1. 4-1 Common Stock Valuation Part I: Difficulties Uncertain cash flows Uncertain cash flows Equity is the residual claim on the firm’s cash flows Equity is the residual claim on the firm’s cash flows Life of the firm is forever Life of the firm is forever Required Rate of Return (the discount rate, r ) is not easily observed Required Rate of Return (the discount rate, r ) is not easily observed

2. 4-2 Discounted Cash Flow Valuation You own a share of stock today. What do you get for holding it for one period? You own a share of stock today. What do you get for holding it for one period? Dividend Dividend Price when you sell the stock: P 1 Price when you sell the stock: P 1 What Determines P 1 ? What Determines P 1 ?

3. 4-3 Discounted Cash Flow Valuation So we can substitute the above formula into the formula for P 0. What determines P 2 ?

4. 4-4 Discounted Cash Flow Valuation The price of a stock equals the present value of all the firm’s forecasted dividends discounted by the required rate of return, r. The price of a stock equals the present value of all the firm’s forecasted dividends discounted by the required rate of return, r. We use 3 different sets of assumptions about future dividends to simplify the above formula. We use 3 different sets of assumptions about future dividends to simplify the above formula.

5. 4-5 (I) Zero Growth Dividend Model Firm’s dividends are constant over time. Firm’s dividends are constant over time. No growth in the dividend No growth in the dividend Stream of constant cash flows forever Stream of constant cash flows forever Price equity as a perpetuity Price equity as a perpetuity

6. 4-6 Common Stock Valuation: Zero dividend growth model A firm’s dividend is expected to stay constant forever at $1 per share. The required rate of return is 10% per year. A firm’s dividend is expected to stay constant forever at $1 per share. The required rate of return is 10% per year. What is the current price of the stock? What is the current price of the stock?

7. 4-7 (II) Constant Growth Dividend Model Forecasted Dividends grow at a constant rate Forecasted Dividends grow at a constant rate Only need to forecast the dividend growth rate and not an indefinite number of dividends Only need to forecast the dividend growth rate and not an indefinite number of dividends Stream of constant growing cash flows forever Stream of constant growing cash flows forever Price equity as a growing perpetuity Price equity as a growing perpetuity

8. 4-8 Common Stock Valuation: Constant Growth Dividend Model A firm just paid a $10 per share dividend. Future dividends are expected to grow at an annual rate of 5% per year. The required rate of return is 10% per year. A firm just paid a $10 per share dividend. Future dividends are expected to grow at an annual rate of 5% per year. The required rate of return is 10% per year. What is the current price of the stock? What is the current price of the stock?

9. 4-9 For many firms (especially those in new or high-tech industries), dividends are low and expected to grow rapidly. As product markets mature, dividends are then expected to slow to some “steady state” rate. For many firms (especially those in new or high-tech industries), dividends are low and expected to grow rapidly. As product markets mature, dividends are then expected to slow to some “steady state” rate. How should stocks such as these be valued? How should stocks such as these be valued? Answer: We return to the fundamental theory of value - the value today equals the present value of all future cash flows. Put another way, the non-constant growth model suggests that P 0 = present value of dividends in the non-constant growth period(s) + present value of dividends in the “steady state” period.

10. 4-10 (III) Differential Growth Dividend Model Forecasted Dividends grow at a constant rate, g 1 for a certain number of years and then grow at a second growth rate, g 2. Forecasted Dividends grow at a constant rate, g 1 for a certain number of years and then grow at a second growth rate, g 2. Example: The dividend of a company has just been paid out, and equals $1. During the next 18 years the dividend will grow at 14% per year. After this high growth period the dividend will grow at 10% per year forever. What is the price of the stock if the required return is 15%? Example: The dividend of a company has just been paid out, and equals $1. During the next 18 years the dividend will grow at 14% per year. After this high growth period the dividend will grow at 10% per year forever. What is the price of the stock if the required return is 15%?

11. 4-11 Answer Create Create timeline with relevant dividends D 1 =$1 D 1 =$1 x 1.14 = $1.14 D 18 =$1 D 18 =$1 x (1.14) 18 (1.14) 18 = $10.57 D 19 =D 18 D 19 =D 18 x (1.10)=$11.63 PV PV growing annuity with C=D 1, C=D 1, r = 15%, g=14% PV t=18 PV t=18 growing perpetuity, with C=D 19, C=D 19, r = 15%, g=10% Discount Discount perpetuity an additional 18 years

12. 4-12 Rearranging the dividend growth model P 0 = D 1 / (r – g) P 0 = D 1 / (r – g) r – g = D 1 / P 0 r – g = D 1 / P 0 r = D 1 / P 0 + g r = D 1 / P 0 + g total return = dividend yield + capital gains yield total return = dividend yield + capital gains yield Dippy Inc. is selling for $20 and is expected to pay a dividend of $1 next year, growing at 10% per year. What is the total return on this stock? Dippy Inc. is selling for $20 and is expected to pay a dividend of $1 next year, growing at 10% per year. What is the total return on this stock? Answer: $1 / $20 + 10% = 15% Answer: $1 / $20 + 10% = 15%