A method of distributing a firm's earnings to shareholders such that the shareholders can select when they want to claim the income for tax purposes is a:

The answer is: Dividend

Explanation:

Dividend is described as the distribution of profits among the shareholders of the company in the form of payment. When a profit is earned, the corporation reinvests in the business and also pays a part of the profit to the shareholders as dividend.

When the shareholders receive dividend, they have to pay income tax and corporate income tax deduction is not received by the corporation for the dividend.