PV
Photovoltaics (PV) is a technology that converts sunlight directly into electricity through the photovoltaic effect, a process in which photons from light excite electrons in semiconducting materials, generating an electric current.[1][2] The effect was first demonstrated in 1839 by French physicist Alexandre-Edmond Becquerel using an electrochemical cell, marking the initial observation of light-induced voltage generation.[3][4] Early PV devices relied on materials like selenium, but practical silicon-based solar cells emerged in 1954 at Bell Laboratories, achieving about 6% efficiency and enabling initial applications in space satellites and remote power systems.[5] Subsequent advancements in crystalline silicon, thin-film technologies, and multi-junction cells have improved efficiencies to 15-25% for commercial modules, with laboratory records exceeding 47% for concentrated systems.[2][6] PV's defining characteristics include modularity, scalability from portable panels to utility-scale arrays, and no moving parts or emissions during operation, though production involves energy-intensive processes and reliance on rare earth materials.[7][8] The technology's most notable achievements encompass dramatic cost reductions—module prices falling over 89% since 2010—and explosive global capacity growth, surpassing 1 terawatt installed by 2022 and projected to multiply further due to manufacturing scale and supply chain efficiencies, primarily in Asia.[7] Controversies include supply chain vulnerabilities, with over 80% of production dominated by a few firms facing geopolitical risks, and debates over lifecycle environmental impacts, such as mining for silver and cadmium in certain thin-film variants, alongside intermittency requiring grid integration or storage solutions.[7] Despite these, empirical data affirm PV's role as the fastest-expanding electricity source, driven by direct conversion physics rather than subsidies alone, contributing to energy diversification amid fossil fuel constraints.[8][9]Places
United States
Pleasant Valley is the name of several communities across the United States, often abbreviated as PV locally. The town of Pleasant Valley in Dutchess County, New York, had a population of 9,799 according to the 2020 United States Census.[10] Nestled in the Hudson Valley, it functions as a quiet residential area with parks and streams.[11] In Pennsylvania, Pleasant Valley Township in Potter County recorded a population of 76 in the 2020 census, reflecting its status as a small rural township. Larger unincorporated areas bearing the name exist elsewhere in the state, but they lack independent municipal status. Prairie Village, Kansas, abbreviated PV, is a suburban city in Johnson County adjacent to Kansas City, Missouri. Incorporated in 1951 after platting in 1941, it had an estimated population of 22,856 in 2025, following a 2020 census figure near 22,900.[12][13] Providence Village, Texas, also known as PV, is a master-planned community in Denton County developed starting in 2000 and incorporated in 2010. Its 2020 census population was 7,691, growing to an estimated 10,350 by July 2024.[14][15] Paradise Valley, Arizona, commonly abbreviated PV, is an affluent town in Maricopa County with a 2020 census population of 12,658.[16] It spans 15.4 square miles, predominantly zoned for single-family housing.[17]International locations
Puerto Vallarta, a resort city on Mexico's Pacific coast in the state of Jalisco, is widely abbreviated as PV in travel, tourism, and informal contexts. Situated within Banderas Bay, it features a municipal population of 291,839 as recorded in Mexico's 2020 census. The city originated as a fishing village in the early 20th century and gained prominence as a tourist hub following infrastructure developments in the 1960s, including its airport opening in 1970.[18][19][20] In Spain, PV serves as the standard abbreviation for País Vasco, the autonomous community in the north comprising the provinces of Álava, Biscay, and Gipuzkoa, with a regional population of 2,200,341 as of January 1, 2023. This abbreviation appears in administrative, media, and geographic references to the area, which borders France and the Bay of Biscay. No significant boundary changes or renamings have occurred post-2020.[21]Politics
Political parties
The Partij voor de Vrijheid (PVV), or Party for Freedom, is a Dutch political party established in February 2006 by Geert Wilders after his split from the center-right People's Party for Freedom and Democracy (VVD).[22] The PVV promotes right-wing populist positions, including stringent restrictions on immigration—particularly from Muslim-majority countries—opposition to what it terms "Islamization" of Dutch society, reductions in foreign aid, and resistance to deeper European Union integration or adoption of the euro.[23][24] These stances have garnered support amid public concerns over cultural integration and housing pressures from migration, though critics from mainstream outlets have labeled them inflammatory.[25] In the November 22, 2023, general election, triggered by the collapse of the prior coalition, the PVV secured 37 seats in the 150-member House of Representatives—more than doubling its previous 17 seats—and emerged as the largest party with around 23.5% of the vote, reflecting voter dissatisfaction with established parties on issues like asylum inflows exceeding 45,000 annually.