Disciplining Prospective Accounting
By Humphrey Nash

Abstract: A mechanism that disciplines a prospective accounting model for publicly traded companies is explored.   This mechanism emerges naturally from the synthesis of management and capital market perspectives.   The discipline creates a relevant and reliable accounting measure.

Introduction

In laboratory measurements, materials are weighed by "taring".   In this process an empty container is placed on the scales and the scales are set to zero.   The material to be measured is then placed in the container on the scales.   The new weight indicated will automatically take into account the container's weight.   "Taring" produces a reliable and relevant measure of the material.   It separates the weight of the material (new information) from the weight of the container (old information).

Is there a way to "set the scales" so that we obtain relevant and reliable measurements within a prospective accounting model?   Surprisingly, the answer is yes.   The mechanism for doing this follows from the definitions of relevant and reliable.   Before we explore these definitions we must first describe a simple prospective accounting model.
   

Prospective Accounting

One model of prospective accounting is based on the capital budgeting technology familiar to most accountants.   In this model, the value of an endeavor (expenditure, project, line of business, or entire enterprise) is the present value of the expected net cash flows associated with that endeavor.

Such a value for the entire enterprise (company or corporation) can form the basis for a financial accounting and reporting model.   For example, we can define assets as the present value of cash inflows and liabilities as the present value of cash outflows.   We can define shareholder equity as the excess of assets over liabilities or equivalently as the present value of expected net cash flows.   We will call both the process and the result of obtaining such values a "valuation".   The period change in such values or valuations is the value added.

This simple model works fine in theory.  Will it work in practice?   Can it be made to produce relevant and reliable accounting measurements?   It seems impossible.

Disciplines

In algebra, if we have more unknowns than bits of information there is no unique solution, no reliable or relevant answer.   For example, if we are given one equation or constraint

Y = 2X + 3

with two unknowns, there is no unique solution.   One can produce any value for Y by choosing a suitable value for X.   If we have another bit of information or constraint in the form of a second equation, say Y = -X, then the pair of simultaneous equations

Y = 2X + 3

Y = -X

has a unique solution for Y and a unique solution for X, namely, Y = +1 and X = -1


Prospective accounting depends on expected cash flows.   Expected cash flows would seem to be unconstrained, providing no unique or reliable solution to the valuation problem.  Is there an additional constraint or bit of information, which would produce a unique solution?   The answer is yes.   We want the valuation to be relevant to end-users.

The end-users are shareholders.   Management and analysts also use financial reports but they act on behalf of shareholders and must adopt the shareholder's perspective.  Shareholders want to know the realizable value of their shares.   This requires that reported shareholder equity (the company valuation) be of the same general magnitude as the capital market valuation.   There is also a stronger link.

The company valuation depends on two things: expected cash flows and a discount rate.   The expected cash flows normally arise from cash flow models similar, if not identical to those used for capital budgeting decisions.   The discount rate is (or should be) the shareholder's cost of capital.   The share price is the capital market measure of the cost of capital for that enterprise.   For any given set of cash flows (dividends or capital gains) to the shareholder , the lower the share price the higher the cost of capital, the higher the share price the lower the cost of capital.

The company valuation depends directly on the market valuation because market valuations reflect the cost of capital.   We will accord the capital market complete credibility in determining its cost of capital.   The method for doing this is the dual validation.   This method disciplines prospective accounting by providing a relevant and reliable solution to company valuation and a unique solution for the cost of capital.

Dual Validation

The dual validation requires a double linkage of the cash flow model to historic experience.   It requires simultaneously that the cash flow model fit past cash flows and that the company valuations based on that model fit past market valuations.   Formulas and a procedural diagram for the dual validation are shown in Appendix B

I. Cash Flow Validation

First, the cash flow model, used to project all future expected cash flows, would have to produce an exact retrospective match to the total prior five-year actual net cash flow.   This model would not have to be a perfect model in the sense of matching each separate year's cash flows.   In fact, we do not want it to, since we want a simplified and stable model of reality, not the impossible complexity and variability of reality itself.   More to the point is that actual annual past cash flows may not be as reliable as expected annual past cash flows.  This is due to,

1. year-to-year fluctuations in reported results due to extraordinary items and to extraordinary experience
2. year-end fluctuations in accounts due or receivable
3. the greater reliability inherent in the longer base period (5 years) used in the model
4. the addition of knowledge, understanding, structures, and relationships to the model
5. the fact that the cash flow model is specifically designed to reliably represent the underlying patterns.

