JRJ Corporation 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, i.e., 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 JRJ issue to raise $2,000,000 cash?

Question

Quizplus · Accepted Answer

The current JRJ bond pays $120 in interest annually ($60 every 6 months). If the same yield is expected for the new bonds, this means that investors would require a 6% annual yield ($120 ÷ $1,000). The new bonds pay $80 in interest annually ($40 every 6 months) so they would need to be priced at $1,333.33 ($80 ÷ 6%).

To raise $2,000,000, JRJ would need to issue $2,000,000 ÷ $1,000 = 2,000 of these new bonds.

However, the question asks how many new bonds must be issued, not how many dollars of new bonds. So we need to divide the total dollar amount by the price per bond:

$2,000,000 ÷ $1,333.33 = 1,500

Finally, we need to add the existing bonds that are still outstanding:

$2,000,000 ÷ $1,333.33 = 1,500 
1,500 + 1,096 = 2,596

Therefore, JRJ would need to issue 2,596 new bonds to raise $2,000,000. The correct answer is B.

JRJ Corporation Recently Issued 10-Year Bonds at a Price of $1,000