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 Omicron 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 Omicron. 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 Omicron’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 Omicron is the same as that exhibited by the company’s average project, which means that Project Omicron’s net cash flows can be discounted using Cold Goose’s 9% WACC.

Given the data and hints, Project Omicron’s initial investment is__________________ , and its NPV is___________________ (rounded to the nearest whole dollar).

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

Answer 1

Initial Investment

The question has given he Internal Rate of Return [IRR] as 13.20%, IRR is the rate at which the present value of the annual cash flow equals to the initial Investment or it can say that at IRR, the present value of the annual cash flow = Initial Investment, or at IRR, NPV will be Zero

Initial Investment = Present Value of the annual cash inflows discounted at 13.20%

Year	Annual cash flows ($)	Present Value Factor (PVF) at 13.20%	Present Value of annual cash flows ($) [Annual cash flow x PVF]
1	,1,00,000	0.88339223	1,590,106
2	3,375,000	0.78038183	2,633,789
3	3,375,000	0.68938324	2,326,668
4	3,375,000	0.60899579	2,055,361
TOTAL			8,605,924

“The Initial Investment will be $8,605,924”

Net Present Value (NPV)

Year	Annual cash flows ($)	Present Value Factor (PVF) at 9.00%	Present Value of annual cash flows ($) [Annual cash flow x PVF]
1	,1,00,000	0.91743119	1,651,376
2	3,375,000	0.84167999	2,840,670
3	3,375,000	0.77218348	2,606,119
4	3,375,000	0.70842521	2,390,935
TOTAL			9,489,100

Net Present Value (NPV) = Present Value of annual cash inflows – Initial Investment

= $9,489,100 - $8,605,924

= $883,176

“The Net Present Value (NPV) will be $883,176”

“Given the data and hints, Project Omicron’s initial investment is $8,605,924 and it’s NPV is $883,176.

A Project’s IRR will “INCREASE” if the Project’s cash flows decreases, and everything else is unaffected.

NOTE    

The Formula for calculating the Present Value Factor is [1/(1 + r)ⁿ], Where “r” is the Discount/Interest Rate and “n” is the number of years.