2.3 The Present Value Model Under Uncertainty

Chapter 2 Accounting Under Ideal ConditionsNic Festarini, Alex Leon, Ben McRae, Matt Spark

2.1 Overview

OverviewPresent Value Model- Under certainty and uncertaintyReserve Recognition AccountingHistorical Cost AccountingThe Non-Existence of True Net IncomeA Matter of Principles by Al RosenCICA Handbook: Section 1100

2.2 The Present Value Model Under Certainty

The Present Value ModelWidely used in Economics, Finance and Accounting

Provides relevant information to financial statement users

Determines firms future prospects and aids in investment decisions

Example of the Present Value Model Under Certainty Consider P.V. Ltd. is a one asset company with no liabilities. Assume the asset will generate end of year cash flows of $150 in both year 1 & 2, and then have a zero value after that. Assume the economic interest rate is 10%. Determine the present value of the firms cash flows and balance sheets at year 0 and year 1.

Example of the Present Value Model Under Certainty Balance Sheet As at Time 0Capital Asset, at expected PV$260.33Shareholders Equity$260.33

Example of the Present Value Model Under Certainty Net revenues are capitalized into asset value

Similar to a savings account

Net IncomePA0 = 260.33 * 0.1PA0 = $26.03

Accretion of discount

Example of the Present Value Model Under CertaintyBalance Sheet at the End of Year 1AssetsShareholders EquityCash$150Opening Value$260.33Capital Asset, at PV$136.36Net Income$ 26.03$286.36$286.36

Important PointsDividends

Net book value = Present value

Relevant and Reliable

Arbitrage Profits

Net income plays no role in firm valuation

2.3 The Present Value Model Under UncertaintyIllustrative example with concepts carrying over from 2.1

States of Nature (States)States of Nature: Uncertain future events such as the state of the economy.

States of nature are a conceptual device to model uncertain/uncontrollable future events whose realizations affect cash flows of a firm

ExampleState 1: Economy is bad (probability 0.5)State 2: Economy is good (probability 0.5)Note: No one can control which of the states is realized; hence they are called states of nature

States of Nature ContinuedAt time 0, no one knows which state will occur and we assume that the set of possible states is publicly known and complete.

Assume that the state probabilities are objective and publicly knownEx: If we imagine a long-run sequence of repetitions of our two-state economy, the bad state will occur with relative frequency of 0.5.Note: The implication of an objective probability here is that any particular outcome tells us nothing about what the state probabilities are.

Ideal ConditionsIdeal conditions under uncertainty are characterized by:

1. A given, fixed interest rate at which the firms future cash flows are discounted2. A completely and publicly known set states of nature3. State probabilities objective and publicly known4. State realization publicly observable

ExampleTaking into account that the economy can be in a bad state or a good state during each year. If it is in a bad state, cash flows will be $100 for the year. If it is in the good state, however, cash flows will be $200 for the year. Assume that during each year the bad state and the good state each occur with probability 0.5.

Example ContinuedBalance Sheet As at Time 0Capital Asset, at expected PV$260.33Shareholders Equity$260.33

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Example ContinuedInvestors may be averse to risk

Expected value of the firm at the end of year 1 will be $236.36 or $336.36 depending on whether the bad state or the good state happens in that yearSee calculations on subsequent slides

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Example ContinuedAccretion of discount is based on expected net income for year 1Calculated as: 0.10 * $260.33 = $26.03

Under uncertainty, net income consists of expected net income plus or minus abnormal (unexpected) earnings for the year

Income Statement for Year 1 (Bad State)Accretion of Discount$26.03Less: Abnormal earnings:Expected Cash Flow (0.5 * $100 + 0.5 * $200)$150Actual Cash Flow$100($50.00)Net Loss($23.97)

Example ContinuedBalance Sheet As at End of Year 1 (Bad State)Financial AssetShareholders EquityCash$100.00Opening Value$260.33Capital AssetEnd of Year Value$136.36Net Loss($23.97)$236.36$236.36

Example ContinuedAccretion of discount is based on expected net income for year 1Calculated as: 0.10 * $260.33 = $26.03

