# Equity Valuation. Lecture Notes # 8. 3 Choice of the Appropriate Discount Rate 2. 4 Future Cash Flows: the Dividend Discount Model (DDM) 3

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1 Equity Valuation Lecture Notes # 8 Contents About Valuation 2 2 Present-Values 2 3 Choice of the Appropriate Discount Rate 2 4 Future Cash Flows: the Dividend Discount Model (DDM) 3 5 The Two-Stage Dividend-Growth Model 5 6 Dividends and Earnings 5 7 The EVA Model 8 8 Alternative Valuation Techniques 9 9 Applications: Boeing and Exxon 0 0 Practice Problems

2 Investments: Notes 8, c by Yalçın 2 About Valuation Sometimes we can observe a market value for the security, and we are interested in assessing whether it is overvalued or undervalued (Eg: stock analysts) Sometimes there is no market value and we are trying to construct one for bargaining or transaction purposes (Eg: a corporation wants to sell a division What should the price be?) Both of these situations call for equity valuation, and this is the most common kind of valuation problem 2 Present-Values The stock is bought, held for some period of time (dividends are collected) and then sold The share is valued as the present value of the expected dividends and the proceeds from the sale: intrinsic value, V Dividends are paid annually, and the time-0 dividend (D 0 ) has just been paid The stock will be bought and held for one year The present value is = E(D + P ), + k If = P 0 = expected rate of return coincides with the discount rate k: + k E(D + P ) P 0 Two main issues arise in the valuation problem: Choice of the appropriate discount rate 2 Estimation of future cash-flows 3 Choice of the Appropriate Discount Rate The discount rate can be found using the CAPM From the SML: k = r f + β[e(r M ) r f ]

3 Investments: Notes 8, c by Yalçın 3 Consider the following valuation problem for ConEdison at the beginning of 994 The beta for ConEdison is: β CE = 75 The average annual rate of return on the SP 500 index, 82-94, is: E(r M ) = 497 The risk-free rate (annual rate) is r f = 075 We have k = = 30 4 Future Cash Flows: the Dividend Discount Model (DDM) Assume constant growth of dividends Dividends are expected to grow at a constant rate g forever: E(D 2 ) = E(D )( + g), E(D 3 ) = E(D )( + g) 2, The present value of all the cash-flows generated by the stock is given by = E(D ) + k + E(D 2) ( + k) 2 + E(D 3) ( + k) 3 + = D 0( + g) + k = D 0( + g) k g + D 0( + g) 2 ( + k) 2 + D 0( + g) 3 ( + k) 3 + = E(D ) k g Note that this result is valid only when k > g If g > k, the present value of the dividends is infinite Note that, based on the model above, the expected rate of capital gains on a stock equals E(V ) = E(D 2) E(D ) E(D ) Hence, we have = E(D )( + g) E(D ) E(D ) k = E(D ) + E(V ) = E(D ) + g = g The expected rate of return on a stock is the sum of expected dividend yield and expected capital gains, where the latter coincides with the growth rate of dividends

4 Investments: Notes 8, c by Yalçın 4 A growth stock is one whose expected rate of return is mainly due to the expected growth of cash flows Conversely a value stock is one whose expected rate of return is mainly due to the expected dividend yield In the case of ConEdison, 993 dividends amounted to \$50, or, disregarding compounding issues, an annual dividend of D 0 = 2 Then, we can proxy the rate of growth of dividends g with the expected growth rate of earnings for the next five years (from analysts forecasts): g = 5% In summary, = 2 05/(30 05) = 2592 This theoretical valuation is remarkably close to the actual price of \$2675 < P 0 is equivalent to the asset plotting below the SML > P 0 is equivalent to the asset plotting above the SML The intrinsic value of a stock is very sensitive to changes in k and g: d dk = k g and For ConEdison we have d dg = + k + g d dk k g = 234 and d dg = 329 This means that if k increases by %, the price of ConEdison drops by 234% If g increases by %, the price of ConEdison increases by 329%

