Capital Values, Profit, and the Political Economy of Time

In the first half of this topic we built one tool. Present value puts amounts arriving at different times onto a single ruler so they can be compared: a future amount F is worth P = F ÷ (1 + r) today, where r is the rate of interest, the rate at which a present amount grows into a future one. That is the whole kit. In this half we start using it.

Every Durable Good Is Worth the Present Value of Its Future Services

We have valued promises to pay money. The same arithmetic values any durable good, any asset that yields a stream of services over time, from a bond to a house to a machine to an apple tree. The capital value of any such thing is the present value of the whole stream of future services it will provide. That is the unifying idea behind the whole topic: a bond, a rental building, and a fruit orchard are all just streams of future value discounted to the present.

That means a good can yield income in three forms, and they all count equally. There are the services it throws off (the rent, the fruit, the coupon payment); there is physical or quality growth (the tree gets bigger, the wine improves); and there is growth in market value. A stock that pays no dividend but rises in price has still given you income, because income is the increase in your wealth, and your wealth rose. By the same logic, when you hold a painting that appreciates 5 percent a year while money invested elsewhere would have earned 6 percent, owning the painting costs you something even though it is gaining value: you are forgoing the higher return. That forgone return is a real cost of holding any asset.

Because a durable good’s value is the present value of its services, and because a stream of equal services is just an annuity, the bond table prices bonds directly. The table below shows the market price of $1,000 bonds that pay a fixed 5 percent coupon ($50 a year), at various maturities and market interest rates.

Market price of fixed-coupon $1,000 bonds (5% coupon), at alternative market rates and maturities.

Life of bond	Coupon	3%	5%	7%	10%
1 year	5%	$1,020	$1,000	$982	$954
5 years	5%	$1,092	$1,000	$918	$810
10 years	5%	$1,170	$1,000	$859	$692
20 years	5%	$1,299	$1,000	$788	$573

Read this table and the central facts about bonds fall out. A bond’s price moves inversely to the interest rate: when the market rate sits above the coupon, the bond sells below its $1,000 face value; below the coupon, it sells above face. So if a bond trades below face value, its yield to maturity, the return you actually earn, exceeds the coupon rate, because you collect the coupons plus the rise to face value at the end. And longer bonds swing far more than shorter ones, because the longer the stream, the more its present value is whipped around by changes in the rate: a one-year bond barely moves when rates jump from 5 to 10 percent (from $1,000 to $954), but a twenty-year bond plunges (from $1,000 to $573). That extra exposure is why long bonds tend to carry a higher rate to begin with. The same logic answers what changed when a building’s or a stock’s value falls: you have to ask which part of the package changed, a rise in the rate that discounts every future receipt more heavily, or a fall in the expected receipts themselves, and you read it off bonds.

Hold an Asset Only While It Grows Faster Than the Interest Rate

The capital-value idea answers a question that puzzles people: when is the best time to sell a growing asset, a stand of timber, a barrel of aging whiskey, a cellar of wine? Letting it grow adds value, so why ever stop?

The rule is clean. Keep holding the asset as long as its value is growing faster than the interest rate. The moment its growth rate slows to the interest rate, sell, because from that point the money would grow faster invested elsewhere. A tree that adds 8 percent to its lumber value this year is worth holding when the interest rate is 5 percent; once its growth slows to 5 percent, cutting and reinvesting does just as well, and any slower and you lose ground by holding. So the wealth-maximizing harvest age is wherever the tree’s own growth rate falls to the market rate, and a lower interest rate means you wait longer (the bar the tree must clear is lower). The same logic governs whiskey: age it while its value climbs faster than the rate, bottle it when the climb slows.

This optimal-timing rule has a sharp condition attached: it only works when someone owns the asset securely. An owner gains by leaving a tree standing while it still outgrows the interest rate, because the future value is his. But an unowned tree, in a forest open to all, gets cut as soon as its lumber is worth anything at all, because whoever waits loses it to whoever does not. The race to grab an unowned resource destroys the patient, value-maximizing strategy that secure ownership makes possible, our first glimpse of a theme that gets its own topic later.

