Arbitrage-free means, in loose terms, that no market participant is in a position to make earnings from nothing. When valuing a firm, which only has a limited lifespan, its end-date must be determined. Brealey and Myers 2003, p. Firstly, that does not agree with the picture that can be empirically observed, and secondly, you fall into a logical contradiction if you assume that constant dividends can be paid for all eternity from a taxable, levered firm. We are then dealing with a financing policy based on market values.
A First Glance at Business Values 27 In theorem 1. The textbook formula has no practical value in the case of uncertain debt ratios. Our calculation proves that this relation is valid independent of whether the cost of equity and the debt ratio are certain or uncertain. We see two ways of obtaining this information if there is no reference firm available that is actually free of debt. If the company fails to meet financial performance expectations, if one of its big customers jumps to a competitor, or if interest rates take an unexpected turn, the model's numbers have to be re-run. Beyond time T , the cash flows do not flow any more, which is why the value of the firm must disappear.
The length of a time interval is not dependent upon the situation in which our model will be used. We usually distinguish between income taxes for example, personal income tax , value-based taxes for example, real-estate tax and sales taxes for example, value-added tax and numerous others. We are convinced that whoever does otherwise risks being accused of having no scientific ground to stand on. In connection to the fundamental representation of this relation, we will analyze how numerous conceivable forms of financing policy affect the value of firms and derive each appropriate valuation equation. Can we, for instance, ascertain that deterministic cost of equity also results from deterministic average cost of capital? This might surprise the attentive reader, due to the principle we assumed earlier.
First the cost of capital that is now relevant has to be defined again. They are not only usual, but extremely advantageous. Certain paradigms dominate finance theory today. This problem shows what can go wrong in the case of an infinite rent i. The Capitalization of Cash Flow Method is most often used when a company is expected to have a relatively stable level of margins and growth in the future — it effectively takes a single benefit stream and assumes that it grows at a steady rate into perpetuity.
Surprisingly, there is no definition of this term to be found in the literature that is precise enough to be used with logical operations to get valuation equations, in particular in a multiperiod context. It deals with a third way, other than certainty equivalents and cost of capital, of incorporating risk into the valuation equation. The academics are then naturally required to live up to the expectations placed on them and must actually be in a position to develop the necessary adjustment equations. They are at best suitable, or unsuitable. You can try to rehabilitate the firm, that is, to re-establish the profitability through suitable restructuring measures. This reference firm should differ neither with respect to its investment policy, nor in regard to its accruals from the actual firm — as a rule a levered firm — to be valued, see assumption 2.
We will be working with a linear tax scale and take neither allowances nor exemption thresholds into consideration. Since corporations do not have personal liability, we can disregard the owners having to make payments from their private pockets in very unfavorable situations. In contrast to a levered firm in which this must all be explained in detail, the circumstances of an unlevered firm are clear and simple. This leads us to the following definition: Definition 2. And this is the reason why considerable efforts must be made to move in a direction away from the fundamental theoretical understanding, which derives from assumptions demanding a great deal of simplification.
The practice-orientated reader will regard our course of action as rather far from reality. One such form of financing policy seems to us to be fully plausible with high leverage at least for the time being. . Our critical colleagues may want to object at this point that the knowledge of future anticipated returns in the valuation of firms depicts all too heroic an assumption; one which cannot actually be met in real life. The use of a terminal growth rate may seem sloppy or conservative, but in valuing a small business with an appropriately high discount rate, the value of cash flows 11-plus years out is going to be worth very little today. It is after all conceivable that the differences in value of the forms of finance specified by us are relatively small. It is relatively clear what one means when speaking of taxes while doing a business valuation.
Andreas Löffler is chair of Banking and Finance at the Universität of Hannover. These include, for instance, expected utility, the concept of perfect markets, the postulate that the markets are free of arbitrage and the equilibrium concept, just to name a few. If it is decided to understand cost of capital as return in the sense of definition 1. The discounted cash flow approach is based on a concept of the value of all future earnings discounted back at the risk these earnings might not materialize. That is a far-reaching assumption, and we are entirely aware of the resulting limitations.
But I would be cautious as a potential buyer in using this approach to value a small company. The assertion that any claim, complicated as it may be, is also traded in this case the market is called complete , is not necessary to prove the fundamental theorem of asset pricing. With autonomous financing the taking out and redemption of debt followed a static, pre-given plan, which did not take any kind of random developments into consideration. Since a firm cannot be financed autonomously as well as based on market values, we have a contradiction. If one thinks of the American corporate income tax, one effectively envisages the tax profit.