Step 1: Think of goodwill as an unrecorded asset:
Goodwill built up over years of good service, location, and reputation is never shown in the books at its true worth — it only becomes relevant in money terms when the partners' shares are about to change.
Step 2: Connect this to fairness among partners:
Without valuing it, an incoming partner would get a free ride on the firm's existing reputation, or an outgoing partner would leave without being paid for the reputation he helped build — valuation at admission, retirement, death, or ratio change prevents this.
Final Answer:
Valuation of goodwill is needed to ensure fair compensation between partners whenever profit-sharing rights are reconstituted — admission, retirement, death, or a change in ratio.