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# Appendix BDerivation of Steady-State Valuation Multiples

Three different theoretical steady state valuation approaches are discussed in Chapter 5. This appendix provides a concise derivation and discussion of the three, e.g., the accounting approach, the discounted free cash flow approach and the market consistent approach.

## The Accounting Approach

The most common steady state valuation formula originates in the accounting literature, often called the residual income or Edwards–Bell–Ohlson (EBO) approach.1 This approach expresses the steady-state value of a firm in terms of accounting earnings and the book value of equity directly. Its starting point is the Dividend Discount Model (DDM).

The DDM assumes that the value of the firm to shareholders is equal to the sum of the discounted expected dividends the firm will generate for shareholders in the future.

Equation B.1 Dividend discount model

${V}_{0}={D}_{0}+\frac{{\stackrel{ˆ}{D}}_{1}}{\left(1+\text{CoC}\right)}+\frac{{\stackrel{ˆ}{D}}_{2}}{{\left(1+\text{CoC}\right)}^{2}}+\frac{{\stackrel{ˆ}{D}}_{3}}{{\left(1+\text{CoC}\right)}^{3}}+\dots$

where ${V}_{0}$ is the current market value of equity (or market capitalization) of the firm, ${\stackrel{ˆ}{D}}_{t}$ is the expected dividend to be received at time t and CoC is the firm's cost of capital, assumed constant.

The EBO is a transformation of the DDM requiring that all balance sheet changes first flow through earnings. In this case, the book value of the firm evolves according to the following formula: ${B}_{t+1}-{B}_{t}={E}_{t+1}-{D}_{t+1}$. Making the appropriate substitutions:2

${V}_{0}={B}_{0}+\frac{{\stackrel{ˆ}{E}}_{1}-\text{CoC}*{B}_{0}}{\left(1+\text{CoC}\right)}+\frac{{\stackrel{ˆ}{E}}_{2}-\text{CoC}*{\stackrel{ˆ}{B}}_{1}}{{\left(1+\text{CoC}\right)}^{2}}+\frac{{\stackrel{ˆ}{E}}_{3}-\text{CoC}*{\stackrel{ˆ}{B}}_{2}}{{\left(1+\text{CoC}\right)}^{3}}+\dots$

where ${\stackrel{ˆ}{B}}_{t}$ is the expected book ...

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