Stock Valuation One Period Valuation Model To value

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 + ke) + P 1/(1 + ke) where – P 0 = the current price of the stock – Div = the dividend paid at the end of year 1 – ke = required return on equity investments – P 1 = the price at the end of period one

One Period Valuation Model • P 0 = Div 1/(1 + ke) + P 1/(1 + ke) – Let ke = 0. 12, Div = 0. 16, and P 1 = $60. • P 0 = 0. 16/1. 12 + $60/1. 12 • P 0 = $0. 14285 + $53. 57 • P 0 = $53. 71 – If the stock was selling for $53. 71 or less, you would purchase it based on this analysis.

Generalized Dividend Valuation Model • The one period model can be extended to any number of periods. – P 0 = D 1/(1+ke)1 + D 2/(1+ke)2 +…+ Dn/(1+ke)n + Pn/(1+ke)n • If Pn is far in the future, it will not affect P 0 • Therefore, the model can be rewritten as: – ∞ t P 0 = S D /(1 + k ) t e t=1

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.

The Gordon Growth Model Some firms try to increase their dividends at a constant rate. P 0 = D 0(1+g)1 + D 0(1+g)2 +…. . + D 0(1+g)∞ (1+ke)1 (1+ke)2 (1+ke)∞ D 0 = 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: P 0 = D 0(1 + g) D 1 = (ke - g) (ke – g)

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.

Gordon Model: Example • Find the current price of Coca Cola stock assuming dividends grow at a constant rate of 10. 95%, D 0 = $1. 00, and ke is 13%. – P 0 = D 0(1 + g)/ke – g – P 0 = $1. 00(1. 1095)/0. 13 - 0. 1095 = – P 0 = $1. 1095/0. 0205 = $54. 12

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.

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.

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

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 projected to be $1. 13? – P 0 = P/E x E – P 0 + 23 x $1. 13 = $26.

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, firmspecific factors that might contribute to a longterm PE ratio above or below the average are ignored.

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.

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.

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.

Estimating Growth: Table 1 Stock Prices for a Security with D 0 = $2. 00, ke = 15%, and Constant Growth Rates as Listed Growth(%) 1 3 5 10 11 12 13 14 Price $14. 43 17. 17 21. 00 44. 00 55. 50 74. 67 113. 00 228. 00

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 a 5% growth rate changes with different estimates of the required return.

Estimating Risk: Table 2 Stock Prices for a Security with D 0 = $2. 00, g = 5%, and Required Returns as Listed Required Return(%) 10 11 12 13 14 15 Price $42. 00 35. 00 30. 00 26. 25 23. 33 21. 00

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.