Final answer:
The statement is false; a new partner's direct purchase of an existing partner's interest changes the composition of the partners' equity.
Step-by-step explanation:
The statement that the admission of a new partner does not change the composition of the partners' equity if the new partner purchases the old partner's interest by paying the old partner directly is false. When a new partner buys out an existing partner's interest directly, it affects the individual holdings of the partners' equity but does not affect the total equity of the business. The total equity remains the same, but the allocation amongst partners changes. The new partner assumes the equity position of the outgoing partner, altering the composition of ownership. An example reflecting a similar concept can be drawn from real estate equity: Freda owns a house valued at $250,000 with no bank liabilities, which means her equity interest in the property is $250,000 in its entirety. Comparably, if a new person were to buy part of Freda's house, directly from her, the equity in the house wouldn't change, but the composition of who holds that equity would.