Discount
A discount is a reduction in the price of a product or service from its usual or list cost, often provided as an incentive to encourage purchases, prompt payments, or larger orders.[1] In commerce and business, discounts play a key role in marketing strategies by boosting sales volume, building customer loyalty, clearing excess inventory, and fostering competitive pricing, though overuse can erode profit margins and perceived value.[2] Various types of discounts exist, such as those based on trade, quantity, loyalty, promotions, and seasons. In finance and investing, a discount describes a situation where a security, such as a bond, trades below its par value or intrinsic worth, typically due to factors like rising interest rates or credit risk.[3] Discounting, a related concept, involves calculating the present value of future cash flows by applying a discount rate that accounts for the time value of money and risk, essential in valuation models like discounted cash flow (DCF) analysis.[4] Financial instruments like zero-coupon bonds are sold at a deep discount to their face value, with the difference representing implied interest upon maturity.[5] In mathematics and decision theory, a discount factor is a multiplier used to adjust the value of future outcomes to their present value, often in models of time preference or intertemporal choice.[4] In arts and entertainment, "Discount" refers to a punk rock band from Florida active in the 1990s,) and a 2014 French comedy-drama film directed by Louis-Julien Petit about supermarket workers.[6]Commerce and retail
Price reductions and allowances
In commerce and retail, a discount refers to a reduction from the list price or standard rate of goods or services, typically applied at the point of sale or through post-sale allowances to incentivize purchases and facilitate transactions.[7][1] This practice allows sellers to adjust pricing dynamically based on market conditions, buyer relationships, or inventory needs, while buyers benefit from lower costs that enhance affordability.[8] These informal allowances evolved with the Commercial Revolution, but it was the 19th-century Industrial Revolution and rise of mass retail that standardized fixed price reductions, enabling department stores and early chains to clear excess inventory from scaled production and attract a broader consumer base.[9][10] Key mechanisms for implementing discounts include functional discounts, which provide price reductions to intermediaries such as wholesalers for handling distribution tasks like storage, transportation, and resale. Trade discounts offer reductions to channel members, such as retailers, for their roles in marketing and selling products.[11] Promotional discounts, in contrast, are short-term cuts designed to drive immediate sales spikes, often tied to marketing campaigns or clearance efforts.[12] Representative examples illustrate these mechanisms in action: seasonal sales events like Black Friday, where U.S. retailers commonly apply discounts of up to 50% on electronics, apparel, and holiday items to stimulate year-end demand and liquidate stock.[13] Loyalty program reductions, such as those in Starbucks Rewards, grant points per purchase redeemable for free products, effectively lowering costs for repeat customers and fostering retention.[14] Economically, discounts boost consumer demand by making products more accessible, often increasing overall sales volume and market penetration in competitive sectors.[15] However, they can erode profit margins per unit if the incremental revenue from higher volumes fails to compensate for the price cut, necessitating careful calibration to avoid long-term financial strain.[16]Types of discounts
Cash discounts are offered to encourage prompt payment of invoices, typically within a short period following the transaction. For instance, the common term "2/10 net 30" allows buyers a 2% reduction on the invoice amount if paid within 10 days, with the full amount due in 30 days otherwise.[17] This mechanism improves cash flow for sellers by incentivizing early settlement while providing buyers with a cost-saving opportunity.[18] Quantity or volume discounts provide progressive price reductions based on the scale of purchase, rewarding bulk buying to boost sales volume and utilize economies of scale. These often follow tiered structures, such as a 10% discount for orders exceeding 100 units or escalating benefits for larger quantities like 20% off for 500 units.[19] Such discounts are prevalent in wholesale and manufacturing sectors to encourage larger orders from distributors or retailers.[20] Promotional discounts are temporary incentives designed to stimulate demand, clear excess inventory, or attract new customers through limited-time offers. Common forms include coupons for percentage-based savings, bundle deals combining products at reduced rates, and flash sales offering deep cuts for purchases within hours or days.[21] These tactics create urgency and can significantly increase short-term sales velocity.