Pastoral Grazing Land Valuation:

In the need to find the best applied, yet theoretical and normative, income-approach and method
process to deriving the value for investment purposes, of a pastoral-zone-grazing-enterprise
(PZGE), and the land it operates upon, in the arid and semi-arid regions of far-western
Queensland, Australia, a relationship path is chosen. A path that looks deeply at the long-term
moving-average ratios, looking-through-the-cycle (LTTC), between the livestock-production
ability of the land itself, and its relationship with gross-revenue; and thus, the earnings-before
interest-and taxation (EBIT) cash-flows (or, net-operating-profit-before-taxation): because that
important EBIT number, is what pays any debt, dividends, capital-expenditure, and taxes.

This income approach and method of ‘value-of-agricultural-investment-in-land’ (V^2), is how
the inherent risk in this type of asset investment is priced accurately, and to a high degree of
probability. The price that emerges is a fundamental-value, or a fair-investment-value (FIV),
at the ‘point-of-indifference’ (POI), where the buyer and seller can agree, and are price
indifferent as to transacting; where net-present-value (NPV) is equal to zero.

Flowing-on from pricing the asset as a going-concern, the agistment/rent/leasing amount is also
discoverable (on an annualised basis): from this same POI metric; where the LTTC, all-risks
yield (ARY) is found: as is the likely affordable, minimum cost-of-debt (kD) in pricing risk.
The master-key to unlocking both the V^2, as a present-value (PV), and the further derived,
‘expected-value-of-real-assets-pastoral’ (EVORA-Pastoral) valuation framework (EPVF, a
Framework), is via the discovery of a unitless, scalar-fractal attractor as a multiple of gross
income, called ‘lambda’ (λ). This λ measures and frames the inherent risk; from seasonal
weather/climate, and the expected produce of annual meat-markets. The λ is derived from
‘two old bankers sayings on debt-leverage’, from around the Federation Drought mid-point (circa
1901), and the relationship between revenue and live-stock, and between debt and livestock,
and the loan-to-valuation (LVR) ratios of total livestock value to total asset value, and thus,
total-assets to total livestock value (all LTTC), and also a mathematical, universal truth.

This discovery of λ is achieved using different methods, within and via a framework of various
distilling systems of methodology; covering applied mathematics and statistics, applied
finance and theory of applied-valuation, applied accounting theory and the mathematics of
management, and economic theory and applied agricultural economics. Some of these methods
applied are, the Law of Large Numbers, Gaussian versus Pareto (80/20) statistics, time-value
of-money (TVM), present-value (PV), and net-present-value (NPV) in the discounted-cash
flow (DCF) methods for valuing an expected income-stream, and also measures of a market’s
range of trading: expectations and stability across time, via Time-Series-Analysis, and Monte
Carlo-Simulation. This λ risk-metric, is essential and fundamental to pricing risk, accurately.

The source sample-data (#1,098-samples, across 61-years), once analysed, was found to be
completely Right-skewed and non-linear; and part of a dynamical system with many moving
parts. The adoption of the LTTC approach to the data had the effect of removing much noise
from the analysis and final result, by bringing the data more towards the middle of the likely
range, and thus made any Pareto, Pearson and Gaussian statistics less volatile, and variable.

The five (5) key-findings are: a) there is a constant universal relationship between the addition
of two numbers, and their answer; such that the unitless scalar multiple of λ, can be deduced:
if a + b = c, becomes λ = c / a = (b / a) + 1: which in turn leads mathematically to, total-assets
minus total-livestock equals, land plus ‘all-things-necessary’ (LATN); or, (λ2 – λ); b) there is
an embedded long-term relationship between the gross-revenue, and the value of the land, and
also the value of agistment/rent/leasing; c) the LTTC, as a central-limit-theorem (CLT)
approach, is important to remove excess noise from the data; d) to price risk of a PZGE
correctly, for investment-purposes, an economic FIV is found at the POI; and, e) that an
appropriate mid-term (i.e. around mid-year-5) level of debt and E(kD) may be targeted, that fits
within expected cash-flows and likely livestock asset values (if the debt be called upon).

The likely users, and likely uses, of this V^2 and EPVF income method and framework of
valuing a PZGE for investment-purposes, and pricing the FIV risk within (LTTC), are
graziers/farmers, financiers, and professional-services firms such as valuers, lawyers,
accountants, and other stakeholders focussed on the arid and semi-arid regions, and those
looking to find value, with an appropriate return on investment, and to compare to the current
market-price-value (MPV), to quantify the gap-premium, so as not to pay too much, initially.

The actionable contributions to the gap in the knowledge, in this specialised area of valuation
theory and applied-valuation are: a) the ability to price the risk in any PZGE, accurately; b) to
derive an income approach and method (V^2) as part of a larger PZGE valuation framework,
to find the normative, theoretical, and hypothetical FIV; for both the ‘going-concern’ enterprise
of total-assets-less-cash (TALC), and the LATN; where the livestock (LSTK) are at PV prices.