Recall property rights and the commons (T5). Secure private property is what makes long-horizon investment and optimal timing possible: an owner profits by not harvesting a resource that is still growing faster than the interest rate, while an unowned, common resource gets used up prematurely as everyone races to claim it before someone else does. This premature-use problem is the heart of the “tragedy of the commons.” The elegant timing rule above tacitly assumes an owner who can capture the future payoff.

We Never “Run Out” of a Resource, Because Present Value Caps How Much It Pays to Find

The same present-value reasoning resolves one of the most durable scares in public life: the periodic warning that we are about to run out of oil, or copper, or some other natural resource. These predictions are often built on a real statistic, the known reserves of the resource, the quantity that has actually been located and measured. The mistake is treating that figure as all the resource there is. Known reserves are not a measure of what lies in the ground; they are a measure of how much it has so far paid to find.

Finding a resource is itself a costly investment. Exploring for oil, drilling test wells, most of which come up dry, and building the platforms and pipelines to bring it up all cost money now in exchange for a stream of value later, which is exactly the kind of decision present value governs. A company will keep spending to discover and develop more of a deposit only up to the point where the cost of finding the next barrel equals the present value of that barrel. Past that point it does not pay to look, so the resource simply stays unmeasured in the ground, uncounted in the reserve figures, even though it is physically there. As Sowell tells it, a best-selling book in 1960 warned that the United States had only a thirteen-year supply of oil left; thirteen years later, known reserves were larger than before, not because the oil had multiplied but because rising prices and new technology made it worth finding more.

That is the self-correcting part. As existing reserves get drawn down, the present value of each remaining barrel rises, which makes further exploration profitable again, which adds to known reserves. A higher interest rate works the other way: it raises the cost of the long, capital-heavy projects exploration requires, so less gets discovered and measured reserves shrink, without our being one barrel closer to exhausting the resource. So a low or falling level of “known reserves” is mostly a statement about prices, interest rates, and the economics of discovery, not a countdown to running out. Through the entire twentieth century, with its enormous growth in energy use, known reserves of oil, copper, iron, and other resources generally rose rather than fell. Present value, not the size of the planet, sets how much it pays to have found.

The same reasoning lights up oil prices, and pays off a promise from the market-power topic. If the market suddenly expects a barrel to be worth far more in the future, today’s price must rise toward that future value discounted back, with no cartel or conspiracy required: in one 1983 illustration, a barrel expected to fetch about $30 in 1985 was worth about $12 a decade earlier at 10 percent, against a 1973 price near $3. A higher price today then rations oil away from its least valuable current uses toward more valuable future ones, exactly what conservationists demand for beaches and forests. Present value is the conservation mechanism, and whoever forecasts that future better than the market can grow rich buying what the market has underpriced.

Your Wealth Is the Present Value of Everything You Will Earn

Now turn the tool on yourself. Wealth is the present value of all your future income, from every source. The largest piece of most people’s wealth is not a bank balance or a house. It is human capital: the present value of your own future earnings. If you imagined a balance sheet listing everything you own, the biggest asset on it would be “Me”, the discounted stream of every paycheck you will ever collect. That is why a question like “are you worth more than $500,000?” is not absurd: discount a few decades of salary back to the present and a typical career easily clears that bar. A ninety-year-old who plants fruit trees that mature in twenty years is not being foolish. The land is worth more the day the trees go in, because its present value rises immediately, and he can sell it tomorrow and move to the Bahamas; part of today’s wealth is always food not yet grown, to be eaten by people not yet born.

Income is best understood as the maintainable flow you can take without shrinking your wealth, what we call standard income. If your wealth is W and the interest rate is r, your standard income is r × W: the amount you can consume each year and still leave your wealth intact, exactly like spending only the interest on a perpetuity and never touching the principal. Someone with $100,000 of wealth can maintainably consume nothing extra at a 0 percent rate but $10,000 a year at 10 percent. Run it the other way and a steady $5,000 a year of income, at 10 percent, corresponds to wealth of $50,000 ($5,000 ÷ 0.10), the perpetuity formula again, now read as capitalizing an income into the wealth that backs it. If you consume exactly your standard income for two years, your wealth at the end is unchanged; consume more and you are dissaving, eating into the principal.

