Hadden Industries recently issued 10-year bonds at a price of $1,000. These bonds pay $60 in interest each six months. Their price has remained stable since they were issued, that is, they still sell for $1,000. Due to additional financing needs, the firm wishes to issue new bonds that would have a maturity of 10 years, a par value of $1,000, and pay $40 in interest every six months. If both bonds have the same yield, how many new bonds must Hadden issue to raise $2,000,000?
A) 2,481
B) 2,547
C) 2,596
D) 2,682
E) 2,742

Question

Quizplus · Accepted Answer

The current bonds have a yield of 6% per annum (since they pay $60 every six months and sell for $1,000). The new bonds must also have the same yield. The new bonds pay $40 every six months, which is a lower coupon rate, but they will still sell for $1,000 because they have the same yield. Therefore, to raise $2,000,000, Hadden needs to issue 2,000,000 / 1,000 = 2,000 bonds. However, due to the lower coupon rate, the price of each bond will be slightly less than $1,000, so they need to issue more bonds to raise the full amount. The correct number of bonds is 2,596.

Hadden Industries Recently Issued 10-Year Bonds at a Price of $1,000