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- 1. Valuation of Bonds andEquities The value of any business asset depends on its expected future cash flows. If you buy a bond you are effectively buying a stream of cash flows.
- 2. Bond with face (nominal) value of €100: couponrate of 8% with 5 years to maturity.If the yield to redemption on this type of bond is 10% at the moment how much should you pay for it? 0 1 2 3 4 5 ? 8 8 8 8 108
- 3. Get the PV of the cash flowsof the bond @ 10%Annuity of €8 p.a. for 5 yearsPV = 8 X 3.791 = 30.33€100 at the end of 5 yearsPV = 100 X 0.621 = 62.10The value of the bond is €92.43
- 4. Topics Covered How To Value Common Stock Capitalization Rates Stock Prices and EPS
- 5. Stocks & Stock MarketCommon Stock - Ownership shares in a publicly held corporation.Secondary Market - market in which already issued securities are traded by investors.Dividend - Periodic cash distribution from the firm to the shareholders.P/E Ratio - Price per share divided by earnings per share.
- 6. Stocks & Stock MarketBook Value - Net worth of the firm according to the balance sheet.Liquidation Value - Net proceeds that would be realized by selling the firm’s assets and paying off its creditors.Market Value Balance Sheet - Financial statement that uses market value of assets and liabilities.
- 7. Valuing Common Stocks Expected Return - The percentage yield that an investor forecasts from a specific investment over a set period of time. Sometimes called the market capitalization rate or the cost of capital. E ( Div1 ) + E ( P ) − P0Expected Return = r = 1 P0
- 8. Valuing Common StocksExample: If Fledgling Electronics is selling for $100 per share today and is expected to sell for $110 one year from now, what is the expected return if the dividend one year from now is forecasted to be $5.00? 5 + 110 − 100Expected Return = = .15 100
- 9. Valuing Common StocksThe formula can be broken into two parts. Dividend Yield + Capital Appreciation Div1 P − P0Expected Return = r = + 1 P0 P0
- 10. What is the value of a share? If an investor buys a share it is worth the PV of the future cash flows it gives her. If she plans to hold the share for one year (period). (Note I have dropped E() for convenience.) P + D1 1 P = 0 (1 +r )
- 11. Valuing Common StocksExample Current forecasts are for XYZ Company to pay dividends of $3, $3.24, and $3.50 over the next three years, respectively. At the end of three years you anticipate selling your stock at a market price of $94.48. What is the price of the stock given a 12% expected return?
- 12. Valuing Common Stocks Example Current forecasts are for XYZ Company to pay dividends of $3, $3.24, and $3.50 over the next three years, respectively. At the end of three years you anticipate selling your stock at a market price of $94.48. What is the price of the stock given a 12% expected return? 3.00 3.24 350 + 94.48 .PV = + + (1+.12) (1+.12) 1 2 (1+.12) 3PV = $75.00
- 13. Value of Shareholders Funds If an investor buys a share it is worth the PV of the future cash flows it gives her. If she plans to hold the share for 2 years the following formula applies. Div1 Div2 + P2 P0 = + (1 + r )1 (1 + r ) 2
- 14. If the investor she sells to at t2 plans to hold the share for H years its value is : Div3 Div4 DivH + PH P2 = 1 + 2 + ...+ H−2 (1 + r) (1 + r) (1 + r)Substituting this into the previous equation gives:
- 15. Substituting this into the previous equation gives Div1 Div2 Div H + PH P0 = + +...+ (1 + r ) (1 + r ) 1 2 (1 + r ) HThis logic can be applied to the investor who buys the sharein year H and so on terminal value PH is so far in the future that it can be until the ignored. Thus, the valueof a share is theoretically equal to the PV of all the futuredividends discounted at the cost of capital
- 16. The Dividend Discount Model: Assume an investor holds a share for one year and sells Let (1+r) = ρE To another investor who also holds the share for 1 year.. d 3 + V3 d 4 + V4 V2 = V3 = ........... d 2 + V2 ρE ρE d1 + V1 V1 =V0 = ρE ρE d V ∞ d d V d d d V dtV0 = 1 + 1 ρE ρE = 1 + 2 + 22 = 1 + 2 + 3 + 3 ... = ∑ ρE ρE ρE 2 ρE ρE ρE ρE 2 3 3 t =1 ρE t 4 d t TV4 V0 = ∑ t + 4 t =1 ρ ρE E
- 17. The Basic Dividend Valuation Model is: ~ ] ∞ E t [ d t+τPt = ∑ τ (PVED) τ =1 RF The value of a share is the present value of all the dividends that It pays to infinity.
