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# The Debt Tax Shield

Let’s start with the corporate tax rate, and this is just a very brief example that will show you the tax shelter, the tax break that you have when you get debt in your capital structure.

 No Debt With Debt \$200.0 \$200.0 \$100.0 \$100.0 \$100.0 \$100.0 \$0.0 \$8.0 \$100.0 \$92.0 \$35.0 \$32.0 \$65.0 \$59.8

Now, as you see there are two companies and they are identical in every possible way. We are only going to look at just a little bit of these companies, the part that is interesting to us. But as you see, in the second column, there are a few numbers that, for a company that has no debt and in the third column, there are few numbers for a company that has debt.

That company that has debt we are going to assume something very simple. It has \$100 million of debt; it pays an 8% interest on that debt. Which means that 8% of 100 or, or \$8 million pays over and repeatedly. Every year it pays \$8 million of interest on the 100 million Dollars of debt. That is simply calculated as the principal that is the \$100 million of debt, multiplied by 8%, that gives me an \$8 million annual payment and would, just to make this very simple because it is not important for where we are going. Are we going to assume that the company is going to be paying these forever? It pays repeatedly every year it pays \$8 million.

8% Interest Rate

Annual Interest: \$100m X (0.08) = \$8m

Perpetual payments

Now, compare column two and column three. We have two companies with the same revenue, two companies with the same costs, two companies with the same EBIT. EBIT is Earnings before Interest and Taxes, and that is revenues minus cost. And as you see, both companies have the same, \$100 million. And here comes the difference. The first company has no debt and that means that it pays actually no interest, therefore the earnings before taxes, after interest but before taxes are 100 million. Now the other company does pay interest and, as we said before, it pays eight million every year, which means that, in this particular year, it is going to pay eight million and after you consider those, the earnings after interest but before taxes are 92 million. Now, notice what happens in the next line. Because the companies have, after interest but before taxes, they have different profits, one has 100 million and the other 92. And because we calculate the taxes on 35% on whatever profits, each company actually had. Well, the first company’s going to pay 35% of 100 million is going to pay 65 million, but the second company is going to pay 35% on 92 million, and that is 32.2. And, therefore, the net income of the company that the total the profit, the bottom-line of the company is going to be 59.8. Now, notice that one company seems to be more profitable than other than the other. That is the company that pays no interest seems to be more profitable. Well, that, that is actually not the right way to think about it. For now, the only thing that matters is that one company pays \$35 million in taxes. And the other pays \$32.2 million in taxes. So notice that when you compare Company 1 with Company 2, one pays 35 million, the other pays 32.2, and therefore there is a 2.8 million difference. That is a tax saving that the second company gets for having debt, and therefore for paying interest and that \$2.8 million, some people refer to that as a tax shield.

Note the impact of debt on corporate taxes

Tax Savings = \$35.0m – \$32.2m = \$2.8m

Hence the after-tax interest is \$8.0m – \$2.8m = \$5.2m

Hence the company effectively pays \$5.2m / \$100m = 5.2%

That is because I have a debt because I have interest, I have to pay interest; I do not get to pay \$2.8 million in taxes. That a company just like me that would have no debt has to actually pay. So that difference between 35 million and 32.2. 2.8 million is what some people would refer to as a tax shelter.

Now, notice the following. I am paying \$8 million in interest, but I get a tax break relative to a company that pays no interest of 2.8. Therefore, if I subtract 2.8 from eight, I get 5.2. That is what some people would say that is what I am effectively paying in terms of interest because I am actually paying 8 million, but I am getting a tax break of 2.8. Therefore, at the end of the day, when I aggregate these things, I am paying 5.2. As if I am paying 5.2, relative to the 100 million of debt that I have in my capital structure, then I am effectively paying 5.2%. Or after tax, I’m paying 5.2%. So keep in mind this number. I am paying 8 million dollars in interest; I get a tax break of 2.8. I am effectively paying 5.2 million dollars after the tax break, which means that my interest rate is 8% but after the tax break is actually 5.2%.

There is another way of looking at that. And the other way of looking at that, remember what we defined before, as the, as the after-tax cost of debt. It was one minus TC multiplied by RD. Well, one minus TC is one minus 0.35. 0.35 is the corporate tax rate. 8% is the interest on the debt. And if you calculate 1 minus 0.35, multiplied by8%, guess what you get? You get exactly 5.2%, that is why we call 1 minus TC times RD the after-tax cost of debt.

(1-tc) X RD  = (1-0.35) X (0.08) = 5.2%

Hence (1-tc) X RD is the after-tax cost of debt

Therefore, if you compare the 5.2% we calculated by multiplying 1 minus 0.35 times 8%, that is exactly the same number we had arrived before, by looking at how much we are effectively paying in terms of cash, 5.2 million, relative to the 100 million that we have in terms of debt. Therefore, bottom line is, when you pay interest, you get a tax break. That tax break actually saves taxes that you have to pay, reduces the cost of debt. Therefore, there is a before tax and an after-tax cost of debt. In terms of our notation, RD is the before-tax cost of debt. And one minus the C multiplied by RD is the after-tax cost of debt. That’s why in the, if you if you remember the notation that we used before, in the first term that was associated with debt, there was a 1 minus TC, but in the second term associated with equity, there was no 1 minus TC. The reason is you get no tax break when you pay dividends; you only get a tax break when you pay interest on, on the debt. We will get back to this, but for now, keep in mind. Interest actually gives you a tax break; a tax break reduces the cost of debt. Therefore, there is a before tax and an after tax the cost of debt.