[22] Functional and trade discounts facilitate pricing in supply chains by providing successive reductions to intermediaries for their roles in distribution and resale. Functional discounts compensate entities like wholesalers for handling logistics and storage, often at rates such as 20% off list price, while trade discounts go to retailers for marketing and selling efforts, typically adding another 10%.[23] For example, a manufacturer might apply a 20% functional discount to distributors followed by a 10% trade allowance to retailers, ensuring competitive end pricing without altering the suggested retail value.[24] In modern e-commerce, discount codes exemplify these types, such as 20% off for first-time purchases to onboard new users or volume-based codes for bulk online orders.[25] Discount stores often institutionalize volume discounts as a core strategy to maintain low prices on everyday goods.[19]Discount retailers
Discount retailers are low-margin, high-volume businesses that sell a wide range of goods at reduced prices compared to traditional department stores or supermarkets, focusing on efficiency to pass savings to consumers. These stores emerged in the United States following World War II, with early pioneers like E.J. Korvette opening in 1948 as one of the first modern discount department stores, challenging established retail norms by offering self-service and lower prices without frills. The model gained momentum in the 1950s amid postwar economic growth and suburban expansion, leading to a boom in the early 1960s when major chains such as Kmart, Walmart, and Target launched their first locations in 1962, capitalizing on consumer demand for affordable variety.[26] This period marked the shift toward discount retailing as a dominant force, with stores emphasizing cost-cutting over luxury service. Operational strategies of discount retailers center on bulk purchasing from suppliers to secure low costs, minimalistic store designs to reduce overhead, and pricing models that prioritize volume over high profits per item. Many adopt everyday low pricing (EDLP), where consistent low prices eliminate the need for frequent sales, as exemplified by Walmart's approach, which relies heavily on private-label products that offer 10-30% savings compared to national brands.[27] In contrast, some use high-low pricing, featuring regular deep discounts on select items to drive traffic, though EDLP has proven more effective for building long-term customer loyalty in high-volume operations. These tactics, combined with limited product assortments and efficient supply chains, allow retailers to maintain slim margins—often 1-3% net—while achieving scale through thousands of locations. Globally, discount retailing has adapted to local markets with notable success in Europe through chains like Aldi, founded in 1946 by brothers Karl and Theo Albrecht, who transformed their mother's grocery into a discount model emphasizing private brands that enable prices up to 50% lower than traditional supermarkets.[28] In the U.S., dollar stores represent a modern evolution, with Dollar General operating over 20,000 locations as of 2025, targeting rural and low-income areas with small-format stores stocked with essentials at $1 or less to maximize accessibility.[29] Despite their resilience, discount retailers face intensifying challenges from e-commerce, particularly since the 2010s when Amazon's online discount model accelerated the closure of thousands of physical stores by offering convenience and competitive pricing without geographic limits.[30] This competition has forced adaptations like click-and-collect services, though traditional discounters struggle with the shift as online sales erode up to 20% of brick-and-mortar traffic in some categories. Economically, discount retailers play a vital role in enhancing consumer affordability, contributing to substantial annual savings estimated in the hundreds of billions across the U.S. retail sector through pervasive price reductions and promotions.[31] By serving diverse income groups, including a growing share of middle- and high-income shoppers seeking value amid inflation, these chains democratize access to goods and stimulate broader economic activity via high turnover.Finance and economics
Financial discounting
Financial discounting is the process of determining the present value (PV) of future cash flows or amounts by accounting for the time value of money (TVM), a fundamental principle stating that a sum of money is worth more today than the same sum in the future due to its potential earning capacity through investment or other opportunities.[32] This adjustment reflects the opportunity cost of capital, where funds available now can be invested to generate returns, making future payments less valuable in present terms.[33] The core idea originates from early economic theories on interest and money's temporal value, first conceptualized in the 16th century by Martin de Azpilcueta in the School of Salamanca, who linked money's worth to inflation and scarcity, and later developed in the 18th century by Richard Cantillon, who analyzed interest rates as reflecting time preferences in lending and borrowing.