[26][27] This outcome enabled the PVV to join a center-right coalition government sworn in on July 2, 2024, led by independent Prime Minister Dick Schoof, which has advanced policies tightening asylum rules and prioritizing nitrogen emission cuts for farmers over urban expansion.[28] The party's influence has prompted debates on source credibility, as Dutch public broadcasters and international media often frame its gains through lenses of extremism despite empirical polling showing broad resonance with native voters' priorities.[29] In Latin America, Partido Verde (PV) entities include Mexico's Ecologist Green Party of Mexico (PVEM), founded in 1986 by Jorge González Torres as an environmental advocate but registered nationally in 1993.[30] The PVEM has allied opportunistically with dominant forces, such as the PRI in the 1990s–2010s for gubernatorial wins and later Morena under President López Obrador, securing roles like Senate seats despite supporting policies like airport expansions conflicting with ecological goals; it obtained about 7–8% in standalone legislative races but leverages coalitions for influence.[31][32] In the June 2, 2024, elections, as part of the Sigamos Haciendo Historia alliance, the PVEM helped deliver a congressional supermajority to Morena, though independent analyses highlight its pragmatic shifts—e.g., backing fossil fuel subsidies—over rigorous green agendas, raising questions about ideological consistency amid corruption probes into allied figures.[33] Brazil's Partido Verde (PV), formed in 1986 post-military rule, emphasizes environmentalism, federalism, and human rights as a centrist option, achieving modest vote shares (around 1–2% in recent nationals) while critiquing deforestation under varying administrations.[34] These PV-labeled groups illustrate varied applications, from populist nationalism in Europe to alliance-driven environmentalism in the Americas, with electoral success tied to contextual voter priorities rather than uniform ideology.Governmental and legal terms
In French and other civil law jurisdictions influenced by French legal traditions, PV abbreviates procès-verbal, denoting an official written record or report documenting verbal statements, proceedings, or factual observations made in the presence of a public authority, such as a magistrate, police officer, or administrative official.[35] This instrument serves as prima facie evidence in judicial or administrative processes, capturing details like witness testimonies, inspections, or deliberations to ensure accountability and verifiability in legal actions. Its procedural role emerged within the codified framework of French law, particularly through the civil procedure elements of the Napoleonic Code enacted on March 21, 1804, which standardized documentation practices to replace pre-revolutionary inconsistencies and promote uniform evidentiary standards across administrative and criminal matters.[36] In the United States criminal justice system, PV refers to a probation violation, defined as the failure of a supervised offender to adhere to court-mandated conditions of release, including regular reporting to a probation officer, refraining from criminal activity, submitting to drug testing, or completing rehabilitative programs.[37] Upon allegation of a PV, courts conduct hearings to determine breach, potentially resulting in sanctions ranging from warnings and modified terms to revocation and reincarceration for the original suspended sentence.[37] Bureau of Justice Statistics data indicate that probationers committing violations exhibit elevated recidivism risks, with federal offenders released to probation showing rearrest rates approaching 50% within eight years, underscoring the causal role of non-compliance in reoffending patterns.[38] Empirical analyses reveal that lenient handling of PVs, such as through high probation officer caseloads exceeding evidence-based thresholds, correlates with increased recidivism, as reduced monitoring intensity diminishes deterrence and intervention efficacy.[39] Conversely, stricter enforcement via intensive supervision—characterized by lower caseloads, frequent contacts, and integrated services—has demonstrated recidivism reductions of up to 17% in models like Intensive Supervision Probation with Services, by enhancing compliance through swift accountability rather than mere surveillance.[40] However, inefficiencies arise when revocations prioritize technical violations over substantive crimes, contributing to cyclical incarceration without proportional public safety gains, as evidenced by supervision failures accounting for nearly 200,000 annual admissions despite comprising few new arrests.[41] This highlights a tension in policy design, where under-enforcement empirically fosters higher reoffense while over-enforcement risks resource strain without addressing root behavioral drivers.[42]Science and technology
Biology and medicine
