Wednesday, September 12, 2007

Present Value Calculator

Topic: Handy annuity calculator for doing back-of-the-envelope design...

Present & Future Value Calculator

PVoa = PMT [(1 - (1 / (1 + i)^n)) / i]


PVoa = Present Value of an Ordinary Annuity
PMT = Amount of each payment
i = Discount Rate Per Period
n = Number of Periods

Annuity calculations are explained with intuitive graphics at this Investopedia link.

Let's say your energy efficiency measure is projected to save $7,000 per year. About how much should we be willing to spend to obtain this savings?

Projecting lifecycle of 20 years and a conservative 5% rate of return, the present value of $7,000 is calculated using the 'Present Amount of an Ordinary Annuity' calculator, at the lower left of the page link above. Plugging $7,000 into the 'Payment Amount' field, 5% into the 'Interest Rate' field, and 20 years into the 'Number of Payments' field results in about $87,200 of net present value. For a new project, this amount may be a justifiable first-cost premium to realize the savings, all other factors equal.

However many companies have a much shorter time frame for justifying capital improvements, and/or may value their cost of capital more highly than 5% -- note that here a higher interest rate reduces the net present value.

For comparison,

  • What is the present value of 20 years worth of $7k savings at a 7% rate of return?
    Answer = $74,200, about $13,000 less than at a 5% return rate.
  • What is the present value of 7 years worth of $7k savings at a 6.5% rate of return?
    Answer = $38,400, a bit more than half of the previous
  • Above answers are rounded to the nearest hundred dollars.
Thanks to the University of Illinois at Chicago


Charles Peake said...
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Rozer Layer said...

The present value of an annuity-due is used when the investor purchases an annuity that pays at the beginning of each period. Thanks for your nice post over present value calculator.

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