Question

1. Assume that a company issues 15-years bonds (call it bonds A) at their par value of $1,000. These bond have $70 in interest every quarter

These bonds are selling at $1000 issue price. This company realizes that to expand their business to the surrounding area.

They need an additional $5,000,000 in long-term debt. They decided to issue 12-year, $1,000 par value bonds (Call it bonds B) that pay only $40 in interest every quarter. Assume also that A and B will provide bondholders with the same yield, how many new bonds must the city issue to raise $5,000,000? (Ignore the day or two difference between the bonds' issue dates and any bond flotation costs.)

Answer 1

As bonds A are selling at a price equal to its par value, the YTM of such bonds will be the same as its coupon rate. The coupon rate for bonds A every quarter is $70/$1000= 7%. As the issue of bonds B is expected to provide the bondholders with the same rate of yield, the following would hold true as follows:

P0= 40/(1+r) + 40/(1+r)^2 +...+40/(1+r)^48 + 1000/(1+r)^48, where P0= present price of bond, r= yield to maturity= 7%.

By solving the above equation, we get P0= $510.35.

Therefore, $50,00,000/$510.35= 9,797 new bonds must be issued by the city to raise $50,00,000.