Why a dollar today is worth more than a dollar tomorrow

The choice

Suppose someone offers you $100, and lets you choose when to take it: today, or one year from now. Receiving it today gives you an additional choice. Grant opens his video on this topic with the same choice, and his answer is the one this page builds on: money you hold now is money you can put to work now.

That is the whole principle. A dollar received today can be used today: invested, lent, spent on equipment that produces income, or used to pay down a debt that charges interest. A dollar received a year from now can only start doing any of that a year from now. The year in between is lost. What the money would have produced in that year is what you give up by waiting, and giving up the best alternative is what economists call an opportunity cost.

The time value of money is that opportunity cost, measured. It is why money at different dates cannot simply be added or compared at face value. A dollar is not just an amount. It is an amount at a time.

A worked example: when waiting stops costing you

This example is hypothetical, and it follows the one in Grant's video. Assume that money put to work earns 10% a year, and that the later payment is just as certain to arrive as the earlier one, so the only difference between the two is time.

1. 1Today

   Take the $100 today

   You hold $100 and put it to work.

   Take the $100 in a year

   You hold nothing yet.

2. 2During the year

   Take the $100 today

   The $100 earns 10%, or $10.

   Take the $100 in a year

   Nothing to put to work. The $10 is never earned.

3. 3One year from now

   Take the $100 today

   You hold $110.

   Take the $100 in a year

   You receive $100 and hold $100.

Same $100, same date at the end. The early dollar ends $10 ahead, and that $10 is the opportunity cost of waiting.

At the end of the year, the $100 taken today has become $110. The $100 taken later is still $100. Both were "$100" when they were offered, and one is now worth $10 more. Nothing appears on any statement for that $10: it is a return that was never earned, which is why opportunity cost is easy to miss.

The same arithmetic tells you how large a later payment must be before waiting stops costing you. The later payment has to match what the earlier money would have grown to:

At a 10% return, $110 a year from now and $100 today are worth the same. Anything less than $110 later is worse than $100 now. Anything more is better.

Waiting longer costs more than proportionally, because each year's return also earns a return in the following years:

1. Amount received today$100
2. ×1 + 10% return, year 11.10
3. =Value at the end of year 1$110
4. ×1 + 10% return, year 21.10
5. =Value at the end of year 2$121

The amount the earlier money reaches by the later date, in dollars. A later payment must reach at least this to be worth as much.

Amount today

The money received now, in dollars.

Annual return

What the money can earn in a year if it is put to work, as a percentage. In this example it is an assumption, 10%, and the same promise of payment is assumed to be equally certain either way.

Two years of waiting cost $21, not $20. The extra dollar is the second year's 10% earned on the first year's $10. This is compounding, and it is why long delays matter much more than short ones.

Run the arithmetic backward and you get the other half of the idea: $110 a year from now is worth $100 today ($110 ÷ 1.10), and $121 two years from now is also worth $100 today. Turning a later amount into its equal today is called finding its present value, the subject of the next topic in the path.

Where accounting uses it

One place US GAAP applies this principle directly is a sale whose payment timing amounts to a loan. Under ASC 606-10-32-15, a business adjusts the price of a sale for the time value of money when the agreed timing of payments gives the customer, or the business, a significant benefit of financing. The objective in 606-10-32-16 is to record revenue at the cash selling price: what the customer would have paid in cash when the goods were delivered.

Here is the same arithmetic in that setting. Brookfield Tools, a hypothetical seller, delivers equipment whose cash price is $100, and lets the customer pay $121 in two years instead. Assume 10% is the right financing rate and the financing is significant. Brookfield records $100 of revenue. The other $21 is not revenue for the equipment. It is the price of lending the customer $100 for two years, and ASC 606-10-32-20 requires it to be presented as interest income, separately from revenue.

1. Revenue at the cash selling price$100
2. Interest income, year 1 (10% of $100)+$10

   Reported as interest, not revenue.

3. Interest income, year 2 (10% of $110)+$11

   The second year earns on the first year's interest too.

4. Cash the customer pays at the end of year 2$121

Grey bars are totals. Green bars with a plus sign add; clay bars with a minus sign subtract. The thin line marks zero.

Assumes the 10% is the appropriate financing rate and the financing is significant. Both are judgments the standard governs.

There is a practical expedient. Under ASC 606-10-32-18, a business may choose not to make the adjustment if, at the start of the contract, it expects the customer to pay within one year of delivery. The relief is optional. It does not mean the financing effect within a year is always small: at a high rate it can be significant.

A common misconception

The most common explanation is that a dollar today is worth more because of inflation. Inflation is a real reason a later dollar can be worth less, because it may buy less. But it is not the reason this page describes. In the example, prices never change, and the early $100 is still worth $10 more, because it earned a return that the late $100 could not.

The same goes for risk. A promise to pay later might not be kept, and a payment that might not arrive is worth less than a certain one. That is a separate discount, for uncertainty. The example removes it on purpose by assuming both payments are equally certain. Time value, inflation and risk can all make a later dollar worth less, and a market interest rate usually reflects more than one of them. Keeping them apart tells you which question you are answering: how long you wait, what the money will buy, or whether it will come at all.

Where the principle stops

The principle assumes the earlier money would be put to work. If you have no use for it and nowhere to earn anything on it, money today and money later are close to equal. Even then, money today is usually at least as good, because you can simply hold it until the later date, unless holding it costs something, such as safekeeping.

The return used to compare amounts is an assumption, and the answer depends on it. At 5%, $100 today is worth $105 in a year, not $110. The right rate is the return available on alternatives of similar risk, and choosing it is a judgment, not something this page settles.

Finally, this page explains why amounts at different dates differ in value. It does not cover how to calculate present values for longer or uneven streams of payments, or how ASC 606 and Subtopic 835-30 measure and present a financing component in detail. Readers applying the standard should read ASC 606-10-32-15 through 32-20 in full.