1. FIN 614: Financial Management Larry Schrenk, Instructor

2. 1.Some Methods and Issues 2.Stock Valuation 1.Constant Dividend Model 2.(Constantly) Growing Dividend Model 3.Mixed Model

3. Discounted Dividend Model (DDM) A Discounted Cash Flow Model (DCF) P/E Ratio Methodologies Other Ratio Methodologies Capital Asset Pricing Model (CAPM) Relative Valuation Free Cash Flow A Discounted Cash Flow Model (DCF)

4. Stock Cash Flows Uncertain: Determined by the Board of Directors Not Required Proceeds from Sale of Stock Uncertain Contrast: Bond Cash Flows are Fixed Difficulties in Stock Valuation: Dividend Cash Flows not Known in Advance Life of Stock is Essentially Forever Hard to Determine Required Rate of Return for a Stock

6. Motivation Dividends are the cash flows derived from common stock. The price is the present value of cash flows. Thus, the price of a common share should be the present value of its dividends Problems Dividends (especially far future ones) are not easily estimated.

7. Constant Model Dividends remain constant Growth Model Dividends change at a constant rate Mixed Model Dividends change at different rates

8. If dividend is constant, then stock is a perpetuity.

9. If a stock is always expected to pay an annual dividend of $4.00 and r = 7%, then

10. If dividend is changing at a constant rate, then stock is a growing perpetuity.

11. If a stock has just paid an annual dividend of $4.00, and the dividend is expected to increase (infinitely) at 2% (r = 7%), then

12. The same methodology applies if the dividend is expected to decline. If a stock has just paid an annual dividend of $4.00, and the dividend is expected to decrease (infinitely) at 2% (r = 7%), then

13. Both Patterns Possible But not likely to apply to very many firms Generally, dividends change at different rates over time A high growth firm might increase is cash flows at 30% for a few years, but this could not be sustained for any extended period.

14. What will be IBM’s dividend 12 years from now? No matter what you said…You’re only guessing! No Rational Way to Estimate Long Term Dividends

15. To alleviate this problem, we divide the forecast of dividends into two periods: Short Term Prediction/Horizon Long Term Prediction/Horizon Short Term Long Term 0123t d0d0 d1d1 d2d2 dtdt d3d3

16. Period over which we can reasonably estimate the expected dividends: As specific dollar amounts, or E.g., $4.00 $4.15 $4.25 $4.90 As subject to some growth forecast E.g., $4.00 growing at 10% for 4 years Dividend ‘Smoothing’

17. Period over which we cannot predict dividends. We cannot ignore the long term, For many firms the long term provides much of the value of the firm. NOTE: The more value is derived from the future, the harder to use the DDM as a method.

18. Estimate the long term dividends as growing at a constant rate or reasonable growth rate. Estimate as constant or growing perpetuity. Infinite growth rate cannot be very large. One good estimate is the long term growth for the economy, perhaps 3 or 4%.

19. 1)Value of the short term dividends as PV of the individual dividends. 2)Value of the long term dividends as a delayed growing perpetuity. NOTE: It is a delayed growing perpetuity because the long term dividends do not begin until after the short term dividends end. 3)Stock Price = PV short term + PV long term

20. EXAMPLE A firm has just paid an annual dividend of $2.00. That dividend is expected to grow at a rate of 30% for one year, 20% for the next two years, then level off to a long term growth rate of 3%. If the discount rate is 12%, what should be the price of the stock?

21. Data: d 0 = 2 g 1 = 30% g 2-3 = 20% g 4+ = 3% r = 12%

22. Data d 0 = 2; g 1 = 30%; g 2-3 = 20%; g 4+ = 3%; r = 12% Dividend Calculation d 1 = 2(1.30) = 2.60 d 2 = 2(1.30)(1.20) = 3.12 d 3 = 2(1.30)(1.20) 2 = 3.74 d 4 = 2(1.30)(1.20) 2 (1.03) = 3.85

23. The Timeline Short Term Long Term 01234 d0d0 d1d1 d2d2 d4d4 d3d3 2.002.603.123.853.74

24. Data: d 0 = 2; g 1 = 30%; g 2-3 = 20%; g 4+ = 3%; r = 12% Short Term Dividends: d 1 = 2.60 d 2 = 3.12 d 3 = 3.74

25. If Cash Flow Starts at t = 1, PV is at t = 0 If Cash Flow Starts at t = m, PV is at t = m – 1 If Cash Flow Starts at t = 20, PV is at t = 19 PV of perpetuity is one period prior to the first cash flow, So it must be discounted from that period.

26. I promise to pay you $100 per year starting in 5 years (r = 10%). What is the PV? Apply perpetuity formula: PV = 100/0.10 = $1000 This $1000 is in Year 4 dollars. Discount it back to the present N = 4; I% = 10; PV = ?; PMT = 0; FV = -1000 PV = $683.01

27. Data: d 0 = 2; g 1 = 30%; g 2-3 = 20%; g 4+ = 3%; r = 12% Long Term d 4 = 3.85

28. Data : d 0 = 2; g 1 = 30%; g 2-3 = 20%; g 4+ = 3%; r = 12% or Short Term Long Term

30. FIN 614: Financial Management Larry Schrenk, Instructor