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Stock Valuation

Stock Valuation. One Period Valuation Model. To value a stock, you first find the present discounted value of the expected cash flows. P 0 = Div 1 /(1 + k e ) + P 1 /(1 + k e ) where P 0 = the current price of the stock Div = the dividend paid at the end of year 1

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Stock Valuation

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  1. Stock Valuation

  2. One Period Valuation Model • To value a stock, you first find the present discounted value of the expected cash flows. • P0 = Div1/(1 + ke) + P1/(1 + ke) where • P0 = the current price of the stock • Div = the dividend paid at the end of year 1 • ke = required return on equity investments • P1 = the price at the end of period one

  3. One Period Valuation Model • P0 = Div1/(1 + ke) + P1/(1 + ke) • Let ke = 0.12, Div = 0.16, and P1 = $60. • P0 = 0.16/1.12 + $60/1.12 • P0 = $0.14285 + $53.57 • P0 = $53.71 • If the stock was selling for $53.71 or less, you would purchase it based on this analysis.

  4. Generalized Dividend Valuation Model • The one period model can be extended to any number of periods. • P0 = D1/(1+ke)1 + D2/(1+ke)2 +…+ Dn/(1+ke)n + Pn/(1+ke)n • If Pn is far in the future, it will not affect P0 • Therefore, the model can be rewritten as: • P0 = S Dt/(1 + ke)t ∞ t=1

  5. Generalized Dividend Valuation Model • The model says that the price of a stock is determined only by the present value of the dividends. • If a stock does not currently pay dividends, it is assumed that it will someday after the rapid growth phase of its life cycle is over. • Computing the present value of an infinite stream of dividends can be difficult. • Simplified models have been developed to make the calculations easier.

  6. The Gordon Growth Model Some firms try to increase their dividends at a constant rate. P0 = D0(1+g)1 + D0(1+g)2 +…..+ D0(1+g)∞ (1+ke)1 (1+ke)2 (1+ke)∞ D0 = the most recent dividend paid g = the expected growth rate in dividends ke = the required return on equity investments The model can be simplified algebraically to read: P0 = D0(1 + g) D1 (ke - g) (ke – g) =

  7. Gordon Growth Model • Assumptions: • Dividends continue to grow at a constant rate for an extended period of time. • The growth rate is assumed to be less than the required return on equity, ke. • Gordon demonstrated that if this were not so, in the long run the firm would grow impossibly large.

  8. Gordon Model: Example • Find the current price of Coca Cola stock assuming dividends grow at a constant rate of 10.95%, D0 = $1.00, and ke is 13%. • P0 = D0(1 + g)/ke – g • P0 = $1.00(1.1095)/0.13 - 0.1095 = • P0 = $1.1095/0.0205 = $54.12

  9. Gordon Model: Conclusions • Theoretically, the best method of stock valuation is the dividend valuation approach. • But, if a firm is not paying dividends or has an erratic growth rate, the approach will not work. • Consequently, other methods are required.

  10. Price Earnings Valuation Method • The price earning ratio (PE) is a widely watched measure of how much the market is willing to pay for $1 of earnings from a firm. • A high PE has two interpretations: • A higher than average PE may mean that the market expects earnings to rise in the future. • A high PE may indicate that the market thinks the firm’s earnings are very low risk and is therefore willing to pay a premium for them.

  11. Price Earnings Valuation Method • The PE ratio can be used to estimate the value of a firm’s stock. • Firms in the same industry are expected to have similar PE ratios in the long run. • The value of a firm’s stock can be found by multiplying the average industry PE times the expected earnings per share. P/E x E = P

  12. Price Earnings Model: Example • The average industry PE ratio for restaurants similar to Applebee’s is 23. What is the current price of Applebee’s if earnings per share are projected to be $1.13? • P0 = P/E x E • P0 + 23 x $1.13 = $26.

  13. Price Earnings Valuation Method • Advantages: • Useful for valuing privately held firms and firms that do not pay dividends. • Disadvantages: • By using an industry average PE ratio, firm-specific factors that might contribute to a long-term PE ratio above or below the average are ignored.

  14. Setting Security Prices • Stock prices are set by the buyer willing to pay the highest price. • The price is not necessarily the highest price that the stock could get, but it is incrementally greater than what any other buyer is willing to pay. • The market price is set by the buyer who can take best advantage of the asset.

  15. Setting Security Prices • Superior information about an asset can increase its value by reducing its risk. • The buyer who has the best information about future cash flows will discount them at a lower interest rate than a buyer who is uncertain.

  16. Errors in Valuation • Problems with Estimating Growth • Growth can be estimated by computing historical growth rates in dividends, sales, or net profits. • But, this approach fails to consider any changes in the firm or economy that may affect the growth rate. • Competition, for example, will prevent high growth firms from being able to maintain their historical growth rate. • Nevertheless, stock prices of historically high growth firms tend to reflect a continuation of the high growth rate. • As a result, investors receive lower returns than they would by investing in mature firms.

  17. Estimating Growth: Table 1 Stock Prices for a Security with D0 = $2.00, ke = 15%, and Constant Growth Rates as Listed Growth(%) Price 1 $14.43 3 17.17 5 21.00 10 44.00 11 55.50 12 74.67 13 113.00 14 228.00

  18. Errors in Valuation • Problems with Estimating Risk • The dividend valuation model requires the analyst to estimate the required return for the firms equity. • However, a share of stock offering a $2 dividend and a 5% growth rate changes with different estimates of the required return.

  19. Estimating Risk: Table 2 Stock Prices for a Security with D0 = $2.00, g = 5%, and Required Returns as Listed Required Return(%) Price 10 $42.00 11 35.00 12 30.00 13 26.25 14 23.33 15 21.00

  20. Errors in Valuation • Problems with Forecasting Dividends • Many factors can influence the dividend payout ratio. They include: • The firm’s future growth opportunities a • Management’s concern over future cash flows • Conclusion: • Analysts are seldom certain that the stock price projections are accurate. • This is why stock prices fluctuate widely on news reports.

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