The net present value (NPV) and internal rate of return (IRR) methods of investm

Question

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 Cold Goose Metal Works Inc. Last Tuesday, Cold Goose Metal Works Inc. 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 13.2%, but he can't recall how much Cold Goose 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 Year1 $2,200,000 Year 2 $4,125,000 Year 3 $4,125,000 Year4 $4,125,000 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 Cold Goose's 7% WACC. Given the data and hints, Project Gamma's initial investment is (rounded to the nearest whole dollar). ,and its NPV is A project's IRR will if the project's cash inflows decrease, and everything else is unaffected.

Explanation / Answer

IRR is that discount rate at which the NPV is zero, i.e. present value of cash inflows equals cash outflows

We shall first calculate the present value of cash inflows @13.2% as follows:

NPV = Present Value of cash inflows - Cash outflows

0 = $10518351.43 - Cash outflows

Cash outflows = $10518351.43

The initial investment is $10518351.43

At 7% discount rate, the present value of cash outflows would be:

NPV = $12173181.01 - $10518351.43 = $1654829.58

A project's IRR will decrease if the project's cash flows decrease and everything else is unaffected.

Year Cash Inflows PV Factor @ 13.2% Present Value 1 2200000 0.883392226 1943462.90 2 4125000 0.780381825 3219075.03 3 4125000 0.689383238 2843705.86 4 4125000 0.608995793 2512107.65 Total 10518351.43

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