In this video I want to discuss a technique for dealing with projects that have unequal lives when we're comparing different investment projects we would ideally like to compare projects that have the same life. And if you think about it, that makes a lot of sense, if one project lasts for five years and one project lasts for ten years, when the five-year project ends, what are we going to do? Well, we might not be able to do anything, but perhaps we could do something we could replicate the project and. In another video I discussed the concept of replication, which was simply that we would just do project. The shorter term project, a second time until its life was exactly the same as the longer term project here, we're going to talk about a different technique, one that's referred to as equivalent annual annuity. And what this approach does is it takes the NPV from each project and spreads it over the life of the project. So let's, take a look at an example project, a cost, seventy thousand.

And last for. Three years project, B cost, eighty-five thousand and last for six years. Now, the NPV at a weighted average cost of capital. Ten percent is a little over eleven thousand for project, a and a little over 19 thousand for project. Two B. Now, if we were simply accepting the projects based on NPV, we would choose B over a because it has a higher NPV, and therefore adds greater value to the firm, but that's not really fair because project a lasts for half the time of project B. So what are we going to do?

Well?. One way we can deal with this problem is we want to spread the NPV of project an over its three-year lifespan. And we want to take the NPV of project B and spread it over its six-year lifespan. So even though project B has a much higher NPV. It spread over more years.

And project DES has a smaller NPV, but it's spread over only three years as opposed to six. So here I've just shown you how you can do this on your financial calculator, but you could certainly do this in Excel or any other spreadsheet. So. What we're trying to find is the annuity or in terms of the financial calculator, the payment PMT, so, and it's three because the project lasts for three years, we have a 10% cost of capital, and we're going to spread this NPV over these three years. And we compute the payment, or we're computing, the annuity that would result from having eleven thousand two, seventy-seven, forty-four in the account spread over three years. We also do this for project B now, project B lasts for six years and has an NPV of. Nineteen thousand thirteen dollars and twenty-seven cents.

And we calculate this EA a equivalent annual annuity of four thousand, three, sixty-five, fifty-nine. And we can see that once we spread them over the life of the project, an actually has a higher EI a. So even though I had a lower NPV we're spreading this amount of money or this amount of net present value over a much shorter time period. And it turns out that an is the better project. So this is another approach.

We use for dealing. With projects that have unequal lives this equivalent annual annuity where we're spreading the NPV over the life of the projects.

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