# Biological asset valuation

*This is a highly-technical article directed towards finance professionals, accountants, and auditors involved in corporate financial reporting; more specifically, for those professionals who have responsibility with understanding or complying with the ***biological asset valuation*** requirements of IAS 41, Agriculture. In short, the article provides a technical overview of the basic biological asset valuation concepts and methods that finance, accounting, and auditing professionals involved in IAS 41 compliance should know.*

*In my view, there is pervasive de facto non-compliance with the IAS 41 (and conforming in-country accounting standards), and this is usually directly evident in companies’ financial statement disclosures with respect to biological assets. Specifically, many companies make disclosure statements similar to “Biological assets are measured at cost, which management believes to be materially equivalent to fair value less selling costs as required by IAS 41 ‘Agriculture’.” Think about that statement for a moment. IAS 41 requires fair value measurement, but companies making such statements are basically saying they believe cost equals fair value. Hmmm …
*

*What would be the basis for the belief that the cost of biological assets is approximately equal to their fair value? I’ve spoken with a number of controllers and auditors on this issue and the most common answer is something like, “Well, we know a lot about the market price of our agricultural products and we’ve discussed this issue a lot and just think it is safe to *assume* biological asset cost is equal to fair value. And, by the way, our auditors agree with us.” If you were a CFO, controller, or auditor, would feel comfortable making that *assumption in writing … publicly*? If your answer is yes, well ok; it’s a free world. *:- )* But if your answer is no, please read on …*

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#### 1. An overview of biological asset reporting requirements

Definitions. * Biological assets* (BAs) are living plants, animals, or other organisms that meet the financial reporting definition of an asset. *Bearer biological assets* either bear other biological assets (e.g, livestock) or agricultural products (e.g., fruits obtained from fruit trees). To make the definitions more concrete and understand how they relate to agricultural products, consider the following diagram:

Market prices for biological assets. It turns out that, in general, many BAs per se cannot be valued without reference to agricultural products derived from the BAs as we will see later. The basic idea is that there are often no markets for the BAs per se; developed markets usually exist only for the agricultural (or other) products that are obtained from the BAs. So, market prices are not generally observable for BAs.

Basic valuation requirements. IAS 41 *Agriculture* is an international financial reporting standard generally requiring BAs to be measured at IFRS 13 *fair value** less selling costs*. I won’t discuss them here, but there are also related accounting standards promulgated by accounting standard-setters within specific countries that closely parallel IAS 41.

Although other methods of estimating fair value are allowed, IAS 41 allows the *residual value method* for BAs physically attached to land having no active market (e.g., immature plants). The method measures BA fair values based on the fair value of the combined land-and-BA if an active market for the combined assets exists:

There are a number of relatively severe problems with the residual method that tend result in biased estimates of fair value, but I will explain only the most obvious problems: In practice, it is not exactly easy to find a reasonable sample both land-and-BA sale transaction data and *comparable* raw land transaction data.

For example, even if we can find transaction data on sugarcane plantation transaction price data (per hectare)–which includes both the land and partially grown sugarcane–it is usually the case that (*i*) the sugarcane growth stage can vary significantly between properties, and (*ii*) it is very difficult to find comparable raw land transaction data because most land suitable for sugarcane production tends to be in production at the time of a sale; raw land transactions tend to represent land that is not suitable for, or not economically feasible to put into, sugarcane production (e.g., land near highways or cities can have a higher value for alternative uses).

Setting aside the residual method which is unique to IAS 41, the fair value estimation requirements of IAS 41 are basically equivalent to those of IFRS 13:

(1) __Quoted market prices__ from active biological asset markets are considered the most reliable basis for estimating fair value of a specific biological asset (IAS 41, para. 17-19).

(2) __Discounted future cash flows.__ If reliable market prices are not available for a specific biological asset, then present value of expected net cash flows from the asset determined based on a current market-determined discount rate is appropriate (IAS 41, para. 20).

(3) Estimated cost. In the limited circumstance where no substantial biological transformation has occurred in the biological asset, then it is generally appropriate to estimate fair value based on the cost of the biological asset (IAS 41, para. 24).

