A dollar next year is worth 95 cents today

A payment's date is part of its price

A payment of $100 due next year is not worth $100 to you now. Aswath Damodaran, who teaches valuation at NYU Stern, gives three reasons a future dollar is worth less than one in hand. People would rather spend now than wait. Inflation eats away at what the money will buy. And the payment promised for later might never arrive.¹ The one thing you cannot do is line up cash from different years and add it, any more than you can add distances measured in different units. The dollars have to be carried to the same point in time first.¹

The tool that carries them is the discount rate. It is an opportunity cost: the return you could earn on your next best alternative, and so the return you give up by waiting for this payment instead.¹ It helps to attach a real number to it. The safest alternative most investors have is lending to the U.S. government, and on July 31, 2026 a ten-year U.S. Treasury paid 4.75 percent a year.² The Federal Reserve reads the same anchor independently: its ten-year constant-maturity series put the yield at 4.68 percent on July 30. The small gap is a matter of construction and date, a constant-maturity figure a day earlier against the Treasury's par yield, not a disagreement about the rate.³ A Treasury carries almost no risk that the payment fails to arrive, so 4.75 percent is close to the pure price of waiting.

One payment, moved back a year

Start with the rate going forward, where the intuition is easy. A 4.75 percent annual return means $100 today becomes $104.75 in a year, the way 50 miles per hour means you cover 50 miles in an hour. The rate is just how fast money grows. Discounting runs the same rate backward. To end up with $100 a year from now, how much do you need today? Exactly the amount that grows to $100 at 4.75 percent. That is $100 divided by 1.0475, or $95.47. You can check it: $95.47 earning 4.75 percent gains $4.53, which brings it back to $100. So a $100 payment due next year is worth $95.47 now, and the speedometer has done its job and can be put away.

Why divide by 1.0475 rather than subtract 4.75 percent? Because the return compounds. It is earned on the whole balance, and a year of growth multiplies that balance by 1.0475, so a year of discounting undoes the growth by dividing by 1.0475. Subtracting would treat the return as a flat, one-time toll, which is only right for a single year and wrong the moment there are several. Discounting is compounding read in reverse, the same growth factor turned into a divisor.⁴ To move a payment back two years you divide by 1.0475 twice; to move it back t years you divide by 1.0475 raised to the power t. That is the whole formula, and it holds for any cash flow and any rate.

From one payment to a stream

Investments rarely pay once. They pay a stream: a little next year, a little the year after, on down the schedule. Once every payment can be carried back to today, they are all in the same units, so you can finally add them. The present value of a stream is the sum of the present value of each payment, \text{PV} = \frac{CF_1}{(1+r)^1} + \frac{CF_2}{(1+r)^2} + \cdots, each term discounted by its own number of years.¹⁵ The table below runs an illustrative stream, $100 a year for four years, back through the 4.75 percent rate. The cash flows are a teaching example and not a real security. Only the rate is a real figure.

Four hundred dollars of future cash is worth $356.67 today. The missing $43.33 is not a fee anyone charges; it is the return you skip by holding claims on later dollars instead of dollars you could put to work now. Two simplifications keep the table clean. The rate is held flat across all four years, and real schedules can use a different rate for each year. Taxes are ignored, which Damodaran flags as its own decision every time he works an example.¹ Neither changes the machinery, only the inputs you feed it.

Risk lifts the rate and lowers the value

The 4.75 percent came from a Treasury, and that choice was doing quiet work. A Treasury is about as certain as a future payment gets, so its rate carries the price of waiting and almost nothing for the third reason a future dollar is worth less: the chance it never arrives.¹ A company's future cash is not that safe. It might come in below plan or not at all, and a saver deciding whether to fund that company will demand extra return for taking the chance. So a risky payment is discounted at a higher rate: the risk-free figure as a floor, plus a premium for the risk on top of it.⁶

That higher rate is the cost of capital the previous lesson built. It weighed together what a company pays lenders and what its shareholders require, and the shareholder piece is exactly this risk premium sitting above the risk-free rate. The same number now has a second job: it was the hurdle a company's return had to clear, and it is also the rate you discount that company's future cash at. Raising the rate makes every divisor in the table bigger, so the value today falls. Run the same four years of $100 at an illustrative 10 percent, the kind of rate a risky business might face, and the stream is worth about $317 today rather than $357. The riskier the cash, the steeper the discount, and the less a future dollar is worth now.

Valuing cash that never stops

A four-year table has an obvious limit. A healthy company is not expected to pay out for four years and shut down; it is expected to go on producing cash indefinitely. You cannot add infinitely many discounted terms by hand, but you do not have to. A constant payment that continues forever, a perpetuity, has a closed form: the payment divided by the rate, \text{PV} = CF / r.¹⁷ If the payment instead grows at a constant rate g every year, the value has a shortcut too.

Two details decide whether the shortcut gives a sane answer. The CF_1 on top is next year's payment, not this year's, a step ahead of where you are standing. And g has to stay strictly below r. If growth equals or beats the discount rate, the denominator hits zero or turns negative and the formula returns a meaningless value, so this is a hard constraint and not a footnote.⁸ When growth is zero the growing form collapses back to the plain perpetuity, CF / r.⁸

This shortcut is how a full valuation handles the years it cannot forecast one by one. You discount a decade of estimated cash flows in a table, then use a perpetuity to stand in for everything after it, a single figure called the terminal value. Building that full model, projecting the cash flows, choosing a growth rate, and pinning down the cost of capital for one specific company, is a later lesson. The point to carry out of this one is narrower. Every piece of that model is the discounting you just did by hand, run on longer schedules.