# Commercial arithmetic - rule of three and profitability

Often one is confronted with economic calculations and knows what to do theoretically, but one last encountered the simple basics years before in school, training or studies. For this purpose, a little remedy should now be created.

## Rule of three

Whether it is the percentage calculation or the conversion of prices to different quantities or the calculation of the required working hours, mastering the rule of three is a basic requirement for commercial invoices.

A distinction is made between even / proportional and odd / anti-proportional rule of three.

### Even or proportional rule of three

The two assigned variables change in the same direction. So size B doubles / triples / halves etc. when size A is doubled / tripled / halved etc.

Example:
5m of wood are required to produce a chair. 100m of wood are bought for € 55. What are the production costs for a chair?

100m = € 55.00
1m = € 5.50
5m = € 27.50

First count on one unit (in this example 1m)
-> 100m: 100 = 1m
–> 55€ : 100 = 5,50€

In the next step, count on the desired size (5m)
-> multiply by 5 on both sides.

### Odd or anti-proportional rule of three

This behaves in exactly the opposite direction: doubles / triples / halves size A so halves / thirds / doubles size B.

Example:
It takes two workers 30 minutes to produce a chair, and the boss is considering hiring a third party. How long does it take to produce a chair?

2 workers = 30min
1 worker = 60min
3 workers = 20min

Step 1: Bring to a unit ...
-> 2 workers divided by 2 = 1 worker
-> 30min multiplied by 2

Step 2: Bring to the desired size ...
-> 1 worker multiplied by 3 = 3 workers
-> 60min divided by 3 = 20min

You can find a more detailed explanation of how to calculate with the rule of three at the free online tutoring at oberprima.com -> "How to calculate with the rule of three" ## profitability

The profitability shows the percentage of the profit generated from the capital employed. A distinction is made between total return on equity and return on equity. How to calculate profitability is shown under the following sections:

### Return on equity

The return on equity (also known under the term return on equity) is a key figure of the annual financial statement analysis (Balance sheet analysis) and shows the "interest rate" that investors can expect from their invested capital. For the calculation you need the items shown in the balance sheet as equity (EK).

Equity Profitability = Profit / Equity * 100%

### Return on investment

It shows the interest on the entire capital employed (GK) - i.e. equity (EK) and outside capital (FK). The return on equity is more suitable than the return on equity for assessing the company's performance compared to its competitors, because different capital structures do not interfere with the comparison.

GK profitability = (profit + FK interest) / GK * 100%