An important concept in corporate finance is the idea of cash flow. Based on a given investment decision, what will my increase in cash flows be as a result? There are two important metrics which are used to determine the value of an investment decision, and that is the net present value (NPV) as well as the Internal Rate of Return (IRR).

Net Present Value looks at the current value of all expected cash flows by using a discounted cash flow (DCF) model for a given discount rate (the firm's stated required rate of return) and is measured in dollars (or whatever currency the investment is made in). A higher NPV is preferable.

Internal Rate of Return is the rate of return earned on the investment. Another way to look at it is to consider it the discount rate for which the NPV is zero. A higher IRR is preferable.

Often, for two different investment decisions, NPV and IRR will give the same investment decision (Project A has higher NPV and IRR than Project B), but this is not always the case. For example, with uneven cash flows and different initial investment outlays, it is possible to get a seemingly conflicting decision. So what do you do?

If you have enough money to do both projects, you do both (assuming the NPV is positive, you would never do a project with a negative expected NPV). If the projects are mutually exclusive, you take the project with the highest NPV (most valuable at the end of the day).

What else can you learn from the NPV and IRR profiles of two projects? Look at the graph below:

Since NPV varies based on different discount rates, the graph shows how the NPV moves for each project as the discount rate used changes. There are four discount rates of interest. The first is a discount rate of 0, which is the NPV of all cash flows assuming no discounting. The next is the cross over rate which is the discount rate at which the NPV of Projects A & B are equally valuable. Then we have NPV of Projects A & B at 0 at IRR A & B respectively.

Notice that as the discount rate moves, your investment decision (assuming Projects A & B are mutually exclusive) changes. For example, between undiscounted cash flows and the cross over rate, the NPV for Project A is higher. Between the Cross over rate to IRR A (and up to IRR B) the NPV for Project B is higher.

What else can we see from this graph? The undiscounted cash flows of Project A are higher, but as the discount rate increases, the NPV of B becomes larger. You can infer that based on this relationship, Project A probably has larger cash flows relative to its initial investment, however, they occur at a later date (and are therefore more sensitive to discounting) whereas B probably has cash flows occurring relatively sooner.

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5 days ago

## 4 comments:

hi there, I was just reading your article. In the end, which project would you choose?

With all the standard business assumptions (leaving this problem strictly in the realm of mathematics), you would choose the project with the highest NPV if you could only choose one.

It is said that IRR calculations carry an the burden of reinvestment risk and hence is not the right measure, can you elaborate on it?

I am unsure what reinvestment risk means?

Interestingly my papers disagree with your comments here;

Please review my papers and send comments:

1. ” New Method to Estimate NPV from the Capital Amortization Schedule and an Insight into Why NPV is Not the Appropriate Criterion for Capital Investment Decision”… is available in the following link:

https://papers.ssrn.com/abstract=2899648

2. Title: IRR Performs Better than NPV: A Critical Analysis of Cases of Multiple IRR and Mutually Exclusive and Independent Investment Projects

https://ssrn.com/abstract=2913905

Cheers Dr Kannan

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