Final answer:
The goodwill is calculated by subtracting the original capital balances from the total implied value of the partnership after the new contribution. With C contributing $40,000 for a 20% interest, it implies a total partnership value of $200,000. The goodwill of $100,000 is then divided according to the original partners' profit and loss sharing ratios, resulting in a goodwill debit of $80,000.
Step-by-step explanation:
The student is asking about the calculation of goodwill in the context of a partnership. When a new partner is admitted into a partnership and contributions are made that are greater than the value of the actual percentage of ownership acquired, goodwill is recognized. In this case, C contributes $40,000 for a 20% interest. To find the total implied value of the partnership after C's admission we can divide C's contribution by their ownership percentage (0.20), which gives us an implied total value of $200,000 ($40,000 / 0.20). We subtract the original value of the partnership, which is the original capital balances of P, L, and O ($50,000 + $30,000 + $20,000 = $100,000), to get the goodwill of $100,000 ($200,000 - $100,000). Now, because C is acquiring 20% of the partnership, we attribute 20% of the goodwill to C's investment. That leaves 80% of the goodwill, or $80,000, to be divided among the existing partners according to their profit and loss sharing ratios. Therefore, the amount of goodwill to be debited is $80,000. Since this value is not an option in the question, it's likely there is a mistake in the provided answers or the question itself.