You are working on an improved display unit which will be much lighter. If this works, you can expect sales of 50,000 to 100,000 units within the first year of sales; sales in subsequent years will be in the 40-80,000 range). Variable costs of production are expected to be in the range $5.50-6.50/unit, and the selling price/unit will be between $20 and $25. But there are significant technical problems to be solved; if you concentrate all your development efforts in this area, it will be between 18 and 36 months before you can have the product ready for market.

The fixed operating costs of your company are $30,000/month. You will need to seek additional capital to survive until you have a product on the market. Depending on what rate you have to pay for capital, your pre-tax MARR may be anywhere between 20% and 30%.

Using the Monte Carlo method, or otherwise, write a brief report explaining what strategy you should follow, and why. Your grade will depend more on how carefully you document and justify your assumptions than on the accuracy of your calculations. In particular, you should explain what study period you are using.

It's possible to use the `Goldilocks Strategy' of examining the best case, worst case, and median case for each strategy. However, this isn't as good as using the Monte Carlo method -- for some of the input parameters [which?] the PW of each option is a nonlinear function of the parameter value, so looking at three points doesn't give you an adequate idea of the overall distribution of PW.

It's absolutely essential to use the same time period, starting and ending at the same times, for both strategies. It seems tempting to start the time period for the lightweight-display strategy later, perhaps when it goes into production, in order to make the comparison `fair'. But you can't escape the fact that money has a time value that easily.

Anything common to both the strategies can be left out. For example, the nine months between the present and the heavyweight-display strategy going in to production can be omitted, since it's the same for both strategies. You could also omit the fixed costs of $30,000/month, since they're the same in both cases.

Once you've set up the MC method, it's as easy to run 1,000,000 trials as it is to run 100. You should run at least 10,000 to get an adequate sample.

After you've got 10,000 or more present-worths for each strategy, how should you best display them?

One possibility is to just calculate the mean value of each strategy (plotting a graph of the mean value versus number of trials, as we did for the determination-of-pi example, shows the evolution of this mean value with number of trials; this is one way of deciding whether you've done enough trials.)

This choice involves throwing away almost all the information you've generated. You may still have enough -- if one PW is clearly higher than the other, it seems like that would be the sensible choice -- but you can make better use of the additional values you calculated.

The first improvement would be to calculate the variance as well as the mean for each strategy; if the strategy with the higher mean also has a very high variance, it might not be the best choice -- suppose, for example, that it gives a 30% possibility of going out of business, while the strategy with the lower mean value gives no possibility of going out of business.

A more informative picture of the distribution of present value can be obtained by plotting a histogram of the results for each strategy, grouping present value into about ten intervals and counting the number of cases that fall into each interval.

This assignment is due Friday Mar 17.