5 Investments: Notes 8, c by Yalçın 5 5 The Two-Stage Dividend-Growth Model The discussion above assumes that dividends grow at a constant rate forever In practice, firms tend to go through different phases Let g denote the growth rate for the first n years Let g 2 denote the growth rate for the remaining life of the firm We have = D 0 + g k g [ ( ) + n ] g + D 0 ( + g ) n + g 2 + k k g 2 ( + k) n The intrinsic value of the firm equals the present value of a growing annuity plus the present value of a deferred growing perpetuity Example Consider again ConEdison stock at the beginning of 994 Assume g = 05 for the first five years, and then g 2 = 06 forever The intrinsic value is given by = 2 05 ( = = 2864 ) ( ) Dividends and Earnings While the cash flows generated by stock ownership are the cash dividends distributed by the firm, stock valuation is sometimes performed in terms of earnings, rather than dividends Hence, it is important to understand the relationship between the two Assume a constant rate of growth of dividends: + g = D t D t Dividends: constant fraction ( b) of the earnings produced by the firm, b: retention or plowback ratio b: payout ratio D t = ( b) E t

6 Investments: Notes 8, c by Yalçın 6 Earnings: proportional to the physical assets (book value) of the equity shares, S, E t = ROE S t Hence, we have S t = S t + be t = S t + broe S t = S t ( + broe) The capital stock, and hence earnings and dividends, grows at the rate g = broe The rate of growth of dividends increases with b, the retention ratio, and ROE In turn, the rate of return on equity depends on the rate of return on assets, ROA, the book value of equity, S, the book value of debt, Debt, the rate of interest paid on the debt, i, and the tax rate: ROE = S + Debt S = ROA + Debt ROA + ( S + Debt S [ROA i ( t)], ) i ( t) S where (S + Debt)/S = Debt/S Equity is equivalent to a portfolio long + Debt/S in the assets of the firm and short Debt/S in corporate bonds Since interest payments are tax deductible, the rate of return on the corporate bonds is reduced by a factor equal to the corporate tax rate The share price depends on the decision to reinvest in the firm: = E(D ) k g = E(E )( b) k (b ROE) Similarly, we can write the price-earnings ratio as = ( + g)( b) k (b ROE) If ROE = k, = E(E )/k: the current intrinsic value does not depend on b Intuition: k is the rate at which you are borrowing; ROE is the rate at which you are investing If ROE = k, you are breaking even

7 Investments: Notes 8, c by Yalçın 7 If ROE > k, you want to increase b: + as b k/roe < If ROE < k, you want to decrease b: 0 as b Also, note that ROE > k means that the assets of the firm plot above the SML Vice versa, ROE < k means that the assets of the firm plot below the SML E(E )/k: value of the firm when i) ROE = k, and/or ii) b = 0 Difference between P 0 and E(E )/k: value of reinvesting future earnings into the firm, the present value of growth opportunities (PVGO); High PVGO stock: growth stock Low PVGO stock: value stock PVGO P 0 E(E ) k Example 2 Consider Eli Lilly at the beginning of 992 We have and Assume the growth rate of earnings = 450, D 0 = 200 g = 654 for the first five years and the growth rate g 2 = 06 afterwards Also, assume the retention ratio for the first five years to be equal to the current retention ratio b = (45 2)/45 = 5556 In the long-run, the retention ratio is derived from the expected growth rate g 2, using ROA = 8, Debt/S = 232, and i ( t) = 0475: b 2 ROE = g 2

