# Accounting In Perfect And Complete Markets Essay — страница 4

“better” means higher net present value for the owners. Thing 3 establishes the equivalence of “better” and higher income. Since period 1 income is the interest rate times year 0 present value, year 1 income is higher if and only if year 0 present value is higher. Year 2 income is similar since income is the interest rate times year 0 present value time (1 + interest rate). It follows that if the cash flow stream is chosen to increase net present value, every period’s income will also be higher. We have established that valuing assets at their discounted future cash flow and defining accounting income to be the change in owners’ equity minus net contributions to capital implies that more income is better. Thus, a larger accounting income number is associated with greater economic welfare for the firm’s owners. As a consequence, we shall henceforth refer to this approach to calculating accounting income as the economic income approach. Back to the main point at hand. To review, we have (1) a market setting (perfect and complete markets) and (2) an accounting technique for presenting the balance sheet and income statement under which more valuable firms always have higher accounting income in every period. Two problems are immediate, however. Can we count on the existence of perfect and complete markets, and can we use the present value accounting valuation technique? Let’s consider the second of these questions. Other Approaches to Accounting Income MeasurementIn the previous section we valued the asset at its cost, and subsequently carried it at the present value of its future cash flows. The latter is, of course, a forward-looking calculation. Yet accounting rules we see rely heavily on objective, verifiable numbers, minimizing to the extent possible reliance on expectations of future events. What happens to our conclusions if we don’t construct our accounting numbers using the discounted cash flow valuation rule? Rather, suppose we initially book the asset at cost, but use some (arbitrary) conventional depreciation method, such as the sum of the years’ digits method. The first thing we notice is that the equivalence between higher net present value (”better”) and higher income in every period no longer holds. Thing 3 is no longer necessarily true. But not everything is lost. Even if we use other accounting techniques, it is still the case that higher income is associated with better investments. But to get the relationship to hold we may have to add up income numbers from more than one period. To illustrate this idea reconsider the original example with some accounting changes. Balance sheetsYear 0Year 1Year 2Year 3Cash$ 0$26$52.60$79.86Long term asset6030100Owners’ Equity$60$56$62.60$79.86Income StatementsYear 1Year 2Year 3Revenue: Cash Revenue$26$24$22 Interest02.605.26Depreciation expense302010Income$(4)$6.60$17.26 In these financial statements a different valuation rule is used; the asset is not reported at the discounted cash flow amount in every period. Instead, the asset is recorded at its cost (which we assume is equal to its discounted cash flow) less accumulated accounting depreciation (using the sum of the years’ digits method). The main point raised here is that the sum of the income numbers, – 4 + 6.6 + 17.26 = 19.86, remains the same as it did under the discounted cash flow valuation rule. This is a general result and is illustrated further for a scheme which depreciates the entire asset in year 1. Balance sheetsYear 0Year 1Year 2Year 3Cash$ 0$26$52.60$79.86Long term asset60000Owners’ Equity$60$26$52.60$79.86Income StatementsYear 1Year 2Year 3Revenue: Cash Revenue$26$24$22 Interest02.605.26Depreciation expense6000Income$(34)$26.60$27.26 Even under this depreciation scheme the total income remains at 19.86. The examples above illustrate the following facts:1.With discounted cash flow valuation, we know that for better firms:a.income is higher in every period, andb.total income for all three periods is higher. 2.With any consistent valuation scheme (where the long term asset is valued at its cost), we know that total income for all three periods is higher. The second fact follows from the error correcting nature of the double entry accounting system. If income is made higher in one period it must be lower in some future period. For example, one period’s ending inventory becomes the next period’s beginning inventory. Thus, if the former period’s ending inventory is overvalued income in that period is overstated, but the next period’s beginning inventory is also overvalued, so that period’s income is understated. Thus, all is not lost when alternative (and more verifiable and

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