1. Lecture 5 A Variable Growth Rate Model

2. Outline Two stage growth model. Price sensitivity of high P/E stocks. Stocks with negative earnings. Three stage growth model. Comparative analysis.

3. Useful Present Value Formulas The present value of an annuity of $1 per period for T periods. The first payment is at the end of period 1.

4. Useful Present Value Formulas The present value of an annuity that grows at a constant rate g. The first payment is $(1 + g) at the end of period 1.

5. Useful Present Value Formulas The formula will work for g>k and g<k, but it will not work if g=k. If g=k, then the present value of the annuity is T.

6. A Numerical Example g = 35%, k = 15%, and T = 8 years.

7. A Two Stage Growth Model Assumptions: 1. Dividends per share and earnings per share grow at a constant rate g for T years. 2. After time T the growth rate slows down. 3. The stock’s expected price-to- earnings ratio is PER T at the end of period T.

8. A Two Stage Growth Model The value of the stock is > the present value of the expected dividends from period 1 thru T plus > the present value of the expected price at the end of period T.

9. XYZ Stock Numerical Example Assumptions D 0 =.36E 0 = 1.20 ROE = 50%g = 35% T = 8 yearsPER T = 24 k= 15%PER 0 = 90 P 0 = 108.00

10. PV of Expected Dividends The present value of the expected dividends during the first T years is

11. Expected Price in Period T The expected earnings at the end of year T is E T = (1 + g) T E 0 = (13.24)(24) = 317.73 The expected price at the end of period T is P T = E T PER T = (1.35) 8 (1.20) = 13.24.

12. PV of Expected Price in Period T The present value of P T is

13. Value of the Stock The intrinsic value of the stock is The current price is 108.00. XYZ stock appears to be reasonably priced.

14. Sensitivity Analysis Use the two stage growth model and an Excel data table to answer the following questions. “What assumptions do I have to make to justify the current price of the stock?” “Are these assumptions reasonable?” If not, the stock is probably over valued.

15. Price Sensitivity of High P/E Stocks The two stage growth model implies that the prices of high P/E ratio stocks are sensitive to changes in ROE Retention rate. Length of high growth period. Discount rate.

16. Stocks With Negative Earnings Forecast the growth in sales. Estimate the net profit margin in period T. Estimate the price-to-earnings ratio in period T. Discount the price in period T back to today.

17. Three Stage Growth Model Assumptions: (1) The expected price-to-earnings ratio is PER T2 at the end of T 2. (2) Earnings and dividends grow at the rate g 1 from period 1 to T 1. (3) The growth rate in earnings and dividends decrease linearly from g1 to g 2 from T 1 to T 2.

18. Three Stage Growth Model T1T2 g1 g2 Time Growth Rate

19. Example of Three Stage Growth Model Assumptions D 0 = 0.40T 1 = 5 E 0 = 2.00T 2 = 10 g 1 = 30%k = 14% g 2 = 8%PER T2 = 15

20. Comparative Valuation Most analysts value stock using the relative value approach. The positive and negative aspects of a stock are compared with those of stocks with similar characteristics. Analysts then determine which stocks are relatively undervalued.

21. Comparative Valuation Ratios Compared Profitability—EBIT margin, net profit margin, ROA, and ROE. Activity—Asset turnover ratios. Credit—Debt to equity ratio, interest coverage ratio. Growth—Sales per share, cash flow per share, earnings per share.