Understand Finance - Finance Tutorials and Finance How To's

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 k_d is our pretax cost of debt, t is the
tax rate, and the equation outputs upper-case K_d 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.

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.

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
K_d 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 K_d 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 K_d equation to get the after-tax cost.

Now that you understand the cost of debt, check out some other tutorials from this
category. If you have a question, please leave it in the comments section below.