This workout asks us to look at two hypothetical companies with very different gearing ratios, very different leverage ratios.

They're in the same industry, so we have two businesses.

The first one, HighFly Inc. It says, is a young business in a phase of rapid growth, aggressively taken on debt to fuel expansion, and its has a debt to equity ratio of three to one.

So just thinking that through, we know that its total assets is 100, and therefore we know, therefore that splits into 4 pieces of 25.

So the debts must be 75 and the equity must be 25 doing the same calculation for a steady craft enterprises, a well established business with a one-to-one debt to equity ratio.

We can do the same calculation, and we know that the assets are 100, so the debt and the equity must be equal.

I.e. they must be 50 each.

It then says that in the following scenarios, calculate the return on equity value for both companies, assuming the amount of outstanding debtors remain stable, what you observe and comment on it.

So the first one says scenario one, it says at the end of the first year, both companies assets are 105 after interest tax and so on.

Well, we know that their assets were 100, so therefore they must have made a profit, both companies of 5.

We can therefore calculate the opening equity, closing equity, and the return on equity.

So the first thing we do, what's the beginning? Shareholder's equity for High Fly? Well, we know that they have three lots of debt to one lot of equity.

So we can simply take the 100 of assets and we know that it's a 1 to 3 ratio. So we simply divide by 4 to get the equity.

So 25 of equity, 75 of debt.

What's their closing equity figure? We know that the profit is 5.

So this is a simple calculation.

You simply say 25 plus 5, and that gives us closing equity or 30.

And then we can work out our return on equity, which is equal to 5 divided by that opening equity figure of 25 i.e. 20%.

We can do the same thing for steady craft.

We know that their opening equity is equal to 100, but this time simply divide by 2. Because we have half equity and half debt, which gives us opening equity of 50, we know we have the same calculation to do.

So, we say closing equity is 50 plus the profits are 5 during the year 55.

So their return on equity is relatively modest.

It's the 5 of profits divided by the opening equity. So half the amount, only half the amount.

And that's simply because the amount of equity with High Fly, because they're so highly leveraged, is the equity element is so much lower.

However, if we look at scenario two, in this case, total assets have fallen to 95. Therefore they must have made a loss of 5.

The opening assets were 100, closing assets were 95. They must have made a loss of 5.

So for the opening equity, we can just simply link that in to the previous figure of 25.

The closing equity, if they made a loss, must be down now to 25, minus 5 down to 20, and their return on equity is this time minus 5 divided by the opening equity of 25, which gives us a return on equity of minus 20%.

If we do the same thing for steady crafts, then we have opening shareholders equity.

Again, we can just link this in to the previous version and we can do the same calculation. Again, the closing equity must be 50 minus this time.

Five of loss gives us closing equity of 45 and a return on equity figure, again, minus 5 divided by the opening equity figure of 50.

So what we can see is that in the case of where a business makes profit, having a relatively small amount of equity and a large amount of debt being highly leveraged gives us a very healthy return, a much better return than the business which is less aggressively financed, 20% return on equity rather than a 10% return on equity.

However, the flip side is if you make losses, then the risk is increased.

So in this case, the High Fly company, the one with the aggressive debt to equity ratio, makes a return on equity of minus 20% compared to just minus 10%.

For the steadier company, the more the less aggressively financed company.