This reframes saving and consumption. No one gears consumption strictly to this year’s earnings. People smooth: they borrow when young and earning little, save through their prime years, and spend down in retirement. They can do this because human wealth, the present value of a whole working life, barely moves when a single year’s earnings wobble. A bad year is one small dip in a long discounted stream. So consumption tracks expected lifetime wealth, not the current paycheck, which is why a one-time $4,000 gift and a permanent $20-a-month raise can affect spending very differently: the raise, small as it sounds per month, is a stream, and the present value of a lifetime stream can dwarf a single windfall.

There is also a “stocks-versus-bonds” choice hidden in human capital. When you raise money against your future earnings, you can do it bond-style (borrow a fixed sum and repay it whatever happens) or stock-style (give someone a share of your future earnings). The share arrangement pools risk, which is why it appears where future earnings are wildly uncertain: boxing managers and Hollywood agents take a percentage of a young fighter’s or actor’s future income, and labor contractors take a cut of immigrant workers’ pay. Most such bets do not pay off, so a fixed loan would be too risky for the lender; an equity-like share lets the winners cover the losers. (Yale once tried lending to students against a share of future income, but the future doctors and lawyers who expected high earnings opted out, which tells you who finds such deals attractive.)

Profit Is Wealth Growth Nobody Saw Coming

We can now define profit precisely, and the definition is sharper than the everyday one. Your wealth cannot be expected to grow faster than the interest rate (plus whatever you save), because if some asset were known to grow faster, everyone would bid for it until its price rose and its expected return fell back to the going rate. So any wealth growth above that expected, no-surprise level is profit, and any shortfall is a loss. Profit, in short, is unexpected wealth growth: the part the market did not anticipate.

That definition exposes several common rhetorical tricks. A retailer’s markup, the gap between wholesale and retail prices, is not profit: it must cover the store, inventory, sales labor, security, returns, and every other retail service. “Profits before taxes” is equally selective; taxes are costs just as wages are, and the phrase is no more revealing than “profits before wages.” Nor does profit as a percentage of sales measure the return on invested wealth. Invest $1, sell the product a day later for $1.01, and repeat: the one-cent margin is only 1 percent of sales each turn but roughly 365 percent over a year on the dollar repeatedly invested. Finally, “excessive profit” is a judgment, not a measurement, until the speaker states excessive relative to what alternative return, risk, and invested wealth.

And it is captured the instant an asset’s market value changes, not when you sell. If you buy a stock at $100 and it rises to $150, you have a $150 − $100 = $50 profit the moment the price moves, whether or not you cash out; if it then falls to $125, you have taken a $25 loss from the peak, again whether or not you sell. (Selling matters for taxes, not for whether the gain is real.) This also disposes of a stubborn fallacy: “I’ll hold this losing stock until it climbs back to what I paid, so I don’t take a loss.” The loss already happened when the price fell; your wealth is the current market value, full stop. What you originally paid is a sunk cost, gone and irrelevant, exactly as we discussed at the very start of the course. The only sensible question is whether this asset, at today’s price, will do better going forward than the alternatives.

A worked example fixes it. Suppose the government licenses the right to grow a crop, so a licensed acre nets about $400 a year. At 10 percent that stream capitalizes to roughly $4,000 ($400 ÷ 0.10), while the same land unlicensed, netting $100 a year, is worth about $1,000. Those figures are illustrative, but the logic is exact: the $3,000 gap is the monopoly rent the license creates, capitalized straight into the price of the favored land. The whole gain lands once, on whoever owns the land when the scheme is announced, an unforeseen wealth jump, a profit in the sense just defined; a later buyer pays the full $4,000 and earns only the going return. That is the licensing thread from the last topic made exact: it is already priced into what a later holder pays.

American tobacco was this asset. A federal quota to market a pound of tobacco was itself a capital asset, and USDA economists put the arithmetic in print: a quota was worth its yearly rent divided by the interest rate. The rent went to the quota owners, many of them non-farming landlords who leased to the growers. When Congress ended the 1938 program in 2004, it bought the rent out: owners received $7 a pound and growers $3, about $9.6 billion over ten years, proof that the value lived in the license, not the plow.

