In ROE, we use the PAT because it’s a measure of earnings of the equity holders. The earnings of the equity holders are the earnings of the company after tax.
In contrast, in ROCE we are evaluating how effectively we have utilized the capital employed in the company to generate income, over a period of time or in comparison with other companies in the same industry. Here we don’t use the PAT since the tax expenses are fixed by an external source viz. government and it can change from year to year.
For example consider a hypothetical company having same amount of income and expenses (excluding tax expenses) for a consecutive 2 years and the tax rate for the 1st year was 30% and for the 2nd year is 25%, resulting in an incremental PAT in the 2nd year.
If we use PAT for ROCE, the above company shall show a higher ROCE in the second year, which is not because of the effective utilization of the capital employed; but merely because of a change in government policy. Here we cannot say that the company has utilized its capital more effectively in the 2nd year, merely because of a higher ROCE. Therefore, using PAT in ROCE shall not show a correct picture of the effective utilization of the capital employed.
On the other hand, in the above example, the higher ROE in the 2nd year is correct since the earning of the equity holders have been increased due to the reduction in tax expenses.
Hope you understand the concept!