It is critically important to recognize that because there are generally no active, quoted markets for units of *immature* BAs assets until they have been harvested and processed into units of agricultural product (e.g., there are no markets for 1/2-grown coffee beans, oranges, etc.), it follows that IAS 41 generally requires estimation of the risk-adjusted present value of future cash flows associated with the agricultural product units obtained from physical biological asset units to estimate their fair value.

There are, of course, some types of BAs for which there are active futures markets with observable current market prices on BA-related *agricultural products* contracts with delivery dates sufficiently far into the future that correspond to the expected maturation, harvesting, processing, and delivery of the agricultural products. For example, as of this writing, the Nymex #11 sugar futures market has contracts extended out to May 2019; so, two years out. Although observability of futures prices seems to suggest method (1) above is adequate, this is not the case; so, it’s generally necessary to use method (2) as I discuss below.

#### 2. The fundamental problem of biological asset valuation

__The fundamental valuation problem.__ The fundamental problem of estimating the fair value (*FV*) of any asset using discounted cash flow methods can be seen most easily in the simple relationship between current fair value and a single expected future cash flow:

The dependence of cash flows and market risk-adjusted discount rates on *risk factors*, denoted as **x**, emphasizes that the fundamental problem of valuation involves (*i*) identifying relevant risk factors over cash flows, (*ii*) projecting cash flows conditional on risk factor forecasts, and (*iii*) estimating how the relevant risk factors over cash flows are priced in a fair market.

Expected versus actual values. Valuation professionals don’t often make the concept of *fair value* explicit, but it can be shown (trust me on this) that **fair value is an estimate of the expected price**—**not the actual price**–resulting from a transaction negotiated under fair market conditions.

To make sense of this statement, just note that an expected value–a probability-weighted average–is not the same thing as an actual value because in most all real world cases there are random causal factors that cause unpredictable variation around that expectation. It turns out that this distinction is critical in most applications of valuation methods to financial reporting: When fair market prices for a specific asset are not observable, we are not predicting *actual prices*; we are predicting *fair value*, which is a probability-weighted average of actual prices that are generally subject to random variation. Think about this carefully. If prices are subject to random variation, then how can we predict actual prices? *We can’t*: *We can only predict some kind of average*.

Read that last paragraph several times until it makes sense. It is absolutely critical to understanding valuation in general, and BA valuation in particular … as we will see.

__The fundamental valuation problem for biological assets.__ It follows from the above discussions that the fundamental problem of estimating biological asset fair value can be most generally represented as …

… where *t* can be regarded as the current financial reporting data, *T* represents the expected agricultural product delivery date associated with the BA, and the general dependence on risk factors **x** over the physical biological asset and cash flows is explicitly shown. Note that *all factors shown in the right-hand-side of the equation must be estimated* and, as alluded to in the previous section, this can even include cases where there are observable futures prices associated with (the agricultural product from) the BA.

#### 3. Biological asset physical processes and IAS 41

BA physical processes. From practical perspective, it’s generally not (economically) feasible to measure the physical units of a BA, denoted *b*(**x**) above, at a financial reporting date; estimates are needed. This generally means that we need a model of the physical processes associated with the BA, which can then be estimated using statistical methods.

Here is a a basic mathematical model of BA physical processes …

… which is fairly intuitive. At *t* = 0 BA units equal zero, *b* = 0. Then BA units are planted, bred, created, etc.; *z* > 0. BA units grow at a rate of *g* > 0 over time and, at some point, BA units are harvested. Although I will defer the explanation to a future article, it should be reasonably evident to those familiar with statistical methods that, if we have data on *b*, *z*, and *h* over time, we can somehow estimate the growth rate *g*. Let’s move on to how this relates to valuation dynamics under IAS 41.

BA processes and IAS 41. Taking the above BA physical process model, we can easily derive a model of valuation dynamics (i.e., valuation changes over time) under IAS 41. Conceptually, we only need to regard each element of the previous expression as a value and to add a term that captures the residual change in value not accounted for in the other terms:

Ignoring valuation and market pricing of risks for the moment, note that the variables generally depend on a variety of decision variables and exogenous factors influencing the BA; general examples of which would be things such as …

**x** = {*agricultural methods, fertilizer, land quality, weather*}

… where such factors must generally be regarded as *risk factors* over the BA physical and economic processes.

