This workout asks us to calculate the return on equity for a business. It gives us the closing year one balance sheet in summarized form with assets of 107 million, debt of 60 and closing equity of 47. It then shows us further down that the net income for the year was 7 million. Now we know if there was no issuance of debt or repayments of debt, then that increase in net income. That net income will have flowed into assets increasing them from 100 to 107. And the other side of that will have flowed into retained earnings within equity. So if the equity finished at 47 and there was 7 of profits, we can calculate the opening equity, which is the closing 47 minus the profits in the year of 7, giving an opening equity figure of 40. We can then calculate the return on equity based on equity at the beginning of the year, and that is simply the profit for the year divided by the opening equity of 40, and that gives us a return on equity of 17.5%.

We now move on to workout two. Workout two looks at the same company as workout one and has another year of trading. The question tells us that the company again made $7 million of profits during the year. None of that profit was distributed by way of dividends or in any other way returned to the shareholders. There was no change in debt, so there was no debt issuance or debt repayment, and the company made an additional 7 million of profits. It then gives us the closing balance sheet for this business.

So we can see in the balance sheet that assets have increased from 107 million to 114 million, and this is basically because the opening 107 million of assets were increased by the profit that the company made of 7 million to give 114.

We can also see the equity has increased. Again, the opening equity figure of 47 million has increased because the profit has been retained. So we add 7 million of profits and that gives us the closing equity figure of 54 million.

It then asks us to calculate return on equity. So we simply take the net income generated during the year of 7 and divide by the opening equity figure, which we know is the opening 47.

That gives a return on equity figure of 14.9%. However, if we compare that to the return on equity figure for workout one, which is just a little bit further up the spreadsheet that was 17.5% the previous year, whereas now it's fallen to 14.9%. So why has it fallen? Well, the reason why is because although the profit is unchanged, that's 7 million.

The denominator of the fraction, the bottom of the fraction, the equity has fallen, and this causes the percentage return on equity to fall.