In this screencast, I'm going to talk about cash flows and net present value. First of all, what is cash flow? Cash flow is a real or virtual movement of money. Typically, it's generally lumped into sales and expenses, so two general categories. A future cash flow must be discounted to the present value. We're going to talk all about discounting and the need to do this in this screencast. Basically by discounting future cash flows, we can normalize it or allow us to compare to present value. So instead of comparing apples to oranges, or future values to present values, we can just normalize it. So we are comparing apples to apples and oranges to oranges. Different years of a company's operation can have drastically different cash flows. For example, startup costs. Let's start out this discussion by answering this question. Which is worth more, a $100 bill in our hands today or a $100 bill in our hands in 2 years from now. If you selected A, you are correct. A $100 bill is worth more today than a $100 bill in 2 years from now since that a $100 today can be invested and will therefore be worth more than a $100 in 2 years from now. You should have learned about this in the screencast about time value of money. There are two ways of comparing cash flows today versus in the future. First, we could compare the present value of something today versus in the future, or we can compare the future value. So we can compare the future value of today's money to a future value or we could take a future value and normalize it to the present value, and so we can compare present values. Recall these two formulas, we have the future value is equal to the present value times 1 plus the interest rate for that period raised to the number of periods. So that's our future value equation. In terms of present value, we can rearrange this to present value in terms of future value. So these two are the same equation, just rearranged. I've got a little table here. We have an interest rate of 5 percent compounded annually. In terms of the present value, a $100 today obviously is worth a $100. If we use the equation for present value in terms of future value that I showed on the previous slide, we can discount. This is known as discounting the a $100 that we obtained in 2 years to today's worth, and that's known as the present value. So a $100 in 2 years from now is equivalent to a present day value of $90.70. Another way of looking at this is in terms of future value. Obviously, $100 that is given to us in 2 years is going to have a future value of a $100. We can calculate the future value of a $100 today by multiplying by 1 plus the interest rate raised to 2 years, and that means that a $100 today, is going to be equal to a $110.25 because we can take that $100 and we can invest it. In either case, $100 today is worth more than $100 in the future, regardless of if you're comparing this in terms of present value, $100 compared to $90.70, or in terms of future value, $110.25 compared to $100 in the future. Just to reiterate, the $100 future value in the upper right has been discounted. That's the important term, discounting to $90.70 in today's terms. So we can compare apples with apples. Typically, financial folks are interested in looking at present value instead of future value. So you see that term present value used a lot. So we're going to discount something in the future to today's worth and that's known as a present value. Some examples of cash flow in 5 years from now, we will need to replace the furnace in our house for $5,000. So that's 5 years from now we could compute a present day value, a present value for that $5,000, which is a future value. Another example, in 3 years from now, our company will sell a real estate investment for $500,000. This will be a positive cash flow in 3 years from now. Over each of the next 5 years, we can claim $4,000 in depreciation costs. Recall my screencast on depreciation for a particular capital expenditure made recently. We're not actually getting money for them like actual, real money, but they are positive cash flows when recorded internally in the company. You've already considered cash flows in this course. For example, a loan with monthly payments. The monthly payments are cash flows. They're constant cash flows of the same value. A savings account with monthly contributions or withdrawals, the monthly contributions and withdrawals are cash flows. In both of these examples, the periodic cash flows, are constant in value and frequency. Therefore, we used Excel functions PV, present value, FV, future value, and PMT for payment. This is what a cash flow diagram looks like for an amortized loan. We had an initial loan amount and that's a positive cash flow because we get that loan amount. But then over time, we're making constant payments over constant intervals. So these down arrows are the payments. Those are negative cash flows. However, the frequency and values of cash flows do not have to be constant and they don't have to be the same. So we can have different frequency cash flows with different values. An example of this shown in this cash flow diagram. On the X-axis here, going left to right, is the time in months. Those little red figures are the months. We have positive cash flows as up arrows, these are sales revenue or credits. We have negative cash flows going down in this diagram, those are payments or expenses. We can have the cash flows be sporadic over time and they can be different values. So we haven't considered this. You can't really use those PV, FV and payment functions so we have to use a different analysis. In particular, you can use the NPV or net present value function in Excel and that I'll be talking about shortly. So the net present value is the sum of future cash flows and the present value discounted to today's worth. The official definition of net present value. We take the present value of all of our assets and then we add up. It's okay if you don't understand what this summation sign means, it just means we're summing through all periods, 1 through period n, the cash flow in that period divided by 1 plus the interest rate in that period quantity raised to the ith power, where again, i is the period that we're considering. I've got an example of this that's going to show you what I mean by this. Example. We will receive a check for $1000 in 1 year from now. That's going to be a positive cash flow and we will have to pay $500 in 3 years from now. That's going to be negative cash flow. To calculate the net present value for this situation, let's just consider an annual interest rate of 0.05. We can calculate that as we have a $1,000 that we receive in 1 year from now, that's a future value of $1,000. We have to discount it to a present value by dividing by 1 plus the interest rate raised to the number of periods from now, which is 1 year. Three years from now, we're going to have to pay $500. We can discount that in today's terms, $500 in 3 years from now is less than $500 today. So we take our $500 and we discount that, we divide by 1 plus 0.05 raised to the 3rd power, because that's 3 years from now. We sum those 2 and that means the net present value for this situation is $520.46.