Question

Olympic Sports has two issues of debt outstanding. One is a 9% coupon bond with a face value of $20 million, a maturity of 10 years, and a yield to maturity of 10%. The coupons are paid annually. The other bond issue has a maturity of 15 years, with coupons also paid annually, and a coupon rate of 10%. The face value of the issue is $25 million, and the issue sells for 94% of par value. The firm’s tax rate is 35%. (LO13-4) a. What is the before-tax cost of debt for Olympic? b. What is Olympic’s after-tax cost of debt?

Answer 1

Answer:

before tax cost of debt =10.4987% ; after tax cost of debt=6.8242%

Explanation:

Hi, here we have 2 bonds and we need to find the real cash flow of both, in order to do so, we have to find out what was the selling price of each one, and with that in mind, establish the cash flow and its discount rate (which is the cost of each bond).

Bond A-Find out the price

The information provided makes it easy to find the price of this bond, since we have the YTM (yield to maturity), the coupon. To find the price we have to solve for "P" the following equation.

$YTM=\frac{C+\frac{F-P}{n} }{\frac{F+P}{2} }$

Where:

YTM=0.1 (that is 10%)

C= 9 (that is 100x9%)

n= 10 (for 10 years to maturity)

Now, we solve for P.

$0.1=\frac{9+\frac{100-P}{10} }{\frac{100+P}{2} }$

$0.1=\frac{\frac{90+100-P}{10} }{\frac{100+P}{2} }$

$0.1=\frac{380-2P}{1000+10P}$

$100+P=380-2P$

$3P=280$

$P=\frac{280}{3}$

$P=93.333...$

This means that the bond is selling at 93.333...% of its face value, in other words, we get for the $20,000,000 only $18,666,666.67

this is how the cash flow should look like.

Period Cash Flow

0  18.666.667  

1 -1.800.000  

2 -1.800.000  

3 -1.800.000  

4 -1.800.000  

5 -1.800.000  

6 -1.800.000  

7 -1.800.000  

8 -1.800.000  

9 -1.800.000  

10 -21.800.000  

 

Cost (A) 10,0891%

You can easily find the cost in excel by using the "IRR" function.

For the second bond (bond (B)), things are a lot easier, since the problem provides the following info: "the issue sells for 94% of par value". That means that the money received from this bond is $25,000,000x0.94 =$23,500,000.

Now, we do the same (I mean find the real cash flow and find the cost with the MS Excel function "IRR")

It should look like this

Period Cash Flow

0 23500000

1 -2.500.000  

2 -2.500.000  

3 -2.500.000  

4 -2.500.000  

5 -2.500.000  

6 -2.500.000  

7 -2.500.000  

8 -2.500.000  

9 -2.500.000  

10 -2.500.000  

11 -2.500.000  

12 -2.500.000  

13 -2.500.000  

14 -2.500.000  

15 -27.500.000  

 

Cost (B) 10,8264%

now we need to find the before-tax and after-tax cost of the debt.

First we have to find out the percentage participation of each bond in the debt, That is Bond (A) = 20M/45M =44.4% and Bond (B)= 25M/45M=55.6%

The pre-tax cost is:

Before tax cost = 44.4%(10.0891%) + 55.6%(10.8264%) = 10.4987%

After tax cost = 44.4%(10.0891% x (1-35%)) + 55.6%(10.8264% x (1-35%)) = 6.8242%

Check out the MS Excel sheet attached to this document for more details.

Best of luck