# How is ROE higher with leverage?

It’s understandable that debt reduces cost of capital but how would a leveraged ROE be greater than unlevered ROE. Return is affected by interest paid but in an all equity scenario there is no expense deducted from return. There is something missing that I can’t get.

If I take a loan for 10K and throw in my own money of 5K… then I bet on a stock and earn 25% returns (\$3750)… My unlevered return is only 25% but my levered return is 75%.

If I did not take out the loan, I would have earned only \$1250 (25% of \$5000).

R stays the same, E decreases.

E decreases because of dividend distribution, but in the case of no dividends, the ROE should not decrease, right?

Or purchase of Treasury Stock.

I’m assuming that total capitalization remains constant, so an increase in leverage means an increase in liabilities and a corresponding decrease in equity.

If equity doesn’t change, then an increase in leverage means an increase in liabilities and a corresponding increase in assets. If ROA is constant, then R increases while E stays the same. ROE still increases.

I understand your point as a general concept that when leverage increase total percentage of equity would decrease but in the end the values are the same. For example that we have two scenarios

Unlevered ROE:

Return=20

Equity=40

Then ROE=0.5

Levered ROE:

Now let’s assume that we used debt, let’s say 10 with an interest expense of 5% and taxes of 30%, then return is 19.65

At the same time, equity will increase by the increase in N.I, hence it will be 39.65

ROE=0.495

Hence, with leveraged, ROE has decreased.

What did you do with the 10 you received from issuing debt?

10*.05*(1-0.3)=-0.35 to calculate it impact on the I/S

You misunderstand.

You borrowed 10. What did you do with it?

What did you do with the 10 you borrowed?

Hint, hint!!!

I’ll give u an example.

Am a firm I have \$50 in debt and \$50 in equity leading to a total assets of \$100.

Tomorrow if I go to a bank and borrow an additional \$10 (leverage), I’ll have \$60 of debt against \$50 of equity = \$110 of total assets.

Now under scenario 1, my leverage multiplier was 2x. Under scenario 2, the additional \$10 debt increases my assets also by \$10 leading to a multiplier of 2.2 which increases the ROE.

PS - you must look at the DuPont model to understand this better.

it makes sense throught eh DuPont you are right but when you think of it through pure return and equity it is difficult to comprehend. Thanks

It’s not all that difficult through pure return and equity. You simply need to carry the thought process through to completion.

You never did say what you’re going to do with the 10 you borrowed. It’s an important question that needs an answer. It will help you understand this through pure return and equity. Give it a shot.

Pay all the employees bonuses, of course!

We have this expression, Christy and I: We don’t wake up for less than \$10,000 a day.

I gave it a shot but still doesn’t work for me, I do not know what is wrong.

For example if I assumed that I will use the 10 borrowed for purchasing assets, the ratio of D/E will definitely change but ROE will not because the equity value is the same.

So, now you have 110 in assets, vs 100 before.

Most companies use assets to produce income. Will you use the extra 10 in assets to produce income? Or did you simply buy a Lear jet for the CEO so that he can feel important?

ahaa, so now I get your point

when we add debt it will definetly add to company’s operations and accordingly, increase income which in return increase ROE.

But then we have to ask when this debt generate revenue (is it a CAPEX plan that will start operations after five years), just kidding this too much analysis.

Thanks for the clarification

Adding leverage adds income:… I think my original post sums this up.