Opportunity cost of money: what you give up

Money is finite, so committing it to one thing takes it away from everything else. Opportunity cost is the value of the next best thing you gave up. Not the average of the alternatives and not their sum: only the single best one you would actually have chosen.

Two things follow from that definition, and both are easy to miss.

The first is that opportunity cost exists even when no money moves. Cash sitting in an account that pays nothing has an opportunity cost equal to what the same money would have earned in the account you would otherwise have used. So does a car you keep rather than sell, and so does an hour of your evening.

The second is that nothing records it. Your bank statement holds the accounting cost, which is the price. There is no column anywhere for the return you did not get, because no transaction happened. Opportunity cost stays invisible unless someone goes and works it out, which is exactly why it drops out of the decisions that turn on it.

Every money decision has the same shape once you look for it:

• Spending. You give up the price and the growth that price would have produced.
• Holding cash. You give up the extra return the next best home for it would be expected to produce, and you buy certainty and access with the difference.
• Paying down debt. You give up whatever else the money could have done, and you receive the interest you no longer owe.
• Holding one investment. You give up the return of every other investment you could have held instead.

The time value of money puts arithmetic behind all four. A discount rate is an opportunity cost with a decimal point in it.

The price is what leaves your account. The cost is the price plus the growth that money would have produced over the time you would otherwise have held it.

Those two numbers separate fast, because the thing between them is compounding rather than addition. $5,000 at 6 percent compounded monthly reaches $9,096.98 in ten years, so $4,096.98 of the full cost never shows up on any receipt. The multiplier over that decade is 1.819397, and because it multiplies, the gap keeps widening for as long as the money would have stayed put.

Two things about that figure. The 6 percent is an assumption rather than a promise, so the whole number moves with the rate you feed it. And it is a nominal figure, which means $9,096.98 of ten-year money will not buy what $9,096.98 buys today. Choosing the rate, below, is where both of those get handled.

Recurring spending is where the effect is largest and least visible, since each payment is small enough to wave through. $50 a month at the same 6 percent runs to $23,102.04 after twenty years against $12,000 actually paid in, which makes the growth given up, $11,102.04, nearly as large as everything that went out of the door. The future value of an annuity calculator does that for any payment and term, and the compound interest calculator above does it for a lump sum with or without deposits.

One rule keeps this honest: use the horizon you would really have held the money for. If it would have gone on something else in three years, three years is the number. Stretching every purchase to a forty-year horizon makes the arithmetic true and the claim false, because forty years of untouched growth was never the alternative on the table. The horizon is a fact about you, not a dial to turn until the answer looks impressive.

Repaying a balance that charges 18 percent buys a return at that same 18 percent, on every dollar of interest you would otherwise have gone on to pay. Interest you no longer owe is money you keep, in exactly the way interest earned is money you keep, and the two are the same object seen from opposite sides. So the question is never whether to be responsible. It is a rate comparison, and the rate on the debt is one side of it.

Put the same $5,000 in front of both uses over three years. Left on a card charging 18 percent compounded monthly, the balance climbs to $8,545.70, of which $3,545.70 is interest. The same $5,000 invested at 6 percent compounded monthly earns $983.40 over those three years. The debt meter runs more than three and a half times faster, and it runs whatever markets do.

Three details sharpen that comparison rather than complicate it.

• Certainty. The return on a payoff comes out of the loan agreement rather than out of a market, so it does not depend on how investments perform. It is not permanent: most card rates are variable and can be repriced, so what is settled is the interest avoided at whatever rate is in force, not the rate itself forever. An investment return, by contrast, is an expectation with a range around it, and that is worth less than the same number arriving whatever happens. Setting 18 percent contractual against 6 percent expected understates the gap.
• Tax. The general point travels: interest you avoid usually arrives untaxed, while investment returns are usually taxed at some point unless they sit in a sheltered account. The specifics are national and change with legislation. In the United States, personal credit card interest is not deductible for individuals, while mortgage interest and student loan interest run under separate rules of their own. Whatever your country does, compare after tax with after tax rather than headline with headline.
• Access. Money used to repay a card is out of your hands unless the card has room left on it, and an issuer can cut or close a line, so that room is not a buffer you control. It is why a cash buffer is usually treated as coming before either use, and why liquidity carries a value no rate captures.

One case is usually put above the comparison: where an employer matches retirement contributions, the match is a return on the money before any rate question is reached, and few debt rates compete with it. Not every job offers one, and vesting rules decide when it is genuinely yours. In the United States that is typically a 401(k) match, and other countries have their own arrangements, so check what your own scheme actually does. Beyond that, the debt-to-income calculator shows how much of an income the existing payments already claim, which is the first thing to know before deciding how much is genuinely spare.