Income Statement for Year 1 (Good State)Accretion of Discount$26.03Add: Abnormal EarningsExpected Cash Flow (0.5 * $100 + 0.5 * $200)$150Actual Cash Flow$200$50.00Net Income$76.03

Example ContinuedBalance Sheet As at End of Year 1 (Good State)Financial AssetShareholders EquityCash$200.00Opening Value$260.33Capital AssetEnd of Year Value$136.36Net Income$76.03$336.36$336.36

This chapter ignores the complication of risk averse investors by assuming investors are risk neutral. That is, they are indifferent between the sure thing and the 50/50 gamble. As such, the firms market value will be $260.33 at time 0.

Points to ConsiderFinancial statement reliability and volatility are different concepts. While PV calculations are reliable under ideal conditions, net income and balance sheet values are volatile since end-of-period PV depend on which state is realized. Volatility is demonstrated by abnormal earnings in our example, where net income varied from ($23.97) to $76.03 under bad and good state realizations.

Points to Consider ContinuedThe income statement has no information content when abnormal earnings do not persist. Investors have sufficient information to calculate for themselves what realized net income will be, once they know the current years state realization. Net income is predictable conditional on the state of nature

Looking AheadSubjective Probabilities (formally introduced in chapter 3): Individuals must assess state of nature probabilities for themselves, using whatever information is available.A more reasonable assumption than objective probabilities because the future performance of a business entity is much more complex and difficult to predict than a simple two state illustration.

2.4 Reserve Recognition AccountingAn Example of RRA with Husky Energy Inc.

Reserve Recognition AccountingReserve Recognition Accounting (RRA) is a current value standard for oil and gas companies. In 1982, the FASB issued SFAS 69 which required supplemental disclosure of certain information about the operations of publicly traded oil and gas companiesSFAS 69 requires disclosure of the estimated PV of future receipts from a companys proven oil and gas reservesIntended to provide investors with more relevant information

RRA ContinuedWhen estimating future cash flows, SFAS 69 requires that the PV calculations use year-end oil and gas prices (as opposed to prices expected to be in effect when the reserves are lifted and sold). SFAS 69 does not require disclosure of states and nature and their probabilities, only the end results of the expectation calculation.SFAS 69 requires a mandated 10% discount rate to be used, presumable for comparability across firms. The figures apply only to proved reserves

RRA ContinuedRRA is more relevant that historical costs of reserves, however it is by no means completely relevantRRA is not a complete representation since it applied only to proved reservesConcept itself is a matter of judgement, since proved essentially means reasonably certain of recovery under current economy and operating conditions. This definition is thus subject to bias, and estimates are subject to error as shown by substantial adjustments to previous estimates.

RRA ContinuedOil company managers tend to regard RRA with suspicion. As an example, Huskys management states in its SFAS 69 disclosures that its RRA information is not a reliable performance measure and should not solely be relied upon in evaluation company performance.Why use RRA?May want to appeal to a broader spectrum of investors as many multinational oil companies report RRA information.

Basic Problems of RRAThe basic problem is that Husky does not operate under ideal conditions.

1. Interest rates in the economy are not fixed, although FSAS 69 deals with this by requiring a fixed, given rate of 10% for discounting.2. The set of states of nature affecting the amounts, prices, and timing of future production is much larger than the simple two-state example shown previously.3. Objective state probabilities of proved reserve amounts are not available. It is difficult to apply PV accounting when the ideal conditions it requires does not hold.

..Basic Problems of RRA ContinuedThe complex environment in which oil companies operate renders it effectively impossible to prepare estimates that are completely accurate and unaffected by subsequent events. Thus estimates become subject to errors and possible bias that threaten reliability to the point where the benefit of increased relevance is threatened.

