Present and Future Values
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Net present value - NPV

The idea of using the present value to estimate the worth of a sum of money received in the future can be extended to a cashflow. If there are a series of cash amounts that become available on different dates then the best way to gauge their value is to reduce each one to its present value and then sum them to form the ‘Net Present Value’.

That is if $Si is recieved at the end of time period i then the NPV is given by:

NPV= S1/(1+I)+S2/(1+I)^2+S3/(1+I)^3
....Sn/(1+I)^n

That is, the NPV is sum of all of the cash sums each one discounted by the appropriate factor.

In more mathematical terms the NPV is

form1

For example, if an investment promises to generate a cashflow of $100 at the end of the first year, $200 at the end of the second and $500 as a closing payment then the Net Present Value is:

 =100/(1+I)+200/(1+I)^2+500/(1+I)^3

where I is the effective annual rate of interest.

If I is assumed to be 8% then the NPV is $660.98 which should be compared to the total income of $800.

Spreadsheet NPV

Most spreadsheets have an NPV function which will calculate the present value of a cashflow:

 NPV(I,range)

where range is the part of the row or column that holds the cashflow values.

An alternative form is often provided:

 NPV(I,list of values)

where the values are entered directly into the formula.

The cashflows are assumed to arrive at the end of equal periods and the interest rate specified has to be appropriate for this period.

For example, in the case of the cashflows described earlier, the spreadsheet shown in Figure 1 demonstrates the two methods of calculation - calculating the PV for each individual value and then adding the results up or more directly in one step using the NPV function.


npv

Figure 1:

 

The cashflows are entered into B3..B5 and the present values of amount is calculate in column C. The NPV in C7 is obtained by summing the present values listed above. That is in C3 the formula is:

=PV($B$1,A3,,-B3)

which is copied down the column and summed in C7.

Alternatively the formula:

 NPV(B1,B3..B5) 

entered into D7 calculates the NPV of all of the values in one step.

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