13-7: Monte Carlo Simulation Problem 13-16 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 $1,800,000 00-29 0.4 5,207,900 30-69 0.3 6,000,000 70-99 0.3 Probability 0.2 Project Life 3 years 10 years 14 years Random Numbers 00-19 20-79 80-99 0.6 0.2 Probability 0.2 0.6 Sales in Units 130 260 Random Numbers 00-19 20-79 80-99 0.2 320 Probability 0.1 0.8 0.1 Sales Price $13,400 13,500 15,000 Random Numbers 00-09 10-89 90-99 Probability Cost per Unit Random Numbers (Excluding Developmental Costs) $4,700 00-29 6,300 30-69 0.3 7,100 70-99 SSC uses a cost of capital of 17% to analyze average-risk projects, 13% for low-risk projects, and 21% for high-risk projects. These risk adjustments primarily reflect the uncertainty about each project's NPV and IRR as measured by the coefficients of variation. The firm is in the 40% federal-plus-state income tax bracket. 0.3 0.4 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. Round the answer to two decimal places. %% Can you determine the value of OIRR short of actual simulation or a fairly complex statistical analysis? No b. Assume that SSC uses a 17% cost of capital for this project. What is the project's NPV? Round your answer to the nearest cent. Could you estimate ONPV without either simulation or a complex statistical analysis? Novo c. Show the process by which a computer would perform a simulation analysis for this project. Use the random numbers 44, 17, 16, 58, 1; 79, 83, 86; and 19, 62, 6 to illustrate the process with the first computer run. Assume the cash flows for each year are independent of cash flows for other years. Calculate the following values, assuming the computer operates as follows: (1) A developmental cost and a project life are estimated for the first run using the first two random numbers. Developmental costs: $ Project life: years (2) Next, sales volume, sales price, and cost per unit are estimated using the next three random numbers and used to derive a cash flow for the first year. Sales volume: X units Sales price: $ Cost per unit: $ After-tax cash flow for Year 1: $ (3) Then, the next three random numbers are used to estimate sales volume, sales price, and cost per unit for the second year, hence the cash flow for the second year. Sales volume: X units Sales price: $ Cost per unit: $ After-tax cash flow for Year 2: $ (4) Cash flows for other years are developed similarly, on out to the first run's estimated life. Sales volume: units Sales price: $ Cost per unit: $ After-tax cash flow for Year 3: $ (5) With the developmental cost and the cash flow stream established, NPV and IRR for the first run are derived and stored in the computer's memory. IRR: NPV: $ (6) The process is repeated to generate perhaps 500 other NPVs and IRRS. (7) Frequency distributions for NPV and IRR are plotted by the computer, and the distributions' means and standard deviations are calculated. Make a decision about how symmetrical the data would be. The input in the box below will not be graded, but may be reviewed and considered by your instructor. blank 13-7: Monte Carlo Simulation Problem 13-16 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 $1,800,000 00-29 0.4 5,207,900 30-69 0.3 6,000,000 70-99 0.3 Probability 0.2 Project Life 3 years 10 years 14 years Random Numbers 00-19 20-79 80-99 0.6 0.2 Probability 0.2 0.6 Sales in Units 130 260 Random Numbers 00-19 20-79 80-99 0.2 320 Probability 0.1 0.8 0.1 Sales Price $13,400 13,500 15,000 Random Numbers 00-09 10-89 90-99 Probability Cost per Unit Random Numbers (Excluding Developmental Costs) $4,700 00-29 6,300 30-69 0.3 7,100 70-99 SSC uses a cost of capital of 17% to analyze average-risk projects, 13% for low-risk projects, and 21% for high-risk projects. These risk adjustments primarily reflect the uncertainty about each project's NPV and IRR as measured by the coefficients of variation. The firm is in the 40% federal-plus-state income tax bracket. 0.3 0.4 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. Round the answer to two decimal places. %% Can you determine the value of OIRR short of actual simulation or a fairly complex statistical analysis? No b. Assume that SSC uses a 17% cost of capital for this project. What is the project's NPV? Round your answer to the nearest cent. Could you estimate ONPV without either simulation or a complex statistical analysis? Novo c. Show the process by which a computer would perform a simulation analysis for this project. Use the random numbers 44, 17, 16, 58, 1; 79, 83, 86; and 19, 62, 6 to illustrate the process with the first computer run. Assume the cash flows for each year are independent of cash flows for other years. Calculate the following values, assuming the computer operates as follows: (1) A developmental cost and a project life are estimated for the first run using the first two random numbers. Developmental costs: $ Project life: years (2) Next, sales volume, sales price, and cost per unit are estimated using the next three random numbers and used to derive a cash flow for the first year. Sales volume: X units Sales price: $ Cost per unit: $ After-tax cash flow for Year 1: $ (3) Then, the next three random numbers are used to estimate sales volume, sales price, and cost per unit for the second year, hence the cash flow for the second year. Sales volume: X units Sales price: $ Cost per unit: $ After-tax cash flow for Year 2: $ (4) Cash flows for other years are developed similarly, on out to the first run's estimated life. Sales volume: units Sales price: $ Cost per unit: $ After-tax cash flow for Year 3: $ (5) With the developmental cost and the cash flow stream established, NPV and IRR for the first run are derived and stored in the computer's memory. IRR: NPV: $ (6) The process is repeated to generate perhaps 500 other NPVs and IRRS. (7) Frequency distributions for NPV and IRR are plotted by the computer, and the distributions' means and standard deviations are calculated. Make a decision about how symmetrical the data would be. The input in the box below will not be graded, but may be reviewed and considered by your instructor. blank