Question

The Corner Bakery has a bond issue outstanding that matures in 7 years. The bonds pay interest semi-annually. Currently, the bonds are quoted at 101.4 percent of face value and carry a 9 percent coupon. What is the firm's aftertax cost of debt if the tax rate is 30 percent

Answer 1

Answer:

Ans. The after tax cost of this bond is 2.09%

Explanation:

Hi, first we need to establish the cash flow of the bond, so we can find the after tax cost of the bond. After we find the after tax cash flow of the bond, we must use the IRR function of MS Excel to find the semi-annual cost of this debt, but, all after tax debts should be presented in annual basis. Let me walk you through the process. First, let me show you how it should look.

Face Value      100  

price              101,4  

years                7 years  

Coupon                9%  

Coupon                4,5% semi-annually  

tax                      30%  

   

Per       Cash Flow After Tax  

0                 101,4 101,4  

1                   -4,5 -3,15  

2                   -4,5 -3,15  

3                   -4,5 -3,15  

4                   -4,5 -3,15  

5                   -4,5 -3,15  

6                   -4,5 -3,15  

7                   -4,5 -3,15  

8                   -4,5 -3,15  

9                  -4,5 -3,15  

10                  -4,5 -3,15  

11                  -4,5 -3,15  

12                  -4,5 -3,15  

13                  -4,5 -3,15  

14               -104,5 -73,15  

   

Cost of Debt 1,04% semi-annually

Cost of Debt 2,09% annually

Ok, now, as you can see, there are 14 periods, that is because the coupon is paid semi-annually, the way to find the cash flow (I mean, the bond´s coupon) is:

$Coupon (semi-annual)=(Face Value)x\frac{0.09}{2} =4.5$

At the end (period 14), we need to add the face value and the coupon, that is $100+$4.5=$104.5

Now, to find the value of the third column (after-tax cost), we do the following.

$After-tax-Cost=Couponx(1-taxes)=4.5(1-0.3)=3.15$

Now, consider this, you are receiving 101.4 for every 100 of debt, that means that you are receiving more money than the emission value, and paying interests over 100 instead of 101.4, that is why we have to use the IRR excel function to find out the semi-annual cost of debt. That is, 1.04%.

Now, to make this an effective annual rate, we calculate it like this.

$EffectiveAnnualRate=(1+semi-annual Rate)^{\frac{1}{2} } -1=(1+0.0104)^{\frac{1}{2} } -1=0.0209$

Finally, the after-tax cost of this debt is = 2.09%

Best of luck.