[34][35] At its essence, financial discounting reverses the process of compounding interest, where compounding grows a present amount forward in time by adding earned interest to the principal, while discounting reduces a future amount backward to its equivalent today by subtracting the implied interest.[36] This inverse relationship ensures consistency in valuing cash flows across time periods. Discounting methods vary between simple and compound approaches: simple discounting applies a linear reduction based on a flat rate over the period, akin to deducting simple interest upfront from the future value to yield proceeds, whereas compound discounting uses an exponential adjustment to account for interest accruing on interest over multiple periods. The standard formula for compound discounting, which is widely used for its accuracy in multi-period scenarios, derives from the compound interest equation. Starting with the future value formula FV = PV \times (1 + r)^n, where FV is the future value, PV is the present value, r is the periodic discount rate, and n is the number of periods, solving for PV yields: PV = \frac{FV}{(1 + r)^n} This derivation works by isolating PV through division: divide both sides of the future value equation by (1 + r)^n, effectively "undoing" the growth factor to bring the value to the present. For simple discounting, the formula is PV = FV \times (1 - r \times n), but it assumes no reinvestment and is less common for long horizons.[37][38] For instance, discounting a future payment of $100 due in one year at a 5% discount rate using the compound formula gives PV = 100 / (1 + 0.05)^1 \approx 95.24, illustrating how the time value reduces the amount's worth today.[37] In practice, financial discounting applies to loans and credit instruments, where borrowers receive funds upfront but repay a larger amount later, effectively paying a discount fee for the time delay. A key example is bill discounting in banking, where a holder sells a commercial bill of exchange to a bank at a reduced present value before maturity, allowing immediate liquidity; this practice became prominent in the 19th century, with institutions like the Bank of England formalizing bill discounting facilities for brokers around 1830 to support trade finance.[39] Such applications underscore discounting's role in balancing immediate needs against future obligations while incorporating the discount rate as the key input for time-value adjustments.Discount rates
In finance, the discount rate is the interest rate applied to future cash flows to determine their present value, typically comprising a risk-free rate plus a risk premium to account for uncertainty and opportunity costs.[40] This rate embodies the time value of money, where future amounts are worth less today due to potential earnings from alternative investments.[41] Discount rates are categorized into nominal and real types, with nominal rates incorporating expected inflation and real rates adjusting cash flows to exclude it for a purer measure of purchasing power.[42] Market-based rates, such as the London Interbank Offered Rate (LIBOR), were phased out in favor of the Secured Overnight Financing Rate (SOFR) by June 30, 2023, to provide a more robust, transaction-based benchmark less susceptible to manipulation.[43] Central bank policy rates, like the U.S. Federal Reserve's primary credit discount window rate of 4.00% as of November 2025, serve as another type, influencing short-term borrowing costs for depository institutions.[44] The determination of discount rates is shaped by inflation expectations, projected economic growth, and central bank monetary policies aimed at stabilizing prices and output.[41] For instance, in the early 1980s, the Federal Reserve raised its discount rate alongside the federal funds rate to combat double-digit inflation peaking at 14.6% in 1980, successfully curbing price pressures but inducing a recession.[45] In public policy, social discount rates—often set at 3.5% for the first 30 years under UK Treasury Green Book guidelines for long-term projects like environmental initiatives—reflect societal opportunity costs and intergenerational equity, declining to 3% for years 31–75 and 2.5% thereafter.[46] In corporate finance, these rates are frequently derived from the weighted average cost of capital, representing the opportunity cost of deploying funds in a specific project versus alternatives.[41] Higher discount rates amplify the discounting effect in present value calculations, substantially lowering the current worth of distant future cash flows as integrated into formulas like PV = \sum \frac{CF_t}{(1 + r)^t}, where r is the rate.[41] This sensitivity underscores the rate's role in risk assessment, as elevated rates signal greater uncertainty and reduce valuations for long-horizon investments.[40]Applications in valuation
