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Moving Cash Flows: Review

Moving Cash Flows: Review. Formulas. Growing Annuity. Annuities are a constant cash flow over time Growing annuities are a constant growth cash flow over time. What are you worth today?. You will make $100,000 the first year.

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Moving Cash Flows: Review

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  1. Moving Cash Flows: Review

  2. Formulas

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

  4. 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.

  5. 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!

  6. 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 + 100 basis points. • Face or Par Value: $1,000/bond • Maturity: no. of years from issue date until principal is paid • Coupon Rate

  7. Bond Valuation Annuity Formula

  8. 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%

  9. Stock Valuation

  10. 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

  11. Differential Growth Dividend Model • Forecasted Dividends grow at a constant rate, g1 for a certain number of years and then grow at a second growth rate, g2. • 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%?

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

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

  14. 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

  15. 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

  16. 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?

  17. 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%, rE = 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 • 1st investment = 0.6 × $10 = $6, which generates 0.2 × $6 = $1.20 • Per share PVGO1 = -6 + (1.20/0.16) = $1.50 (at t=1) • 2nd investment = 0.6 × $11.20 = $6.72, generating 0.2 × $6.72 = $1.344 • Per share PVGO2 = -6.72 + (1.344/0.16) = $1.68 (at t=2)

  18. 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 • PVGO0 = $1.50 / (0.16 - 0.12) =$37.50 • No-growth dividend value: $10/0.16 = $62.50 • P = $62.50 + $37.50 = $100

  19. 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 • D1 / (rE - g) = $4 / (0.16 - 0.12) = $100 • So the entire firm is worth $100

  20. 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)=-8888.89 • PV(GO) = (-8,888.89)/(0.18-0.02) = - 55,555 • New Policy: P=$555,555 - 55,555 = $500,000

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