Chapter 18 Equity Valuation Models
Fundamental Stock Analysis: Models of Equity Valuation One approach to firm valuation is to focus on the firm's book value, either as it appears on the balance sheet or as adjusted to reflect current replacement cost of assets or liquidation value. Another approach is to focus on the present value of expected future dividends. Basic Types of Models Balance Sheet Models Dividend Discount Models Price/Earning Ratios
Intrinsic Value (IV) Fair value Self assigned value Variety of models are used for estimation Market Price (MP) Consensus value of all potential traders determined on the basis of demand and supply Trading Signal Intrinsic Value and Market Price MP < IV The stock is underpriced Buy MP > IV The stock is overpriced Sell or Short Sell IV = MP The stock is fairly priced Hold
Dividend Discount Models: General Model The dividend discount model holds that the price of a share of stock should equal the present value of all future dividends per share, discounted at an interest rate commensurate with the risk of the stock V o D t ( 1 k ) t 1 t V 0 = Value of Stock D t = Dividend k = required rate of return
No Growth Model V o D k Stocks that have earnings and dividends that are expected to remain constant. Preferred Stock
No Growth Model: Example V o D k E = D = $5.00 k = 15% V 0 = $5.00/0.15 = $33.33
Constant Growth Model The constant-growth version of the DDM asserts that if dividends are expected to grow at a constant rate forever, the intrinsic value of the stock is determined by the formula Vo D Do(1 g) 1 k g k g g = constant perpetual growth rate
Constant Growth Model This version of the DDM is simplistic in its assumption of a constant value of g. There are more-sophisticated multistage versions of the model for more-complex environments. When the constant-growth assumption is reasonably satisfied and the stock is selling for its intrinsic value, the formula can be inverted to infer the market capitalization rate for the stock: k D P 1 0 g
Constant Growth Model The constant growth dividend discount model is best suited for firms that are expected to exhibit stable growth rates over the foreseeable future. In reality, however, firms progress through lifecycles. In early years, attractive investment opportunities are ample and the firm responds with high plowback ratios and rapid dividend growth. Eventually, however, growth rates level off to more sustainable values. Three-stage growth models are well-suited to such a pattern. These models allow for an initial period of rapid growth, a final period of steady dividend growth, and a middle, or transition, period in which the dividend growth rate declines from its initial high rate to the lower sustainable rate.
Estimating Dividend Growth Rates The expected growth rate of earnings is related both to the firm's expected profitability and to its dividend policy. The relationship can be expressed as g ROE b g = growth rate in dividends ROE = Return on Equity for the firm b = plowback or retention ratio = 1 d d = dividend payout ratio
Constant Growth Model: Example Vo k D 1 g E 1 = $5.00 b = 40% k = 15% ROE = 20% Compute the intrinsic value of the stock. Solution: d = 1 b = 60% D 1 = $5 0.6 = $3.00 g = ROE b = 0.2 0.4 = 0.08 V 0 = $3 0.15.08 = $42.86
Specified Holding Period Model V D D D P N (1 k) (1 k) (1 k) 1 2... 0 2 N N P N = the expected sales price for the stock at time N N = the specified number of years the stock is expected to be held
Partitioning Value: Growth and No Growth Components V 0 = No-growth value per share + PVGO V o E k 1 PVGO PVGO Do(1 g) E D E ( k g) k k g k 1 1 1 PVGO = Present Value of Growth Opportunities E 1 = Expected Earnings Per Share Next Year Note: For PVGO to be positive, ROE must be greater than k.
For PVGO to be positive, ROE must be greater than k If PVGO = D 1 k ROE b E 1 k > 0 D 1 k ROE b > E 1 k D 1 > E 1 E 1 k ROE b E 1 k ROE b > E 1 D 1 ROE > (E 1 de 1 )k be 1 = E 1 1 d k be 1 = be 1 be 1 k = k ROE > k
Partitioning Value: Example ROE = 20% d = 60% b = 40% E 1 = $5.00 D 1 = $3.00 k = 15% g = 0.20 0.40 =.08 or 8%
Partitioning Value: Example V o $3 (0.15 0.08) $42.86 NGV o $5 0.15 $33.33 PVGO $42.86 $33.33 $9.52 V 0 = value with growth NGV 0 = no growth component value PVGO = Present Value of Growth Opportunities In this example, ROE > k If ROE = 15%, PVGO = 0. If ROE =10%, PVGO = 15.59
Price Earnings Ratios Stock market analysts devote considerable attention to a company's price-to-earnings ratio. The P/E ratio is a useful measure of the market's assessment of the firm's growth opportunities. Firms with no growth opportunities should have a P/E ratio that is just the reciprocal of the capitalization rate, k. As growth opportunities become a progressively more important component of the total value of the firm, the P/E ratio will increase.
Price Earnings Ratios P/E Ratios are a function of two factors Required Rates of Return (k) Expected growth in Dividends Uses Relative valuation Extensive Use in industry
P/E Ratio: No Expected Growth P P E 0 0 1 E k 1 k 1 E 1 - expected earnings next year - E 1 is equal to D 1 under no growth k - required rate of return P 0 E 1 is called leading P/E ratio; P 0 /E 0 is called the trailing P/E ratio.
P/E Ratio with Constant Growth P 0 D1 E1 d E1(1 b) k g k g k ( b ROE) P0 d 1 b E1 k g k b ROE ( ) d = dividend payout ratio b = retention ratio ROE = Return on Equity
Numerical Example: No Growth E = $2.50 g = 0 k = 12.5% P 0 = E/k = $2.50/.125 = $20.00 P/E ratio = P 0 E = $20 $2.5 = 8 or P/E ratio = 1/k = 1/.125 = 8
Numerical Example with Growth b = 60% ROE = 15% d = (1 b) = 40% E 1 = $2.50 1 + 0.15 0.6 = $2.73 D 1 = $2.73(0.4) = $1.09 P 0 = k = 12.5% g = 9% $1.09 0.125.09 = $31.14 Leading P/E = $31.14 $2.73 = 11.4 Leading P/E = or d = 0.4 = 11.4 k g 0.125 0.09
Pitfalls in P/E Analysis Many analysts form their estimate of a stock's value by multiplying their forecast of next year's EPS by a P/E multiple derived from some empirical rule. This rule can be consistent with some version of the DDM, although often it is not. Often people use average P/E ratio using past data, which ignores the growth opportunity of the firm. Use of accounting earnings also has its problems, e.g., - Historical costs in depreciation and inventory valuation: during high inflation period, the use of historical cost would underestimate cost thus overestimate earnings and underestimate P/E ratio.
Inflation and Equity Valuation Inflation has an impact on real stock returns. Research shows that real rates of return are lower with higher rates of inflation. Remember Fisher effect? r = R i (approximate) Empirical research shows that inflation has an adverse effect on equity values.
Inflation and Equity Valuation One reason is the lower real after-tax earnings and dividends attributable to inflation-induced distortions in the tax system. Often govt. tries to implement contractionary fiscal policy i.e. raise taxes to reduce inflationary pressure.
Practice Problems Chapter 18: 4, 5, 6, 7, 8, 9, 10, 11