Your firm has a new technology that will enable it to be the market leader in a new product segment. You estimate that the project life will be ten years, after which the project will cease operations. Your role is to determine the optimal size of the project as your analysis so far suggests that the larger the scope of the project, the lower will be the revenue growth rate. Specifically, you estimate that at nearly zero investment, the project will have a 30% growth rate but that for every $1 million invested in the project, the growth rate will drop by one percent. As an example, if $5 million is invested in the project, the estimated annual sales growth rate is forecast to be 25%. The other forecasts are as follows:

• Revenues begin in the first year after the initial investment and are equal in the first year to the amount of the initial investment (so if the investment is $5 million, expected revenue in year 1 is $5 million).
• Operating costs are estimated to be 85% of revenues.
• The investment can be fully depreciated straight-line over the ten-years and will have zero salvage value.
• The marginal tax rate is 35%.
• The project requires an investment in working capital in the first year equal to ten percent of the first years expected revenues. In each year of operation, the working capital balance is expected to be ten percent of that years revenue forecast. At the end of the project, the balance of working capital will be recovered.
• The estimated project cost of capital is 12%.

What do you estimate to be the optimal size of the investment in the project? What is the NPV of the project at that investment level?