Poliovirus (PV), a member of the Enterovirus genus in the Picornaviridae family, is a small, non-enveloped, single-stranded positive-sense RNA virus approximately 30 nm in diameter that primarily infects the human gastrointestinal tract and can invade the central nervous system, causing poliomyelitis.[43] First isolated in 1908 by Karl Landsteiner and Erwin Popper through transmission experiments in rhesus monkeys, PV exists in three serotypes (1, 2, and 3), with type 1 being the most prevalent in paralytic cases due to its neurovirulence.[44] Transmission occurs via the fecal-oral route, with initial replication in the oropharynx and intestine; in a small fraction of infections (less than 1%), the virus spreads hematogenously to motor neurons in the spinal cord and brainstem, leading to flaccid paralysis with a case-fatality rate of 2-10% in paralytic forms.[45] Global vaccination efforts, initiated with the inactivated polio vaccine (IPV) in 1955 and the live attenuated oral polio vaccine (OPV) in 1961, have reduced wild poliovirus (WPV) cases by over 99% since 1988, when an estimated 350,000 cases occurred across 125 countries, to just 99 confirmed WPV1 cases in 2024 confined to Afghanistan and Pakistan.[46] [47] However, OPV's use of live virus has led to circulating vaccine-derived poliovirus (cVDPV) outbreaks in under-vaccinated populations, where the attenuated virus regains neurovirulence through mutations; from January 2023 to June 2024, 74 such outbreaks yielded 672 confirmed cases across 39 countries or areas, primarily type 2 cVDPV2, highlighting an unintended consequence of OPV despite its role in initial eradication gains.[48] Transition to IPV in routine immunization aims to mitigate this risk, though challenges persist in maintaining high coverage above 95% to prevent resurgence.[49] Pharmacovigilance (PV) encompasses the science and activities for detecting, assessing, understanding, and preventing adverse effects or other medicine-related problems, including substandard or falsified products, with a focus on post-marketing surveillance to ensure ongoing safety beyond pre-approval clinical trials.[50] Established formally in the 1960s following the thalidomide tragedy, PV systems rely on spontaneous reporting databases like the WHO's VigiBase, mandatory adverse event notifications, and signal detection methods such as disproportionality analysis to identify potential risks.[51] In the European Union, Directive 2010/84/EU, implemented in 2012, strengthened PV by mandating risk management plans, enhanced electronic reporting, and periodic benefit-risk evaluations, expanding scope to include medication errors, off-label use, and pregnancy exposures.[51] Application of PV to mRNA COVID-19 vaccines revealed safety signals not fully anticipated in initial trials, such as excess risks of myocarditis and pericarditis, particularly in young males after the second dose.[52] A 2022 analysis of randomized trial data estimated an excess risk of serious adverse events of special interest at 12.5 per 10,000 vaccinated for combined Pfizer-BioNTech and Moderna vaccines, underscoring limitations in trial sizes for rare events and the value of real-world PV data in refining causal attributions through methods like self-controlled case series.[52] [53] These findings, drawn from systems like VAERS and international registries, challenged early assertions of unequivocal safety profiles by prompting investigations into dose-response relationships and long-term outcomes, though overall vaccine benefits in reducing severe COVID-19 outweighed identified risks in population-level assessments.[54] Persistent PV monitoring remains essential, as evidenced by ongoing signals for anaphylaxis and other events in updated formulations.[55]Chemistry
Polyvinyl chloride (PVC), a prominent polyvinyl compound, is synthesized via free-radical polymerization of vinyl chloride monomer (CH₂=CHCl) in methods such as suspension or emulsion polymerization, yielding a polymer with the repeating unit –(CH₂–CHCl)ₙ–. Patents for PVC production were filed in 1913 by Russian inventor Ivan Ostromislensky, though commercial-scale manufacturing began in 1931 using emulsion polymerization in Germany by IG Farben, followed by U.S. production in 1935.[56] Industrial synthesis achieves monomer conversion yields exceeding 85–95% under controlled conditions of 40–70°C and initiator concentrations of 0.1–0.5 wt%, minimizing unreacted monomer residuals below 10 ppm to mitigate toxicity risks, as vinyl chloride is classified as a human carcinogen by the International Agency for Research on Cancer.[57] PVC exhibits thermoplastic properties including a glass transition temperature of approximately 80°C, tensile strength of 40–60 MPa for rigid formulations, and inherent flame retardancy from 56–57% chlorine content by weight, rendering it insoluble in water and resistant to dilute acids, bases, and many solvents. Additives such as plasticizers (e.g., diisononyl phthalate at 30–50 phr) enable flexible variants, while stabilizers prevent HCl evolution during processing at temperatures up to 200°C. Lifecycle assessments indicate PVC production emits about 1.5–2.5 kg CO₂ equivalent per kg resin, higher than polyethylene due to chlor-alkali electrolysis for monomer precursor, though durability extends service life in piping and coatings, reducing replacement frequency compared to metals in corrosive environments.