In a very real sense the expected cash flows become the standard by which the actual cash flow are judged, not the reverse.   If a past or future year's actual net cash flow is higher than the modeled net cash flow, then we would probably conclude that actual result was better than expected.   We would probably not conclude that the model was unreliable for that year.

The cash flow model would have to kept up-to-date and conform to professional modelers' standards.   Not only would the cash flow model have to conform to the past it would have to conform to the future, or at least the future expected by company management.   Management's cash flow expectations provide half of the information that determines the company valuation.
   

II. Market Price Validation

Second, the average company valuation over the prior five-year time period would be required to exactly match the average market valuation over the prior five years.   This would be accomplished by setting the discount rate for expected cash flows to that value which produces the average market valuation.   This discount rate would vary from company to company and would represent many things: risk, volatility, industry trends, current general market discount rates, management credibility, perceived growth prospects, the quality of earnings projections, etc.   This market discount rate represents the historic cost of capital for the enterprise and is an appropriate general-purpose discount rate (called an implicit rate by accountants).   The historic cost of capital provides the other half of the information that determines the company valuation.

Note that company valuations make use of all future expected cash flows, but such expected cash flows do not include new information or changed expectations of the current year.   This perspective is needed to separate new information from old.   This perspective is the natural perspective arising from performing the dual validation at the start of the year.

Management and the model are given limited credibility in estimating expected cash flows after the five-year validation of the cash flow model (the expected cash flows for the validation period are exact).   The capital market is given complete credibility in pricing accurately and determining its cost of capital over the five-year validation period.

It is not possible for the company to produce a company valuation without some appropriate assumption about the market cost of capital.   It is not possible for the capital markets to determine a cost of capital without some appropriate assumption about expected cash flows.   The dual validation combines the best information from management with the best information from the capital markets.   This approach is superior in that more information and more appropriate information is employed.   This is done in a natural and disciplined way.   The result is to produce more reliable and more relevant information.  This will be clarified in the next section.
   

The Normalization Process

The above method for determining the historic cost of capital seems simple and natural enough, but its ramifications are far-reaching.   We first give a name to the discounting process.   We will call the process by which cash flows are discounted using the historic cost of capital "normalization".

Normalization performs several related functions.   It coordinates expected cash flows, market values, and the cost of capital.   In the process, it disciplines company valuations.   It separates new from old information.   It sets the scales and makes prospective accounting relevant and reliable.

Prospective accounting provides high level processed information about the future in the form of company valuations.   Some of this information about the future may be old information already known to the capital markets.   It is assumed that the capital markets have fully and accurately processed old information over the course of time.   We therefore set the difference between market valuations and the company valuations to zero for the validation period.   This "tares" old information, setting the scales to zero, so that information new to the capital markets may be directly measured and communicated.   It also re-calibrates expected cash flows to so that values are measured in shareholder value units.
   

Normalized Values

Normalization enforces the discipline of capital market pricing within prospective accounting.   Clearly participants in the capital markets are motivated to not over-price since they will lose by doing so.   They also do not want to under-price since they will forego gains (lose) by doing so.   The capital markets are powerfully disciplined, by self-interest, to price accurately.   The strong link between company valuations and market valuations can be used to transfer the discipline of the capital market to prospective accounting.

The historical cost of capital is that rate of discount which, when applied to expected cash flows, produces company valuations matching market valuations.   The level of expected cash flows is not critical, since the historical cost of capital adjusts to any level of expected cash flows.   Hence company valuations are largely independent of expected cash flows arising from a model.   This makes prospective accounting reliable.   This independence is illustrated in Tables I and II in Appendix B.