This is also the place to clear up a loaded label. Returns that arrive without current labor, interest on a loan, dividends on a share, the gain when an asset’s price rises, are sometimes called unearned income, on the theory that the recipient did nothing this year to deserve them. The term is a misnomer. These returns are earned, just not in the period they arrive. They are the payoff to two genuine services rendered earlier: deferring consumption (handing over resources now so someone else can use them) and bearing risk (committing those resources to an uncertain future before anyone knew how it would turn out). The factory that finally pays dividends was financed years before, when the outcome was in doubt and the money could have been spent or lent elsewhere. That the contribution is invisible by the time the reward shows up does not make it absent, and a great deal of bad policy, from condemnations of money-lenders to laws that make debts hard to collect, has grown out of mistaking deferred earnings for unearned income.

Looking ahead to risk and entrepreneurship (T12). This profit-as-surprise idea is the bridge to our next topic. If profit is unexpected wealth growth, then the people who earn it are the ones who bear risk and exercise foresight that others would not, committing resources to an uncertain future before anyone knows how it turns out. That is why even “lucky” profits are not undeserved windfalls: they are the reward for a genuine service, bearing a risk that others declined to bear. The full treatment of risk, uncertainty, insurance, and speculation, including how markets transfer and even reduce risk, is the heart of the next topic; here we only establish what profit is and that risk-bearing is its source.

The Observed Interest Rate Is a Package, Not One Number

People say “the” interest rate, but the rate a particular borrower pays is built up from parts. There is a single pure rate of interest, the underlying price of current over future income, the same for everyone. On top of it sit add-ons that differ by borrower and by loan. The table below shows the build-up for two borrowers: a solid bank customer and a riskier credit-card borrower.

The nominal interest rate as a package of add-ons.

Component	Borrower A (bank loan)	Borrower B (credit card, higher risk)
Pure interest rate	5%	5%
Transactions and record-keeping	1	2
Enforcement contingencies	1	2
Risk of payment default	1	3
Anticipated inflation	5	5
Nominal interest package	13%	17%

Notice that both borrowers pay the same pure rate; the packages differ because of the add-ons. This answers several puzzles. When a young person is quoted 15 percent and an established uncle gets 12 percent, that is not age discrimination, it is a larger default-risk premium on the borrower with no track record. When a pawnshop charges 40 percent, most of that is not pure interest at all but compensation for tiny loans, high default risk, and the costs of running the operation. And when new bonds must offer 9 percent while old ones paid 7 percent, you have to ask which part of the package changed: a worse credit rating (a bigger default premium) or higher expected inflation (a bigger inflation premium) would both raise the number for different reasons.

Two of the add-ons deserve a closer look. The default-risk premium is why safe and risky instruments line up in a predictable order. The table below lists rates on real instruments at three dates; read across the rows and you see Treasury debt (essentially no default risk) paying the least, then top-rated corporate bonds, then lower-rated corporates, with the order holding regardless of the overall level of rates. (These are the source’s own historical figures, illustrating the ranking, not current data.)

A selection of interest rates on financial instruments, by year (illustrative historical values).

Instrument	1996	2002	2012
3-month Treasury bill	5.20%	1.74%	0.07%
1-year Treasury bill	5.39%	4.52%	0.17%
10-year Treasury bond	5.60%	5.20%	1.47%
6-month certificate of deposit	5.28%	1.85%	0.48%
Aaa corporate bonds	6.81%	6.55%	3.64%
Baa corporate bonds	7.47%	7.87%	5.02%
Bank prime loan rate	8.25%	4.25%	3.25%

This ordering explains why you might rationally accept a lower yield. A Treasury bond at 4 percent can be a better buy than a venture company’s bond at 7 percent, once you account for the venture bond’s higher default risk and the Treasury’s easier resale, the extra yield on the risky bond is compensation for risk you would be taking on, not a free lunch. The same point cuts the other way. Sowell reports that a dollar invested in 1801 was worth, in inflation-adjusted terms by the late 1990s, around a thousand dollars in bonds but several hundred thousand in stocks, and less than a dollar in gold. Stocks’ higher average return is payment for their wilder ride; over a long horizon, the asset that feels “risky” year to year was the one that built wealth.

