A law firm provides accounting services for some of its clients. The person who

Question

A law firm provides accounting services for some of its clients. The person who handles this service and her secretary cost the firm an average of $80,000 a year in salary and benefits. Clients are charged a fixed rate of $300 per year for those services, and the firm is billed $50 per client for computer time, postage, and supplies. Now a local accounting firm has offered to provide comparable service for a fee of $600 dollars per client.

a. What profit or loss would the firm realize if 354 clients use its accounting service each year?

b. Assuming 300 clients a year, would the law firm be better off using its own staff, or using the outside accounting firm?

c. At what level of client usage would the two alternatives produce the same profit?

Explanation / Answer

a Annual Fixed Cost of the Accounting services to the firm 80,000.00 Charge to the client 300.00 Billing per client (50.00) Contribution per Client 250.00 Profit or Loss realized by the firm if the Number of clients is 354 Client Revenue - Contribution ( 354 × 250 ) 88,500.00 Less : Fixed Cost 80,000.00 Profit 8,500.00 b At 300 clients per year Using its staff Client Revenue - Contribution ( 300 × 250 ) 75,000.00 Less : Fixed Cost 80,000.00 Profit (5,000.00) Using Outside Acounting firm: Client Revenue ( 300 × 300 ) 90,000.00 Savings in Annual Cost 80,000.00 Less : Cost per client paid to the outside firm ( 600 × 300 ) (180,000.00) Loss (10,000.00) At 300 clients per year , the firm would be better off using its own accounting services c Let V the number of clients where the profits from the two options is equal : Profit if Accounting firm is used : Revenue(300 × V ) 300V Savings in Annual Cost 80,000.00 Less : Cost per client paid to the outside firm ( 600 × V ) 600V Profit 300V + 80,000 - 600V (A) Profit if Accounting firm is not used : Contribution per Client 250V Less : Fixed Cost 80,000.00 Profit 250V - 80,000 ( B ) Now, 300V + 80,000 - 600V = 250V - 80,000 Solving the equation we get , V = 290.9 or 291 Hence, at 291 clients, the profits from both options would be equal

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