Break-Even in Units

Aliyah Brown and two of her colleagues are considering opening a law office in a large metropolitan area that would make inexpensive legal services available to those who could not otherwise afford these services. The intent is to provide easy access for their clients by having the office open 360 days per year, 16 hours each day from 7:00 a.m. to 11:00 p.m. The office would be staffed by a lawyer, paralegal, legal secretary, and clerk-receptionist for each of the two 8-hour shifts.

In order to determine the feasibility of the project, Aliyah hired a marketing consultant to assist with market projections. The results of this study show that if the firm spends $500,000 on advertising the first year, the number of new clients expected each day would have the following probability distribution:

Number of New Clients per Day	Probability
20	0.10
30	0.30
55	0.40
85	0.20

Aliyah and her associates believe these numbers are reasonable and are prepared to spend the $500,000 on advertising. Other pertinent information about the operation of the office is as follows.

The only charge to each new client would be $30 for the initial consultation. All cases that warranted further legal work would be accepted on a contingency basis with the firm earning 30 percent of any favorable settlements or judgments. Aliyah estimates that 20 percent of new client consultations will result in favorable settlements or judgments averaging $2,000 each. Repeat clients are not expected during the first year of operations.

The hourly wages of the staff are projected to be $25 for the lawyer, $20 for the paralegal, $15 for the legal secretary, and $10 for the clerk-receptionist. Fringe benefit expenses will be 40 percent of the wages paid. A total of 400 hours of overtime is expected for the year; this will be divided equally between the legal secretary and the clerk-receptionist positions. Overtime will be paid at one and one-half times the regular wage, and the fringe benefit expense will apply to the full wages.

Aliyah has located 6,000 square feet of suitable office space, which rents for $28 per square foot annually. Associated expenses will be $22,000 for property insurance and $32,000 for utilities.

It will be necessary for the group to purchase malpractice insurance, which is expected to cost $180,000 annually. The initial investment in office equipment will be $60,000; this equipment has an estimated useful life of four years. The cost of office supplies has been estimated to be $4 per expected new client consultation.

Required:

1. Determine how many new clients must visit the law office being considered by Aliyah Brown and her colleagues in order for the venture to break even during its first year of operations. Round your answer to the nearest whole number of clients.

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