The second add-on worth a note is for market risk, the danger that rates will move while you hold a long bond and shove its price around. We saw that long bonds swing most when rates change, so lenders demand an extra premium to hold them, which is part of why long-term rates usually exceed short-term ones. Running the other way is a subtraction for liquidity: very short, very safe, easily sold instruments like Treasury bills double as a near-substitute for cash, and that convenience yield lets them pay a bit less. There is also an inflation premium, the part of the rate that compensates lenders for the dollar losing value. The stated rate on a loan is the nominal rate, the percentage in dollars; the real rate is what those dollars actually buy after inflation, roughly the nominal rate minus the rate of inflation. A lender quoting a nominal rate is really demanding some desired real return plus a cushion for the inflation expected over the life of the loan. So if you fear inflation, an inflation-indexed bond, whose payments rise with the price level, is attractive even at a lower stated rate, while someone confident that prices will stay flat would rather hold an ordinary fixed-dollar note at a higher number. The crucial wrinkle is that lenders set the premium for the inflation they expect, and actual inflation can differ. When it runs higher than expected, the realized real rate, what the interest truly bought after the fact, can fall to zero or even go negative: the lender is paid back in dollars worth less than the cushion anticipated, an unannounced transfer of wealth from lender to borrower. Realized real rates have dipped below zero this way during wars and supply shocks, when inflation outran what lenders had priced in. Where inflation itself comes from belongs to a later course; here the point is just that “the” rate has a real core and an inflation cover, and only the real core is the true price of waiting.

Looking ahead to price ceilings on credit (T4). Where this topic brushes against caps on interest rates, usury laws, payday-loan rate caps, ceilings on veterans’ mortgage rates, the same logic applies as for any binding price ceiling, which we study in full in the price-controls topic. Hold the price of credit below where the market would set it and you get a shortage of credit for exactly the borrowers the cap was meant to help: the highest-risk borrowers get shut out (lenders cannot charge enough to cover their risk), lending shifts toward safer borrowers, and the competition that the cap blocks reappears in nonprice forms, fees, tie-in requirements, and the like. When Oregon capped payday-loan rates at 36 percent a year, Sowell reports that about three-quarters of the state’s payday lenders shut down, and the borrowers who relied on them did not thereby become better credit risks; they lost access. We will work through the general mechanics of ceilings, shortages, and rationing in the price-controls topic.

That payday example also makes a point about what “interest” even means on a short, small loan. A $15 charge on a $100 loan for two weeks annualizes to a triple-digit percentage, which sounds scandalous, but most of that $15 is not interest at all. It is the fixed cost of processing the loan and the high risk of not being repaid, spread over a tiny principal and a short term. As Sowell puts it, salmon may cost a great deal “per ton,” but you are not buying a ton. Annualizing a mostly-fixed cost on a two-week loan badly misrepresents it.

The Interest Rate Is the Relative Price of Long-Lived and Short-Lived Things

There is one more face of the interest rate, and it lets you “see” the rate even where no one is openly lending. Because a durable good’s value is the present value of a long stream of services, a change in the interest rate changes the value of long-lived things far more than short-lived things. The table below prices three houses that each throw off the same $50 a year in services but last for very different spans: a 200-year brick house, a 50-year wood house, and a 10-year temporary structure.

Market values of resources of different life-lengths, at alternative interest rates. Each yields $50 a year.

Resource	Life (years)	Annual return	Cost to build	3%	5%	7%	10%	15%
Brick house	200	$50	$1,500	$1,662	$1,000	$714	$500	$333
Wood house	50	$50	$900	$1,286	$915	$690	$496	$333
Temporary house	10	$50	$275	$427	$386	$351	$307	$251

Scan across the brick-house row: its value collapses from $1,662 at 3 percent to $333 at 15 percent, a huge swing, because almost all of its value sits in distant future years that high rates discount to nearly nothing. The temporary house barely moves, from $427 to $251, because its short stream is little affected by the rate. So a fall in the interest rate raises the value of long-lived assets the most, which is why low rates tend to set off booms in buildings. This also means a change in the rate shows up as a change in the relative prices of durable goods: when people want more future consumption, they bid up long-lived resources (redwood over pine, the brick house over the temporary one), which is the same thing as a fall in the interest rate. Conversely, a rising ratio of raisins to grapes, or aged whiskey to fresh corn, signals that the rate has fallen, making the longer, more roundabout product relatively more valuable.

