5. Rainier Bros. has 12.0% semiannual coupon bonds outstanding that mature in 10

Question

5. 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"? a. 9.29% b. 9.78% c. 10.29% d. 10.81% e. 11.35%

Explanation / Answer

Call price of bonds: $1,060 Old rate: 12.0%

Flotation cost per bond: $45 Years to maturity: 10

Par value of bonds: $1,000 Semiannual periods: 20

Cost of refunding:

Call price per bond............................................$1,060

Flotation cost per bond.......................................$     45

Total investment outlay per bond...........................$1,105

Interest on old bond per year (Old rate × Amount)........$120

Interest per period............................................$60

If the company does not call the bonds, it will have to pay $60 for 20 periods, plus $1,000 at Period 20. If it goes ahead and calls the bonds now, it will have to pay $1,060 + $45 = $1,105 today. We can find the discount rate that equates these cash flows. Here is the time line:

0 1 2 3 ..... 20

-$1,105 $60 $60 $60 $60

$1,000

-$1,105 $60 $60 $60 $1,060

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 5.1469%, rounded to 5.15%. You can do the same thing with Excel. Note that the semiannual savings at this lower rate would be (0.12/2 0.051469) × $1,000 = $8.53. The PV of that amount, discounted back for 20 periods at 5.15%, is $105.00, which is the cost of the refunding. The semiannual discount, when doubled, is the breakeven nominal rate.

Required nominal annual rate to break even: 10.29%

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