# What is the probability of a loss?

1. Profit Analysis. A consumer electronics from produces  a line of battery rechargers for cell phones. the following distributions apply:

Unit price-Triangular with a minimum of \$18.95, most likely value of \$24.95, and maximum of \$26.95

Unit Cost-Uniform with a minimum of \$12.00 and a maximum of \$15.00

Quantity Sold- 10,00-250xUnit price, plus a random term given by a normal distribution with a mean of 0 and standard deviation of 10

Fixed costs- normal with a mean of \$30,000 and a standard deviation of \$5,000

a. What is the expected profit?

b. What is the probability of a loss?

c. What is the maximum loss?

2. R&D Planning. A firm is in the process of assessing the economic prospects for a new bottling machine it is develop- ing. Future research and development expenses could range from \$4 to \$9 million, with a most likely value around \$7 million. The life of the product will be anywhere from 3 to 10 years. Yearly unit sales will range from 100 to 500, with a most likely value around 300. The machines will sell for between \$20,000 and \$25,000 each. The production cost of the machine is expected to be \$13,000 but could be as low as \$11,000 or as high as \$15,000. The firm’s discount rate is 10 percent.a. What is the expected NPV for this new machine over ten years?b. What is the probability of a positive NPV?

3.) HealthClaims.Alargemanufacturingcompanyself-insures its employee health insurance claims. That is, it collects a fixed amount each month from every employee for health care costs and then it pays the entire claim amounts using its own funds to make up the difference. It would like to estimate its total health care payments for the coming year.The total number of employees at the start of the year is 11,124. The firm expects the number of employees to change each month over the coming year by a percentage that is uniformly distributed between ␣2 percent and 5 percent. Employees contribute \$125 each per month toward their health care costs, while the average claim is \$250 per month. The average claim itself is expected to grow by an amount given by a normal distribution with a mean of 1 percent and a standard deviation of 2 percent.a. What is the expected cost to the company of covering employee health care costs in the coming year?b. What is the maximum cost to the company of covering employee health care costs in the coming year?c. What is the probability that costs will not exceed \$20million?