Although the differences between the physical process and valuation dynamics model are subtle and not at all obvious, I will simply point out that those who understand backflush cost accounting will recognize the conceptual similarity. I will otherwise avoid details of BA accounting mechanics here because it’s outside the basic BA valuation scope of the article. For our purposes here, what is important about the above expressions is that we simply understand that changes in BA value are partially–but not wholly–attributable to BA physical asset growth.

#### 5. Example: Sugarcane growth, agricultural product, and valuation functions

In this example, I will move more quickly without much explanation or referencing. Any interested reader is welcome to contact me or post a question on references, theory, logic, evidence, etc. below the article.

Physical asset growth model. Consider a BA physical unit growth function proposed by agricultural scientists to be one reasonable functional form for representing non-linear plant growth:

The function is called the logistic function and has been widely used by scientists in growth modeling for hundreds of years. It’s not necessary to understand much about the above growth function other than that the growth rate *g* > 0, the initial BA value *b*0, and general factor *K* (potentially representing a variety of factors) determine the level and shape of the growth function, for which I show an example in a graph below.

Agricultural product output function. Recall that because there are usually no organized markets for BAs per se (e.g., there are no organized markets for partially grown sugarcane), it is generally necessary to estimate the agricultural product output from the BA. To continue the example, when sugarcane is harvested and milled there is an average proportional loss or difference between the estimated raw sugar content of the unharvested sugarcane and the raw sugar remaining at the end of the harvest/milling process. This can be represented by a simple function where BA units, *b*, are multiplied by two proportions *hm* < 1, the product of which is the estimated agricultural product units:

This represents the agricultural product unit volume–in pounds of raw sugar–associated with the estimated sugar content of the unharvested sugarcane at time *t*, which could, in principle, be sold in an actual spot market.

BA valuation function. A simplified version of the previously shown BA valuation function that suppresses the explicit dependency of the function(s) on the set of risk factors **x** can be written as …

… where, one way or another, we have estimated the expected future price per pound of raw sugar, selling cost, and the risk-adjusted market discount rate.

Graph. Using semi-realistic parameter values obtained from sugar industry data sources for each of the three functions presented above, I constructed the following graphs to show the basic geometric shapes and relationships between the functions:

Values in the graph omit 000 and, so, represent either thousands of pounds of raw sugar or USD thousands (because the global sugar market is priced in USD).

The BA physical unit function shows that over the 18 months spanned by the graph, sugar content of the cane grows slowly at first because the leaf size for maximal solar radiation exposure–used by the cane to convert energy to sugar–has not been achieved. The growth rate then become rapid with sufficient leaf size, and then levels off as the cane matures. The raw sugar agricultural product function can be seen to be proportional to the BA physical unit function. (Note: I realize Brazilian sugarcane can grow to maturity in about 6 months; I made the graphs based on Indian sugarcane data.)

Interestingly,the BA valuation function begins at *t* = 0, the BA inception date, at a value substantially near zero. To understand this, just note that BA value is determined by the risk-adjusted discounted value of the ultimate future cash flow obtained after the BA is harvested, processed, and delivered to the market. In this case, when sugarcane is immature early in the growth phase, there is so little sugar content that the risk-adjusted discounted value of the small cash flow associated with that sugar content is very low. Perhaps most importantly, *this phenomenon generally results in BA fair value being lower than BA cost early in the BA life cycle*. So, as suggested in my introduction, the common management assumption that BA cost approximates BA fair value is problematic.

With this overview of the functions underlying BA valuation, we can turn explicitly to the question of how to estimate the risk-adjusted market discount rate.

