# LECTURE- 4. Valuing stocks Berk, De Marzo Chapter 9

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1 1 LECTURE- 4 Valuing stocks Berk, De Marzo Chapter 9

2 2 The Dividend Discount Model A One-Year Investor Potential Cash Flows Dividend Sale of Stock Timeline for One-Year Investor Since the cash flows are risky, we must discount them at the equity cost of capital.

3 3 The Dividend Discount Model A One-Year Investor P = 1 + re Div P If the current stock price were less than this amount, expect investors to rush in and buy it, driving up the stock s price. If the stock price exceeded this amount, selling it would cause the stock price to quickly fall.

4 4 Dividend Yields, Capital Gains and Total Returns r E Div1 + P1 Div1 P = 1 = + P0 P { 0 P { 0 Dividend Yield P 1 0 Capital Gain Rate Dividend Yield Capital Gain Capital Gain Rate Total Return Dividend Yield + Capital Gain Rate The expected total return of the stock should equal the expected return of other investments available in the market with equivalent risk.

5 5 Example-1:The Dividend Discount Model 3M (MMM) is expected to pay paid dividends of \$1.92 per share in the coming year. You expect the stock price to be \$85 per share at the end of the year. Investments with equivalent risk have an expected return of 11%. What is the most you would pay today for 3M stock? What dividend yield and capital gain rate would you expect at this price?

6 6 A Multi-Year Investor What is the price if we plan on holding the stock for two years? P Div Div + P = re (1 + re )

7 7 The Dividend-Discount Model Equation What is the price if we plan on holding the stock for N years? P Div Div Div P 1 (1 ) (1 ) (1 ) 1 2 N N 0 = + + L N + re + re + re + re This is known as the Dividend Discount Model. Note that the above equation holds for any horizon N. Thus all investors (with the same beliefs) will attach the same value to the stock, independent of their investment horizons. N

8 8 P The Dividend-Discount Model Equation Div Div Div Div 1 (1 ) (1 ) (1 ) = = n L re + re + re n = 1 + re n The price of any stock is equal to the present value of the expected future dividends it will pay.

9 9 The Discount-Dividend Model Constant Dividend Growth The simplest forecast for the firm s future dividends states that they will grow at a constant rate, g, forever.

10 10 Applying the Discount-Dividend Model Constant Dividend Growth Model P r 0 E = r E Div Div P 1 g 1 = + 0 g The value of the firm depends on the current dividend level, the cost of equity, and the growth rate.

11 Example-2: Dividend Growth Model AT&T plans to pay \$1.44 per share in dividends in the coming year. Its equity cost of capital is 8%. Dividends are expected to grow by 4% per year in the future. Estimate the value of AT&T s stock. 11 P 0 D iv r = 1 = = E g \$ \$36.00

12 12 Dividends Versus Investment and Growth A Simple Model of Growth Assuming the number of shares outstanding is constant, the firm can do two things to increase its dividend: Increase its earnings (net income) Increase its dividend payout rate Dividend Payout Ratio The fraction of earnings paid as dividends each year Div t Earnings t = Shares Outstandingt E PS t Dividend Payout Rate t

13 13 Dividends Versus Investment and Growth A Simple Model of Growth Change in Earnings = New Investment Return on New Investment New Investment = Earnings Retention Rate Retention Rate Fraction of current earnings that the firm retains

14 14 Dividends Versus Investment and Growth A Simple Model of Growth Earnings Growth Rate Change in Earnings = Earnings = Retention Rate Return on New Investment g = Retention Rate Return on New Investment If the firm keeps its retention rate constant, then the growth rate in dividends will equal the growth rate of earnings.

15 15 Dividends Versus Investment and Growth Profitable Growth If a firm wants to increase its share price, should it cut its dividend and invest more, or should it cut investment and increase its dividend? The answer will depend on the profitability of the firm s investments. Cutting the firm s dividend to increase investment will raise the stock price if, and only if, the new investments have a positive NPV.

16 Example-3: Dividends Versus Investment and Growth Dren Industries is considering expanding into a new product line. Earnings per share are expected to be \$5 in the coming year and are expected to grow annually at 5% without the new product line but growth would increase to 7% if the new product line is introduced. To finance the expansion, Dren would need to cut its dividend payout ratio from 80% to 50%. If Dren s equity cost of capital is 11%, what would be the impact on Dren s stock price if they introduce the new product line? Assume the equity cost of capital will remain unchanged. 16

17 17 Changing Growth Rates We cannot use the constant dividend growth model to value a stock if the growth rate is not constant. For example, young firms often have very high initial earnings growth rates. During this period of high growth, these firms often retain 100% of their earnings to exploit profitable investment opportunities. As they mature, their growth slows. At some point, their earnings exceed their investment needs and they begin to pay dividends. Although we cannot use the constant dividend growth model directly when growth is not constant, we can use the general form of the model to value a firm by applying the constant growth model to calculate the future share price of the stock once the expected growth rate stabilizes.

