# Does the Net Present Value of Future Cash Flows Increase or Decrease as the Discount Rate Increases?

A higher discount rate reduces net present value.
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Net present value, or NPV, expresses the value of a series of future cash flows in today's dollars. It stems from the observation that there is time value to money -- people must be compensated to induce them to give up some money now in order to receive more money later. That compensation is interest and the required interest rate used in the NPV calculation is called the discount rate. A higher discount rate reduces net present value. Businesses can use NPV to decide in which projects to invest.

## The NPV Equation

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NPV is the sum of periodic net cash flows. Each period's net cash flow -- inflow minus outflow -- is divided by a factor equal to one plus the discount rate raised by an exponent. NPV is thus inversely proportional to the discount factor – a higher discount factor results in a lower NPV, and vice versa. The exponent is the period number: zero for today, one for first future period, two for the second future period, etc. Since the exponent, and hence the divisor, increases with each period, the contribution of each net cash flow in the series to the total NPV decreases with time.

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## The Discount Rate

The discount rate is an interest rate that reduces the value of a future cash flow. The way many businesses look at the discount rate is to consider it the opportunity cost of investing the firm's money in a particular project. In other words, what is the best rate of return the firm would experience if a proposed project's funds were used in a different project instead? If we determine that the discount rate should be, say 5 percent, we can use that rate to determine the NPVs of both projects. The higher NPV wins.

## Money is Good

The NPV calculation works because it assumes certain attitudes about money on which most people agree. The central assumption is that having money now is better than having it later. When you have money now, you know exactly how much you have. Future money carries risk – for example, how can you be sure of the amount you will actually receive? The discount rate must be set high enough to compensate you for this risk. The higher you set the discount rate, the more you value current money over future money.