[58][57] In chemical engineering, the process variable (PV) denotes any directly measurable parameter characterizing a system's state, such as reactor temperature, pH, or reactant concentration, essential for real-time monitoring in continuous processes like distillation or catalytic reactions. PVs are inputs to control loops, where deviations from setpoints trigger adjustments via manipulated variables (e.g., valve positions) using proportional-integral-derivative algorithms, achieving stability within ±0.5–2% of target in industrial applications per ISA standards. For example, in exothermic polymerizations, PV tracking of temperature prevents runaway reactions by modulating coolant flow, with sensor accuracies typically ±0.1°C for thermocouples in pilot-scale units.[59][60] The pivaloyl (Pv or Piv) group, derived from pivalic acid (trimethylacetic acid, (CH₃)₃CCOOH), serves as a bulky protecting group for alcohols in organic synthesis, installed via esterification with pivaloyl chloride under basic conditions (e.g., pyridine catalysis at 0–25°C) and cleaved by hydrolysis or lithium aluminum hydride reduction, offering steric hindrance against nucleophilic attack with deprotection yields >95% in multi-step sequences.[61]Computing
In computing, a physical volume (PV) refers to a physical disk drive, partition, or logical unit initialized for use within a logical volume manager (LVM) subsystem, enabling abstract storage pooling and allocation beyond rigid partitioning schemes. This allows administrators to create volume groups (VGs) from multiple PVs, which are then subdivided into resizable logical volumes (LVs) supporting features like online extension, snapshots, and striping for improved I/O distribution. In IBM AIX, PVs form the foundational layer of LVM, integrated into the base operating system since AIX version 3.1 released in 1989, where they are partitioned to allocate space dynamically while adhering to hardware constraints such as disk geometry and controller limits.[62] Similarly, Linux LVM, originating from code developed in 1998 by Heinz Mauelshagen at Sistina Software and inspired by earlier Unix systems like HP-UX, designates PVs via thepvcreate command to mark devices for metadata storage, typically limiting initial partition sizes to 2 TB without GPT tables due to legacy MBR constraints.[63] These mechanisms prioritize operational flexibility but introduce hardware dependencies, including alignment requirements for SSDs to prevent write amplification and vulnerability to controller caching inconsistencies that can exacerbate data corruption during power failures without battery-backed units.[64]
Redundancy in PV-based systems relies on explicit mirroring or integration with RAID, as LVM alone provides no inherent fault tolerance; a single PV failure in a non-mirrored VG can render the entire LV inaccessible, amplifying risks in high-availability setups. Misconfigurations, such as unsafe LV shrinking without proper backups or extending across mismatched disk types, have led to metadata overwrites and total data loss, as documented in industrial case studies where improper PV initialization on RAID arrays resulted in undetected stripe misalignment and subsequent filesystem corruption during expansion attempts.[65][66] Practical limitations include performance overhead from metadata indirection, with benchmarks indicating 10-50% I/O degradation compared to direct partitioning, particularly under random workloads due to additional seek operations on spinning disks or queue depth saturation on NVMe arrays.[67] In 2025 scalability tests for virtualized environments like Proxmox, LVM configurations scaling to dozens of PVs across 100 TB+ aggregates demonstrated sub-millisecond latency for sequential reads but required tuning stripe widths to mitigate bottlenecks from legacy metadata formats, underscoring hardware constraints like maximum 256 PVs per VG without kernel patches.[68]
In software control systems, a process variable (PV) denotes a measurable physical quantity sampled in real-time feedback loops, such as temperature, pressure, or flow rate, which is compared against a setpoint to compute control outputs via algorithms like PID in programmable logic controllers (PLCs). Within SCADA architectures, PVs are acquired from field devices via remote terminal units (RTUs), digitized through analog-to-digital converters with resolutions typically limited to 12-16 bits, and processed centrally for alarming or actuation, as seen in examples like monitoring steam pressure in power plants where PV deviations trigger valve adjustments.[69][70] Operational mechanics emphasize causal constraints from hardware, including sensor drift (e.g., thermocouples accurate to ±1°C but degrading over time) and polling latencies exceeding 100 ms in bandwidth-constrained networks, which can destabilize loops in fast-dynamic processes like chemical reactors.[71] Scalability challenges arise with thousands of PVs per system, where CPU overhead for scanning and Ethernet protocol overheads limit update rates to 1-10 Hz without distributed edge processing, as evidenced in industrial deployments prioritizing deterministic real-time kernels over general-purpose OSes to avoid jitter-induced instability.[72] These implementations highlight trade-offs, such as trading precision for throughput in resource-limited embedded hardware, rather than idealized continuous models.
