Two Computer EngineersDan and Susan are first met in college, and both had a bachelors degree in Computer Engineering. They had put in several years as maintenance engineers in a large chip manufacturing company. About $6$ months ago, they were able to exercise their first stock options. That was when they decided to quit their safe, steady job and pursue their dreams of starting a venture of their own. In their spare time, almost as a hobby, they had been collaborating on some research into a new chip that could speed up certain specialized tasks by as much as $25\%.$ At this point, the design of the chip was complete. While further experimentation might improve the performance of their design, any delay in entering the market now may prove to be costly$,$ as one of the established players might introduce a similar product of their own. The duo knew that now was the time to act if at all. They are now facing an important decision. After having discussed different financial scenarios, the two computer engineers felt it was time to finalize their cash flow projections and move to the next stage decide which of two possible projects they should undertake.They estimated that they would need to spend about $$1,000,000$ on plant, equipment and supplies. As for future cash flows, they felt that the right strategy at least for the first year would be to sell their product at dirt$-$cheap prices in order to induce customer acceptance. Then, once the product had established a name for itself, the price could be raised. By the end of the fifth year, their product in its current form was likely to be obsolete. However, the innovative approach that they had devised and patented could be sold to a larger chip manufacturer for a decent sum. Accordingly, the two budding entrepreneurs estimated the cash flows for this project $($call it Project A$)$ as follows:YearProject AExpected Cash flows $($$$)0(1,000,000)150,0002200,0003600,00041,000,00051,500,000$An alternative to pursuing this project would be to immediately sell the patent for their innovative chip design to one of the established chip makers. They estimated that they would receive around $$200,000$ for this. It would probably not be reasonable to expect much more as neither their product nor their innovative approach had a track record.They could then invest in some plant and equipment that would test silicon wafers for zircon content before the wafers were used to make chips. Too much zircon would affect the long$-$term performance of the chips. The task of checking the level of zircon was currently being performed by chip makers themselves. However, many of them, especially the smaller ones, did not have the capacity to permit $100\%$ checking. Most tested only a sample of the wafers they received.Dan and Susan were confident that they could persuade at least some of the chip makers to outsource this function to them. By exclusively specializing in this task, their little company would be able to slash costs by more than half, and thus allow the chip manufacturers to go in for $100\%$ quality check for roughly the same cost as what they were incurring for a partial quality check today. The life of this project too $($call it project B$)$ is expected to be only about $5$ years.The initial investment for this project is estimated at $$1,100,000.$ After taking into account the sale of their patent, the net investment would be $$900,000.$ As for the future, Dan and Susan were pretty sure that there would be sizable profits in the first couple of years. But thereafter, the zircon content problem would slowly start to disappear with advancing technology in the wafer industry. Keeping all this in mind, they estimate the cash flows for this project as follows:YearProject BExpected Cash flows $($$$)0($$$900,000)1650,0002650,0003550,0004300,0005100,000$Dan and Susan now need to make their decision. For purposes of analysis, they plan to use a required rate of return of $20\%$ for both projects. Ideally, they would prefer that the project they choose have a payback period of less than $3\mathrm{.}5$ years and a discounted payback period of less than $4$ years.

Questions:

$1.$ Rank the projects based on each of the following metrics: Payback period, Discounted payback period, NPV$,$ IRR, Profitability Index.

$2.$ Susan believes that the best approach to make the decision is the NPV approach. However, Dan is not so sure that ignoring the other metrics is a good idea. Which of the approaches or metrics would you propose? In other words, would you prefer one or more of these approaches over the others? Explain why.