Rainier Bros. has 12.0% semiannual coupon bonds outstanding that mature in 10 years. Each bond is now eligible to be called at a call price of $1,060. If the bonds are called, the company must replace them with new 10-year bonds. The flotation cost of issuing new bonds is estimated to be $45 per bond. How low would the yield to maturity on the new bonds have to be in order for it to be profitable to call the bonds today, i.e., what is the nominal annual "breakeven rate"?

Question

Rainier Bros. has 12.0% semiannual coupon bonds outstanding that mature in 10 years. Each bond is now eligible to be called at a call price of $1,060. If the bonds are called, the company must replace them with new 10-year bonds. The flotation cost of issuing new bonds is estimated to be $45 per bond. How low would the yield to maturity on the new bonds have to be in order for it to be profitable to call the bonds today, i.e., what is the nominal annual "breakeven rate"?

Answer 1

To determine the breakeven rate at which it would be profitable to call the bonds today, we need to calculate the net cash flow from calling the bonds and issuing new ones.

First, let's calculate the cash flow from calling the bonds. The call price is $1,060 per bond, and there are presumably multiple bonds outstanding. However, the number of bonds outstanding is not given in the question. Therefore, we will assume there is only one bond outstanding for simplicity.

The cash flow from calling the bond would be:
(-$1,060 for call price)

Next, let's calculate the cash flow from issuing new bonds. The flotation cost per bond is $45. Again, we need to assume the number of new bonds issued is the same as the number of old bonds being called.

The cash flow from issuing new bonds would be:
(-$45 for flotation cost)

Now, let's compare the present value of the cash flow from calling the bonds to the present value of the cash flow from issuing new bonds.

Using a financial calculator or spreadsheet, we can set up the following equation:

PV of cash flow from calling the bonds = PV of cash flow from issuing new bonds

In this equation, the cash flows are discounted at the yield to maturity on the new bonds. By solving for the yield to maturity, we can find the breakeven rate.

To solve this equation, we need to know the semiannual coupon rate of the new bonds. Unfortunately, this information is not provided in the question. Assuming the new bonds will also have a semiannual coupon rate of 12.0%, we can proceed with the calculation.

The cash flow from calling the bonds is (-$1,060), and the cash flow from issuing new bonds is (-$45). Therefore, the equation becomes:

-$1,060 = -$45 + (12.0% / 2) * $1,060

Solving for the yield to maturity, we find:

Yield to maturity = (12.0% / 2) - ($45 / $1,060)

Calculating this expression yields the nominal annual breakeven rate you are looking for.