#### 5. Estimating risk factor pricing using (fair) market data

Modern asset pricing theory suggests that to estimate fair market risk-adjusted price—and discount rate—it is necessary to estimate the risk factors to which a biological asset’s cash flows are sensitive:

Recalling the expected, risk-adjusted market price—and related expected risk-adjusted market return—the expected market price and return per unit of risk can be estimated using biological asset price and risk factor data. If market price data is obtained from a fair market, then it follows that risk factor premiums determine the expected fair market (inverse) price of the set of risk factor sensitivities:

So, modern asset pricing theory is really quite simple; even if abstract. Nonetheless, because this article is not about asset pricing theory application, I’m going to make a (huge) assumption about risk pricing below that allows me to avoid actually estimating market risk premiums.

So, with the caveat that we should not do it this way in practice, let’s look at a non-rigorous example roughly showing how to apply the theory to valuing a sugarcane crop; a leading example of BA valuation in Brazil.

#### 6. Example: Sugarcane crop valuation under IAS 41

Raw sugar market risk factor sensitivities. Recall that the fundamental BA valuation problem suggests the fair value of expected future sugar output and related profit stream can be written as …

The notation “**x**” indicates that *risks over expected future sugarcane revenues and costs that are priced in a fair market* must be identified (i.e., some risks are *hedged* or *diversified* and, so, are not *priced* in markets), and then fair market pricing and risk-adjusted expected rates of return must be estimated. For example, economic theory suggests a number of potential risk factors influence the demand for any product (and, so, related production costs as well):

**x** = { *shifting preferences*, *currency purchasing power*, *season*,

* substitutes*, *consumer income*, *consumer population, … * }

Recalling that under asset pricing theory it’s necessary to develop estimates of raw sugar price sensitivity to risk factors, I developed and estimated the following econometric model of Nymex #11 sugar contract *front-month futures price* as a function of global risk factors:

The basic idea here is that because the sugar futures market is a highly organized, deep market, using futures prices to estimate risk factor sensitivities results in more accurate, reliable estimates. In contrast, there are raw sugar spot markets all over the world, but they are by comparison much less organized and much less deep. Consequently, it is usually not clear that all significant risks are being impounded in spot market prices, making any resulting estimates potentially less accurate and reliable.

To see a bit more clearly what the econometric model is predicting, consider the graph of the econometric model in-sample predictions to the actual sugar future market price data (red vertical lines show nominal time bounds of the Great Recession effects on Brazil):

The relatively good fit of the model to actual price data suggests the economic factors identified in the model represent the primary risk factors priced in the raw sugar futures contract market.

Econometric model interpretation and implications. The econometric model explains about 87% of the variation in sugar contract price between 2000 and 2012 as a function of observable global risk factors. Modeling of other risk factors to potentially explain the remaining variation is, of course, possible, but I think the model is sufficient for the example; i.e., the model seems to capture most major risks that are priced in the global sugar market.

The model includes a variable, *time-to-delivery*, that captures average combined rates of time discounting and risk pricing for growth/harvest/milling/transport of raw sugar. That is, it captures the raw sugar price effects of risk factors that are not priced through the other global market factors. As seems normal for raw sugar markets, the estimated marginal effect of time-to-delivery is negative (-.1258) consistent with sugar market being in a contango condition over average over the sample period; implying, importantly, that holding all else equal sugar futures prices are not equivalent to expected future sugar spot prices. Intuitively, the contango condition and related negative risk-adjusted expected rate of return on the long futures position represents the periodic cost of ensuring ownership of the commodity.

Having now estimated raw sugar futures contract risk factor sensitivities and shown that futures prices are generally not equal to expected future spot prices, I will conclude by pointing out that we could use the sensitivity estimates to both predict such future spot prices and to estimate the market risk-adjusted market discount rate; both of which are needed to estimate the value of the sugarcane crop. I will, however, make a huge simplifying assumption: *I assume only the marginal effect of time-to-delivery will have an effect on raw sugar futures and spot prices and that all other risk factors will have no effects*. Basically, I am just making the assumption to keep things focused on BA valuation rather than on application of asset pricing theory.

__Predicting expected spot price from futures price.__ Recall that observed Nymex #11 sugar contract price data represents the rolling market average price of the front-month sugar futures contracts with a time to settlement/delivery of between approximately 15 and 75 days. The basic relationship between futures price *F* at present time *t* for future delivery date *T* and *future expected* spot market price *P* at time *T* can be written as …

… where I use discrete versus continuous time discounting and *r* = *R* – 1 generally represents the net periodic cost of holding the long position with all significant risks impounded into this market discount rate.