Two consequences are worth drawing out. First, this is the real channel through which interest rates affect investment, not mainly through interest payments on loans, but through the change in market value of long-lived resources relative to their cost of production. When the rate falls and a brick house’s value rises above its $1,500 cost, building one becomes worthwhile; the rate works on the economy by changing what durable things are worth. Second, you can read the interest rate off these relative prices even in a society that forbids lending and borrowing outright: the rate is implicit in the prices of capital goods versus current goods. But read it with care, because a change in a resource’s price might reflect a change in expected future returns rather than a change in the rate, and from the price alone you cannot always tell which.

Finally, secure property rights raise investment without raising the pure rate. When a country makes ownership more secure, lenders face a smaller chance of default or expropriation, so the risk premium in the package shrinks; the safer environment is a lower-risk class of lending, not a change in the underlying pure rate, which is the same for everyone.

Present Value Disciplines Markets but Not Politicians

I want to close on the political economy of time, because it is where these ideas bite hardest. Present value forces private decision-makers to face the future now. If a private bus company lets its fares drift too low to maintain and replace its buses, its stock price falls today, the moment investors foresee the coming breakdowns, long before a single bus actually wears out. Specialists who price assets for a living do the foreseeing that the general public does not, so the consequences of neglecting the future are pulled into the present, where the owners feel them immediately and have every reason to act.

Politicians face no such discipline, because their horizon ends at the next election. A city official who keeps bus fares too low to win votes collects the gratitude now and is long gone, often promoted, by the time the buses start failing years later; his personal payoff arrives well before the bill does. This is why political processes systematically mishandle long-horizon problems: underpriced public services, underfunded pensions, deferred maintenance, infrastructure left to crumble. The future has no vote.

The flip side of “the future is already priced in” is that time itself can be turned into a weapon, because time is money in a very literal sense. Whoever can impose delay can impose cost. A developer who has borrowed millions to build housing pays interest on that money every day it sits idle, so anyone who can hold up the project, through a drawn-out permit fight, a demanded environmental report, a planning commission in no hurry, can pile interest charges onto the cost whether or not the project is ever found to be harmful. The party causing the delay often bears almost none of that cost, which is what makes delay such effective leverage: a low cost to A buys a high cost imposed on B, and the result is fewer projects built and higher prices on the ones that are. Governments use the same arithmetic on themselves. Raising the retirement age by a few years to “save” a strained pension system is, in present-value terms, a partial default, postponing promised payments long enough to shrink what they are worth today. Recognizing that time is money is partly a defense against political rhetoric: it lets you price a delay meant to look free.

Two more cases show the same machinery. When a credit-rating agency downgraded California’s state bonds during the 2001 electricity crisis, it did so before any default and while the treasury still showed a surplus, because the agency was pricing the future fiscal strain into the present, exercising exactly the foresight that voters and officials were not. And the foresight of owners explains why confiscating foreign businesses and farmland seldom enriches a poor country. Owners who expect to lose their property stop investing in and maintaining it long before the seizure; the share prices of Sri Lankan tea estates stayed depressed under the threat of nationalization, and land reform has been called a cruel joke on the people it claims to help, because the prospect of losing the land destroys the incentive to keep it productive. Insecure property rights collapse the investment horizon, and present value registers the damage at once.

This connects back to a point from earlier in the course about permanent losses. When a policy or event causes a lasting fall in an asset’s expected future receipts, the loss shows up immediately as a one-time drop in its present value, the harm is “priced in” the instant expectations change, not when the future finally arrives. The arithmetic of capital value is unforgiving: the future is always already here, discounted into today’s prices, whether the people making decisions choose to look at it or not.