# Equivalent Annual Costs

In the previous articles we have seen how we can convert a possible future stream of cash flows to its present value today to make investment decisions. We choose amongst competing projects and the one with the highest NPV is usually selected. But sometimes this may not be the appropriate thing to do.

**Example:**

Consider the fact that the firm has to choose between two types of software to run its day to day operations. Now both these software are identical in the sense that they do the same job in pretty much the same manner. However, their costs are different and so is the duration of their licenses.

Software A costs $20,000 upfront, has a life of 4 years and the company will have to pay $2,500 as annual maintenance charge to the vendor. Software B, on the other hand costs $10,000 upfront requires an annual maintenance charge of $3000 for 3 years which is the duration of its license. Now, how does the company make a financially prudent decision and choose the more cost effective software.

**The Problem:**

Under normal circumstances, this would have been a pretty straightforward decision. The NPV of both the software could have been computed. Since we are talking about costs and not revenues, we would have selected the one with the lowest NPV. But there is a slight problem. The life of both the software is different. One will have to be renewed after 4 years while the other will have to be renewed after 3 years. So, the value of a future cash flow is contingent upon the decision that we make now. So, just looking at the NPV will be making a decision with incomplete information! The bottom line is that since the life of both these software is different, we can’t really decide amongst them on the basis of NPV alone.

### The Concept of Equivalent Annual Costs

Here we have the concept of equivalent annual costs to the rescue. The approach to the problem is simple if we look at it from this point of view. We now have lump sum NPV’s which can be derived from the costs that have been stated above.

Assuming a discount rate of 10%, the NPV of software A and software B is $25,386 and $15,873 respectively. Our common sense approach would tell us to chose software B because of its lower NPV, but we just discussed why that would not be a wise choice because the duration of their licenses is different.

So, instead we start to view them as if we have taken these software on rent. This means that we will convert the NPV for software A into an annuity for 4 years, whereas that of software B for 3 years. By doing so, we will be able to bring both the costs down to an annual level. It is like choosing between software A or software B on the basis of which has the lowest annual rental payment. This nullifies the fact that they have different license durations.

### Solution with Equivalent Annual Costs

Now, if we consider the present value of software A as $25,387, assume a 10% discount rate, the annual cost would be $8,008 for a period of 4 years.

Similarly, the present value of software B is $15,873, assuming the same 10% discount rate, the annual cost of software B would be $6,382 for a period of 3 years.

Since, the costs are annual, the number of years really do not matter. We are therefore facing a choice between an annual rent of $8,008 and $6,382. $6,382 is the lower rent and therefore software B is a more financially prudent choice.

Now, just to clarify, we are not taking the software on rent. We are buying it outright. The assumption regarding renting out the software was a metaphor to ensure that the concept of equivalent annual costs becomes easier to understand.

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