# Understanding NPV ( Net Present Value )

Net present value takes into account the time value of money. All projected after-tax cash flow from a proposed investment is discounted to the present values using a minimum acceptable rate of return.

## User Inputs

• Discount Rate

An important issue in forecasting the time value of money in budgeting decisions is establishing the appropriate discount rate to use for calculating the present value of cash flows.

We’ll need to determine some minimum acceptable rate of return on the money invested. This target rate to use as the basis for present value calculations may be at or above the cost of capital.

This is entered in cell B1 of the example below. We need to see a 12% minimum rate of return to consider this investment acceptable.

• Initial Investment

Since our initial investment occurs immediately, it does not need to be discounted.

Our net present value in this case will be calculated as the sum of the discounted net cash flows minus the initial investment.

In our example, assume we are considering an investment having a \$20,000 initial cost, entered in cell B10.

• · Cash Flow

For the purpose of simplicity, the analysis in this example will be based on annual after-tax cash flow.

In practice, our cash flow will often be measured in shorter increments, such as months and quarters.

In Row 4 of our example below, we’ll project net cash flows after taxes over the next four years to be \$4,800, \$7,200, \$9,600, and \$10,800 respectively.

## Understanding Net Present Value "the Old Fashioned Way"

In general, our investment is acceptable if it has a positive net present value. We’ll see this in cell B10, the net present value returned when we calculate it all out is \$3,722.

Since the sum of the discounted net cash flows, \$23,722 (in cell B8), is greater than the initial cost of \$20,000 (in cell B9), the investment is acceptable in this analysis.

If subtracting the initial cost from the sum of the discounted net cash flows turned out to be a negative value, then the return on investment would not have been adequate to satisfy our minimum acceptable rate of return.

Let’s have a look at the formulas:

Looking back at the first illustration, notice that the values in Row 5 range from .89

at the end of the first year, to .64 at the end of the fourth year.

This represents the value of a dollar we have today at the end of each projected year.

The syntax for the calculations in Row 5 are:

1 / (1 + Discount Rate ) ^ Year Number

The ^ (caret) is the exponentiation operator.

The Discounted Cash Flow is the result of multiplying Row 4 (net cash flow) by Row 5.

## The NPV Function

Excel provides a NPV (net present value) function to perform the discounting process with a single formula.

The following formula has been entered in cell E10 and demonstrates that the NPV function can be applied to return the same value as the result in cell B10 from the long calculation method.

=NPV(B1,B4:E4)-B9

The Excel NPV function has an assumption that the first cash flow must occur at the end of one period.

Therefore, we subtract the initial investment to get a net present value.

Here’s the syntax for the formula:

=NPV( DiscountRate , CashFlow ) – InitialInvestment