Samuel and Darci are partners. The partnership capital for Samuel is $50,000 and that of Darci is $60,000. Josh is admitted as a new partner by investing $50,000 cash. Josh is given a 20% interest in return for his investment. The amount of the bonus to the old partners is

A) $0
B) $18,000
C) $8,000
D) $10,000

Josh's investment of $50,000 for a 20% interest implies a total partnership valuation of $250,000 ($50,000 / 20%). Before Josh's investment, the total capital was $110,000 ($50,000 for Samuel + $60,000 for Darci). The new total capital after Josh's investment is $160,000. The difference between the implied total valuation ($250,000) and the actual total capital after investment ($160,000) is $90,000, which represents the implied value of the old partners' interest post-Josh's investment. The bonus to the old partners is the difference between the implied value of their interests and their actual capital contributions, which is $90,000 - $110,000 = -$20,000. However, since this calculation does not directly lead to the options provided, let's correct the approach:Josh's $50,000 investment for a 20% interest values the partnership at $250,000. Subtracting the total capital after Josh's investment ($160,000) from this valuation gives us the implied increase in value due to Josh's investment, which is $90,000. However, since Josh only contributed $50,000, the difference of $40,000 is the bonus to the old partners. This bonus is then allocated based on their original capital contributions, which are not directly asked for in the question. The correct approach to find the bonus to the old partners involves recognizing that Josh's investment increases the total value of the partnership, and the excess of the partnership's value over the actual cash contributed by Josh is considered a bonus to the old partners. However, the calculation provided here mistakenly concludes with an incorrect interpretation of the bonus calculation. The correct calculation should determine the bonus based on the increase in valuation attributable to Josh's investment relative to the existing partners' capital. Given the options and the correct understanding that Josh's investment implies a total value increase, the actual bonus calculation should reflect how much additional value the old partners are credited with due to Josh's investment, which is not accurately captured in the initial explanation. The correct answer involves calculating the total value of the partnership after Josh's investment and determining the bonus based on the proportionate share of the old partners in the increased valuation. Since the initial calculation led to confusion, let's clarify:The correct calculation is as follows: If the partnership is valued at $250,000 after Josh's investment, and he owns 20%, the existing partners' share is 80%, or $200,000. Before Josh's investment, the old partners had a combined capital of $110,000. The bonus to the old partners is the difference between the new valuation of their shares ($200,000) and their original capital ($110,000), which is $90,000. This bonus is attributed to the increase in the valuation of the partnership due to Josh's investment, reflecting the premium over the actual cash he contributed. Given this, the options provided do not directly match the corrected explanation, indicating a need to reassess the calculation based on the correct premise for determining the bonus to the old partners. The essence of the bonus calculation lies in assessing the increase in the partnership's value attributable to the new partner's investment and how this increase benefits the existing partners.