25.5.B.2. Internal Rate of Return (IRR)

• Definition: Discount rate at which NPV is zero. • Formula: 0=∑¿

The Internal Rate of Return (IRR) represents the discount rate that makes the net present value (NPV) of all cash flows from a particular investment equal to zero. In simpler terms, if you discount future cash flows back to the present using the IRR, the total amount you get will equal your initial investment, meaning you're neither making nor losing money on the investment.

Imagine you invest in a lemonade stand. If you want to know what rate of return you're getting, you can calculate the rate at which the present value of your lemonade sales equals the cost you paid to set up the stand. If that rate is, say, 10%, that's your IRR, showing that you're breaking even at that discount rate.

• Decision Rule: o If IRR > Required Rate of Return: Accept the project. o If IRR < Required Rate: Reject.

The decision rule for IRR is straightforward: compare the calculated IRR to the minimum required rate of return set by the organization. If the IRR exceeds this required rate, the investment should be accepted, as it's expected to yield a good return exceeding the cost of capital. Conversely, if the IRR is lower than the required return, the investment is deemed unattractive and should be rejected.

Think about a savings account that offers 2% interest. If you find an investment that promises a return of 5% (its IRR), you'd choose the investment because it exceeds your savings account interest rate. But if it only offers a return of 1%, you would likely pass on that investment, preferring your savings account instead.

• Advantages: o Considers time value of money. o Easy to compare with cost of capital.

One of the major advantages of the Internal Rate of Return is that it takes into account the time value of money, which means it acknowledges that money available today is worth more than the same amount in the future. This makes IRR a relevant metric in assessing an investment's profitability over time. Moreover, IRR provides a simple way to compare different investments against the cost of capital, making it easier for managers to make informed decisions.

Consider the decision to buy a new smartphone. If the smartphone costs $1,000 now but is expected to save you$250 a year in costs, you want to know how long it will take before those savings cover the phone's cost and how that compares to other potential purchases. By calculating the IRR, you get a clear picture of whether this is a smart investment compared to other options.

• Disadvantages: o May produce multiple IRRs for non-conventional cash flows. o Difficult to calculate manually.

While IRR is a useful metric, it has its downsides. For projects with non-standard cash flows (for example, cash inflows and outflows occurring at different times), the calculation can yield multiple IRRs, complicating the decision-making process. Additionally, calculating the IRR, especially manually or without financial software, can be challenging and time-consuming, which may discourage its use in some cases.

Imagine you're trying to calculate your savings from several projects, but different projects yield cash in different amounts and times throughout their life. It's like trying to navigate a maze with multiple exits—sometimes you end up at a dead end because your calculations lead you to more than one 'answer,' making it hard to choose the right path.

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