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.)

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.

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