Internal rate of return (IRR)

[Lorenzo Incarnato s220426]

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Abstract

The Internal Rate of Return (IRR) is a powerful discounted cash flow method used in capital budgeting and corporate finance to estimate and evaluate the profitability of potential investments. Keeping in mind the formula for the Net present value (NPV), the IRR is defined as the discount rate that makes the present value of the costs (negative cash flows) of an investment equal to the present value of the benefits (positive cash flows). In other words, the IRR is the discount rate that gives a net present value of zero when applied to the expected cash flow of a project. This rate of return is called internal because the formula predicts a rate that depends only on the project, more precisely on the project's cash flows, and does not depend on external factors such as market interest rates or inflation. One of the main advantages in using the internal rate of return to evaluate project investments, compared to other methods such as the Payback period or the Benefit-cost ratio, is that IRR reflects the time value of money. In general, due to the relationship between NPV and IRR, the higher the Internal Rate of Return of a project, the more desirable the investment to be made. This article shows also the limitations of the internal rate of return; however, when the IRR is unique, it provides relevant information about the return on investment and is also used as a measure of investment efficiency. In fact, according to academic research, three-quarters of Chief Financial Officers use the IRR method to evaluate capital projects.

Time value of money

100 000$ today has the same value one year from now? This paragraph explains, including examples, one of the core concepts in finance which is the Time Value of Money (TVM).

The TVM is the concept for which a certain sum of money available today can be invested and grow according to the interest rate, generating a higher amount of money in the future. This close connection between money and time is called the Time Value of Money and it is straightly related to the interest rate concept, Before answering the initial question, it is necessary to understand the concept of interest rate [%], which is the amount of interest due per period, as a proportion of the amount deposited/borrowed.

In order to clearly understand the concept of the Time Value of Money, it is necessary to introduce three fundamental terms: the present value (PV), the interest rate (r), and the future value (FV).

   The Present Value [$]: is the sum of money available right now.
   The Future Value [$]: is the value of a current asset (present value) at a future date based on an assumed rate of growth (interest rate). 

So, it is easy to understand that the answer to the initial question is: NO. In fact, applying the formula of the future value (FV):

$FV = PV (1 + r) = 100.000$ (1 + 0.03) = 103.000$$

Example to answer the initial question: 100 000$ invested today with an interest rate of 4% yearly will match to 104 000$ next year. If the present value is not invested, the value of money erodes it over time because you have lost the additional money it could have earned over that time if invested.

Hence, a certain sum available in the present could be invested and grow according to the interest rate. The amount of money cumulated in the meantime is the Time Value of Money, mathematically TVM = FV - PV.