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Simulation Singleton Supplies Corporation (SSC) manufactures medical products for hospitals, clinics, and nursing homes. SSC may introduce a new type of X-ray scanner designed to identify certain types of cancers in their early stages. There are a number of uncertainties about the proposed project, but the following data are believed to be reasonably accurate.

Probability Developmental Costs Random Numbers 0.3 $2,000,000 00–29 0.4 4,000,000 30–69 0.3 6,000,000 70–99 Probability Project Life Random Numbers 0.2 3 years 00–19 0.6 8 years 20–79 0.2 13 years 80–99 Probability Sales in Units Random Numbers 0.2 100 00–19 0.6 200 20–79 0.2 300 80–99 Probability Sales Price Random Numbers 0.1 $13,000 00–09 0.8 13,500 10–89 0.1 14,000 90–99 Probability Cost per Unit (Excluding Developmental Costs) Random Numbers 0.3 $5,000 00–29 0.4 6,000 30–69 0.3 7,000 70–99 SSC uses a cost of capital of 15% to analyze average-risk projects, 12% for low-risk projects, and 18% for high-risk projects. These risk adjustments primarily reflect the Chapter 11: Cash Flow Estimation and Risk Analysis 463 uncertainty about each project’s NPV and IRR as measured by their coefficients of variation. The firm is in the 40% federal-plus-state income tax bracket.

a. What is the expected IRR for the X-ray scanner project? Base your answer on the expected values of the variables. Also, assume the after-tax “profits” figure that you develop is equal to annual cash flows. All facilities are leased, so depreciation may be disregarded. Can you determine the value of σIRR short of actual simulation or a fairly complex statistical analysis?