Table I (not on Website)in Appendix B shows the results of modeling expected net cash flows with a linear fit to actual net cash flows for the five-year validation period.   It also shows the fit of company valuations (labeled expected stock value) to actual stock market values for the five-year validation period.   A cost of capital of 6.17% was used to equate these values (found by the Microsoft Excel goal seek function).   After the validation period, modeled expected cash flows were a linear extension of the cash flows for the validation period.     The resulting expected stock values after the validation period formed a linear extension of the values for the validation period.   The reported company valuation at year-end 2001 would be $2,836,764

Table II (not on Website) in Appendix B shows a similar development where each year's net cash flows is $100,000 higher than in Table I after the year 2000.   The past actual cash flows and the past market valuations are the same as in Table I.   The cost of capital has increased to 9.52%.   The reported company valuation at year-end 2001 would be $2,993,670.   The company valuation has increased somewhat, not due to the increased earnings per se but due to the incidence of those earnings.   In fact, many valuations in Table II are lower than in Table I.   Hence the company valuation is generally not sensitive to expected cash flows.   In this Table, it is assumed that the market was made aware of the higher expected cash flows after the year 2000, i.e., it was not new information.


If we did not increase the discount rate from 6.17% to 9.52% to validate share values then the year-end 2001 company valuation would be $3,967,720.   This is shown in Table III of Appendix B.   All other company valuations would also be substantially increased.   This would only be appropriate if the capital markets and management were not aware of the extra $100,000 of net cash flow, i.e., it was new information.   Such new information would have to be disclosed and would have to have a real existence as a fact of experience, contract, management action or commitment.  Upon disclosure the market valuation would be expected to increase to $3,967,720 (the expected stock value).

This insensitivity of company valuations to expected cash flows (in the absence of new information) arises from the dual validation and produces a high degree of reliability.   The company valuation is the expected standard and, as such, conveys useful information to the market.   Company valuations will exhibit greater stability than market valuations.   Market valuations may differ from company valuations, but the burden may now be on the market to reconcile valuations.   It is expected that changes in actual share prices will track reported value added.

Normalization expresses values and changing values in shareholder terms.   It separates new information from old information and provides decision useful information to the capital markets.   Normalization makes prospective accounting relevant.

   

Un-normalized Values

Normalization re-calibrates most information about the future to agree with market valuations.   However, some information about the future contained in the expected cash flows may be new information not yet known to the capital markets.   This information does not enter into the calculation of the historical cost of capital and is not normalized.   Table III in Appendix B illustrates the effect of new information.   Normalization does not simply "mark to market value".   If normalization did only this it would be empty since it would not be using company information.   It differs in at least four respects.

First, the historic cost of capital is a stable average based on expected cash flows.   This is different from a spot rate.   A spot rate would exactly reproduce the market value and would cancel out all company information.   The goal is not to reproduce market values, but to produce a company valuation that conveys expected cash flow information.

Second, any pattern within the expected cash flows will emerge as a trend in the company valuations.   Normalization leaves patterns intact.   In fact, normalization leaves all expected cash flows intact changing only their present value.

Third, the actual current year results, as they differ from expected, will change the company value unaffected by normalization.   For example, a cash windfall during the year will, in the absence of loss or destruction, be utilized or invested in some way.   The cash is thus converted into future expected cash flows, hopefully with a present value greater than the cash amount.

Fourth and most important, new expectations are not normalized.   New expectations from the current year have no affect on the historic cost of capital and the historical cost of capital can not adjust to offset new expectations.
   

New Expectations

It is difficult for a model to spontaneously generate new expected cash flows.   The model would require some help from management in the form of new decisions or revised assumptions.   If management changes the assumptions for the model then the historic cost of capital will not offset those changes.   Nor do we want it to.   We want to fully measure the value added by those changes.   This is a fundamental reason for using a historic cost of capital.   It provides a standard from which we can measure change.

Not only do we want to measure the effect of assumption changes, we generally want the assumptions to change as much as possible.   We want management to take actions and make decisions that will add value.   We want to measure the long-term value of those actions or decisions, so that adding value to the company coincides with value-added measures.   We want to free management from the tyranny of short-term or backwards accounting.

