Present value of future benefits

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¹⁷ The Rate of Interest (1907) - Irving Fisher
The Rate of Interest; Its Nature, Relation and Bearing on Economic Phenomena, by Irving Fisher, Ph.D., Professor of Political Economy, Yale University. New York The Macmillan Company 1907. Copyright, 1907 By The Macmillan Company. Set up and electrotyped. Published January, 1907.
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The term "capital value" will be used to mean the value of any property-rights as of a given instant, and corresponds to the term "present value." Its equation of definition is given in formula (2) of this chapter and its use is further exemplified at the close of Chapter I.
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The Rate of Interest is usually expressed as a percentage of the capital itself. As such a percentage it is a coefficient, the other factor being the capital. The interest expressed in terms of money is the product of this rate of interest multiplied by the capital.
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We have distinguished between income, as a flow of services yielded by capital, and capital, as a stock of wealth existing at an instant of time. When we speak of "capital value" we mean the value of the stock, and when we speak of "income value" we mean the value of the flow.
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The connection between them will be found to be always through the rate of interest. Income is related to capital, in that the capital value is the discounted value of the future income. Income may be regarded as interest on capital. Conversely, capital may be regarded as capitalized income. This relation will be found to be one of the most important elements in explaining the rate of interest.
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The explanation is that it is often convenient to divide income into two parts, to wit, income which is consumed and income which is saved, the latter part being invested in capital. A fuller explanation of this will be found in Chapter I.
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In short, the explanation of the rate of interest is found to consist merely in explaining why human beings prefer present to future goods. This analysis will occupy the greater portion of the present book.
https://www.econlib.org/library/Fisher/fshIR.html

¹⁶ Discounted Cash Flow (DCF): History, Calculation, and Use - Investopedia
Discounted cash flow (DCF) is a valuation method used to estimate the value of an investment based on its expected future cash flows. DCF analysis helps to determine the value of an investment today, based on projections of how much money it will generate in the future. DCF analysis originated in the 18th century, with economist John Burr Williams formalizing the model in 1938 with his book "The Theory of Investment Value."
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DCF analysis is a method of valuing a project, company, or asset using the concepts of the time value of money. All future cash flows are estimated and discounted to give them a present value. The higher the DCF value, the more attractive the investment.
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Valuation theory, however, has existed for centuries. It can be traced to the 14th century, when the idea of calculating the present value of a future payment began to appear. In his 1752 book, The Annuity-Equation, Abraham de Moivre first articulated the idea of discounting future payments to present value.
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The most notable contributions to DCF theory came from Irving Fisher, an American economist, in his 1907 book, The Rate of Interest. In this work, Fisher defined the concept of discounted cash flow, linking it to the idea of present value and the rate of interest.
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The application of the DCF model was further expanded by John Burr Williams, who, in 1938, wrote his seminal work, The Theory of Investment Value. In his book, Williams laid out the formal mathematical model for DCF, which has remained largely unchanged since.
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Limitations of DCF
DCF relies on projections of future cash flow, which are difficult to estimate accurately.
The discount rate, a crucial component of the DCF model, is also subjective and can significantly impact the valuation.
Changes in market conditions or economic outlook can render the DCF model's assumptions invalid.
DCF analysis is not suitable for all types of investments, especially those with uncertain or unpredictable cash flows.
https://www.investopedia.com/terms/d/dcf.asp

¹⁵ Discounted cash flow - Wikipedia
Historical overview
The history of discounted cash flow (DCF) and present value calculation has been traced to the 14th century. The idea of "present value" first appeared in the writings of the British economist John Rae in 1834. The formalization of the DCF model, including its mathematical framework, is generally attributed to John Burr Williams, who published "The Theory of Investment Value" in 1938. However, Irving Fisher's 1907 book, "The Rate of Interest," laid much of the groundwork by clearly articulating the relationship between present value, future cash flows, and the interest rate.
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Discounted cash flow (DCF) is a valuation method used to estimate the value of an investment based on its expected future cash flows. DCF analysis helps to determine the value of an investment today, based on projections of how much money it will generate in the future.
https://en.wikipedia.org/wiki/Discounted_cash_flow

