Question

Com Inc's bonds currently sells for $1,200. They pay semiannual coupon, have a 15 year maturity, and a $1,000 par value, but they can be called in 5 years at $1,050. Assume that no costs other than the call premium would be incurred to call and refund the bonds, and also assume that the yield curve is horizontal, with rates expected to remain at current levels on into the future, YTM is 10%. What is the annual coupon rate? (round to 2 decimal places).

Answer 1

The annual coupon rate of Com Inc's bonds is determined by calculating the semiannual coupon payment that would equate the bond's present value with its current market price, considering a 10% annual YTM, and then annualizing this figure.

Step-by-step explanation:

The annual coupon rate of Com Inc's bonds, which is sought by the investor, can be calculated by understanding the nature of semiannual coupon payments and recognizing that the bond's price reflects the present value of these payments, given the bond's yield to maturity (YTM) of 10%. We must establish the semiannual yield, which would be 5% (since 10% annual YTM divided by 2), and find the coupon payment that would make the present value of the bond's remaining cash flows equal to its current price of $1,200.

Once the semiannual coupon payment is found, it can be multiplied by 2 to obtain the annual coupon payment. Dividing this annual payment by the bond's par value of $1,000, then multiplying by 100, gives us the annual coupon rate. The process involves a financial calculator or spreadsheet function to input the known variables (current price, par value, YTM, and number of periods) and solve for the unknown coupon payment.