Adidas issued 10-year,8% bonds with a par value of $200,000,where interest is paid semiannually.The market rate on the issue date was 7.5%.Adidas received $206,948 in cash proceeds.Which of the following statements is true?
A)Adidas must pay $200,000 at maturity and no interest payments.
B)Adidas must pay $206,948 at maturity and no interest payments.
C)Adidas must pay $200,000 at maturity plus 20 interest payments of $8,000 each.
D)Adidas must pay $206,948 at maturity plus 20 interest payments of $8,000 each.
E)Adidas must pay $200,000 at maturity plus 20 interest payments of $7,500 each.

Question

Quizplus · Accepted Answer

The par value of the bond is $200,000, so at maturity, Adidas must pay back that amount. The bond has an 8% coupon rate, meaning it will pay $8,000 in interest ($200,000 x 0.08) per year, paid semiannually, or $4,000 every six months. There will be 20 interest payments over the life of the bond (10 years x 2 semiannual periods per year). The market rate on the issue date was 7.5%, so investors were willing to pay more than the face value of the bond to receive the higher coupon rate. The fact that Adidas received $206,948 in cash proceeds indicates that the bond was issued at a premium (i.e., investors paid more than the face value for the bond). The premium can be calculated as the present value of the future cash flows of the bond (i.e., the $200,000 face value plus the 20 semiannual interest payments of $4,000 each) at the market rate of interest (7.5%) multiplied by the face value of the bond. Therefore, the premium on the bond is:

Premium = ($4,000 x 20) x (1 - 1/(1+0.075)^20) / 0.075 x $200,000 = $6,948

The fact that Adidas received $206,948 in cash means that it received the face value of the bond ($200,000) plus the premium ($6,948). Therefore, at maturity, Adidas must pay back the face value of the bond ($200,000) plus the 20 semiannual interest payments of $8,000 each, or a total of $360,000 ($200,000 + $8,000 x 20).

Adidas Issued 10-Year,8% Bonds with a Par Value of $200,000,where