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NONCONSTANT GROWTH

Many companies grow at rapid or irregular rates for several years before finally settling down. Obviously we can t use the constant-growth dividend discount model in such cases. However, we have already looked at an alternative approach. Set the investment horizon (Year H) at the future year by which you expect the company s growth to settle down. Calculate the present value of dividends from now to the horizon year. Forecast the stock price in that year and discount it also to present value. Then add up to get the total present value of dividends plus the ending stock price. The formula is

The stock price in the horizon year is often called terminal value

Estimating the Value of United Bird Seed s Stock

Ms. Dawn Chorus, founder and president of United Bird Seed, is wondering whether the company should make its first public sale of common stock and if so at what price. The company s financial plan envisages rapid growth over the next 3 years but only moderate growth afterwards. Forecast earnings and dividends are as follows:

Thus you have a forecast of the dividend stream for the next 3 years. The tricky part is to estimate the price in the horizon Year 3. Ms. Chorus could look at stock prices for mature pet food companies whose scale, risk, and growth prospects today roughly match those projected for United Bird Seed in Year 3. Suppose further that these companies tend to sell at price-earnings ratios of about 8. Then you could reasonably guess that the P/E ratio of United will likewise be 8. That implies

You are now in a position to determine the value of shares in United. If investors demand a return of r = 10 percent, then price today should be

Thus price today should be about $25.70 per share. United Bird Seed is looking forward to several years of very rapid growth, so you could not use the constant-growth formula to value United s stock today. But the formula may help you check your estimate of the terminal price in Year 3 when the company has settled down to a steady rate of growth. From then on dividends are forecast to grow at a constant rate of g = .05 (5 percent). Thus the expected dividend in Year 4 is and the expected terminal price in Year 3 is

the same value we found when we used the P/E ratio to predict P3. In this case our two approaches give the same estimate of P3, though you shouldn t bet on that always being the case in practice.