## Valuing the Corporation

Three approaches are commonly used in corporation valuation: the income approach, the asset-based approach, and the market approach.

### Learning Objectives

Distinguish between the income, asset-based, and market approaches for corporate valuation

### Key Takeaways

#### Key Points

- Income approaches include Discount or capitalization rates, Capital Asset Pricing Model (CAPM), Modified Capital Asset Pricing Model, and Weighted average cost of capital (“WACC”).
- The asset approach to business valuation is based on the principle of substitution: no rational investor will pay more for the business assets than the cost of procuring assets of similar economic utility.
- The market approach to business valuation is rooted in the economic principle of competition: in a free market the supply and demand forces will drive the price of business assets to a certain equilibrium.

#### Key Terms

**net asset value**: Net asset value (NAV) is the value of an entity’s assets less the value of its liabilities, often in relation to open-end or mutual funds, since shares of such funds registered with the U.S.**discounted cash flow**: In finance, discounted cash flow (DCF) analysis is a method of valuing a project, company, or asset using the concepts of the time value of money. All future cash flows are estimated and discounted to give their present values (PVs)–the sum of all future cash flows, both incoming and outgoing, is the net present value (NPV), which is taken as the value or price of the cash flows in question.**corporation**: a group of individuals, created by law or under authority of law, having a continuous existence independent of the existences of its members, and powers and liabilities distinct from those of its members

Corporation valuation is a process and a set of procedures used to estimate the economic value of an owner’s interest in a business. Valuation is used by financial market participants to determine the price they are willing to pay or receive to perfect the sale of a business. In addition to estimating the selling price of a business, the same valuation tools are often used by business appraisers to resolve disputes related to estate and gift taxation, divorce litigation, allocate business purchase price among business assets, establish a formula for estimating the value of partners’ ownership interest for buy-sell agreements, and many other business and legal purposes.

Three different approaches are commonly used in business valuation: the income approach, the asset-based approach, and the market approach. Within each of these approaches, there are various techniques for determining the value of a business using the definition of value appropriate for the appraisal assignment. Generally, the income approach determines value by calculating the net present value of the benefit stream generated by the business (discounted cash flow ); the asset-based approach determines value by adding the sum of the parts of the business (net asset value); and the market approach determines value by comparing the subject company to other companies in the same industry, of the same size, and/or within the same region.

### 1. Income approaches

- Discount or Capitalization Rates

A discount rate or capitalization rate is used to determine the present value of the expected returns of a business. The discount rate and capitalization rate are closely related to each other, but are distinguishable. Generally speaking, the discount rate or capitalization rate may be defined as the yield necessary to attract investors to a particular investment, given the risks associated with that investment.

- Capital Asset Pricing Model (CAPM)

The Capital Asset Pricing Model (CAPM) is one method of determining the appropriate discount rate in business valuations. The CAPM method originated from the Nobel Prize winning studies of Harry Markowitz, James Tobin, and William Sharpe. The CAPM method derives the discount rate by adding a risk premium to the risk-free rate. In this instance, however, the risk premium is derived by multiplying the equity risk premium times ” beta,” which is a measure of stock price volatility. Beta is published by various sources for particular industries and companies. Beta is associated with the systematic risks of an investment.

- Modified Capital Asset Pricing Model

The Cost of Equity (Ke) is computed by using the Modified Capital Asset Pricing Model

CAPM Model ke = Rf + B ( Rm-Rf) + SCRP + CSRP Where: Rf = Risk free rate of return (Generally taken as 10-year Government Bond Yield) B = Beta Value (Sensitivity of the stock returns to market returns) Ke = Cost of Equity Rm= Market Rate of Return SCRP = Small Company Risk Premium, CSRP= Company specific Risk premium

- Weighted Average Cost of Capital (“WACC”)

The weighted average cost of capital is an approach used to determine a discount rate. The WACC method determines the subject company’s actual cost of capital by calculating the weighted average of the company’s cost of debt and cost of equity. The WACC must be applied to the subject company’s net cash flow to total invested capital.

