$3.$ Understanding the IRR and NPV

The net present value $($NPV$)$ and internal rate of return $($IRR$)$ methods of investment analysis are interrelated and are sometimes used together to make capital budgeting decisions.

Consider the case of Fuzzy Button Clothing Company:

Last Tuesday, Fuzzy Button Clothing Company lost a portion of its planning and financial data when both its main and its backup servers crashed. The company$$s CFO remembers that the internal rate of return $($IRR$)$ of Project Gamma is $11\mathrm{.}3\%,$ but he can$$t recall how much Fuzzy Button originally invested in the project nor the project$$s net present value $($NPV$).$ However, he found a note that detailed the annual net cash flows expected to be generated by Project Gamma. They are:

Year

Cash Flow

Year $1$ $$2,000,000$

Year $2$ $$3,750,000$

Year $3$ $$3,750,000$

Year $4$ $$3,750,000$

The CFO has asked you to compute Project Gamma$$s initial investment using the information currently available to you. He has offered the following suggestions and observations:

$$ A project$$s IRR represents the return the project would generate when its NPV is zero or the discounted value of its cash inflows equals the discounted value of its cash outflows$$when the cash flows are discounted using the project$$s IRR.

$$ The level of risk exhibited by Project Gamma is the same as that exhibited by the company$$s average project, which means that Project Gamma$$s net cash flows can be discounted using Fuzzy Button$$s $7\%$ WACC.

Given the data and hints, Project Gamma$$s initial investment is $,$ and its NPV is $($rounded to the nearest whole dollar$).$