds sell for at issuance?

Each 1000 par value bond will sell at issuance for $110.71

Explanation:

A zero coupon bond is a bond that does not pay interest and is issued at a heavy discount which is a compensation for the interest payment. The value of the zero coupon bond today is calculated using the present value of the face value of zero coupon bond. The formula to calculate the present value of the zero coupon bonds is,

PV = Face value / (1+r)^t

As the required rate is quoted in annual terms, we will divide it by 2 to calculate the semi annual required rate and multiply the time (annual) by 2 to calculate the semi annual periods in 25 years.

Semi annual required rate = 9% / 2 = 4.5%

Semi annual periods (t) = 25 * 2 = 50

PV = 1000  /  (1+0.045)^50

PV = $110.70965 rounded off to $110.71