A field can become more valuable between one harvest and the next without growing an additional blade. Its boundary has not moved; its soil has not improved; its owner still expects the same rent. What has changed is the price at which buyers exchange money today for the right to receive money later. The rise belongs in the owner’s fortune, although it records no addition to the field. The earlier plate’s reservoir therefore needs a second gauge: one for the things held, another for the value attached to holding them. Capitalization connects the two by bringing an expected future into the present. Its arithmetic can be exact while the future it prices remains unsettled.
The connection begins with a payment and a date. Suppose, in an invented example, that one hundred and five dollars will certainly arrive a year from now, and that five percent is the available annual return on an otherwise equivalent claim. One hundred dollars today can buy that future payment; the extra five compensates the passage between the two dates. To value a payment two years away, the same operation must be performed twice. At the same rate, one hundred and ten dollars and twenty-five cents due in two years is worth one hundred today. A stream of payments can be valued by carrying each back from its own date and adding the resulting present amounts. The dates are part of the property being priced. Receiving the same sum later changes the bargain.
A perpetual payment makes this bridge unusually visible. Imagine an enforceable claim paying one hundred dollars at the end of every year forever, with no costs, growth or uncertainty. At five percent it is worth two thousand. A buyer paying that price receives one hundred each year while retaining a claim worth two thousand if the conditions remain unchanged; the income is five percent of the purchase. The reciprocal of the rate is the multiple: twenty years’ income capitalized into the price paid now. If the required rate becomes four percent, the same stipulated stream is worth twenty-five hundred, or twenty-five years’ income. The holder gains five hundred in value without receiving an extra dollar of annual payment. The new buyer, paying more for the same hundred, obtains the lower yield.
The perpetuity’s simplicity depends on its extraordinary promise. Let the one hundred arrive for only five years, with nothing to sell or recover at the end, and its value at five percent is about four hundred and thirty-two dollars and ninety-five cents. Dividing by the rate would instead report two thousand, because it would silently add every payment after the fifth year. A bond poses a different account: five annual coupons of fifty dollars, followed by repayment of a thousand with the last coupon, are worth a thousand at five percent. The principal belongs in the final payment. A finite asset may have a resale value, a salvage value, or an obligation to pay for its removal; each enters at its date and with its sign. The multiple is a shortened account of these terms, and becomes misleading when the terms disappear from view.
The flow to be capitalized is what the claim can deliver after the expenditures required to sustain it. A building’s rent cannot all be treated as an indefinitely spendable return if repairs, vacancies and replacement must be paid from it. A business’s recorded earnings need examination for the same reason: some may have to remain in the business to support the future earnings on which its price rests. Conversely, a benefit need not arrive as a cash payment. A house occupied by its owner supplies shelter; a controlling shareholding may supply powers that a small passive holding does not. Fisher’s account expressly allowed benefits of use, control and possession. These possibilities widen the account and make its specification more demanding. They do not provide a convenient cash figure for every benefit, or prove that every observed price is the sum a particular forecast would justify.
The future introduces a second source of movement alongside the rate. Expected rents may rise because a place becomes useful to more people, or expected profits fall because a rival has found a cheaper way to serve the same customers. Payments may also become less secure. Fisher repeatedly set risk aside when stating the simple discount calculation; that assumption deserves to remain visible when the calculation is used. A certain hundred and a precarious hundred do not become equivalent merely because they have the same number written beside them. Valuation must account for the uncertainty as well as the timing, through assumptions about possible payments and the prices attached to their risks. A single capitalization rate compresses those judgments. It cannot make them disappear.
A fall in a quoted interest rate consequently does not dictate the movement of every fortune. In the original perpetual example, lowering the rate from five to four percent raises value by a quarter, provided the hundred remains unchanged. Now let the expected constant payment fall to seventy at the same time. Capitalizing that smaller payment at four percent gives seventeen hundred and fifty, below the original two thousand. The lower rate and the poorer prospect work in opposite directions. Nor can a change in the rate on a safe loan automatically be inserted as the same change in the return required on a doubtful enterprise. The familiar statement that lower rates raise asset values is a comparison with other relevant conditions held fixed. It is useful precisely because it names one influence without pretending to describe the whole movement.
Even the word “dollar” carries an assumption about the future. A stream fixed in money can buy less when the prices of consumption rise. A stream fixed in purchasing power instead requires changing money payments. Discounting the latter at a rate appropriate to the former would mix two standards, much as adding the reservoir to its annual inflow mixes two dimensions. The numerator and the rate must speak the same language of prices and time. The same care is needed with taxation and with debt: the payments available to a shareholder after interest and taxes differ from the receipts of the enterprise before those charges. A large multiple may reflect expected growth, a low required return, or the choice of an earnings figure that is temporarily depressed. Its magnitude alone cannot identify which.
Capitalization gives the fortune a contingent size without making it imaginary. If a buyer will pay twenty-five hundred for the claim, its owner has an opportunity unavailable to someone who holds no such claim. The owner may exchange it for other resources, subject to the costs and conditions of sale. A lender may recognize some of it as security. The change in the account can therefore change what the owner can do even while the annual payment stays still. Yet an offer for one holding is not an assurance that every holder could sell everything at that price simultaneously. The number has a date, a market and a scale. Its reality is the reality of a valued position in those circumstances.
The origin of the position remains a separate question from its valuation. A valuable claim may arise from producing something useful, holding scarce land, receiving an inheritance, or acquiring a protected right to charge others. Capitalization follows the expected benefits of whichever claim exists. It does not distinguish a payment people gladly make for an additional service from one they must make to cross a privately controlled obstruction. A change in law can enlarge or diminish either claim, just as a change in technology can alter the opportunities beneath it. The valuation records the expected consequences for its holder. To infer social contribution from that figure requires an account of how the benefits arise, who pays for them, and what would happen under another arrangement. The multiple supplies none of those conclusions by itself.
The multiple prices a future; it cannot certify how that future was earned.
A fortune’s size is thus a fact about claims valued under particular conditions, and the conditions are part of the fact. The field, the title, the expected rent, the relevant rates and the opportunities of exchange all belong in the account. Calling the number conditional keeps its components open to examination; calling it wealth recognizes the command its holder may exercise through them. The mistake is to let a rising valuation stand without argument for more things produced, a greater service performed, or a stronger title to the resulting gain. Having brought the future into the present, the next plate must decide how to enter it beside everything else a person owns and owes. The multiple leads to the ledger, where a single total conceals several different kinds of certainty.