$3.$ 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.

Cute Camel Woodcraft Company lost a portion of its planning and financial data when its server and its backup server crashed. The company$$s CFO remembers that the internal rate of return $($IRR$)$ of Project Zeta is $11\mathrm{.}30\%,$ but he can$$t recall how much Cute Camel originally invested in the project nor the project$$s net present value $($NPV$).$ However, he found a note that contained the annual net cash flows expected to be generated by Project Zeta. They are:

Year

Cash Flow

$1$ $$2,000,000$

$2$ $$3,750,000$

$3$ $$3,750,000$

$4$ $$3,750,000$

The CFO has asked you to compute Project Zeta$$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.

$$ The level of risk exhibited by Project Zeta is the same as that exhibited by the company$$s average project, which means that Project Zeta$$s net cash flows can be discounted using Cute Camel$$s $10\mathrm{.}00\%$ desired rate of return.

Given the data and hints, Project Zeta$$s initial investment is$$10,081,684,$ and its NPV is$$262,116($both rounded to the nearest whole dollar$).$