The rate is the whole argument. Change it and the same decision flips, so picking it deserves more thought than the arithmetic that follows it. Four rules cover most cases.

• Use the return you would genuinely have got. Not the best return available to anyone, and not the best year you remember. If the money would have sat in a savings account, the savings rate is the honest number.
• Match the risk. A certain return and an uncertain one are not comparable at face value. The uncertain one has to clear the certain rate by a risk premium before it wins, which is the same operation as marking its expected return down to what it is worth as a certainty. Running it the other way, adding the premium to the risky side, rewards an option for being risky. Risk and return covers the adjustment.
• Take the highest honest hurdle first. Anyone carrying expensive debt has that rate as the hurdle for anything else the money could do, since paying it down already returns that rate without market risk. The cash buffer and any employer match, above, are the usual exceptions.
• Work after inflation. A return that buys less each year is not the return you think you are earning.

That last rule hides a small trap. Real and nominal rates compound together rather than adding, so $(1 + r_{\text{real}})(1 + i) = 1 + r_{\text{nom}}$ and the familiar subtraction is only an approximation. At 6 percent with 3 percent inflation the real rate is 2.9126 percent rather than 3 percent, overstated by 0.0874 percentage points. That is a rounding error at these levels and a serious one when rates are high, because the overstatement equals the real rate multiplied by the inflation rate, so it grows as either one grows. The real return calculator converts either way, and inflation and purchasing power covers what the adjustment is doing.

Whichever rate you settle on, match both sides throughout. Compare after tax with after tax, and today's prices with today's prices.

Opportunity cost is a lens, not a verdict, and four failures all come from forgetting that.

Treating a purchase as a pure loss. It is a trade, not a leak. The framework prices what you gave up and says nothing about what you got, and a trip you would remember for thirty years can beat a fund balance comfortably. The number is an input to the decision rather than the decision.

Assuming the money would have been invested. This is the flaw sitting inside every calculation that turns a daily coffee into a retirement. The arithmetic is right and the premise usually is not, because money that did not go on coffee would mostly have gone on something else rather than into a fund left alone for forty years. Only count an alternative you would actually have taken.

Confusing it with sunk cost. Opportunity cost looks forward, at money you still hold. Money already spent has no opportunity cost left, so it cannot argue for finishing a project or holding a losing position out of loyalty to what it already ate. The only live question is what the money and time you have now could do next.

Charging cash for the job it is doing. An emergency fund is expected to earn less than a stock fund over a long horizon, and that difference is not an error waiting to be corrected. It is the price of the money being there on the day something breaks, and that price buys something real. The same goes for a deposit being saved for a house next year. Money with a job and a date has a different next best use from money with neither.

One pattern runs through all four: comparing against a fantasy alternative instead of the one you would have chosen.

Most decisions do not need the arithmetic. Three filters catch the ones that do.

• Size. Is the amount large next to what you have? A big one-off is worth ten minutes.
• Repetition. Does it recur? A small monthly amount can end up costing more than a single large purchase, because every payment starts compounding of its own and more keep arriving. Whether it does is a question of size and term, so work it out rather than assume it either way.
• Horizon. Would the money otherwise have been left alone for years? If it was going to be spent in a few months anyway, the growth given up is small and the sum is not worth doing.

Fail all three and the honest move is to decide and get on with it, because deliberating has an opportunity cost of its own.

For the decisions that pass, three habits do the work of a spreadsheet.

Write down one hurdle rate and reuse it. Most people have a single obvious next best use, usually a savings rate, an expected portfolio return, or the rate on their most expensive debt. Choosing it once takes the argument out of every later decision.

Use the rule of 72 for mental arithmetic. Divide 72 by the rate to get the doubling time, so 6 percent doubles money in roughly twelve years. Something you would otherwise have held for twenty-four years costs about four times its price, and you can get there without opening anything. It is an approximation, closest for rates in the middle single digits and looser at either extreme, so use it to decide whether a number is worth computing rather than as the number.

Ask the question backwards. Instead of "should I spend this?", ask "if this money were already invested and growing, would I sell it to buy this?" It is the same trade seen from the other side, and it is much harder to answer carelessly. When the answer is close, the compound interest calculator at the top of this page settles the number.

This is one instance of a general idea in economics, where the cost of any choice is the value of the best option given up rather than the money spent: opportunity cost.