## After tax cost of debt formula

The cost of debt formula is the before tax cost of debt multiplied by 1 minus the company’s tax rate.

A-T Cd = Cd * (1 – t)

In the cost of debt formula you have two variables that must be inputted in order to solve the after tax cost of debt.

## Tax Rate

The tax rate can be found on a public company’s annual reports. The best way to find the tax rate that is representative of the company’s future tax rate is by using more than one year of historical data. 5 to 10 years of data should be enough to estimate a company’s future tax rate. Therefore, finding the tax rate of a company is quite simple.

## Cost of Debt

However, finding a company’s cost of debt can be more challenging. In theory, there are three ways to find a company’s cost of debt (before tax cost of debt).

## Cost of Debt Strategy 1

The first, and usually the most accurate estimate of a company’s before tax cost of debt is it’s average cost of its current outstanding debt. A company’s outstanding debt (bonds issued) will give a strong estimate of a company’s average cost of debt

For example, if Company A has the three following bonds outstanding: Bond A $100M @ 5% interest rate, Bond B $200M @ 7% interest rate and Bond C $200M @ 6% interest rate. In order to calculate the cost of debt for Company A use a weighted average of the outstanding debt. Here is cost of debt of Company A, using the data above: ((100/500) * 5%)+((200/500) * 7%)+((200/500)*6%) = 6.2%. Using this technique, the cost of debt for Company A would be 6.2%.

## Cost of Debt Strategy 2

The second way to estimate a company’s cost of debt is by looking at the company’s historical income statements and balance sheet in order to calculate their historical interest payment to debt ratio. This strategy to calculate the cost of debt is acceptable and used widely by students and professional analyst.

Let’s look at an example! Company A has historically paid the following interest (income statement 2017: 300,000, 2016: 200,000, 2015: 250,000, 2014: 100,000, 2013: 180,000. Over the same years, Company A has had the following debt outstanding (long-term debt on balance sheet). 2017: 7M, 2016: 4M, 2015: 5M, 2014: 3M, 2013: 3.5M. Please see the steps to calculate the cost of debt below.

Step 1, calculate the interest rate paid for every year:

2017: 300,000/7,000,000 = 4.28%

2016: 200/4,000 = 5%

2015: 250/5,000 = 5%

2014: 100/3,000 = 3.3%

2013: 180/3,500 = 5.14%

Step 2, calculate the average rate over the 5 years:

Cost of debt = (4.28% + 5% + 5% + 3.3% + 5.14%)/5

Cost of debt = 4.54%

As we can see from the calculation above, the historical interest rate calculation to solve the cost of debt is simple and easy to understand.

## Cost of Debt Strategy 3

Finally, the third strategy t that allows us to solve for cost of debt in the after tax cost of debt formula is using a government rate plus corporate debt premium. This strategy uses the current government risk free interest rate and adds a premium for the risk of the company. The rate is then used in the cost of debt formula. For example, if Company A is expected to pay a 3% premium above the current government risk free rate of 3%, their estimated cost of debt is 6% (3% + 3%). This strategy is simple but it is not very accurate since only one data point is being used to solve for the cost of debt.

## After Tax Cost of Debt Formula in Action

Now, we know how to find the tax rate and the cost of debt we can use the after tax cost of debt formula to solve for a company’s after tax cost of debt. Once again, the after tax cost of debt formula is:

A-T Cd = Cd * (1 – t)

For example, you find out using the historical interest rate strategy that Company A’s cost of debt is 4.54%. You also know from historical data that there average marginal tax rate over the last 5 years has been 35%. Use this information to calculate the after tax cost of debt of Company A. In this case, A-T Cd = 4.54% * (1-35%), A-T Cd = 2.95%. Therefore, Company A’s after tax cost of debt is 2.95%, which is much lower than the 4.54% before tax cost of debt.

## Conclusion

The tax advantage to using debt is immense and very beneficial for a company who is looking to add value and pay the least amount of money possible to its capital providers. This should tell you that most companies should use debt to fund their expansion projects. By paying less to its capital providers the company will be able to add more value to its shareholders and continue to grow at a faster rate. However, we know that debt increases a company’s risk to go bankrupt. For this reason, having too much debt can be very dangerous. Finding the optimal debt to equity ratio (capital structure) of your company is essential. This will be discussed in other pages of this website.

In conclusion, leverage is important for both companies and individuals. Leverage is an optimal way to access cheap capital and expand a growing business. Many successful entrepreneurs and business man have used leverage throughout their career as a way to fund risky projects. Why use your money when you can use someone else’s at a very low cost?