Mathematics
The Cauchy principal value, denoted PV, provides a rigorous method for evaluating improper integrals exhibiting singularities on the integration path, particularly in real and complex analysis. For a function f with an isolated singularity at x_0 on the real line, the PV is defined as \mathrm{PV} \int_a^b f(x) \, dx = \lim_{\epsilon \to 0^+} \left( \int_a^{x_0 - \epsilon} f(x) \, dx + \int_{x_0 + \epsilon}^b f(x) \, dx \right), provided the limit exists; this symmetric exclusion of the singular neighborhood ensures cancellation of divergent contributions from opposing sides.[73][74] Introduced by Augustin-Louis Cauchy in his foundational work on residue calculus and definite integrals during the 1820s, this construction derives from first-principles limits that preserve analytic continuation properties without ad hoc regularization.[73] In complex analysis, the PV extends Cauchy's integral theorem to contours indented around poles on the real axis, yielding \mathrm{PV} \int_{-\infty}^\infty \frac{f(z)}{z - c} \, dz = \pi i \sum \mathrm{Res}(f, \text{upper}) - \pi i \sum \mathrm{Res}(f, \text{lower}) for c real and f holomorphic off the axis, with convergence guaranteed by the symmetry when the indentation radius vanishes./10:_Definite_Integrals_Using_the_Residue_Theorem/10.05:_Cauchy_principal_value) This framework underpins proofs of convergence for singular integrals, such as those arising in potential theory, where the PV aligns with the Sokhotski–Plemelj formula linking boundary values of analytic functions. Applications to Fourier transforms leverage PV to regularize oscillatory integrals; for instance, the Fourier transform of \mathrm{PV}(1/x) equals -\pi i \mathrm{sgn}(\xi), enabling rigorous inversion and Plancherel-type theorems via distributional limits rather than unsubstantiated formal manipulations.[74][73] Within distribution theory, the PV defines tempered distributions for functions like $1/x, acting on test functions \phi \in \mathcal{S}(\mathbb{R}) via \langle \mathrm{PV}(1/x), \phi \rangle = \lim_{\epsilon \to 0^+} \int_{|x| > \epsilon} \frac{\phi(x)}{x} \, dx, which exists by the oddness of the kernel and evenness of \phi(0); this extends to higher-order singularities through finite-part regularization, verifiable by density arguments in Schwartz spaces.[74] Such constructions facilitate algebraic manipulations under differentiation—e.g., \frac{d}{dx} \mathrm{PV}(1/x) = -\mathrm{PV}(1/x^2)—and underpin microlocal analysis without reliance on non-analytic extensions. These purely mathematical utilities emphasize PV's role in ensuring well-posedness of linear operators on function spaces, grounded in limit theorems independent of physical interpretations.[73][74]Physics
Phase velocity, denoted v_p, is the velocity at which a specific phase of a wave form propagates through a medium, defined as the ratio of the angular frequency \omega to the wave number k, given by v_p = \omega / k.[75][76] This arises from the wave equation for a plane wave \exp(i(kx - \omega t)), where constancy of phase kx - \omega t = constant implies dx/dt = \omega / k.[75] In non-dispersive media, such as electromagnetic waves in vacuum, v_p = c, the speed of light, approximately $3 \times 10^8 m/s.[75] The value of v_p derives from the dispersion relation \omega(k), which links frequency and wavenumber in a given medium; for dispersive media, where \omega is nonlinear in k, v_p varies with frequency.[75] It differs fundamentally from group velocity v_g = d\omega / dk, which represents the propagation speed of a wave packet's envelope and thus the transport of energy or information.[75] In electromagnetism, for instance, plane waves in free space yield v_p = v_g = c, but in dispersive structures like waveguides operating above cutoff frequency, v_p > c while v_g < c, ensuring no causal violation as v_g \leq c.[75] This relation follows from the waveguide dispersion \omega^2 = \omega_c^2 + c^2 k^2, where \omega_c is the cutoff angular frequency, leading to v_p = c / \sqrt{1 - (\omega_c / \omega)^2}.