The 7 percent, semiannual coupon bonds offered by House Renovators are callable in two years at $1,035. What is the amount of the call premium if the bonds have a par value of $1,000?

Question

Quizplus · Accepted Answer

The call premium is the amount the issuer pays above the face value of the bond to call it back early. In this case, the call premium can be calculated as follows:

Call premium = Call price - Face value
Call price = $1,035
Face value = $1,000
Coupon rate = 7%

The bonds are semiannual, so they pay 3.5% every six months. Over the next two years, there will be four payments of $35 each ($1,000 x 7% x 6/12). The present value of these payments can be calculated using the annuity formula:

PV = PMT x (1 - (1 + r)^-n) / r
PV = $35 x (1 - (1 + 3.5%)^-4) / 3.5%
PV = $135.699

To calculate the call premium, we need to discount the present value of the remaining coupon payments back to the call date, which is two years from now. Using the semiannual discount rate of 3.5%, we get:

Call premium = PV x (1 + r)^n - Face value
Call premium = $135.699 x (1 + 3.5%)^4 - $1,000
Call premium = $1,035.08 - $1,000
Call premium = $35.08

Therefore, the answer is B, $35.

The 7 Percent, Semiannual Coupon Bonds Offered by House Renovators