A company receives an order for five custom-made microchips at a price of $7,500

each. The company will produce the chips one by one using a complex process which

has only a 67% chance of producing a defect-free chip at each trial. After five defectfree

chips are produced the process will be stopped.

A cost accountant at the company has prepared the following cost report: The cost of

production includes a $14,800 fixed cost and a $2,700 unit variable cost. Thus if X

number of chips are produced, the total cost of production would be 14800 + 2700 X

dollars. The revenue minus the cost of production will be the profit.

After some analysis, the finance manager of the company says that the risk may be too

high and thinks the order should not be accepted.

i. What distribution will the number of chips produced, X follow?

ii. What is the expected value and standard deviation of X?

iii. What is the expected value and standard deviation of the profit?

iv. What is the break-even X

v. What is the probability that accepting the order will result in a loss?

vi. A popular measure of risk in a venture is value at risk, which is the loss suffered

at the 5th percentile of the return from the venture. In this problem, find an integer

x such that P(X > x) is approximately 5%.

vii. For the x value found in vi, calculate the loss, and thus the value at risk.

viii. Express the value at risk as a percentage of the expected value of the profit.

ix. What is your assessment of the risk and reward in the order? Should the company

accept the order?