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Home Economic Trends Net present value solved a 400-year-old landlord-tenant negotiation problem.

Net present value solved a 400-year-old landlord-tenant negotiation problem.

by xyonent
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In 1628 Ambrose Ackroyd Lease and Interest TableAckroyd served as trustee of Trinity College from 1615 to 1625, and for some years as senior treasurer (the modern equivalent of “chief financial officer”), and the first table in his book focuses on a particular situation.

Ackroyd’s unusual table i considers a very special situation: a party owns an annuity with a maturity of 21 years, some of which have already matured, and the annuity owner wishes to make a payment to extend the term of the annuity to 21 years. Suppose someone owns an annuity paying £1 per year for 21 years, with 14 years having matured, leaving 7 years remaining. Ackroyd’s first table shows how much would need to be paid to “mature” the annuity to 21 years; in this case it is £3, 5s and 11p, as shown in the “14” row of the table.

This is an example of a “net present value” or “present discounted value” calculation: how much you must pay today to receive an income some years in the future. Ackroyd’s book was just one of several books containing this kind of formula printed in England in the first decades of the 17th century. These authors did not invent the formula to convert a stream of future payments into a present value. The mathematics dates back at least several centuries to Leonardo of Pisa (who was known as “Fibonacci”). But why is this calculation important in this place and time? In fact, authors continued to use his book more than a century later, asking, “Who was Ackroyd, anyway?”

William Dillinger tells the story: “Mr. Eckroyd’s Table: Economic Calculation and Social Custom in the Early Modern Countryside” Modern History JournalMarch 2024, 96:1). Peter Dizikes A short, easy-to-read summary MIT News (June 6, 2024).

This social problem arose as a result of skyrocketing price inflation. Dellinger writes:

Compared with prices during the decade 1501–1510, the average price of foodstuffs in England rose 3.0 times between 1551 and 1560, 5.0 times between 1601 and 1510, and 6.5 times between 1651 and 1660. This was a radical departure from the previous experience, where prices had remained broadly stable and had fallen slightly between 1400 and 1500.

Thus, the rents paid by tenant farmers remained essentially stable for over a century. Raising rents was seen as an act of social aggression, which tenant farmers could and did resist through protests and court cases. But as price inflation took hold, nominal rents became smaller and smaller. Landlords, including the Church of England and ecclesiastical institutions such as Trinity College, were squeezed. Again, raising nominal rents seemed socially and politically impossible. So landlords responded by increasing the fees charged for taking out or renewing a lease, so-called “penals.” The amount of these one-time “penals” was linked to the profitability of the land over the life of the lease, which was determined by a combination of past experience and land surveys.

As Dellinger emphasizes, 17th-century England was a time and place where the logic of supply and demand or market outcomes did not even feature in social debate. Instead, it was a time when payments were judged in terms of fairness, taking into account the social roles and obligations of the parties. In this context, a book with the formula for net present value arose as a solution to the social negotiation problems that landlords and tenants faced after inflation had dramatically disrupted the previous annual payments of fixed nominal rents. Ackroyd’s 1628 book was mostly tables and very little text, but many of the surviving copies appear to have a Latin inscription at its beginning. Dellinger explains:

The poem, which consists of four elegiac couplets, does not appear to have originated from any earlier source. A fairly literal translation is as follows:

Deviations and frauds often torment us, but the straightforward rules of arithmetic teach us [us] What is useful and right? Nature has taught man to deceive. Perhaps art will prevent the treachery of fraud. Let the swarm of swindlers, the quarrelsome, raise their voices in protest. [against this book]Buyers, sellers, consultations [it]You’d be careful [to do so]Those who promote fair exchange between people should avoid any ill will if they wish to avoid praise for it.

