In this video we're going to revisit the calculation of return on assets or ROA.

One of the things that we'll see is that the common way to measure it which is

simply net income divided by total assets is actually too

simplistic and it messes up a key feature that we want

ROA to supply when we're using this as a measure of our operating performance.

Remember that what we would ideally like this to measure is how well did we

do with our assets independent of how the assets were financed,

that is how much was debt versus how much was equity.

Our denominator in the calculation is total assets,

so that's fine because assets equals liabilities plus owners' equity.

Only the sum matters not how much is one versus the other.

The problem is the numerator of our calculation.

In the calculation of net income there is a subtraction for interest expense.

That subtraction is going to be bigger,

the more debt we have,

and so the numerator is impacted by

how much debt versus equity there is in the capital structure.

That's what we want to fix.

How to fix it?

Well, we're just going to add that interest expense back and look at

what income was before the interest expense.

The only difficulty with that calculation is interest expense also

impacted the tax expense because interest expense is tax deductible.

So, we need to add back the interest expense in a way that also adjusts for that.

And so, what we're going to do is add back the after-tax cost of interest.

This is referred to as de-levering or un-levering the firm's capital structure.

What would we have done if it was in all equity firm for example?

So, here we've got an example calculation.

One firm has no debt,

the other firm has some debt but they've got the same total amount

of assets and the same pretax, pre-interest income.

But the firm with debt is showing the subtraction for interest expense of $50.

So, if we want to un-lever that we can just add $50 to it's bottom line,

50 plus 162.5 is not going to equal 195.

This is because the interest expense also impacted the taxes.

If the tax rate is 35 percent what we have to add back

is the extra interest expense and the taxes that were saved.

So, we have to add back one minus the tax rate,

or 65 percent of the interest expense.

Once we do that,

now we're on equal footing.

So, a more improved or sophisticated version of the calculation of return on assets,

starts with income but adds back the after tax cost of interest.

Again, the idea of that is here's how much income we had before we

doled out any of it to any of the stakeholders divided by,

here's how much assets we had independent of how

much of it supplied by debt holders versus equity holders.

This is what we're really trying to get at.

Coming up with how big the interest expense was is relatively straightforward,

the tricky part of this is what's the right tax rate to use.

Now, what does this more sophisticated version of ROA do

to our understanding of how ROA and ROE are different?

Well, it changes it a little bit.

Now, ROA is income before interest.

That's not the same denominator that we're doing in ROE because

shareholders have to pay out some of that to the debt holders in the form of interest.

So, the numerator is different and the denominator is

different because in ROE we're just looking at shareholders investment,

ROA we're looking at the total investment.

So, how does leverage impact those two things?

In a similar way that we talked about before, but slightly different.

And here's the intuition for how leverage works.

Suppose we went out and we borrowed some money at six percent.

We took the money and we invested it in

something and we actually earned 10 percent with our investment.

Well, with the 10 percent return we could pay off what we owe to debt holders,

and we still have four percent left over.

Who gets that four percent?

Well, we do. And that adds to the return that we

generated without adding any to the investment that we made,

and so our return on our investment goes up.

The more debt we had,

the happier we would be as long as we can

generate a bigger return than what we have to pay out on the debt.