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This open access book discusses firm valuation, which is of interest to economists, particularly those working in finance. Firm valuation comes down to the calculation of the discounted cash flow, often only referred to by its abbreviation, DCF. There are, however, different coexistent versions, which seem to compete against each other, such as entity approaches and equity approaches. Acronyms are often used, such as APV (adjusted present value) or WACC (weighted average cost of capital), two concepts classified as entity approaches.

This book explains why there are several procedures and whether they lead to the same result. It also examines the economic differences between the methods and indicates the various purposes they serve. Further it describes the limits of the procedures and the situations they are best applied to. The problems this book addresses are relevant to theoreticians and practitioners alike.

Open Access

### 1. Introduction: A Stochastic Approach to Discounted Cash Flow

Abstract
The valuation of firms is an exciting topic. It is interesting for economists engaged in either practice or theory, particularly for those in finance. Among practitioners, it is investment bankers and public accountants, who are regularly confronted with the question of how a firm is to be valued. The discussion about shareholder value Rappaport set off indicated that you cannot tell from the numbers of traditional accounting alone whether the managers of a firm were primarily successful or did poorly. Instead, the change in the value of the firm is used in order to try and determine exactly this. That suffices for the practitioner’s interest. The reasons why academics involve themselves with questions of valuation of firms are different.
Lutz Kruschwitz, Andreas Löffler

Open Access

### 2. Basic Elements: Cash Flow, Tax, Expectation, Cost of Capital, Value

Abstract
Valuation is being talked about everywhere. Finance experts, CPAs, investment bankers, and business consultants are discussing the advantages and disadvantages of discounted cash flow (DCF) methods since years. This book takes part in the discussion, and intends to make a theoretical contribution to it.
Lutz Kruschwitz, Andreas Löffler

Open Access

### 3. Corporate Income Tax: WACC, FTE, TCF, APV

Abstract
There is a variety of problems in the valuation of firms. That is why the evaluator has to make some simplifications in order to come up with a result. That also goes for the theory of valuation. We will take the first step in assuming that the firm has no debt. In simplifying with this assumption, we shall see that a number of economic problems can be discussed. In the next step we will turn to indebted firms.
Lutz Kruschwitz, Andreas Löffler

Open Access

### 4. Personal Income Tax

Abstract
We now shift gears. While in the last chapter we worked on the basis that the firm was taxed, but that the financiers were free from taxes, we now suppose that the financiers have to pay income tax, but that the firm is spared.
Lutz Kruschwitz, Andreas Löffler

Open Access

### 5. Corporate and Personal Income Tax

Abstract
In the last chapter of this book we would like to look into the question of how to evaluate a firm if taxes are raised both at the investor and at the company level. Attentive readers of Chaps. 2 and 3 might expect a discussion on different strategies of financing policy (Chap. 2) and of dividend policy (Chap. 3). But, we are not going to do this. We will also, however, not dwell on the innumerable variations of possible combinations in this context, rather we will restrict ourselves to a manageable example. At the end, we will only discuss how to proceed in the cases of further possible financing and dividend policies.
Lutz Kruschwitz, Andreas Löffler

Open Access

### 6. Proofs

Abstract
Lutz Kruschwitz, Andreas Löffler

Open Access

### 7. Sketch of Solutions

Abstract
The first strategy requires an investment of $$\frac {1}{(1+\kappa _{t,t+2})^2}$$ and the second one gives a payment of $$\frac {1}{(1+\kappa _{t,t+1})(1+\kappa _{t+1,t+2})}$$ which is, by assumption, more. By investing again and again the investor will get infinitely rich.
Lutz Kruschwitz, Andreas Löffler