Accounting In Perfect And Complete Markets Essay — страница 3

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cash flows. Thus market values and discounted cash flows are equivalent under perfect and complete markets. Before proceeding, we note that market value accounting may not in general work well. Imagine that markets were not perfect. In particular, what if the current owner of the asset knew the discounted cash flows, but outsiders did not? They might attribute a larger or smaller value to the asset than the owner, so the market price would not be equal to the current owner’s discounted cash flows from holding the asset. Thus the market value would not necessarily be a good way to value the asset. What if the markets were not complete? That’s even easier, there is no market price! So, in cases where markets do not work well, market value accounting will not (or can not)

represent the value of the assets to the firm. Applying this valuation rule to our example, the asset will be valued now (year 0) as follows:$60 = 26(1.10) + + . Similarly, the asset value at year 1 is:$40 = 24(1.10) + . All we need to construct financial statements is a valuation rule and we have one, so here are the financial statements. Balance sheetsYear 0Year 1Year 2Year 3Cash$ 0$26$52.60$79.86Long term asset6040200Owners’ Equity$60$66$72.50$79.86Income StatementsYear 1Year 2Year 3Revenue: Cash Revenue$26$24$22 Interest02.605.26Depreciation expense202020Income$6$6.60$7.26 Check that all the numbers are sensible. Since no dividends were paid, the cash received earns interest at 10%. So interest earned in year 2 is 10% of $26. In year 3, interest earned is 10% of (26 + 2.60

+ 24) = $5.26. Depreciation is reported in the usual way: it is equal to the difference between ending and beginning asset value adjusted for acquisitions and disposals (of which there are none). Since the values are established in perfect markets, depreciation when calculated this way reflects the change in value to the firm. Thus, this method of depreciating is commonly referred to as economic depreciation. Depreciation expense results because some of the future cash flows have been realized, and so are no longer available to the owner of the asset. Some of the future cash flows have been converted to cash on hand. For example, year 1 depreciation is 60 – 40 = 20. In this example, the sequence of depreciation expense numbers turns out to be equal to those obtained under the

familiar straight line depreciation approach, but this is purely a coincidence: the depreciation numbers follow from the valuation of the asset. There are four things about these financial statements we want to be sure we understand. Thing 1 — The assets are reported using the discounted value of future cash flows. That’s the rule which allowed the construction of the statements; and, further, that was the only rule we required to make a complete set of statements. Thing 2 — Since discounted cash flow calculations are forward-looking, there is a demand to do accruals. Cash accounting cannot accomplish proper valuation and income determination. Thing 3 — Each period’s accounting income is equal to the interest rate times beginning owners’ equity. Note, for example,

that year 3 income is $7.26 which is 10% of year 2 owners’ equity of $72.60. It is easily verified that the other years work the same way. This relationship is a sensible one which follows from our perfect and complete market structure. All assets can be traded for dollars and all dollars earn the same rate of return (in this case 10%). (Certainty and risk neutrality are important here, as well.)Thing 4 — We have a clean surplus accounting relationship which is maintained. In every period ending owners’ equity is equal to beginning owners’ equity plus accounting income for the period. For example, year 3 owners’ equity ($79.86) is equal to year 2 owners’ equity ($72.60) plus year 3 income ($7.26). Of course, in general owners’ equity would be adjusted for dividends

and contributions of capital, but we don’t have any of them here. A tangential question that arises is why more accounting income may be better. First let’s attach some meaning to the term “better.” In perfect and complete markets the owners of the firm prefer higher net present value to lower. They can rearrange their holdings in the marketplace to suit their own consumption preferences. Higher net present value of their share of the firm increases the opportunities available to them. This is the rationale for using maximum net present value as the criterion in capital budgeting and other problems in finance — higher net present value is always preferred to lower in the presence of sufficient market opportunities. In the market setting of our discussion, then,