So far you have learned how to find the present value of future lump sum cash flow. Next, let's learn how to find present value of multiple cash flows. That is cash flows are more than once in the future. For example, you're supposed to receive $100 next year, $200 in two years, and $300 in three years. This kind of stream of cash flows is called multiple cash flows. In order to find present value of multiple cash flows, you need to find present value of each cash flow first and then sum the present values of each cash flow. The general form of calculating PV of multiple cash flows is the formula in the slide. That is PV = CF1/(1+r) raised to the power of 1 + cash flow in time 2 divided by the 1 + r, raised to the power of 2 +, so and so, up to cash flow in time n divided by 1 plus rate raised to the power of n years. Let's take a look at an example. Suppose you have an opportunity to invest in a business that will pay you $100,000 in one year, $200,000 in two years, $300,000 in three years, and $400,000 in four years. You can earn 10% per year compounded annually on a mutual fund that has similar risk. That means that the discount rate, you need to apply to this investment opportunity is 10%. In order to find the present value of these cash flows, you need to find the present value of each cash flow first. We can present these cash flows in a diagram as it is shown in this slide. First, let's find PV of CF in year 1 using Excel. Why donâ€™t you just start Excel in your computer and open Excel template. Since we are looking for PV we are going to use template for PV. In the template for PV, type in 100,000 for FV. Next type in 10% for RATE, and 0 for PMT. Next type in 1 for NPER. Then you get PV of 90,909.09. That is, $100,000 in 1 year, is equal to, $90,909 as of today. As you already learned, PV calculated in Excel is negative, but you interpret that as a positive value. Next, let's find PV of CF in Year 2. We're going to use the same PV template. What you need to do is to change the value for FV from 100,000 to 200,000. And the value for NPER from 1 to 2. And you get PV of 165,289.26, that is $200,000 in two years is equal to $165,289 as of today. Next, let's find PV of cash flow in time 3. In the previous solution, you need to change FV from 200,000 to 300,000, and NPER from 2 to 3. In the same template you need to change the value for FV from $200,000 to $300,000. And the value of NPER from 2 to 3. And you get PV of 225,394. That is $300,000 in 3 years is equal to $225,394 as of today. Next, let's find PV of cash flow in year 4. In the same template you need to change the value for FV from 300,000 to 400,000 and the value of NPER from 3 to 4. Then you get PV of 273,205. That is $400,000 in year 4 is equal to $273,205, as of today. Now you need to add all PVs. As you can see in this table, PV of 4 years of cash flows is $754,798. If you're asked to pay less than this amount of PV for the business, then investment opportunities worth to take. For example if the cost of investment is $700,000. Your profit is $754,798 - $700,000 of cost. So the profit is $54,798 which is called the Net Present Value or NPV for short. NPV is what you really earn after considering the cost of capital of 10%.