This paper addresses five foundational concepts in finance: the Net Present Value (NPV) decision rule and its relationship to cost-benefit analysis and the Valuation Principle; the Law of One Price and its implications for financial securities; the Time Value of Money and why future cash flows are worth less than present ones; the distinction between annuities and perpetuities and the methods used to calculate their present values; and the special case of growing perpetuities, including real-world examples and the theoretical implications of growth rates exceeding discount rates.
The Net Present Value (NPV) decision rule states that an investment should be accepted if its net present value is greater than zero, and rejected otherwise. The NPV of an investment is the present value of its cash inflows minus the present value of its cash outflows. One may compute NPV by identifying all cash flows, determining and applying the appropriate discount rate, and summing all of the resulting present values.
This approach is closely related to cost-benefit analysis, in that both methods weigh the benefits of an investment against its costs — NPV simply expresses that comparison in present-value terms. The Valuation Principle examines earnings, revenues, cash flow, equity, dividends, and other indicators in order to determine the overall value of a company. That total value is then divided by the number of outstanding shares to arrive at a per-share value, providing a basis for comparing an investment's cost against its expected return.
The Law of One Price is a theory holding that a given item will have the same price across markets once exchange rates are taken into consideration. This principle is particularly relevant when the item in question is a security, commodity, or other traded asset.
When the Law of One Price does not hold, different prices can exist in different markets. In that situation, an arbitrageur can purchase the asset in the cheaper market and simultaneously sell it in the higher-priced market, earning a risk-free profit. This arbitrage activity continues until prices converge. Therefore, when purchasing power parity is absent, market participants will exploit price discrepancies through arbitrage until a single equilibrium price is restored across markets.
The Time Value of Money, also referred to as the present discounted value, is a concept suggesting that money available today is worth more than the same amount of money in the future, because money held in the present has earning capacity. As long as money can earn any interest, a given sum today is worth more than the same sum received at a later date.
For this reason, future cash flows must be discounted back to the present before they can be meaningfully compared to current costs or benefits. The future value of an asset is a function of its present value multiplied by the applicable interest rate — with the exact calculation depending on whether interest is simple or compounded.
"Fixed payments, present value formulas explained"
"Infinite growing payment streams and their value"
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