Question

Jay's Bakery has a bond issue outstanding that matures in eight years. The bonds pay interest semiannually. Currently, the bonds are quoted at 97.8 percent of face value and carry a coupon rate of 5.7 percent. What is the aftertax cost of debt if the tax rate is 21 percent?

Answer 1

Answer:

Ans. The after tax cost of this debt is 4.8526% annual.

Explanation:

Hi, first we have to establish the amount to pay for each coupon. In our case, the coupon is paid semi-annually, so the coupon is:

$Coupon=\frac{CouponRate}{2} *100=\frac{0.057}{2} *100=2.85$

we also need to take into account that this is an eight years bond, we need to change years into semesters, so 8 years = 16 semesters.

We´re going to need MS Excel to find this value (Function "IRR"), Please see the attached excel sheet for further clarifications.

This is what it should look like

Price  97,8  

Coupon  5,70% annual

Coupon  0,0285 semi-annual

taxes  21%  

time             8 years

time            16 semesters

Period Cash Flow

     0 97,8

      1 -2,85

      2 -2,85

      3 -2,85

      4 -2,85

      5 -2,85

      6 -2,85

      7 -2,85

      8 -2,85

      9 -2,85

     10 -2,85

     11 -2,85

     12 -2,85

    13 -2,85

    14 -2,85

    15 -2,85

    16 -102,85

Using the "IRR" function, we get 3.0255%, but this discount rate is semi-annual, and the answer we are looking for has to be effective annual, therefore, we need to use the followiong formula.

$r(Annual)=(1+0.030255)^{2 } -1=0.061425$

So our discount rate (cost of this debt) before taxes is 6.1425% annual. In order to find the after tax cost of this debt, we have to use the following formula.

$AfterTaxCost=Before TaxCost(1-Taxes)=0.061425*(1-0.21)=0.048526$

Therefore, the after tax cost of this debt is 4.8526% annual.

Best of luck.