# UT FIN 357 - Chapter 6. Valuing Stocks v4 (53 pages)

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## Chapter 6. Valuing Stocks v4

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- Pages:
- 53
- School:
- University of Texas at Austin
- Course:
- Fin 357 - Business Finance

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Valuing Stocks Chapter 6 Finance 357 J David Miller 2017 Valuing Types of Stocks Zero Growth When a stock pays the same dividend each period this is a zero growth stock Div1 Div 2 Div 3 The dividends form a basic perpetuity 2 No Growth Example Walmart stock is expected to pay a dividend of 2 50 next year and the same dividend each year forever The discount rate is 5 What should the stock be selling for today P0 Div r P0 2 50 05 50 3 Valuing Types of Stocks Constant Growth We have constant growth with each dividend grows by the same percentage Div1 Div 0 1 g Div 2 Div1 1 g Div 0 1 g 2 Div 3 Div 2 1 g Div 0 1 g 3 This is just a growing perpetuity so we can use the formula to find the present value of this kind of stock Div1 P0 R g 4 Constant Growth Example Intel will pay a dividend of 1 50 next year and is expected to grow its dividend by 4 per year every year after The discount rate is 5 What should the stock be selling for today P0 Div r g P0 1 50 05 04 150 5 Valuing Types of Stocks Differential Growth When dividends grow at different rates over different periods of time we call this differential growth For example the dividend of a company grows at 15 per year for the next 4 years and then slows to 6 growth per year forever after These are multi step problems because the dividends at each growth rate must be discounted separately 6 Differential Growth Example Nike just paid a 1 00 It expects its dividend to grow by 10 annually for the next 2 years After which its dividend will grow by 3 per year forever The discount rate is 5 How much is the stock worth today Next year it will pay 1 x 1 10 1 10 The next year it will pay 1 10 x 1 10 1 21 The next year it will pay 1 21 x 1 03 1 25 Now that we have the dividends we need to find the PV of each one 1 10 1 05 1 05 1 21 1 05 2 1 10 Dividend 3 is a little special We must consider Div3 and all the dividends thereafter 7 Differential Growth Example cont d Nike just paid a 1 00 It expects to its dividend to grow by 10 annually for the next 2 years After which its dividend will grow by 3 per year forever The discount rate is 5 How much is the stock worth today The dividends starting in year 3 will grow by 3 per year so we need to use a growing perpetuity 1 25 05 03 62 50 Using Div3 r g 62 50 is at time 2 so we must discount it back to time 0 62 50 1 05 2 56 69 Now we just add the PVs together Price of the stock 1 05 1 10 56 69 58 84 8 Where does g come from Until now we have assumed that stocks dividends grow at rate g But where does this number come from Businesses grow by making investments in projects equipment etc If the amount we invested was the same as our depreciation then earnings would remain the same This means that Net Investment will only be positive if some earnings are not paid out as dividends 9 Quick Note on EPS EPS can be retained by a company reinvested or it can be paid out to the shareholders as a dividend EPS Payout Dividend Retained Earnings Retention Rate 1 Payout Rate Payout Rate 1 Retention Rate 10 Earnings Growth How do earnings grow 11 Earnings Growth Example Our company reported earnings of 2 000 000 for the year just ended We plan to retain 45 of the earnings and reinvest them into the firm Throughout our history we have averaged a 20 return on equity and we estimate that will continue Based on this information at what rate do we expect earnings to grow over the next year 12 Earnings Growth Example Our company reported earnings of 2 000 000 for the year just ended We plan to retain 45 of the earnings and reinvest them into the firm Throughout our history we have averaged a 20 return on equity and we estimate that will continue Based on this information at what rate do we expect earnings to grow over the next year 2 000 000 X 45 900 000 in Retained Earnings Reinvestment 900 000 X 20 180 000 in earnings growth 180 000 2 000 000 9 earnings growth This is exactly what we would get using the formula 13 How do we calculate return Return on a stock is calculated by adding the dividend yield and the growth rate 14 Dividend Yield vs Capital Gains Yield Our total return can be broken down into two parts Dividend Yield and Capital Gains Yield Dividend Yield 15 Capital Gains Yield Return Example A certain stock is selling for 20 per share The next dividend will be 1 one year from now You also expect the earnings to grow at 10 per year after this forever What is the Dividend Yield and Capital Gains Yield What rate of return does this stock offer you 16 Return Example A certain stock is selling for 20 per share The next dividend will be 1 one year from now You also expect the earnings to grow at 10 per year after this forever What is the Dividend Yield and Capital Gains Yield What rate of return does this stock offer you R Div P0 g R 1 20 10 R 5 10 15 17 The Big Question If all these formulas are correct why do companies that don t pay dividends have any value 18 Future Dividend TechnoCorp just earned 1 50 per share It is a young company and is reinvesting its earnings to grow the company The company will grow EPS at 10 per year for 10 years It is expected that 11 years from now the company will have a payout ratio of 50 and EPS and dividends will grow by 5 per year forever What will the dividend in year 11 be and what is the value of the stock now if the discount rate is 12 19 Future Dividend TechnoCorp just earned 1 50 per share It is a young company and is reinvesting its earnings to grow the company The company will grow EPS at 10 per year for 10 years It is expected that 11 years from now the company will have a payout ratio of 50 and EPS and dividends will grow by 5 per year forever What will the dividend in year 11 be and what is the value of the stock now if the discount rate is 12 NOTE There are no dividends until year 11 Find the expected earnings in 10 years PV 1 50 N 10 I Y 10 FV 3 89 EPS at the …

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