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Published byMariah Tull Modified about 1 year ago

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Moving Cash Flows: Review

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Formulas

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Growing Annuity Annuities are a constant cash flow over time Growing annuities are a constant growth cash flow over time

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What are you worth today? You will make $100,000 the first year. You expect to work for 40 years, get 9% raises every year and 20% per year on investments.

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Cash Flow Timing When does the first cash flow occur relative to the present value of the _______ –Perpetuity? Growing perpetuity? –Annuity? Growing annuity? One period later!

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Review: Bond Features Coupon Payments: Regular interest payments –Semi annual for most US corporate bonds –Types of Coupon payments Fixed Rate: 8% per year Floating Rate: 6-mo. Treasury bill rate basis points. Face or Par Value: $1,000/bond Maturity: no. of years from issue date until principal is paid Coupon Rate

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Bond Valuation Annuity Formula

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What is the price of a $1000 bond maturing in ten years with a 12% coupon that is paid semiannually if the YTM is 10%

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Stock Valuation

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Common Stock Valuation is Difficult Uncertain cash flows –Equity is the residual claim on the firm’s cash flows Life of the firm is forever Rate of return (the appropriate discount rate) is not easily observed

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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. Example: The dividend of a company was $1 yesterday. During the next 18 years the dividend will grow at 14% per year. After that the dividend will grow at 10% per year. What is the price of the stock if the required return is 15%?

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The second dividend regime is a growing perpetuity The first dividend regime is a growing annuity

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Now, we need to sum the two dividend regime values.

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EPS and Dividends Dividends (share repurchase) are a function of… –Ability to pay: Cash flow uncertainty –Decision to pay: Managerial uncertainty Why does a manager retain earnings? –Has better investment opportunities than the shareholder –Makes a sub-optimal decision for the shareholder What is a “better investment opportunity”? –Investment has a NPV>0

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Value a firm that retains earnings? Fundamental valuation equation: Sum of the discounted cash flows First component: PV(no-growth earnings stream) –Remember EPS=Net income/Shareholders equity Second component: PV of growth opportunities –Look for pricing shortcuts: perpetuity, annuity, etc. Rule: As long as PV(GO) > 0, price increases

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One Time Investment Opportunity Firm expects $1 million in earnings in perpetuity without new investments. Firm has 100,000 shares outstanding. Firm has investment opportunity at t=1 to invest $1 million in a project expected to increase future earnings by $210,000 per year. The firm’s discount rate is 10%. What is the share price with and without the project?

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Constant Growth, Constant Investing Firm Q has EPS of $10 at the end of the first year and a dividend pay-out ratio of 40%, r E = 16% and a return on investment of 20%. The firm takes advantage of its growth opportunities each year by investing retained earnings. PV(GO) model –1 st investment = 0.6 × $10 = $6, which generates 0.2 × $6 = $1.20 –Per share PVGO 1 = -6 + (1.20/0.16) = $1.50 (at t=1) –2 nd investment = 0.6 × $11.20 = $6.72, generating 0.2 × $6.72 = $1.344 –Per share PVGO 2 = (1.344/0.16) = $1.68 (at t=2)

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Constant Growth, Constant Investing (cont) Relationship between PV(GO)’s? –1.68 = (1+g) × 1.5 g=0.12 Is there an easier way to estimate g for this case? –G=ROI x Investment Rate=0.2 x (1-0.4)=0.12 PVGO 0 = $1.50 / ( ) =$37.50 No-growth dividend value: $10/0.16 = $62.50 P = $ $37.50 = $100

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Constant Growth, Constant Investing (cont) Can we price this firm a different way? –Since the investment grows at a constant rate we can immediately estimate g –Investment rate x ROI = 0.6 × 20% = 12% Then estimate PV(GO) as a growing perpetuity based on dividends rather than cash flow –D 1 / (r E - g) = $4 / ( ) = $100 So the entire firm is worth $100

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Another Example Firm X currently has expected earnings of $100,000 per year in perpetuity. Firm X is switching its policy and wants to invest 20% of its earnings in projects with a 10% return. The discount rate is 18%. No-growth price: P=$100,000/0.18 = $555,555 PV(GO) is a constant growth perpetuity –What’s g? g=Investment rate x ROI = 0.2 × 10% = 2% –What is the first year’s investment cash flow? Invest $20,000 and receive $2,000 forever –-20,000+(2,000/0.18)= –PV(GO) = (-8,888.89)/( ) = - 55,555 New Policy: P=$555, ,555 = $500,000

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