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# 3. Understanding the IRR and NPV The net present value (NPV) and internal rate of return...

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 Cute Camel Woodcraft Company:

Last Tuesday, Cute Camel Woodcraft 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 Zeta is 14.6%, 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 detailed the annual net cash flows expected to be generated by Project Zeta. 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 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 9% WACC.

Given the data and hints, Project Zeta’s initial investment is _______ , and its NPV is ___________ (rounded to the nearest whole dollar).

A project’s IRR will___(decrease/increase/stay the same)____ if the project’s cash inflows decrease, and everything else is unaffected.

NPV = -initial investment + PV of future cash flows

Present value = Future value/(1+i)^n

i = interest rate per period

n= number of periods

IRR is the at which NPV is zero

=>

0 = -initial investment + 2000000/1.146 + 3750000/1.146^2 + 3750000/1.146^3 + 3750000/1.146^4

=>

initial investment = 2000000/1.146 + 3750000/1.146^2 + 3750000/1.146^3 + 3750000/1.146^4

= 9266329.61

NPV = 9266329.61 + 2000000/1.09 + 3750000/1.09^2 + 3750000/1.09^3 + 3750000/1.09^4

= 1277115.34

A project’s IRR will decrease if the project’s cash inflows decrease, and everything else is unaffected.

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