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All right, so 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.

Now, as you see there, there,

there are two companies and, and they're identical in every possible way.

We're only going to look at just a little bit of these companies, the,

the part that is interesting to us.

But as you see, in the second column, there's a few numbers that, for

a company that has no debt.

And in the third column there's few numbers for a company that has debt.

That company that has debt we're 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 basically pays over and over and over again.

Every year it pays $8 of interest on the 100 million, excuse, 8, 8 million.

Dollars of interest on that $100 million of debt.

And 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's not really important for where we're going.

Are we going to assume that the company is going to be paying these forever?

It pays over and over and over, every year it pays $8 million.

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 basically 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's going to pay eight million and after you take that into account,

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, 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.

And that is the company that pays no interest seems to be more profitable.

Well, that, that's 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's a 2.8 million difference.

That is a tax saving that the second company gets.

For having debt, and therefore for paying interest.

And, and that $2.8 million, some people refer to that as a tax shield.

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.

So if I subtract 2.8 from eight, I get 5.2.

That is what some people would say.

That is what I'm effectively paying in terms of interest,

because I am actually paying 8 million, but I'm getting a tax break of 2.8.

So at the end of the day, when I aggregate these things, I'm paying 5.2.

As if I'm paying 5.2, relative to the 100 million of

debt that I have in my capital structure, then I'm effectively paying 5.2%.

Or after tax, I'm paying 5.2%.

So keep in mind this number.

I'm paying 8 million dollars in interest, I get a tax break of 2.8.

I'm effectively paying 5.2 million dollars after the tax break which means that,

yes my interest rate is 8% but after the tax break is actually 5.2%.

Now there's 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.

So if you compare the 5.2% we calculated by multiplying 1 minus 0.35 times 8%,

that's exactly the same number we had arrived before,

by looking at how much we're effectively paying in terms of cash,

5.2 million, relative to the 100 million that we have in terms of debt.

So 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.

And so there's 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 to debt, there was a 1 minus tc, but

in the second term associated to 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'll 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.

And so there's a before tax and an after tax.

Cost of debt.

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