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Chapter 2

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Wilfrid Laurier University
Bixia Xu

FAT Chapter 2 – The Present Value Model Under Certainty The Present Value Model Under Certainty • Certainty: the future cash flows of the firm and the interest rate in the economy are publicly known with certainty o Denoted as ideal conditions • Relevant financial statement information gives information to investors about the firm’s future economic prospects • Under ideal conditions, the firm’s dividend policy will not affect its value o Called dividend irrelevancy o As long as investors can invest any dividends they receive at the same rate of return as the firm earns on cash flows not paid in dividends, the PV of investor’s overall interest in the firm is independent of the timing of dividends o This holds because there is only one interest rate in the economy o Under dividend irrelevancy, cash flows are just as relevant as dividends, because cash flows establish the firm’s dividend-paying ability o As a result, the financial statements are entirely relevant • The firm’s net income plays no role in firm valuation under ideal conditions o Future cash flows are known and hence can be discounted to provide balance sheet valuations o Net income is then perfectly predictable o In effect, under ideal conditions, the balance sheet contains all the relevant information and the income statement contains none o There is no information in the current net income that helps investors predict future economic prospects of the firm, as these are already known to investors and are capitalized into asset valuation • Reliable financial statement information faithfully represents what it is intended to represent o Under ideal conditions, since future cash flows and the interest rate are known with certainty, any attempt by management to hide assets and liabilities, or bias inputs into the present value calculations, and any errors would be immediately discovered • Under the ideal conditions of future cash flows known with certainty and the economy’s risk- free interest rate given, the present value of an asset or liability will equal its market value o Arbitrage: if market prices for identical goods and services are such that it is possible to make a profit by simply buying in one market and selling in another • If a firm has more than one asset, the market value of the firm would be sum of its value of its financial assets plus the present value of the joint future receipts from its capital assets, including its intangibles, less present value of any liabilities o At the points after time 0, the firm’s market value continues to equal the sum of its financial assets plus capital assets, net of liabilities o Dividend policy affects the amount of financial assets, as retained dividend will earn a return on reinvested assets • Summary o Under the ideal conditions of future cash flows known with certainty and a given interest rate in the economy, it is possible to prepare completely relevant and reliable financial statements o The process of arbitrage ensures that the market value of an asset equals the present value of its future cash flow o The market value of the firm is then the value of its net financial assets plus the value of its capital assets (less any other liabilities) The Present Value Model Under Uncertainty • Uncertain future events such as the state of economy are called states of nature, or states for short • No one can control which of the states is realized • Assume that the set of possible states is publicly known and complete • Assume that the state realization is publicly observable • Assume that the state probabilities are objective and publicly known o Objective: probability of the state remains regardless of the state realization this period • Ideal conditions under uncertainty are characterized by o A given fixed interest rate at which the firm’s future cash flows are discounted o A complete and publicly known set of states of nature o State probabilities objective and publicly known o State realization publicly observable • Abnormal earnings / unexpected earnings: reduction in earnings as a result of bad-state realization • Under uncertainty, net income consists of expected net income +/- abnormal earnings • Dividend irrelevancy continues to hold • Abnormal earnings do not persist o The effect dissipates completely in the year in which they occur • It continues to be the case that financial statement is both completely relevant and reliable o Relevance holds because balance sheet values are based on expected future cash flows, and dividend irrelevancy holds o Reliability holds ideal conditions ensure that present value calculations faithfully represent the firm’s expected future cash flows • Volatility: values depend on which state is realized • There are still 2 ways of calculating balance sheet current values: expected PV directly or market values • The income statement has no information content when abnormal earnings do not persist o Net income is predictable conditional on the state of nature • Income statements can be informative o Subjective probabilities: state probabilities are no longer objective o Since the probabilities are subjective, so are the resulting expected values o Which means, the value of the firm is also subjective • When state probabilities are subjective, the income statement can provide information about what these probabilities are • Summary o The definition of ideal conditions must be extended to include a complete and publicly known set of states of nature, with future cash flows known conditionally on state realization o Ideal conditions now specify the objective state realization o The logic of the PV model under certainty then carries over, except that market values are based on expected cash flows, assuming investors are risk neutral o The major difference between the certainty and uncertainty cases is that expected and realized net income need no longer be the same under uncertainty, and the difference is called abnormal earnings o Financial statements based on expected present values continue to be both relevant and reliable  Relevant because they are based on expected future cash flows  Reliable because financial statement faithfully represent the expected future cash flows and, in each case, management omission, error, and bias are not possible o All the conclusions are independent of the firm’s dividend policy, since dividend irrelevancy continues to hold Reserve Recognition Accounting (RRA) • Present value accounting applied to oil and gas reserves is known as reserve recognition accounting (RRA) • RRA seem to conform to the theoretical present value model under uncertainty, except that it is necessary to make changes to previous estimates Critiques of RRA • Provisions such as including only proved reserves, period-end prices are used rather than prices expected when the reserves are lifted and sold, and the interest rate is 10% are made • These provisions reduce relevance, since the extent to which the resulting present value predicts future cash flows and their risk is reduced o RRA is more relevant historical costs of reserves, it is by no means completely relevant • Reliability concerns remain o RRA is not a complete representation since it applies only to proved reserves o “Proved” means “reasonable certainty” of recovery under current economic and operating conditions o RR
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