A five-year, $500,000 bond was issued on 1/11/11. The stated rate of interest wa

Question

A five-year, $500,000 bond was issued on 1/11/11. The stated rate of interest was 10%, and the effective rate of interest was 14%. The interest is paid semiannually. Which of the following statements is correct? Please explain how you got the answer.

A.) This bond was issued at a premium, and the semiannual cash payment is $25,000 per period.

B.) This bond was issued at a discount, and the annual cash interest payment is $25,000.

C.) This bond was issued at a discount, and the semiannual cash payment is $25,000 per period.

D.) This bond was issued at a premium, and the annual cash payment is $25,000 per period.

Explanation / Answer

The first thing you want to do is calculate the coupon payment using the stated interest rate. This bond pays semiannual payments at 5% each period (10% annual/2). Therefore the coupon payment is $25,000 each period or $50,000 each year. We can thereby rule out options B and D because the cash payment is $25,000 semiannually, not annually. The next thing you want to do is notice that the effective rate of interest is 14%. Whenever the effective rate is greater than the stated rate, the bond must have been issued at a discount. Imagine, if you will, a bond issued at par of $1000. When that bond matures, I am going to get $1000 face value. I am also going to get cash payments of 10% per year (stated rate). If the effective interest rate is 14%, this implies I got it at a discount because the only way that I could get more than 10% interest on this bond is if I paid less than $1000 for it (because if I paid $1000 for it, I would only get 10% interest from the coupon payments). Therefore, the answer is C. Don't forget to rate! Thanks.

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