Thompson Enterprises has $5,000,000 of bonds outstanding. Each bond has a maturity value of $1,000, an annual coupon of 12.0%, and 15 years left to maturity. The bonds can be called at any time with a premium of $50 per bond. If the bonds are called, the company must pay flotation costs of $10 per new refunding bond. Ignore tax considerations--assume that the firm's tax rate is zero.

The company's decision of whether to call the bonds depends critically on the current interest rate on newly issued bonds. What is the breakeven interest rate, the rate below which it would be profitable to call in the bonds?

Call premium: $50 Old rate: 12.0%

Flotation cost per bond: $10 Years to maturity: 15
Amount of issue: $5,000,000 Number of bonds: 5,000
Par value of bonds: $1,000
Cost of refunding:
Call premium per bond * number of bonds = $250,000
Flotation cost = $10 * Number of bonds issued = $ 50,000
Total investment outlay: $300,000
Interest on old bond per year = Old rate * Amount = $600,000

If the company does not call the bonds, it will have to pay $600,000 per year for 15 years, plus $5,000,000 at Year 15. If it goes ahead and calls the bonds, it will have to pay $300,000 + $5,000,000 = $5,300,000 today. We can find the discount rate that equates these cash flows. Here is the time line:
0 1 2 3 ... 15
−300000 $600,000 $600,000 $600,000 $ 600,000
−5000000 $5,000,000
−5300000 600000 600000 600000 $5,600,000

If you enter these cash flows in the cash flow register of a calculator and then press the IRR key, you will get the breakeven rate, which is 11.1583%, rounded to 11.16%. You can do the same thing with Excel. Note that the annual savings at this lower rate would be (0.12 − 0.111583) × $5,000,000 = $42,084.78. The PV of that amount, discounted back for 15 years at 11.16%, is $300,000.

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"?

4. a. Someone in the 36 percent tax bracket can earn 9 percent annually on her investments

in a tax-exempt IRA account. What will be the value of a one-time $10,000 investment
in 5 years? 10 years? 20 years?
b. Suppose the preceding 9 percent return is taxable rather than tax-deferred and the taxes
are paid annually. What will be the after-tax value of her $10,000 investment after 5, 10,
and 20 years?

Discussion: “Investment Performance." – Corporate Investment Analysis

To determine the breakeven interest rate, we need to compare the cost of calling the bonds with the cost of issuing new refunding bonds.

Let's break down the costs involved in each scenario:

1. Calling the bonds:
- Each bond has a maturity value of $1,000 and an annual coupon of 12.0%. This means the coupon payment per bond is ($1,000 * 12.0%) = $120 per year.
- The company must pay a premium of $50 per bond when calling the bonds.
- There are $5,000,000 of bonds outstanding, so the total premium cost would be ($50 * 5,000,000) = $250,000.
- Additionally, the company must pay flotation costs of $10 per new refunding bond.
- Therefore, the total cost of calling the bonds would be $250,000 (premium cost) + ($10 * 5,000,000) (flotation costs) = $250,000 + $50,000,000 = $50,250,000.

2. Issuing new refunding bonds:
- The new refunding bonds would need to have a coupon rate equal to the breakeven interest rate, which we are trying to find.
- The maturity value and the number of years left to maturity would remain the same as the existing bonds, which is $1,000 and 15 years, respectively.
- The flotation costs for issuing new refunding bonds would be $10 per bond.

Now, to find the breakeven interest rate, we need to calculate the coupon payment per bond for the new refunding bonds and compare it with the cost of calling the bonds:

Coupon payment per bond for the new refunding bonds = $1,000 (maturity value) * breakeven interest rate

Cost of issuing new refunding bonds = $10 (flotation cost per bond) * 5,000,000 (number of bonds)

For the breakeven interest rate, the coupon payment per bond for the new refunding bonds should be equal to the cost of calling the bonds:

$1,000 (maturity value) * breakeven interest rate = $10 (flotation cost per bond) * 5,000,000 (number of bonds)

Simplifying the equation:

breakeven interest rate = ($10 * 5,000,000) / $1,000

breakeven interest rate = $50,000,000 / $1,000

breakeven interest rate = 50,000

Therefore, the breakeven interest rate is 50,000%.