$($All answers were generated using $1,000$ trials and native Excel functionality.$)$

Orange Tech $($OT$)$ is a software company that provides a suite of programs that are essential to everyday business computing. OT has just enhanced its software and released a new version of its programs. For financial planning purposes, OT needs to forecast its revenue over the next few years. To begin this analysis, OT is considering one of its largest customers. Over the planning horizon, assume that this customer will upgrade at most once to the newest software version, but the number of years that pass before the customer purchases an upgrade varies. Up to the year that the customer actually upgrades, assume there is a $0\mathrm{.}50$ probability that the customer upgrades in any particular year. In other words, the upgrade year of the customer is a $($discrete$)$ random variable. For guidance on an appropriate way to model upgrade year, refer to Appendix $13\mathrm{.}1.$ Furthermore, the revenue that OT earns from the customer's upgrade also varies $($depending on the number of programs the customer decides to upgrade$).$ Assume that the revenue from an upgrade obeys a normal distribution with a mean of $$100,000$ and a standard deviation of $$25,000.$

Using the template in the file OrangeTech, complete a simulation model that analyzes the net present value of the revenue from the customer upgrade. Hint: Excel's NPV function computes the net present value for a sequence of cash flows that occur at the end of each period. To correctly use this function for cash flows that occur at the beginning of each period, use the formula $=$NPV$($discount rate, flow range$)+$ initial amount, where discount rate is the annual discount rate, flow range is the cell range containing cash flows for years $1$ through n$,$ and initial amount is the cash flow in the initial period $($year $0).$ Use an annual discount rate of $10\%.$

Click on the datafile logo to reference the data.

The datafile logo$.$

$($a$)$ What is the average net present value that OT earns from this customer?

Round your answer to the nearest whole number. Do not round your intermediate calculation.

$

$($b$)$ What is the standard deviation of net present value?

Round your answer to the nearest whole number. Do not round your intermediate calculation.

$$\backslash$table$[[,$A$,$B$],[1,$Orange Tech,$],[2,,],[3,$Parameters,$],[4,$Annual Upgrade Probability,$0\mathrm{.}5],[5,$Upgrade Year,$],[6,$Discount Rate,$10\%$