Fair value of sugarcane crop. Based on the sugar futures econometric model shown above, the above futures-spot price relationship, and the expectation of futures price conditional on risks at 12/31/2010 of US $.2422 per pound, the expected future sugar spot price at 3/15/2011 is …

… where (by the simplifying, unrealistic assumption) I use the time-to-delivery marginal effect as the risk-adjusted market discount rate; again showing the normal contango market condition for raw sugar and related *negative* risk-adjusted expected rate of return from holding a long position in the futures contract.

Suppose we need to estimate the fair value of a sugarcane crop at a financial reporting date of 12/31/2010 where the raw sugar spot market delivery date is expected to be 3/15/2011. First we need estimates of the BA and related agricultural product output inherent in the BA at the 12/31/2010 financial reporting date. Using (hypothetical) data and estimates we obtain from plant scientists, plantation managers, and commodity traders, we estimate the raw sugar content of a sugarcane crop planted on 9/17/2010 (measured in thousands of pounds) to be …

Using this estimate, the estimate of expected future spot price per pound of raw sugar of US $.2359, estimated selling costs at 2% of spot price, and the estimated risk-adjusted market discount rate, the estimated IAS 41 fair value of the sugarcane crop at the 12/31/2010 financial reporting date would be …

… in USD thousands (US$ 34,800). *O fim*.

#### 7. Summary and final thoughts

In addition to providing an overview and examples of biological asset (BA) valuation under IAS 41, I’ve basically demonstrated a number of things that don’t seem widely understood among professionals responsible for developing, reporting, and auditing estimates of biological asset (BA) fair values under IAS 41:

- BA fair value is, in principle, not equivalent to BA cost.
- BA fair value is, in principle, not equivalent to BA futures market price.
- BA fair value must be estimated from expected BA agri-product cash flows.
- BA / agri-product physical unit models are necessary for BA valuation.
- BA fair value depends on a broad set of BA risk factors.
- All significant BA risk factor sensitivities must be estimated.
- Risk-adjusted discount rates must depend on (fair) market risk premiums.

Unless I’m mistaken about the general level of understanding of BA valuation issues, that represents a fairly extensive set of important ideas that are not widely understood among professionals with BA valuation-related responsibilities.

Why would this be the case? I think we all know the reason: As the business world becomes more complex, all our professional education, training, and experience becomes more and more specialized and–hence–narrower. Consider the remarkable scope of fields addressed in this article: financial accounting and reporting, agricultural production, commodity markets, financial derivatives, asset pricing theory, mathematics, and econometric methods. Roughly speaking, it would take a professional lifetime to become an expert in any one of these fields.

This all suggests that the problem with BA valuation has mainly to do with how we are all educated, trained, and experienced. I will address this issue in future articles, but for the time being I will leave the (very patient, diligent) reader with food for thought on what I believe is the basis for a solution to the problem:

“At a more advanced level, we have such tools as the equation or formula which enable [us] to learn in a few hours fundamental and pervasive features of the behavior of things which [we] could otherwise learn only imperfectly with great labor or not at all.” E. L. Thorndike

Or, if the reader would prefer, a quote from someone a bit more closely associated with the modern financial world …

“It has been my experience that competency in mathematics, both in numerical manipulations and in understanding its conceptual foundations, enhances a person’s ability to handle the more ambiguous and qualitative relationships that dominate our day-to-day financial decision-making.” Alan Greenspan

Thought provoking, no? Let’s continue the discussion below and in future articles / discussions. After all, no problem solves itself. :- )

MMc

São Paulo

**Caveats.** Please note: (i) views presented above are my own and do not reflect those of others; (ii) like anyone, I’m not infallible and am responsible for any errors; (iii) I greatly appreciate being informed of any significant errors in facts, logic, or inferences and am happy to give credit to anyone doing so; (iv) the above article is subject to revision and correction; and, (v) the article cannot be construed as investment or financial advice and is intended merely for educational purposes. MMc