The time value of money is the principle that an amount of cash is worth more the sooner it arrives, because cash held now can be put to work over the intervening period. Present value moves a future amount back to today, and future value moves a present amount forward, and both are the same arithmetic read in opposite directions.
Federal benefit-cost guidance states the rule in four sentences. In order to compute net present value, it is necessary to discount future benefits and costs, this discounting reflects the time value of money, benefits and costs are worth more if they are experienced sooner, and all future benefits and costs, including nonmonetized benefits and costs, should be discounted (Office of Management and Budget, Circular A-94, section 8). The same passage adds the direction of travel: the higher the discount rate, the lower is the present value of future cash flows.
The Formula Is a Tool, Not a Theory
Accounting standards treat the arithmetic as a device for measurement rather than as a claim about how the world works. The present value formula is a tool used to incorporate the time value of money in a measurement, and in their simplest form present value techniques capture the amount that an entity demands, or that others demand from it, for money that it will receive or pay in the future (FASB Concepts Statement No. 7, paragraph 19).
The same paragraph goes further than most textbook treatments. The present value of estimated future cash flows is implicit in all market prices, including the historical cost recorded when an entity purchases an asset for cash, and that relationship, readily apparent when applied to financial assets like loans or bonds, extends to all assets and liabilities recognized in the financial statements (FASB Concepts Statement No. 7, paragraph 19). On that reading the time value of money is inside a historical cost figure whether or not anyone discounted anything.
A Figure the Standard Works Out
The standard runs its own example rather than leaving the idea abstract. Using the rate of interest for 10-year default risk-free assets, 5 percent, the present value of the assets in that example that represent cash to be received 10 years hence is $6,139 (FASB Concepts Statement No. 7, paragraph 112). Its own footnote records what the face amount was: $6,139 is the present value of $10,000 discounted for 10 years at 5 percent (FASB Concepts Statement No. 7, footnote 13).
That single figure is the whole idea. The standard describes the asset in question as the promise of an amount certain of receipt in 10 years, no risk premium has been applied to it at that point in the example, and the amount still measures well below its face because of when it arrives (FASB Concepts Statement No. 7, paragraph 112).
It Is Not the Same Thing as Inflation
The two are routinely collapsed into one, and the standard separates them explicitly. The time value of money, inflation, and uncertainty interact with one another, and they do not cancel each other except by coincidence (FASB Concepts Statement No. 7, paragraph 109).
The example it gives is the clearest test. A dollar of cash flow due 10 years hence and indexed to inflation is not worth a dollar today, because the indexed amount returns the cost of inflation but does not provide for the time value of money, which exists even when inflation does not (FASB Concepts Statement No. 7, paragraph 109). Marketplace participants demand a real, inflation-free interest rate after removing the effects of inflation from their expectations.
The Time Value Is Only One Ingredient of a Present Value
A present value measurement that fully captures the economic differences between the assets in that example would necessarily include five elements, and the time value of money is only one of them. It enters represented by the risk-free rate of interest, alongside an estimate of the future cash flow, expectations about possible variations in the amount or timing of those cash flows, the price for bearing the uncertainty inherent in the asset or liability, and other, sometimes unidentifiable, factors including illiquidity and market imperfections (FASB Concepts Statement No. 7, paragraph 23). The five elements as a set, and what an entity assembles them into, are worked through in cost of capital.
Where Accounting Deliberately Ignores It
Several measures in daily use are built to leave it out, which is a design choice rather than an oversight, and knowing which ones is the practical half of the concept.
The accounting rate of return ignores it outright, and what that costs the measure is set out in the accounting rate of return equation. Plain payback ignores it too while discounted payback does not, and the difference between the two is drawn in the formula for the payback period. Leaving it out is also one of the stated assumptions behind the contribution model, listed in cost-volume-profit analysis.
Where the arithmetic is required rather than optional, it appears under other names. The net present value rule is in NPV, a stream of equal payments is handled in annuity, a stream with no end is in perpetuity, and the rate a below-market loan is deemed to carry for tax purposes is in imputed interest.
Common Questions
Discounting and compounding. Discounting moves a future amount back to a present value, which is the operation federal guidance requires before benefits and costs occurring at different dates can be compared (Office of Management and Budget, Circular A-94, section 8). Compounding is the same relationship run forward, producing the amount a sum today grows to by a later date.
Because certainty and timing are separate questions. In the standard’s own example the promise is of an amount certain, and it still measures at $6,139 rather than $10,000, a figure the footnote confirms as the present value of $10,000 discounted for 10 years at 5 percent (FASB Concepts Statement No. 7, footnote 13). Risk changes the number further. Time changes it first.
That depends on what the measurement is for. In a present value built to capture economic differences the time value component is represented by the risk-free rate of interest, and the price for bearing the uncertainty inherent in the asset or liability is a separate element of the same measurement rather than part of that rate (FASB Concepts Statement No. 7, paragraph 23). How a required return gets assembled from those pieces is in cost of capital.
Accountably places offshore accountants inside US CPA and EA firms, working in the firm’s own systems and under the firm’s own review. Discounted measurements, lease and impairment calculations and the schedules behind them are the kind of work that gets deferred when the team is short of hours, and adding reviewed capacity is the part of that problem staffing can solve.