The epigraph positions Ackroy’s book as a tool for fighting fraud and promoting fair trade. This tool is presented as a convenience to both buyers and sellers, landlords and tenants, who seek fair, prudent, and honest business transactions. In rental disputes, both landlords and tenants may be guilty of certain frauds and deceptions (Fraus): Landlords use coercive tactics such as demanding exorbitant fines and selling reversionary leases to discourage unfair economic practices, while tenants hide the value of their property or resort to unfair practices to deny landlords their fair share. Arithmetic can promote justice and harmony by enabling rational economic practices and curtailing unjust practices.

In other words, we today tend to think of the net present value formula as part of financial decision-making, and that’s true. When an investor considers buying a stock, he or she has to think about whether the payment now is equal to the return expected from owning that stock over the long term. When a bank lends money, the bank is calculating whether the amount of their payment now (to you) is equal to the amount they’ll pay back over the long term. When you buy a home, you think about whether the price you pay is justified by the set of benefits you expect to receive while owning the home, and the expected resale value included in that figure. When a government considers a program to build infrastructure, improve child nutrition, or reduce pollution, part of the analysis is comparing the amount spent now with the value received over the long term. Dellinger cites financial historian William N. Goetzman’s 2016 book, “The ‘net present value’ method is the most important tool in modern finance.”

But in the 17th century, the net present value formula served a different social function: Most people didn’t understand the details of the mathematics, but they understood the basic ideas well enough to believe that the mathematics represented rules that limited the opportunistic behavior of both sides.

However, as Dellinger points out, this interpretation is correct but incomplete. The specific interest rates that Ackroyd used to determine the present value of the “fine” payments were fairly high, ranging from 11 to 13%. If one discounts future benefits using the relatively high interest rates, the present value of those payments becomes relatively small. Thus, while the wealthy and political supporters were able to rent land from the Church of England at these preferential interest rates, those without power looking to rent land on the market proved less protected. Dellinger sees sharp parallels between the use of “net present value” in the 1600s and the use of algorithms for decision-making today. He writes:

But there is something surprisingly modern about the way that the Eckroyd Tables encoded economic equality in arcane calculations. Most notably, those arcane pages of numbers were empowered to determine what was fair and just on behalf of people who had no understanding of how mathematics worked. …We can assume that the majority of churchgoers found the arcane tables almost incomprehensible, as did, on the evidence…some of the church officials tasked with using them. From one quarter it could be argued that the Eckroyd Tables table Viewed from another perspective, as an evolution of medieval notions of fair prices, their adoption might be seen as an important early chapter in what Rodrigo Ochigame recently called “the long history of algorithmic fairness.”

Today, the use of “black box algorithms” – opaque computational procedures – to make socially controversial decisions is a common phenomenon. In many fields, complex questions about what is fair (fair interest rates, fair use of public resources or distribution of public benefits, fair punishments, etc.) are entrusted to algorithms, underpinned by the belief that they are less susceptible to human biases and errors. …

From one point of view, these calculative techniques succeeded in producing a mutually acceptable and sustainable solution to the problem of dividing up agricultural income on church land, providing landlords with a way to gradually increase their income in line with inflation, while at the same time protecting tenant farmers from arbitrariness and exploitation. table It now works like a synthetic habit.

At the same time, the introduction of the discount table for church land was also an element of other significant transformations in landlord-tenant relations. Most notably, the shift from a system in which tenants paid based on a fixed “ancient” rent to a system based on the surveyed profitability of the land. This dramatic transformation was undoubtedly to the disadvantage of tenants. The institution of the discount table for church land protected church tenants from the worst consequences of this change. But at the same time, one can reasonably assume that church policy justified this change and exacerbated the erosion of customary protections for tenants of non-church land. Since many of those who benefited from favorable church leases were relatively wealthy and well-connected, the institutionalization of Acroyd’s algorithm may have actually helped to entrench existing disparities. This is a pattern that would be repeated in the subsequent history of algorithmic adjudication. In other words, the calculated fairness was a form of collusion, a deal concluded between a subset of interested parties without taking into account, and often to the detriment of, the views of many others who were not part of the equation.

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