Final answer:
Berns's new capital balance after admitting Ola, who invested P1,000,000 for a 1/4 interest in the partnership, is calculated by determining the value increase in Berns's share based on the profit-sharing ratio. Berns's original balance plus his share of the increase totals P2,300,000.
Step-by-step explanation:
To determine Berns's new capital balance after Ola is admitted to the partnership with an investment, we first calculate the total value of the partnership before Ola's investment. The capital balances of Berns and Ruiz are P2,000,000 and P1,500,000, respectively, totaling P3,500,000. Ola invests P1,000,000 for a 1/4 (25%) interest, thereby valuing the entire partnership at P4,000,000 (4 times P1,000,000). This implies that the existing partners' interest is now worth P3,000,000 (75% of P4,000,000). To find Berns’s new capital balance, first the increase in value of his share is determined, and then this is added to his original capital balance.
Berns's share of the increase is calculated based on his profit-sharing ratio, which is 3/5 of the increased value. The increase in value for the existing partnership is P500,000 (P3,000,000 minus P2,500,000 original total). Berns's share of this increase is 3/5 of P500,000, which is P300,000. Therefore, Berns's new capital balance is P2,000,000 (original) plus P300,000 (increase), totaling P2,300,000.