On the other hand, any revised assumptions would require explicit disclosure and justification; the effect of those changes will have to be disclosed in detail and in total.   It is expected that assumption revisions will be made only infrequently and then only under legitimate circumstances.   No assumption lock-in will be required.   Valuations can thus be responsive to changing circumstances and expectations.   At first it may seem unnatural to allow assumptions changes to affect reported results.   However, it is more unnatural for a changing outlook not to affect values.   Indeed, this is precisely the information that the shareholder needs.

Normalization preserves and captures changing experience or new expectations.   Normalization re-calibrates old expectations so that they, in essence, become the standard from which we measure change.   The scales are set to zero to measure change.

Normalized prospective accounting communicates new forward-looking information to the shareholder.   This information is expressed in shareholder value terms so that the shareholder can make appropriate decisions.  This makes the accounting relevant.

    

Observation

Simulations performed by the author indicate that a disciplined prospective accounting system is stable and reliable.   Accounting and financial reporting can be simplified and made more relevant to end-users thus benefiting management, capital markets, and the accounting profession.   Further details may be found in the draft proposal: Accounting For The Future, by the author.
   

Conclusions

The dual validation provides a simple, natural, and unequivocal mechanism for coordinating company and market information and determining shareholder value.   This can make a prospective accounting model relevant and reliable.

Appendix A
Formulas and Procedures

Dual Validation Formulas

Let,

CVt = Company Valuation at time t
Et = Expected cash flow at time t for prior year
H = Historic cost of capital for the previous five-year period
At = Actual cash flow at time t for prior year
MVt = Market value at time t

The Expected cash flows must match the Actual cash flows,

E-5 + E-4 + E-3 + E-2 + E-1 = A-5 + A-4 + A-3 + A-2 + A-1

This is the cash flow validation.


The Company Valuation is defined as,

CV0 = E1 / (1+H) + E2 / (1+H)^2 + E3 / (1+H)^3 + E4 / (1+H)^4 + …

Where the historic cost of capital H is determined from,

CV-5 + CV-4 + CV-3 + CV-2 + CV-1 = MV-5 + MV-4 + MV-3 + MV-2 + MV-1

This is the market price validation.

Notes

1. The company valuation uses all future cash flows not just cash flows for the validation period.   Hence the cost of capital normalizes all modeled cash flows.

2. The company and market valuations could be year-end valuations.   Average valuations over four quarters might be more reliable and eliminate any seasonal effects.

3. There are two unknowns: the company valuation and the cost of capital.   There are two bits of information: expected cash flows and capital market prices.   We simultaneously solve for both unknowns.

Appendix B

Go out of the box

Appendix C
Value Added and Taring

Whenever we combine or compare cash flows or values from different times an appropriate interest adjustment must be made for the time value of money.   We discount future cash flows and/or accumulate past cash flows using a cost of capital.   If we compare a current valuation with a prior valuation then the prior valuation must be increased by interest on that prior valuation.   In the context of a prospective accounting model designed for shareholder reporting the appropriate interest rate is the shareholder's historic cost of capital.   Hence Value Added is defined by

Value Added = CV0 - CV-1 * (1+H)

Where

CV0 = Current Company Valuation
CV-1 = Prior Company Valuation
H = Historic cost of capital

The historic cost of capital is determined by the capital market's pricing mechanism.   It represents an average yield expected by the market (if it didn't the pricing mechanism would kick in).   Hence roughly half the time the actual yield will exceed the cost of capital and half the time it will fall short.   This applies to individual companies and to the capital market as a whole.   On average, a company will add value half the time and lose value half the time.   On average, half the companies will be adding value and half will be losing value.   On average, the market will add value half the time and will lose value half the time.   Expected value added is zero.  The scales are set to zero.   Hence value added "Tares" financial measurement.

In this sense value added provides an actual-to-expected measure.   The shareholder can immediately judge the progress of the company.   He does not have to assess the meaning of absolute results.   Any positive value added represents progress.   More important, the value added per share represents the expected (past and/or future) increase in share price.   Value added provides a relevant and reliable measure.