- 18. Valuing Common StocksDividend Discount Model - Computation of today’s stock price which states that share value equals the present value of all expected future dividends.
- 19. Making the Basic DDMpracticalIf we assume all dividends are the same forever this implies we forecast no growth and will then value the stock as a PERPETUITY. D1 P0 = r
- 20. Valuing Common StocksThis essentially assumes that the companydoes not grow.No earnings are retained so all earnings arepaid out as dividends. D1 EPS1 Perpetuity = P0 = or r r Assumes all earnings are paid to shareholders.
- 21. This is essentially the P/E ratiomethod of valuing a stockRe-arranging the above equation we get EPS1 P0 = r EPS1 1 P0 ⇒r = or = =P P0 r EPS1 E
- 22. Constant Dividend Model This is obviously unrealistic since it assumes that no earnings are retained and there is no growth. Accordingly, we need to adjust this formula for the value of growth.
- 23. Constant Growth ModelConstant Growth DDM - A version of the dividend growth model in which dividends grow at a constant rate (Gordon Growth Model). Div1 P0 = r −g
- 24. Dividends Growth at aconstant rate g d1 = d0(1+g)If the most recent dividend paid was 100 and the growth rate is 8%.The next dividend is d1 = 100(1.08) = 108In two years time the dividend d2 is100(1+g)2 = 100(1.08)(1.08)=116.6
- 25. Where does g come from? It come from retained earnings which are reinvested at the cost of capital. This increases subsequent earnings and dividends.
- 26. Valuing Common Stocks If a firm elects to pay a lower dividend, and reinvest the funds, the stock price may increase because future dividends may be higher.Payout Ratio - Fraction of earnings paid out as dividendsPlowback (Ploughback) Ratio - Fraction of earnings retained by the firm.
- 27. Valuing Common Stocks Growth can be derived from applying the return on equity to the percentage of earnings plowed (ploughed) back into operations.g = return on equity X plough back ratio The ploughback ratio is 1 – payout ratio
- 28. g is a sustainable growth level Sustainable Growth Rate - Steady rate at which a firm can grow: plowback ratio X return on equity
- 29. NotationBVP: Book value per sharePayout Ratio: The proportion of earnings paid out. DPS=EPS X Payout RatioREPS: Retained Earnings Per Share: that part of earnings per share not paid in dividends and ploughed back into the business = EPS X Ploughback RatioROE: Return on Equity = EPS/BVP
- 30. ExampleAn all equity company has 1,000,000 shares and a book value of €10mThe BVP is €10If we assume the ROE is 10% the EPS is 0.1 X 10 = €1 or 100 centIf we assume the payout ratio is 40% the DPS is 40 cent.
- 31. Summary of Accounts: year 0 Number of SharesNet Income (NI) 1000000 1000000 EPS 1Dividend 400000 1000000 DPS 0.4Retained Earnings 600000 1000000 REPS 0.6Book Value (BV) 10000000 1000000 BVP 10ROE = NI/BV 0.1
- 32. How Growth affects earnings and dividendsT BVP EPS Payout DPS REPS ROE g (cents) Ratio0 €10 100 0.4 40 60 10%1 €10.6 106 0.4 42.4 63.6 10% 6%2 €11.23 112.36 0.4 44.94 67.42 10% 6%3 €11.91 119.1 0.4 47.64 71.46 10% 6%
- 33. Summary of Accounts: Year 3 Number of SharesNet Income (NI) 1191016 1000000 EPS 1.191Dividend 476406.4 1000000 DPS 0.476Retained Earnings 714609.6 1000000 REPS 0.715Book Value (BV) 11910160 1000000 BVP 11.91ROE = NI/BV 0.1
- 34. Valuing Common StocksExample Our company forecasts to pay a $5.00 dividend next year, which represents 100% of its earnings. This will provide investors with a 12% expected return. Instead, we decide to plough back 40% of the earnings at the firm’s current return on equity of 20%. What is the value of the stock before and after the plowback decision?