In valuation, discounting techniques are essential for assessing the worth of assets, projects, and investments by converting future cash flows into their present value equivalents, accounting for the time value of money.[47] One primary application is the Net Present Value (NPV) method, which calculates the difference between the present value of cash inflows and the present value of cash outflows over a period.[48] The NPV formula is given by: \text{NPV} = \sum_{t=1}^{n} \frac{\text{CF}_t}{(1 + r)^t} - C_0 where \text{CF}_t represents the cash flow at time t, r is the discount rate, n is the number of periods, and C_0 is the initial investment.[49] To compute NPV for a 3-year project with an initial investment of $100,000, annual cash inflows of $40,000, $50,000, and $60,000, and a 10% discount rate, first discount each inflow: year 1 as $40,000 / (1.10)^1 = $36,364; year 2 as $50,000 / (1.10)^2 = $41,322; year 3 as $60,000 / (1.10)^3 = $45,078. Summing these gives $122,764, and subtracting the initial investment yields an NPV of $22,764, indicating a profitable project.[48] The Discounted Cash Flow (DCF) model extends this principle to estimate the intrinsic value of a company or stock by projecting future free cash flows and discounting them to the present.[50] In stock valuation, analysts forecast earnings or free cash flows, apply a discount rate reflecting the company's risk, and sum the present values to derive equity value. For instance, a company with projected annual free cash flows of $100 million growing at 5% indefinitely, discounted at 8%, might be valued at approximately $3.3 billion using the Gordon Growth Model variant of DCF, where value = (next year's cash flow) / (discount rate - growth rate).[51] This approach is widely used in mergers, acquisitions, and equity analysis to determine if a stock is over- or undervalued.[52] Another key application is the Internal Rate of Return (IRR), defined as the discount rate that makes the NPV of all cash flows equal to zero, solved iteratively through trial and error or numerical methods.[53] IRR is employed in capital budgeting to rank and select projects by comparing the rate to a hurdle rate, such as the cost of capital; projects with IRR exceeding this threshold are typically accepted.[53] Its use in capital budgeting gained prominence in the 1950s as firms shifted toward discounted cash flow techniques for more rigorous investment appraisal, replacing simpler payback methods.[54] Discounting is routinely applied in bond pricing, where the bond's value equals the present value of its future coupon payments plus the principal repayment at maturity, discounted at the yield to maturity.[55] For a bond with a $1,000 face value, 5% annual coupon, 10 years to maturity, and a 6% yield, the price is the sum of discounted coupons ($50 annually) and the discounted principal, resulting in a value below par (e.g., approximately $928) due to the higher yield.[55] In project appraisal, such as for infrastructure like highways, future toll revenues are discounted to evaluate feasibility; for example, projected annual toll collections of $50 million over 30 years for a toll road, discounted at 7%, might yield a present value of $620 million to justify the $400 million construction cost in public-private partnerships.[56] In modern contexts, discounting incorporates environmental, social, and governance (ESG) factors, with post-2020 adjustments often applying lower discount rates to green projects to reflect reduced risk premiums for sustainable investments, enhancing their NPV attractiveness.[57] Similarly, in cryptocurrency applications, discounting is used to value non-fungible tokens (NFTs) by estimating future yields from royalties or resale rights; for an NFT with projected 10% annual royalty streams on secondary sales, discounted at a high crypto-specific rate like 20% to account for volatility, the present value might justify an initial mint price of $10,000.[58] Discount rates in these applications are selected based on the underlying risk profile.[50]Mathematics and decision theory
Discount factors
In mathematics, the discount factor represents a multiplier applied to future cash flows or values to express their present equivalence, accounting for the time value of money. For discrete compounding periods, it is defined as d = \frac{1}{(1 + r)^n}, where r is the interest rate per period and n is the number of periods. This factor ensures that a future value FV discounted back to the present yields PV = FV \cdot d.[59][60] The derivation of the discrete discount factor follows directly from the compound interest formula. Starting with the accumulation relation FV = PV \cdot (1 + r)^n, solving for the present value gives PV = FV \cdot \frac{1}{(1 + r)^n}, identifying d = \frac{1}{(1 + r)^n} as the scaling multiplier that equates future and present values. For continuous compounding, the discount factor emerges as the limit of frequent discrete compounding: as the number of compounding intervals approaches infinity, (1 + \frac{r}{m})^{mt} \to e^{rt}, so the inverse discount factor is d = e^{-rt}, where t is continuous time. This form simplifies differential equations in mathematical models of growth and valuation.[60][61] The discount factor exhibits key properties as a monotonically decreasing function of both r and n (or t in the continuous case), reflecting how higher rates or longer horizons reduce the present weight of future amounts. For illustration, consider r = 0.05:| n | Discount Factor d |
|---|---|
| 1 | 0.952 |
| 2 | 0.907 |
| 3 | 0.864 |
| 4 | 0.823 |
| 5 | 0.784 |