### 2. Asset-Based Approaches

The value of asset-based analysis of a business is equal to the sum of its parts. That is the theory underlying the asset-based approaches to business valuation. The asset approach to business valuation is based on the principle of substitution: no rational investor will pay more for the business assets than the cost of procuring assets of similar economic utility. In contrast to the income-based approaches, which require the valuation professional to make subjective judgments about capitalization or discount rates, the adjusted net book value method is relatively objective.

### 3. Market Approaches

The market approach to business valuation is rooted in the economic principle of competition: that in a free market the supply and demand forces will drive the price of business assets to a certain equilibrium. Buyers would not pay more for the business, and the sellers will not accept less than the price of a comparable business enterprise. It is similar in many respects to the “comparable sales” method that is commonly used in real estate appraisal. The market price of the stocks of publicly traded companies engaged in the same or a similar line of business, whose shares are actively traded in a free and open market, can be a valid indicator of value when the transactions in which stocks are traded are sufficiently similar to permit meaningful comparison.

## Discounted Dividend vs. Corporate Valuation

The dividend discount model values a firm at the discounted sum of all of its future dividends, and does not factor in income or assets.

### Learning Objectives

Calculate a company’s stock price using the discounted dividend formula

### Key Takeaways

#### Key Points

- P = D1 / ( r – g ). P is the current stock price, g is the constant growth rate in perpetuity expected for the dividends, r is the constant cost of equity for that company, and D1 is the value of the next year’s dividends.
- The equation can also be understood to generate the value of a stock such that the sum of its dividend yield (income) plus its growth ( capital gains ) equals the investor ‘s required total return.
- There are also problems with the model, such as the presumption of a steady and perpetual growth rate less than the cost of capital may not be reasonable.

#### Key Terms

**Miller-Modigliani hypothesis**: The Modigliani–Miller theorem (of Franco Modigliani, Merton Miller) forms the basis for modern thinking on capital structure. The basic theorem states that, under a certain market price process (the classical random walk), in the absence of taxes, bankruptcy costs, agency costs, and asymmetric information, and in an efficient market, the value of a firm is unaffected by how that firm is financed.

The dividend discount model (DDM) is a way of valuing a company based on the theory that a stock is worth the discounted sum of all of its future dividend payments. In other words, it is used to value stocks based on the net present value of the future dividends. The equation most always used is called the “Gordon Growth Model. ” It is named after Myron J. Gordon who originally published it in 1959, although the theoretical underpin was provided by John Burr Williams in his 1938 text *The Theory of * *Investment* * Value*.

### The variables and equation are:

- P is the current stock price.
- g is the constant growth rate in perpetuity expected for the dividends.
- r is the constant cost of equity for that company.
- D1 is the value of the next year’s dividends.
- There is no reason to use a calculation of next year’s dividend using the current dividend and the growth rate, when management commonly disclose the future year’s dividend, and websites post it.

[latex]\text{P}=\frac { { \text{D} }_{ 1 } }{ \text{r}-\text{g} }[/latex]

Income plus capital gains equals total return:

The equation can also be understood to generate the value of a stock such that the sum of its dividend yield (income) plus its growth (capital gains) equals the investor’s required total return. Consider the dividend growth rate as a proxy for the growth of earnings and by extension the stock price and capital gains. Consider the company’s cost of equity capital as a proxy for the investor’s required total return.

Income + Capital Gain = Total Return

Dividend Yield + Growth = Cost of Equity

[latex]\frac {\text{D} }{ \text{P}} +\text{g}=\text{r}[/latex]

[latex]\frac {\text{D} }{ \text{P}} =\text{r}-\text{g}[/latex]

[latex]\frac {\text{D} }{ \text{r}-\text{g}} =\text{p}[/latex]

### Problems with the Model

- a) The presumption of a steady and perpetual growth rate less than the cost of capital may not be reasonable.
- b) If the stock does not currently pay a dividend, like many growth stocks, more general versions of the discounted dividend model must be used to value the stock. One common technique is to assume that the Miller-Modigliani hypothesis of dividend irrelevance is true and, therefore, replace the stocks’s dividend D with E earnings per share. However, this requires the use of earnings growth rather than dividend growth, which might be different.
- c) The stock price resulting from the Gordon model is hypersensitive to the growth rate chosen.