18 18 Changing Growth Rates P N = Div r E N + 1 g Dividend-Discount Model with Constant Long-Term Growth P Div Div 1 2 N N = + + L N N 1 + re (1 + re ) (1 + re ) (1 + re ) re g Div 1 Div

19 19 Limitations of the Dividend-Discount Model There is a tremendous amount of uncertainty associated with forecasting a firm s dividend growth rate and future dividends. Small changes in the assumed dividend growth rate can lead to large changes in the estimated stock price.

20 20 Total Payout and Free Cash Flow Valuation Models Share Repurchases and the Total Payout Model Total Payout Model PV 0 = PV (Future Total Dividends and Repurchases) Shares Outstanding 0 Values all of the firm s equity, rather than a single share. You discount total dividends and share repurchases and use the growth rate of earnings (rather than earnings per share) when forecasting the growth of the firm s total payouts.

21 21 The Discounted Free Cash Flow Model Discounted Free Cash Flow Model Determines the value of the firm to all investors, including both equity and debt holders Enterprise Value = Market Value of Equity + Debt Cash The enterprise value can be interpreted as the net cost of acquiring the firm s equity, taking its cash, paying off all debt, and owning the unlevered business.

22 22 The Discounted Free Cash Flow Model Valuing the Enterprise Unlevered Net Income Free Cash Flow = EBIT (1 τ ) + Depreciation Capital Expenditures Increases in Net Working Capital Free Cash Flow Cash flow available to pay both debt holders and equity holders Discounted Free Cash Flow Model V0 = PV (Future Free Cash Flow of Firm) c P 0 + Cash Debt = V Shares Outstanding

23 23 The Discounted Free Cash Flow Model Implementing the Model Since we are discounting cash flows to both equity holders and debt holders, the free cash flows should be discounted at the firm s weighted average cost of capital, r wacc. If the firm has no debt, r wacc = r E. V FCF FCF FCF V 1 (1 ) (1 ) (1 ) 1 2 N N 0 = + + L N + rwacc + rwacc + rwacc + rwacc Often, the terminal value is estimated by assuming a constant long-run growth rate g FCF for free cash flows beyond year N, so that: N V N FCFN = = rwacc gfcf ( rwacc gfcf ) g FCF FCF N

24 Example:4-Discounted Free Cash Flow

25 Textbook Example 9.7 (cont'd)

26 26 The Discounted Free Cash Flow Model Connection to Capital Budgeting The firm s free cash flow is equal to the sum of the free cash flows from the firm s current and future investments, so we can interpret the firm s enterprise value as the total NPV that the firm will earn from continuing its existing projects and initiating new ones. The NPV of any individual project represents its contribution to the firm s enterprise value. To maximize the firm s share price, we should accept projects that have a positive NPV.

27 27 Valuation Based on Comparable Firms Method of Comparables (Comps) Estimate the value of the firm based on the value of other, comparable firms or investments that we expect will generate very similar cash flows in the future. Valuation Multiple A ratio of firm s value to some measure of the firm s scale or cash flow The Price-Earnings Ratio P/E Ratio Share price divided by earnings per share Trailing Earnings Earnings over the last 12 months Trailing P/E Forward Earnings Expected earnings over the next 12 months Forward P/E

28 28 Valuation Multiples Forward P/E P Div / EPS Dividend Payout Rate EPS r g r g = = = 1 E E Firms with high growth rates, and which generate cash well in excess of their investment needs so that they can maintain high payout rates, should have high P/E multiples.

29 29 Problem Example-5: valuation multiple Best Buy Co. Inc. (BBY) has earnings per share of \$2.22. The average P/E of comparable companies stocks is Estimate a value for Best Buy using the P/E as a valuation multiple. Solution The share price for Best Buy is estimated by multiplying its earnings per share by the P/E of comparable firms. P 0 = \$ = \$43.73

30 30 Enterprise Value Multiples Valuation Multiples V FCF / EBITDA = EBITDA r g wacc FCF This valuation multiple is higher for firms with high growth rates and low capital requirements (so that free cash flow is high in proportion to EBITDA).

31 31 Example-6:Valuation Multiples Best Buy Co. Inc. (BBY) has EBITDA of \$2,766,000,000 and 410 million shares outstanding. Best Buy also has \$1,963,000,000 in debt and \$509,000,000 in cash. If Best Buy has an enterprise value to EBITDA multiple of 7.7, estimate the value for a share of Best Buy stock.

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