8 Investments: Notes 8, c by Yalçın 8 Hence b 2 = g 2 ROE = (8 0475) = 2847 The cost of capital for Eli Lilly is estimated at k = 378 Based on this information, we can compute the present value of the cash flows for the first five years: ( ) = The theoretical value at time 5 is computed according to the second part of the formula for the two-stage dividend formula V 5 = ( ( + g ) 5 ( b 2 )) + g 2 k g 2 ( + k) 5 V 5 = ( 2847) ( + 378) 5 = 4944 Note that since we are not the given dividend growth g div, we cannot use the first term D 0 ( + g div ) 5 = E(D 5 ) of the 2-stage formula directly Instead, we can compute the expected date-5 dividend and the growth after date 5 from the earnings growth: E(D 5 ) = ( + g ) n ( b 2 ), where we used the earnings growth g until year 5 to get the expected earnings at date 5, and the estimated payout ( b 2 ) after year 5 for the expected dividends after year 5 Hence, the theoretical value at time 0 is given by = V 5 = = 609 which should be compared to an actual price of \$79 in February 992 We can now calculate the present value of growth opportunities as PVGO = 79 (45 654)/378 = The EVA Model In recent years an alternative formulation of the dividend growth model has gained popularity: the Economic Value Added or EVA model

9 Investments: Notes 8, c by Yalçın 9 The EVA model is based on the intuition that the current value of the firm depends on the current market value of the assets in place,, plus the discounted value of the cash flows generated by the future assets in place in excess of the cost of equity: where and hence Since t= S t (ROE k) ( + k) t = = + t= S t (ROE k) ( + k) t, S t+ = S t + be t+ = S t ( + broe) t= the EVA formula implies that S t = ( + broe) t (+b ROE) t(roe k) (ROE k) = S ( + k) t 0 k (b ROE) (ROE k) = + k (b ROE) = S ROE( b) 0 k (b ROE) Note that ROE = E(E ), and hence = E(E )( b) k (b ROE), which is the dividend-discount model expressed in terms of earnings 8 Alternative Valuation Techniques In practice, the cash-flow analysis described before is complemented by information based on industry ratios Price-earnings ratio: given the average price-earnings ratio for the industry, we can calculate the intrinsic value of the stock We have = ( Similarly, we can use the average market-to-book ratio: = ( ) )

10 Investments: Notes 8, c by Yalçın 0 Also, we can use the average price-to-sales ratio: = ( Note that we can also relate cash-flow analysis to these other valuation techniques For the price-earnings ratio, we have = D 0 + g k g where D 0 / = b: pay-out ratio For the market-to-book ratio, we have ) = ( b) + g k g, = D 0 + g k g = ROE, where / = ROE: rate of return on equity For the price-to-sales ratio, we have where / = π: profit margin = D 0 + g k g = π, These theoretical ratios can be compared to the actual ones to have a better understanding of the relationship between the actual and the theoretical valuation 9 Applications: Boeing and Exxon Example 3 At the beginning of 995 Boeing had the following ratios: P 0 / = 2709 P 0 / = 239 P 0 / = vs vs vs ( ) ( ) ( ) = 85 = 257 = 8 Hence, based on these comparisons it is hard to tell whether Boeing is undervalued or overvalued relative to the rest of the industry

11 Example 4 Consider Exxon at the beginning of 995 We have b = 74, expected growth rate g = 06 We also have k = 3 ROE = 5 and π = 047 We can calculate theoretical ratios We have / = = 529 / = = 229 / = = 79 These theoretical ratios can be compared to actual ratios of 702, 244, and 78 Hence, we may conclude that Exxon is slightly overvalued 0 Practice Problems The Two-Stage Dividend Growth Model The Patagon Company currently does not pay any dividends, and is not expected to pay any dividend for the next six years Seven years from now Patagon is expected to pay the first dividend of \$05 per share At that point the rate of return on assets is expected to be ROA = 20% The debt-equity ratio is expected to equal D/E = 3, with an after-tax cost of debt of 45% The expected payout ratio is ( b) = 06 Patagon s beta is 2, the risk free rate is 5% and the premium on the market is 6% Calculate the expected value of the stock seven years from now, E(V 7 ) Also, calculate the current value of Patagon, Assume Patagon stock is fairly priced, calculate the component of the expected rate of return between year zero and year one which is due to the dividend yield, and that which is due to capital gains Redo your calculations for the expected rate of return between year seven and year eight

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