[75] Experimental validation in waveguides confirms these predictions; for example, phase shifts measured via multi-emitter setups on elastic guided waves yield v_p values matching theoretical dispersion curves, with errors below 1% in controlled lab conditions using piezoelectric transducers at frequencies around 100 kHz.[77] In earth-ionosphere waveguides for very low frequency (VLF) signals, phase velocity measurements from 1964 NIST experiments showed deviations from free-space values due to ionospheric height variations, with v_p / c \approx 1.1 to 1.3 depending on propagation mode, derived from observed phase delays over transatlantic paths.[78] Anomalies, such as apparent superluminal v_p in plasmas or metamaterials, align with causality via sub-luminal v_g, as verified in microwave waveguide tests where energy arrival times respect relativistic limits.[79]Economics and finance
Present value
Present value (PV) in finance refers to the current worth of a future sum of money or series of cash flows, discounted to account for the time value of money, which arises from opportunity costs, inflation, and risk aversion.[80] This concept quantifies how a rational investor prefers money today over equivalent amounts in the future, as present funds can be invested to generate returns.[81] Empirical support stems from observed market behaviors, such as positive yields on risk-free bonds, implying positive time preferences.[82] The standard formula for the present value of a cash flow stream is PV = \sum_{t=1}^n \frac{CF_t}{(1 + r)^t}, where CF_t denotes the cash flow at time t, r is the discount rate, and n is the number of periods; for a single future value FV, it simplifies to PV = \frac{FV}{(1 + r)^t}.[80] This discounting approach originated in early modern Europe with the development of compound interest tables in the 1610s–1620s, enabling systematic calculations for annuities and leases, building on ancient annuity contracts but formalized through printed mathematical aids for present value assessments.[83] By the 18th century, annuity tables incorporating these methods became widespread for valuing life annuities and perpetual rents.[84] In capital budgeting, PV forms the basis for net present value (NPV) analysis, where NPV equals the PV of expected inflows minus outflows; projects are accepted if NPV exceeds zero, reflecting value creation over the cost of capital.[85] For instance, consider a 2025 project requiring an initial outlay of $1,000,000 and generating annual cash inflows of $300,000 for five years, discounted at a 5% real rate adjusted for projected 2% inflation (yielding a nominal rate of approximately 7%). The PV of inflows calculates as approximately $1,243,000, resulting in a positive NPV of $243,000, justifying acceptance assuming the rate reflects market opportunity costs.[86] The choice of discount rate r is critical, with market-implied rates derived from government bond yields providing empirical benchmarks; as of October 2025, the 10-year U.S. real interest rate stands at about 1.57%, though longer-term yields suggest 2–3% real rates incorporating growth expectations.[87] However, policy models like the 2006 Stern Review on climate change employed a 1.4% consumption discount rate, criticized by economists such as William Nordhaus for undervaluing present consumption relative to uncertain future damages, thereby inflating the PV of distant costs and biasing toward aggressive intergenerational transfers that ignore higher market-revealed rates (often 3–5% real in integrated assessments).[88][89] Such low rates, prevalent in some environmental policy frameworks, deviate from observed private discount rates and risk premia, potentially leading to suboptimal resource allocation by overprioritizing hypothetical future scenarios over verifiable current opportunities.[90]| Year | Cash Flow | Discount Factor (7%) | Present Value |
|---|---|---|---|
| 0 | -$1,000,000 | 1.000 | -$1,000,000 |
| 1 | $300,000 | 0.935 | $280,500 |
| 2 | $300,000 | 0.873 | $261,900 |
| 3 | $300,000 | 0.816 | $244,800 |
| 4 | $300,000 | 0.763 | $228,900 |
| 5 | $300,000 | 0.713 | $213,900 |
| Total NPV | $243,000 |