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# Lease Purchase Calculator

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## How to Calculate Net Present Value

Net present value (NPV) is the present value of all future cash flows of a project. Because the time-value of money dictates that money is worth more now than it is in the future, the value of a project is not simply the sum of all future cash flows. Those future cash flows must be discounted because the money earned in the future is worth less today. In order to calculate NPV, we must discount each future cash flow in order to get the present value of each cash flow, and then we sum those present values associated with each time period. ###### Where:
• = Cash Flow at time t
• = discount rate expressed as a decimal
•  = time period

You can think of NPV in different ways, but I think the easiest way is to think of it is as the sum of the present value all cash inflows, i.e. cash you earn from the project, less the present value of all cash outflows, i.e. cash you spend on the project. This way of thinking about NPV breaks it down into two parts, but the formula takes care of both of these parts simultaneously. The way we calculate the present value is through our discount rate, r, which is the rate of return we could expect from alternative projects. Say you have a dollar. If you don’t invest that dollar, you will still have that same dollar bill in your pocket next year; however, if you invest it, you could have more than that dollar one year from now. The alternative project is investing the dollar, and the rate of return for that alternative project is the rate that your dollar would grow over one year.

Just by thinking of things intuitively by the time value of money, if you have a time series of identical cash flows, the cash flow in the first time period will be the most valuable, the cash flow in the second time period will be the second most valuable, and so forth. This means that the present value of the cash flows decreases. Now, this is not always the case, since cash flows typically are variable; however, we must still account for time. The way we do this is through the discount rate, r, and each cash flow is discounted by the number of time periods that cash flow is away from the present date. This means that our cash flow for the first time period of the project would be discounted once, the cash flow in the second time period would be discounted twice, and so forth. To discount a cash flow, simply divide the cash flow by one plus the discount rate, raised to the number of periods you are discounting. This methodology follows from compound interest. Let’s take a look at an example.

#### Example  