Take a seat, grab your calculator, and get ready for an easy tutorial. Generally, we're either going to find the cost of debt for a firm by looking at their cost of bank loans or their cost of bonds. The most important concept to remember here is that either way, we're looking for the after-tax cost of debt! Remember that interest is tax-deductible for a company, so it is very important to always find that after-tax cost of debt.
Let's take a look at how this all fits together when we find the cost of bank loans. Assume our local grocery store has a line of credit with a bank at a pretax cost of 9%. Furthermore, the grocery store is in the 34% tax bracket. Believe it or not, we're almost done already! We have a very simple equation to find the after-tax cost of debt.
In this equation, the lower-case kd is our pretax cost of debt, t is the tax rate, and the equation outputs upper-case Kd which is our after tax cost of debt.
Going back to our grocery store example, we are given the pretax cost of debt as 9% and the tax rate at 34%. Easy enough! Let's run that through our equation to find the after-tax cost of the bank loans.
That simple equation tells us that the grocery store has an after-tax cost of bank loans of 5.94%. Believe it or not, that's all there is to it!
To understand how we find the cost of bonds, we are simply finding the yield-to-maturity first to find our pretax cost of bond financing. The next step is to run that through our cost of debt equation above to get our after-tax cost of bonds. If you are unfamiliar with finding the yield-to-maturity, please take a look at our tutorial on the subject.
When we are dealing with the cost of bonds, it is important to note that the firm will have to pay floatation costs. The floatation costs are simply the fee that the company pays the investment banker to issue the bonds. The following table shows you exactly what you will need for each problem.
P/YR |
The number of coupon payments the bond makes each year. It is generally 2 since bonds usually make semiannual payments. |
N |
The number of compounding periods. Usually it is the number of years times 2 if the bonds make semiannual coupon payments. |
PMT |
The coupon payments in dollars that the bonds make. These are cash outflows for the company so put them in as negative. |
PV |
This is the net price that the firm receives when they sell a bond. In other words, it is the price minus floatation costs. It is a cash inflow so put it in as a positive number. |
FV |
The par value of the bond that the firm will have to pay back to investors. It is a cash outflow and should go in as a negative number. |
I |
This is what we're solving for! It is the pretax cost of the bond. |
Sample Problem 1.
Understand Corporation has recently issued 15 year bonds. The bonds sold at par but floatation costs amounted to 5% of par. The bonds have a 12% coupon rate and make semiannual coupon payments. The firm is in the 35% tax bracket. What is the cost to the firm for these bonds?
Solution.
Let's put all of this into a table to see what we're working with.
P/YR |
The bond makes semiannual coupon payments so P/Y=2. |
N |
There are 15 years until maturity, with 2 payments each year. Multiply 15 years by 2 payments per year to get N=30. |
PMT |
The bond pays 12% of par each year in coupon payments. So, $1000 times 12% tells us that it will pay $120 per year. However, since P/Y is 2, divide the 120 by 2 to get $60. It is a cash outflow so it has to be negative. |
PV |
The bonds sold at par value of $1,000. However, the firm had to pay floatation costs of 5% or $50 per bond. The amount the firm actually receives is thus $1,000 - $50 = $950. |
FV |
Remember that with bonds, the firm will have to pay the par value back at the end as a cash outflow. So the FV = -$1,000. |
I |
We'll solve for this in the next step! |
Texas Instruments BAII Plus |
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Hewlett-Packard 10BII |
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Our calculator spits out a value of 12.76%. Remember that this is our pretax cost. We want the after-tax cost so we just run it through our Kd equation. When all is said and done, you should get a final answer for this problem of 8.29% You're getting the hang of it! Test your skills with some of these practice problems.
Practice Problem 1.
Studious Inc. has decided to borrow $25,000 from their local bank. The bank will charge them 7.5% for this loan and the firm is in the 34% tax bracket. What is the cost for the firm after taxes?
Solution.
Hopefully you just ran the numbers through the Kd equation given above and found their after-tax cost of 4.95%
Practice Problem 2.
Just Sweatpants, a fancy uptown clothing company, has recently borrowed some money from the local bank at an after-tax cost of 8.7%. They are in the 34% tax bracket. What is the firm's cost for this loan?
Solution.
Your answer should be 8.7% believe it or not! Remember that when we find the cost of debt, we always want the after-tax value. This problem gave you the after-tax number up front! I'm sorry. I know we're here to build trust, but I have to prove that point somehow.
Practice Problem 3.
Collegiate Corporation has recently issued 10 year bonds with an 8% coupon rate. The bonds will make semiannual coupon payments and the company is in the 30% tax bracket. If the bonds sell at par and floatation costs amount to 3%, what is Collegiate Corporation's cost for this bond issue?
Solution.
Did you get 5.92%? Good! If you got an answer of 8.45%, run that through your Kd equation to get the after-tax cost.
Now that you understand the cost of debt, check out some other tutorials from this category. Also, use our UnderstandFinance Forums to get any of your questions answered!