# Present Value

IMAGINE YOU’RE a teenager, your older sister is heading off to college and she wants to take the car you share. She offers to buy you out, and says she’ll pay you \$5,000 five years from now, after she graduates. But you’d rather be paid today.

What’s a reasonable sum to ask for? The right number might be around \$4,500. If you got \$4,500 today and invested it, you’d have \$5,000 after five years, assuming you could earn a 2.13% after-tax annual return over the intervening period.

In Wall Street lingo, the future value would be \$5,000 and the present value would be \$4,500. Present value calculations crop up all the time in the financial world:

• When we use a retirement calculator to estimate how much we need to hit our target nest egg, we’re calculating the present value of the future sum we desire. Let’s say we hope to retire in 30 years with \$1 million and we think we can earn 4% a year. The present value of that \$1 million is \$308,319. Most of us don’t have that sort of money to sock away today, so instead we calculate how much we need to save regularly to hit that \$1 million—which turns out to be \$1,436 a month.
• When our employer offers to cash us out of our pension by paying us a lump sum today, it’s telling us what it considers to be the present value of those future monthly pension payments. Hint: The offer may not be especially generous.
• When research analysts argue that a company’s shares are undervalued, they typically forecast the company’s earnings for the years ahead, calculate the present value of that stream of future earnings and then compare that present value to the company’s current stock market value. The analysts likely expect the company’s earnings to grow over time. But they also apply a discount rate to those future earnings, because \$1 of earnings in the years ahead is less valuable than \$1 today.

As you’ll gather from the above examples, we often aren’t comparing just two numbers, a present value and a future value. Rather, we’re cooking up a single number for today that reflects a string of future numbers. Such calculations can be complicated, which is why folks rely on online calculators, spreadsheets and financial calculators to do the math for them.

Be warned: Present value calculations are only as good as the interest rate they assume. For instance, a calculator might indicate that we only need to make a single investment today of \$6,502 to have \$50,000 for our toddler’s college education—which sounds like a good deal, until we notice that the assumed return for this present value calculation is an optimistic 12% a year.

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