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Calculating Net Present Value [Investing
Posted on December 15, 2016 @ 09:56:00 AM by Paul Meagher

If you asked me to invest $100,00 in your business in exchange for $25,000 paid out each year for the next 5 years, you might think that was a good offer. I would be making an extra $25,000 at the end of 5 years in return for the capital I invested today.

There is a potential problem with this offer that has to do with the fact that you have to compare that $25,000 earned after 5 years with what I might make if I invested my $100,000 in some other investment vehicle that returned a certain percentage of my money as profit each year. We can think of this "certain percentage" as an interest rate on my money.

If my initial investment of $100,000 has an interest rate of 8% applied each year over the next 5 years, and the interest-derived total is greater than the overall amount that would be returned by investing in your business, then it is not rational for me invest in your business. I would be losing money relative to the interest rate I'm looking for.

The comparison of a set of investment related cashflows to a discounted interest rate is captured simply and elegantly in the Net Present Value (NPV) formula that looks like this:

You might find it easier to appreciate how this formula works if you see how the NPV calculation can be implemented in the popular PHP web scripting language. In the PHP script below, after we implement the npv function we call the npv function with an interest rate and cash flow series that evaluates the investment offer described above.

<?php
/**
* Calculates total present value of a time series of cash flows.
*/
function npv($rate$cashflows) {
  
$total 0.0;
  foreach (
$cashflows AS $time=>$cashflow
    
$total += $cashflow pow($rate$time);
  return 
sprintf("%01.2f"$total);
}

// interest rate 
$rate      0.08
// cashflow series 
$cashflows = array(-1000002500025000250002500025000);
// calculate npv
$npv       npv($rate$cashflows);
// print npv result
echo "NPV is $ $npv<br />";
?>

The output of this script is: NPV is $ -182.25. This tells us that we would be losing $182.25 if we made this investment, relative to an interest rate of 8 percent. If we used a more achievable "interest rate" of 4 percent instead, then the NPV is $ 11295.56 which is a positive return that we might be inclined to invest in (would depend on what the NPV of our other potential investments are). The NPV of our investment is a more realistic assessment of what the investment return would be after 5 years that the undiscounted amount of $25,000.

Personally I find some of the terminology used to describe NPV a bit confusing. It may be easier to understand what NPV is all about if you play around with different interest rates and cashflow series using excel or a program like the one above. Note that in the program above the first value in your cashflow series is the proposed investment amount and is always negative. After that are the cashflows you expect for each year of the investment. You can learn more about the Net Present Value formula in How to Evaluate a Business Investment Proposal (where I got the formula displayed above). I encourage you to plug the interest rate and cash flow series in their example into the script above to convince yourself that it can be used to calculate NPV.

If someone asks you what the NPV of your investment offer is, you could say that it is X assuming an interest rate/discount rate of Y percent. That would tell an investor more about your investment offer than simply giving them the non-discounted amount that they might make after Z years. It tells them more because it is compared against an interest rate that might otherwise be earned on an invested amount.

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