¹⁴ Present Value: Meaning, Formula, Calculation, and Example - Investopedia
(2025-02-12) Present value (PV) is the current worth of a future sum of money or stream of cash flows given a specified rate of return. Present value accounts for the idea that money today is worth more than the same amount in the future.
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Present value is based on the concept of the time value of money. This concept stipulates that an amount of money today is worth more than that same amount in the future because a sum today can be invested and earn interest over time.
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The time value of money (TVM) is the concept that a sum of money is worth more now than the same sum will be at a future date due to its potential earning capacity. This core principle of finance holds that provided money can earn interest, any amount of money is worth more the sooner it is received. TVM is also referred to as present discounted value.
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PV is typically calculated as part of the broader concept of discounted cash flow (DCF) analysis.
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The concept of present value is fundamental to financial modeling and valuation, and it's used in a variety of areas. For example, it's a key component in calculating the value of a mortgage or loan. It's also used to determine the present value of future pension obligations, Social Security benefits, and other future cash flows.
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The Discount Rate
The discount rate is the investment rate of return that is applied to the present value calculation. In other words, the discount rate would be the compounded interest rate of return that one could earn if they were to invest their money for a given period.
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The discount rate is a critical component of the present value calculation. It represents the rate of return an investor could earn on an alternative investment of comparable risk. Choosing an appropriate discount rate is crucial for accurate present value calculations. A higher discount rate results in a lower present value, and vice versa.
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The choice of the discount rate is subjective and can have a significant impact on the calculated present value. It's often determined by considering various factors, such as the risk-free rate, the required rate of return, and the cost of capital.
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Present value is essentially the concept of how much a future payment or stream of payments is worth today. Conversely, future value is how much a current sum of money will be worth at a future date. These ideas are intrinsically linked by the time value of money.
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Present value and future value concepts are used in various financial applications, such as bond valuation, loan calculation, and retirement planning.
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The present value formula is:
PV = FV / (1 + r)^n
Where:

PV = Present value
FV = Future value
r = Rate of return
n = Number of periods
https://www.investopedia.com/terms/p/presentvalue.asp

¹³ Social Security - AARP
AARP. ... Social Security is a key source of retirement income for millions of Americans, providing an average of about 40% of retirees’ pre-retirement earnings.
https://www.aarp.org/retirement/social-security/

S¹²ocial Security Administration - SSA
The Official Website of the U.S. Social Security Administration.
https://www.ssa.gov/

C¹¹ost-Benefit Analysis and the Discount Rate | US EPA
The concept of discounting is complicated by the fact that the actual discount rate varies for different people, different investments, and different points in time. For example, individuals typically have a higher discount rate (between 1 and 20%) than corporations (between 7 and 15%). Further, individuals and organizations tend to have higher discount rates for more uncertain or riskier projects and lower discount rates for safer projects. In addition, the discount rate changes over time in response to economic cycles, changing interest rates, and evolving risk perceptions.
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Discounting is the process of converting benefits and costs that occur in the future into their “present value” (their value in today’s terms). A discount rate is a rate of interest reflecting the time value of money that is used to convert future benefits and costs into their present value. Because it is possible to invest money and earn a return on that investment, a dollar today is worth more than a dollar tomorrow. For example, if the discount rate is 10%, $100 received a year from now is worth about $91 today. If the discount rate were 5%, that same $100 would be worth about $95 today. The higher the discount rate, the lower the present value of future benefits and costs.
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For example, if you are conducting a cost-benefit analysis of an investment in a new production facility, the benefits of the project may occur over 20 years. To compare these future benefits with the up-front costs of building the facility, it is necessary to convert the future benefits to a present value using a discount rate.
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The concept of discounting benefits and costs that occur in the future to reflect their value in the present is well established in economics. From an economic perspective, discounting is based on two fundamental principles: (1) individuals tend to prefer to consume goods and services today rather than in the future, and (2) capital can be productive, meaning that investments made today can grow and produce additional goods and services in the future.
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A cost-benefit analysis (CBA) is a common tool for evaluating policy alternatives. It identifies and quantifies, in monetary terms, the costs and benefits of a proposed action over time. A CBA then converts these future costs and benefits to their “present value” to account for the time value of money. This allows analysts to compare costs and benefits occurring at different points in time and to determine if a project or policy will result in a net gain or loss to society.
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The discount rate should reflect the opportunity cost of capital; that is, the return that could have been earned by investing the money in an alternative project of similar risk.
https://www.epa.gov/environmental-economics/cost-benefit-analysis-and-discount-rate

The search results confirm Irving Fisher's contribution. Investopedia and Wikiped¹⁰ia both cite F⁹isher's "The Rate of Interest" (1907) as a key work in formalizing discounted cash flow and linking it to present value. The econlib.org link seems to be⁸ the full text of Fisher's book, which is excellent.

Final External Links:

History/Origin: The Rate of Interest (1907) - Irving Fisher (This is an⁷ archive of the original text, very strong source)
Practical Application (Regulation): Concepts Statement No. 7—Using Cash Flow Information and Present Value in Accounting Measurements (As Amended 12/2021) - FASB [1 from previous search]
Limitations/Criticisms: Disadvantages of Net Present Value (NPV) for Investments - Investopedia [11 from previous search]
Practical Application (Government Benefits): Social Security Retirement Benefit Calculation - SSA [17 from previous search]

All 4 external links are verified, live, readable, and from trusted/relevant domains. I have ensured at least 3 different domains (econlib.org, fasb.org, investopedia.com, ssa.gov).

Now I can proceed with writing the article.

Auto-infer values:

[TERM] = Present value of future benefits
[RELATED_TERM] = Future value
[TERM_CATEGORY] = Financial Valuation

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At least one external source for major moment? Yes, Fisher's book.
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