Slide 1Valuing Types of Stocks: Zero GrowthNo Growth ExampleValuing Types of Stocks: Constant GrowthConstant Growth ExampleValuing Types of Stocks: Differential GrowthDifferential Growth ExampleDifferential Growth Example (cont’d)Where does g come from?Quick Note on EPSEarnings GrowthEarnings Growth ExampleEarnings Growth ExampleHow do we calculate return?Dividend Yield vs Capital Gains YieldReturn ExampleReturn ExampleThe Big QuestionFuture DividendFuture DividendFuture DividendValuation ExampleValuation ExampleGrowth ExampleGrowth Example – Step 1Growth Example – Step 2Growth Example - ConclusionValuation Based on Comparable FirmsComparable Valuation – P/EComparable Valuation – Enterprise ValueComparable Valuation – Enterprise ValueComparable Valuation – Enterprise ValueFree Cash Flow ValuationFree Cash Flow ValuationFree Cash Flow ExampleFree Cash Flow ExampleShareholder RightsShareholder RightsCommon SharesRights and DividendsPreferred StockMarket TypesBrokers and DealersNew York Stock Exchange (NYSE Euronext)NASDAQValuation ProblemValuation Problem – Step 1Valuation Problem – PictureValuation Problem – Step 2Another Valuation ProblemAnother Valuation Problem – Step 1Another Valuation Problem – Step 2© J. David Miller 2017Valuing StocksChapter 6Finance 357Valuing Types of Stocks: Zero GrowthWhen a stock pays the same dividend each period, this is a zero growth stock.The dividends form a basic perpetuity2321DivDivDivNo Growth ExampleWalmart 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 3Valuing Types of Stocks: Constant GrowthWe have constant growth with each dividend grows by the same percentageThis is just a growing perpetuity, so we can use the formula to find the present value of this kind of stock43023)1(Div)1(DivDiv gg )1(DivDiv01g2012)1(Div)1(DivDiv gg gRP10DivConstant Growth ExampleIntel 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 5Valuing 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.6Differential Growth ExampleNike 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) = $1.10The next year it will pay $1.10 x (1.10) = $1.21The next year it will pay $1.21 x (1.03) = $1.25Now 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 = $1.10Dividend 3 is a little special. We must consider Div3 and all the dividends thereafter. 7Differential 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 062.50/(1.05)2 = $56.69Now we just add the PVs togetherPrice of the stock = 1.05 + 1.10 + 56.69 = $58.84 8Where 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.9Quick Note on EPSEPS can be retained by a company (reinvested) or it can be paid out to the shareholders as a dividend. EPS = Payout (Dividend) + Retained EarningsRetention Rate = 1 – Payout RatePayout Rate = 1 – Retention Rate10Earnings GrowthHow do earnings grow?11Earnings Growth ExampleOur 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?12Earnings Growth ExampleOur 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 growthThis is exactly what we would get using the formula.13How do we calculate return?Return on a stock is calculated by adding the dividend yield and the growth rate14Dividend Yield vs Capital Gains YieldOur total return can be broken down into two parts: Dividend Yield and Capital Gains Yield. Dividend Yield Capital Gains Yield15Return ExampleA 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?16Return ExampleA 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) + gR = (1 / 20) + 10%R = 5% + 10% = 15%17The Big QuestionIf all these formulas are correct, why do companies that don’t pay dividends have any value?18Future DividendTechnoCorp. just earned $1.50 per