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 $$osts Random Numbers

$0\mathrm{.}3$ $$2,000,00000-29$

$0\mathrm{.}44,000,00030-69$

$0\mathrm{.}36,000,00070-99$

Probability Project Life $($Years$)$ Random Numbers

$0\mathrm{.}2300-19$

$0\mathrm{.}6820-79$

$0\mathrm{.}21380-99$

Probability Sales in Units Random Numbers

$0\mathrm{.}210000-19$

$0\mathrm{.}620020-79$

$0\mathrm{.}230080-99$

Probability Sales Price Random Numbers

$0\mathrm{.}1$ $$13,00000-09$

$0\mathrm{.}813,50010-89$

$0\mathrm{.}114,00090-99$

Cost per Unit

$($Excluding

Probability Developmental Costs$)$ Random Numbers

$0\mathrm{.}3$ $$5,00000-29$

$0\mathrm{.}46,00030-69$

$0\mathrm{.}37,00070-99$

SSC uses a cost of capital of $15\%$ to analyze average$-$risk projects such as this one. The firm is in the $25\%$ federal$-$plus$-$state income tax bracket.

What is the expected IRR for the X$-$ray scanner project? Base your answer on the expected values of the variables. $($Hint: You'll need to calculate the expected value of each variable. To make your calculations easier, note that because these distributions are symmetric, the expected value is also equal to the middle value.$)$ 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. Do not round intermediate calculations. Round your answer to two decimal places.

$\%$

Can you determine the value of $\backslash$sigma IRR short of actual simulation or complex statistical analysis?

What is the project's NPV$?$ Do not round intermediate calculations. Round your answer to the nearest dollar.

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Could you estimate $\backslash$sigma NPV without either simulation or a complex statistical analysis?

Show the process by which a computer would perform a simulation analysis for this project. Assume the computer has generated the random numbers used in parts $(1)$ and $(2).$

$(1)$ Use the random numbers $11$ and $32$ to determine the project's life and development costs; these will be the same for all sample years.

$(2)$ Use $8,28,$ and $19$ as random numbers to determine the unit sales, sales price per unit, and cost per unit in the first year, respectively. Calculate the net income. Repeat this for Year $2$ by using the random values $37,87,$ and $70$ to determine the unit sales, sales price per unit, and cost per unit in the second year. Repeat this for Year $3($and any subsequent years$)$ by using the random values $3,27,$ and $69$ to determine the unit sales, sales price per unit, and cost per unit in the third year, respectively.

$(3)$ What is the NPV for this sample? Do not round intermediate calculations. Round your answer to the nearest dollar. Use a minus sign to enter a negative value, if any.

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