2.5 Historical Cost Accounting

Comparison of Different Measurement Bases

Present-day accounting practice can be considered as a mixed measurement modelIt can be argued that Historical Cost accounting is more useful than Current Value Accounting (Dichev and Tang 2008)Past performance is the best indicator of future performanceStatement of Earning is primary F/S

Comparison of Different Measurement BasesCurrent Value accounting includes volatility and reliability concernsFirms operate in an constantly changing environmentSamuelson (1965), who demonstrated that when markets work well, market prices fluctuate randomly Balance Sheet is of greater importanceHowever, volatility impacts F/S as volatility reflects the firms environment

Characteristics: Relevance vs. ReliabilityIt is necessary to trade them offDifferent measurements bases imply different tradeoffsHistorical CostRelevance LowReliability HighCurrent ValueRelevance HighReliability Low

Characteristics: Revenue Recognition Current Value implies earlier Revenue Recognition than under Historical CostCurrent value accounting values assets & liabilities as changes constantly occur in current value Recognition as changes in current value occurHistorical cost accounting values inventories at cost and A/R at selling priceRecognition as inventory is sold

Characteristics: Recognition LagRecognition Lag refers to the timing of revenue recognition lags behind changes in economic valueCurrent Value Low Recognition LagChanges in economic value occur as recognizedHistorical Value High Recognition LagChanges in economic value occur through realization

Characteristics: Matching of Costs & RevenuesHistorical CostMatching is primarily used as net income is accomplished through the use of accrualsAccrualsResult of the matching of realized revenues with the associated costsAccruals smooth out cash flows to allocate them over related periods

Characteristics: Matching of Costs & RevenuesMatching is reasonably reliable yet vagueness is presentConsider Amortization of Capital Assets:IAS 16, amortization should be charged systematically over the assets useful life and reflect the pattern of benefit consumptionHowever, useful life and benefit consumption are largely subjective estimates

Characteristics: Matching of Costs & RevenuesCurrent ValueMatching is not required, as net income is an explanation of changes in current valueValues of assets & liabilities is driven by:Market ForcesThe firms response to these forces

2.6 The Non-Existence of True Net Income

The Non-Existence of True Net IncomeCurrent Value accounting F/S require that all the firms assets and liabilities be prepared based on the current valueNet income is the change in the firms current value during the periodHowever under real world conditions Net income does not exist as a well-defined economic constructLack of objective state probabilities

The Non-Existence of True Net IncomePresence of Incomplete Markets market values need not exist for all firm assets and liabilitiesReady market values is not available, results in an impossible income measure Income is not well defined when markets are incomplete (Beaver & Demski 1979)However, net income is not information impact when conditions are ideal

Concept of Net IncomeFrustrating difficulty of agreeing on accounting policiesDifferent users will desire tradeoffs between relevance and reliabilitySeveral different accounting policiesFascinating lack of well-defined concepts of net incomeJudgment is critical in the process of asset valuation and income measurementProvides the basis of the accounting profession

Additional Reading:A Matter of PrinciplesAl Rosen

Financial Statements in CanadaDifficult to interpretDo investors require education to understand a companies financial statements?Several alternatives for reportingVarious methods can lead to misunderstandings amongst investorsDepreciation policiesInventory costing

Current Problems Investor PerspectiveNot familiar with Canadian GAAPInability to explain GAAPs impact on the financial statementsEPS and EBITDA figures are being misinterpreted

Accounting Text BooksOld text books can become misleading extremely quickly with the fast changing principles in accountingPrinciples once deemed useful and current, can quickly become outdated in Canadian GAAP

CICA Handbook: Section 1100Generally Accepted Accounting Principles

CICA HB: S1100This section describes what constitutes GAAP principles for private enterprisesProvides guidance on sources to consult when selecting accounting policies and determining appropriate disclosuresThe primary sources of GAAP in descending order of authority:Sections 1400-3870Accounting Guidelines

CICA HB: S1100Accounting guidelines set out how existing sections shall be applied in specific cases Sections and accounting guidelines sometimes have illustrative material such as examples and decision treesPart 1 of the handbook may be an important source to consult on matters not covered by Part 2

CICA HB: S1100Consistent accounting policies used for similar transactions unless GAAP requires or permits categorization of items for which different policies may be appropriateSpecific GAAP recommendations from the primary sources override the concepts in section 1000

Jeopardy