# How to calculate the average shareholder's equity?

We get the conclusion from a website:
ROE and ASE
The average shareholders' equity calculation is the beginning shareholders' equity plus the ending shareholders' equity, divided by two. The resulting formula is:

``````(Beginning shareholders' equity + Ending shareholders' equity) ÷ 2 = Average shareholders’ equity
``````

The concept may be built directly into the return on equity formula, where the average is stated in the denominator, as follows:

``````Net income ÷ ((Beginning shareholders' equity + ending shareholders' equity) ÷ 2) = Return on equity
``````

Take `aapl`'s financial statements as an example:
I download and format the raw data (delete items unrelated with the roe calculate ) as below:

income statement income

``````+------------------------------+--------+--------+
| year                         | 2022   | 2021   |
+------------------------------+--------+--------+
| net income                   | 99803  | 94680  |
+------------------------------+--------+--------+
``````

balance statement balance-sheet

``````+------------------------------+---------+---------+
| year                         | 2022    | 2021    |
+------------------------------+---------+---------+
| common stock                 | 64849   | 57365   |
+------------------------------+---------+---------+
| retained earnings            | -3068   | 5562    |
+------------------------------+---------+---------+
| comprehensive income         | -11109  | 163     |
+------------------------------+---------+---------+
| shareholders' equity         | 50672   | 63090   |
+------------------------------+---------+---------+
``````

main ratios ratios

``````+--------------------------+---------+---------+
| year                     | 2022    | 2021    |
+--------------------------+---------+---------+
| return on equity (roe)   | 160.90% | 144.10% |
+--------------------------+---------+---------+
``````

We get all numbers to calculate roe on 2022:

``````Net income = 99803  (2022)
Beginning shareholders' equity =  63090 (2021)
ending shareholders' equity = 50672  (2022)

Return on equity on 2022 = Net income ÷ ((Beginning shareholders' equity + ending shareholders' equity) ÷ 2)
= 99803 ÷ ((63090+50672) ÷ 2)
= 175%
``````

And 99803/50672 = 197%.
How can the webpage say aapl's roe on 2022 is 160.90% ?

The average equity is the four continious quarter `shareholders' equity`,the concept of ttm. For aapl's 2022 year 3 quarter:
``````average equity = (50.67+58.11+67.4+71.93)/4 = 62.0275