# Chapter 10 Video: EV

Uncertainty In Future Events

Transcript Area

In this el…excel tutorial I’m going to be talking to you about expected value. I want you to know that in..in this particular chapter this is the first of a series of three that will relate to each other. So, you need to watch this video first. Okay, basically what expected value is, is where to calculate it, each outcome is weighted by its probability and the results are summed. So, notice in this project we have 3 different annual benefits that we think are possible plus the probabilities. We also have a couple expected lives in here and their probabilities. We also have an initial cost of \$20,000 and our interest rate is 10%. So, the first thing we want to figure out is the expected value.

Which I said is outcome is weighted by its probability. So, you need to multiply the outcome that you’re looking for times its probability. Which you’ll notice that it’s done here in..in D6. It equals B6 times C6. Which is the outcome we’re looking at times its probability. Now to do the other three columns I can simply drag it down. Notice how increments to B7 times C7 and so on. So, our expected value over benefit is simply the sum of those products. So, it equals sum, highlight that, click and we’re done. Now, if this seems too many clicks, too many calculations for you, another way that you can calculate the same thing is this. I’m going to delete this for you.

You can do equals, sum product, S. U. M. P. R. O. D. U. C. T. And what you do is you highlight your first array, which is the 3 different annual benefits we think we could have, comma, our second array, which is their corresponding probabilities and just close our parentheses and notice we get the same answer. So, go either way, if you feel good to have the steps to understand, go ahead, or you can do this way. Now we need to do the same thing on our life. Notice that we’ve done the multiplication, we’ve drug it down, and then here we’re simply going to sum the product. And you can see that we get 10 years. And I do not need decimals on my years so I’m simply clicking them out. Now that we’ve taken to account our..our different benefits with their different probabilities, our different expected lives with their probabilities, now we can figure out the present worth of our expected values.

So, to do this, what you’re doing now is you’re going to do equals, present value, our rate is the 10 percent found in B3, our year is going to be our expected value for the years and our payment is going to be negative our expected value of our benefits. And remember that sitting back there, already at the present, is the \$20,000 that we invested. So, in this case, we get a present worth of our earned value, or I mean expected value. Sorry I keep saying the earned when it’s expected value, is \$19,000, almost \$20,000. Which means your project is viable because it’s above 0. So, in this tutorial I’ve shown you how to use probability in relationship to..to different benefits that you might have, or different expected values. By using those expected values you can get a better feel for when you have probability mixed in with your economic analysis.