Question

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 Blue Hamster Manufacturing Inc.:

Last Tuesday, Blue Hamster Manufacturing 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 Delta is 11.3%, but he can’t recall how much Blue Hamster 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 Delta. They are:

Year	Cash Flow
Year 1	$1,800,000
Year 2	$3,375,000
Year 3	$3,375,000
Year 4	$3,375,000

The CFO has asked you to compute Project Delta’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 Delta is the same as that exhibited by the company’s average project, which means that Project Delta’s net cash flows can be discounted using Blue Hamster’s 9% WACC.

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

A project’s IRR will (STAY THE SAME/INCREASE/DECREASE) if the project’s cash inflows increase, and everything else is unaffected.

Answer 1

Calculation of NPV and initial investment
		IRR
Year	Cashflow ($)	Discounting factor @ 11.3%	PV of cashflows ($)
0	-x	1	-x
1	1800000	0.898472597	1617250.67
2	3375000	0.807253007	2724478.90
3	3375000	0.725294705	2447869.63
4	3375000	0.651657417	2199343.78
		NPV	8988942.98-x
We know,
At IRR, NPV=0
Let the initial investment be x (since it is an outflow so shown as negative in table)
Equating the equation, to get the initial investment (i.e. x)
8988942.98-x=0
x= $8988942.98
Initial investment= $8988943 (rounded off to nearest whole number)
		NPV
Year	Cashflow ($)	Discounting factor @ 9%	PV of cashflows ($)
0	-8988943	1	-8988943.00
1	1800000	0.917431193	1651376.15
2	3375000	0.841679993	2840669.98
3	3375000	0.77218348	2606119.25
4	3375000	0.708425211	2390935.09
		NPV	500157.46
We know,
NPV= Present value of future cashflows discounted at the required rate of return
NPV= $500157.46
A project's IRR will increase if the project's cashflows increase and everything else is unaffected (as it is a rate of return from the project so as the cashflows increases the IRR will also increase).