IRR

Internal Rate of Return provides a single number summarizing the merits of the project.

The discount rate that equates the net Present value NPV of a stream of cash out flows and inflows to zero.

often, a borrower knows the amount of cash to be received as well as the amounts and due dates of repayments, but te loan does not say the market interest rate (or it says it incorrectly). Finding the market interest rate implied by the receipt of a given amount of cash now in return for a series of promised future repayments requires a process called "finding the IRR". Some people call this the "implicit rate of return".

IRR is the internal rate of return - the interest rate that works to discount a series of cash flows to the NPV. If you know the NPV + cash flows...then what is %? ...this is the IRR.

How to calculate

Use this basic formula

PV (1 + r)^n = FV"

And, solve for r (rate %)

How to choose projects

choose any project that has an IRR greater than the discount rate

Benefits

Do not need to know the discount rate of the project, nor the relevant interest rate to discount the future cash flows. The IRR just depends on the cash flows.

Relation to the NPV rule

the IRR and NPV (net present value) analysis will usually give the same results. If the IRR is greater than the discount rate than it follows that the NPV will be positive and the project should be undertaken.

If you are comparing two projects against one another, however, it is advisable to use the NPV analysis (NPV trumps all other methods in a head-to-head challenge)

Problems with IRR

1. There might be multiple IRRs if there are more than one sign change in cash flows (from + to - and back to +).

2. Scale problem - you might get 100% return, but on a small investment...not as good as 15% return on a massive one. Your goal as a manager is not to increase the % IRR, but to deliver increased NPV of the firm. Some investments are bigger than others, and IRR analysis does not take this into account.

see capital budgeting section for more ...

Incremental IRR

subtract the smaller cash flows from the larger (initial) cash flows (investment)

Used to get around the "scale problem" listed above

Look at project A-project B. Cash flows at t=0, and future cash flows. Then do an IRR of the incremental project. This will tell you the incremental IRR in choosing A over B. Then compare this incremental IRR to the discount rate and see if its worth spending the extra money on A.

Note: you can also do the NPV (net present value) analysis on the incremental cash flows. The results should give you the same indication. If the NPV is positive, then its worth it to spend the extra $ for A.

note - do not, however, compare the IRRs of the two projects directly against each other...or, you will make the wrong decision.