Don Carson and two colleagues are considering opening a law office in a large metropolitan area to make inexpensive legal services available to people who cannot otherwise afford these services. They intend 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. A lawyer, paralegal, legal secretary, and clerk-receptionist would staff the office for each of the two 8-hour shifts.

To determine the feasibility of the project, Don hired a marketing consultant to assist with market projections. The consultant's results 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

10 ..................................................... 0.10

20 ..................................................... 0.30

40 ..................................................... 0.40

60 ..................................................... 0.20

Don and his associates believe these numbers to be reasonable and are prepared to spend the $500,000 on advertising. Other pertinent information about the operation of the office follows.

The only charge to each new client would be $30 for an initial consultation. The firm will accept on a contingency basis all cases that warrant further legal work, with the firm earning 30% of any favorable settlements or judgments. Don estimates that 20% of new client consultations will result in favorable settlements or judgments averaging $15,000 each. He does not expect repeat clients during the first year of operations.

The hourly wages for the staff are projected to be $185 for the lawyer, $50 for the paralegal, $30 for the legal secretary, and $20 for the clerk-receptionist. Fringe benefit expense will be 40% 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 wage.

Don has located 6,000 square feet of suitable office space that rents for $48 per square foot annually. Associated expenses will be $22,000 for property insurance and $32,000 for utilities. The group must purchase malpractice insurance 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 $10 per expected new client consultation.

Required

1. Determine how many new clients must visit the law office that Don and his colleagues are considering for the venture to break even in the first year of operations. (For purposes of this calculation, treat all labor costs as fixed with respect to number of new clients.)

2. Using the probability information provided by the marketing consultant, determine whether it is feasible for the law office to achieve breakeven operations. Specifically, calculate and interpret the expected value of new clients for year 1, based on the probability data given above.

3. Explain how Don and his associates could use sensitivity analysis to assist in this analysis.

4. Assume, for purposes of this question, that the number of new clients is normally distributed around a mean of 3,649.087, with a standard deviation of operating income equal to $5,000,000. Use the NORMDIST function in Excel to respond to the following questions.

a. What is the probability that the firm will at least break even for year 1 (based on number of new clients added)?

b. What is the probability that the firm will generate a minimum of $3,235,760 of pretax income on the basis of new clients added in year 1?

c. Assume now that the mean value of new clients in year 1 is 12,600, with a standard deviation of $5,000,000 (in terms of operating income). Assume, as above, that operating income is thought to be normally distributed around the mean value. Given these assumptions, what is the probability of generating operating income of at least $8,235,760 in year 1 based on the number of new clients added?

d. Assume the facts stated in part (c) above, except that the standard deviation of operating income is $2,500,000 (not $5,000,000). Given these assumptions, what is the probability of generating at least $8,235,760 of operating income in year 1 based on the number of new clients added? How does this result compare to the one obtained above in (c)?