Question

Forever Yours Insurance Company need to raise $40,000,000. They decide to do so through the issuance of consol bonds. Each bond will have an annual coupon of $900. Given the current 7.00% yield to maturity on the firm’s bonds, how many bonds must the firm issue? (Enter your answer rounded to the nearest whole number.)

Answer 1

The company is planning to issue consol bonds. Consol bonds are the bonds that have a perpetual life and, pays a fixed coupon payment.

In the given question, the bond will make annual coupon payment of $900. The current YTM is 7.00%.

Since, these bonds have no fixed life thus, its coupon payments will form a perpetuity. The price of the bond can be calculated using the following formula of perpetuity:

Price of bond = Annual coupon payment / YTM

Price of bond = $900 / 7.00%

Price of bond = $12,857.14286  

Thus, the current price of the bond is $12,857.14286  

The company wants to raise $40,000,000. The current price of the bond is $12,857.14286 . Calculate the number of bonds to be issued using the following formula:

Number of bonds to be issued = Amount to be raised  / Current price of the bond

Number of bonds to be issued = $40,000,000 /12,857.14286  

Number of bonds to be issued = 3111.11111  bonds

Thus, the company must issue 3,111 bonds.