为找到适用于澳大利亚昆士兰州远西部干旱及半干旱地区牧区放牧企业（pastoral-zone-grazing-enterprise，PZGE）及其运营土地的、兼具实用性与理论规范性的最优收益法估值路径与方法流程（用于投资目的价值评估），研究选择了一条关联分析路径。该路径深入探究土地自身牲畜生产能力与总收入之间的跨周期（looking-through-the-cycle，LTTC）长期移动平均比率，以及由此产生的息税前利润（earnings-before interest-and taxation，EBIT）现金流（或税前净营业利润）——因为这一关键的EBIT数值是偿还债务、支付股息、资本支出及税费的基础。

这种名为“土地农业投资价值（value-of-agricultural-investment-in-land，V²）”的收益法，能够精准且高概率地对该类资产投资中的固有风险进行定价。由此得出的价格是无差异点（point-of-indifference，POI）上的基础价值或公平投资价值（fair-investment-value，FIV）——在此点上，买卖双方可达成共识且对交易价格无差异，同时净现值（net-present-value，NPV）等于零。

在将资产作为持续经营实体定价的基础上，放牧费/租金/租赁金额（按年化计算）也可通过同一POI指标得出——该指标同时包含LTTC全风险收益率（all-risks yield，ARY）以及风险定价中可负担的预期最低债务成本（minimum cost-of-debt，kD）。解锁作为现值（present-value，PV）的V²及进一步衍生的“牧用实物资产预期价值（expected-value-of-real-assets-pastoral，EVORA-Pastoral）估值框架（EPVF，一个框架）”的关键，在于发现一个无量纲的标量分形吸引子——它是总收入的倍数，被称为“拉姆达（λ）”。此λ用于衡量并框定季节性天气/气候及年度肉类市场预期产出带来的固有风险。λ的推导基于联邦干旱期中期（约1901年）流传的“两条银行家关于债务杠杆的古老谚语”，以及收入与牲畜、债务与牲畜之间的关系，总牲畜价值与总资产价值的贷款估值比（loan-to-valuation，LVR）（反之亦然，均为LTTC），同时还基于一个数学普遍真理。

λ的发现是通过多种方法在不同方法论提炼体系框架内实现的，涵盖应用数学与统计学、应用金融学与应用估值理论、应用会计理论与管理数学、经济学理论与应用农业经济学。所应用的方法包括大数定律、高斯统计与帕累托（80/20）统计、货币时间价值（time-value of-money，TVM）、现值（PV）、折现现金流（discounted-cash flow，DCF）法中的NPV（用于评估预期收入流），以及通过时间序列分析和蒙特卡洛模拟衡量市场交易范围、跨期预期与稳定性的方法。此λ风险指标对于精准定价风险至关重要且具有基础性意义。

源样本数据（共1098个样本，跨度61年）经分析后发现呈完全右偏且非线性特征，属于具有多个动态组件的动态系统的一部分。对数据采用LTTC方法可将数据拉向更可能的范围中心，从而消除分析及最终结果中的大量噪声，降低帕累托、皮尔逊与高斯统计的波动性与变异性。

五项关键发现如下：a) 两数相加与其结果之间存在恒定的普遍关系，据此可推导出无量纲标量倍数λ：若a + b = c，则λ = c/a = (b/a)+1——这在数学上进一步推导得出总资产减去总牲畜价值等于土地加所有必要资产（all-things-necessary，LATN），即λ² - λ；b) 总收入与土地价值及放牧费/租金/租赁价值之间存在内在长期关系；c) 作为中心极限定理（central-limit-theorem，CLT）方法的LTTC，对于消除数据中的多余噪声至关重要；d) 为正确定价投资目的下PZGE的风险，需在POI处找到经济FIV；e) 可设定合适的中期（即第5年中期左右）债务水平及预期最低债务成本（E(kD)），使其与预期现金流及可能的牲畜资产价值（若债务被要求偿还）相匹配。

V²与EPVF收益法及PZGE投资价值估值框架（含LTTC下FIV风险定价）的潜在用户及用途包括：牧场主/农民、金融机构、估值师、律师、会计师等专业服务机构，以及关注干旱及半干旱地区的其他利益相关者——这些主体旨在寻找具有合理投资回报的价值，并将其与当前市场价格价值（market-price-value，MPV）对比，量化价差溢价，以避免初始投资时支付过高成本。

在估值理论与应用估值这一专业领域，本研究对知识空白的可操作贡献包括：a) 精准定价任何PZGE风险的能力；b) 推导收益法（V²）作为更广泛PZGE估值框架的一部分，以找到规范性、理论性与假设性的FIV——适用于总资产减现金（total-assets-less-cash，TALC）的持续经营企业及LATN，其中牲畜（LSTK）按现值定价。