Exam 12: Probabilistic Risk Analysis

Amy wants to estimate the average number of items per purchase at the express lane of a local grocery store. She has estimated the following probabilities based on a sample size of 50 customers. Determine the expected value, variance, and standard deviation of items per purchase. Items per Purchase Probability 1 0.29 2 0.16 3 0.15 4 0.18 5 0.22

The estimated annual cash flow of an investment project along with associated probabilities are given below. Determine the expected present worth of this annual cash flow series at an interest rate of 11% per year. Year P=0.5 P=0.4 P=0.1 0 \- 57,000 -\ 59,000 -\ 57,500 1 \ 3100 \ 3000 \ 3100 2-6 \ 3250 \ 3000 \ 3100 7 \ 3400 \ 6000 \ 3100

Gopher Manufacturing is considering purchasing new calibration equipment to improve the quality of its processes. The equipment has an initial cost of $66,000 and a market value of $52,000 at the end of its useful life of 10 years. Net annual revenue is estimated based on the production and market conditions and is shown below. If the optimistic and pessimistic values each have an estimated 11% chance of occurring, determine whether the equipment should be purchased on the basis of the expected value of AW. Use a MARR of 8% per year. Optimistic Most likely Pessimistic Net annual revenue, \ /year 93,500 90,000 88,500

The probability distribution of a certain overhead cost is f(x) = 2(1- x)2, where x is production hours per day. Determine the expected value and variance for this distribution if the number of production hours per day ranges from 4 to 11 hours.

Buffalo Manufacturing is considering purchasing new equipment with an initial cost of $65,000 and zero market value at any time of its useful life. The company expects this new equipment to generate additional net revenue of $6700 per year. Due to the harsh environment in which the equipment will be operated, the useful life of the equipment is uncertain. The estimated probabilities of different useful lives are shown below. Calculate the expected present worth and variance of present worth associated with the purchase of the equipment. Assume the company's MARR is 11% per year. Useful life, Years (N) P(N) 3 0.1 4 0.1 5 0.15 6 0.18 7 0.47

Kewpie, Inc. is considering purchasing a new set of packaging and labeling equipment. A comparison of estimated cash flows is shown below. Item =0.2 =0.15 =0.65 Initial investment, \ 210,000 210,000 210,000 Net annual revenue, \ /y=ar 265,000 250,000 240,000 Market value, \ 30,000 32,000 37,000 Project life, years 5 5 5 If straight- line depreciation with a salvage value of $32,000 and a useful life of 5 years is used, determine whether Kewpie should invest in the equipment on the basis of the expected value of after- tax PW. Assume an effective tax rate of 35% and a MARR of 10% per year.

An engineer is considering the size of a reservoir for flood control in the northern part of Germany. The size of the reservoir is closely related to the annual rainfall. In addition, there will be reparation costs from damages when the amount of rainfall exceeds the design capacity. If such damage occurs, it is estimated that the annual reparation cost will be 2.3% of the capital investment. The probabilities of specific amounts of rainfall per year and the estimated investment costs of the reservoir are given below. Using an interest rate of 8% per year and a study period of 11 years, determine the appropriate investment on the basis of AW. Annual Probability of Greater Rainfall Estimated Capital Cnvestment, \ 110 0.6 2,500,000 120 0.2 2,550,000 130 0.1 2,600,000 140 0.055 2,650,000 150 0.045 2,700,000