Question

A manufacturing company is launching a new consumer product. The manufacturing company is considering taking out an insurance policy to cover possible losses incurred by marketing the new product. If the product is a complete failure, the manufacturing company will incur a loss of $80,000. If the product is only moderately successful, the manufacturing company's loss is estimated to be $25,000. At the insurance company, insurance actuaries have determined that the chances that the product would be a complete failure or only moderately successful are 0.01 and 0.05, respectively. a. What premium should the insurance company charge the manufacturing company for a policy to insure the marketing campaign, in order to make an expected profit of $1,000? To make an expected profit of $1,000, the insurance company should charge a premium of $ . (Provide an integer value.) b. Using the answer in part a., compute the standard deviation of the insurance company's net cash flow. The standard deviation of the insurance company's net cash flow is $ . (Provide an integer value.)

Answer 1

a.

Let X be the premium charge by the insurance company.

Net Cash flow in cash of complete failure = X - 80000 with p = 0.01

Net Cash flow in cash of moderate successful = X - 25000 with p = 0.05

Net Cash flow in cash of successful = X    with p = 1 - 0.01 - 0.05 = 0.94

Expected profit = $1000

1000 = 0.01 * (X - 80000) + 0.05 * ( X - 25000) + 0.94 X

1000 = X - (800 + 1250)

X = 2050 + 1000 = $3050

b.

The probability distribution of net cash flow is,

Net Cash flow in cash of complete failure = -76950 with p = 0.01

Net Cash flow in cash of moderate successful = - 21950 with p = 0.05

Net Cash flow in cash of successful = 3050 with p = 0.94

Expected net cash flow, E(C) = 0.01 * -76950 + 0.05 * -21950 + 0.94 * 3050 = 1000

= 92047500

E(C) = 0.01 * (-76950)2 + 0.05*(-21950)2 +0.94 * 30502

Standard deviation of net cash flow = $\sqrt{91047500}$ = $9542 (Rounding to nearest integer)