The correct answer is: A. X and Y equally
Goodwill is an intangible asset that represents the value of a company’s reputation and the likelihood that it will continue to generate future profits. When a new partner is admitted to a firm, the existing partners must agree on how to value the firm’s goodwill. The most common method is to use the book value of the firm’s assets, which is the value of the firm’s assets minus the value of its liabilities. The new partner then contributes an amount of cash or other assets equal to the agreed-upon value of the firm’s goodwill.
In this case, X and Y are partners in a firm sharing profits in the ratio of 3 : 1. They admit Z as a partner with new profit sharing ratio of 2 : 1 : 1. This means that X’s share of the firm’s profits will decrease from 3/4 to 2/5, and Y’s share of the firm’s profits will decrease from 1/4 to 1/5. In order to compensate X and Y for this decrease in their profit shares, Z must contribute an amount of goodwill equal to the difference between the old and new profit sharing ratios. This amount of goodwill is equal to 1/20 of the firm’s total value.
Since X and Y are sharing profits in the ratio of 3 : 1, they will each contribute an amount of goodwill equal to 1/40 of the firm’s total value. This amount of goodwill will be credited to X and Y equally.
Here is a brief explanation of each option:
- Option A: X and Y equally. This is the correct answer.
- Option B: Only X. This is incorrect because Y is also entitled to a share of the goodwill.
- Option C: Only Y. This is incorrect because X is also entitled to a share of the goodwill.
- Option D: None of these. This is incorrect because at least one of the options is correct.