- 35. Valuing Common Stocks Example Our company forecasts to pay a $5.00 dividend next year, which represents 100% of its earnings. This will provide investors with a 12% expected return. Instead, we decide to plough back 40% of the earnings at the firm’s current return on equity of 20%. What is the value of the stock before and after the plowback decision? No Growth With Growth 5P0 = = $41.67 .12
- 36. Valuing Common Stocks Example Our company forecasts to pay a $5.00 dividend next year, which represents 100% of its earnings. This will provide investors with a 12% expected return. Instead, we decide to plough back 40% of the earnings at the firm’s current return on equity of 20%. What is the value of the stock before and after the plowback decision? With Growth No Growth g =.20×.40 =.08 3 5 P0 = = $75.00P0 = = $41.67 .12 −.08 .12
- 37. Valuing Common StocksExample - continued If the company did not plowback some earnings, the stock price would remain at $41.67. With the plowback, the price rose to $75.00. The difference between these two numbers (75.00-41.67=33.33) is called the Net Present Value of Growth Opportunities (PVGO).
- 38. Valuing Common StocksNet Present Value of Growth Opportunities (PVGO) - Net present value of a firm’s future investments.
- 39. Value of a share with growth EPS1 P0 = + PVGO r AND P 1 PVGO = + E r EPS1
- 40. Examples – using a DividendDiscount model to Value shares How much is a share worth if it yield DPS of 100 cent forever. The cost of capital or expected rate of return is 10% Answer: 100/0.1 = 1000 cent or €10
- 41. Suppose the company did notpay a Div in year 3 It reinvests the 100 cent per share at 10%. What happens to the value of the share? First need to consider what happens to dividends Assume that dividends are reinvested at the cost of capital i.e. 10%
- 42. Reinvestment of Profits in year 3 Dividends in year three are zero Dividends from year 4 onwards increase to 110 cent per annum. (The 100 cent yields are return of 10%) Accordingly we have dividends of 100 cent for years one and two. Zero divs for year 3 and a perpetuity of 110 cent from year 4 onwards.
- 43. ∞ dt P0 = ∑ t =1 (1 + R) t DIV1 Div2 DIV3 DiV4 P0 = + + + + ..... (1 + r) (1 + r) (1 + r) (1 + r) 1 2 3 4 DIV1 Div2 DiV4P0 = + + ... + (1 + r) (1 + r) 1 2 r(1 + r)3 100 100 0 110P0 = + + + (1 + r) (1 + r)2 (1 + r)3 r(1 + r)3 1
- 44. Divs 100 100 110PV ofDivs fromyear 4 atyear 3. 1100Value Discount 1.1 1.21 1.331 1000.00 PV 90.91 82.64 826.45
- 45. Why is there no change invalue? Because the investment of retained earnings only yields the same rate of return as the cost of equity. We could use the formula EPS1 P0 = + PVGO r 100 P0 = + 0 =100 0 .1
- 46. Real Growth Opportunity What if the company did not pay any Divs in year three but invested in a positive NPV project For example a project yielding 20 cent per share per annum forever beginning in year 4
- 47. NPV of the project is NPV = − 100 + 20 = 100 0.1
- 48. But this NPV is at year 3 NPV now is 100 x 0.7513 = 75.13 100 P0 = + 75.13 = 1075.13 cent 0.1
- 49. ∞ dt P0 = ∑ t =1 (1 + R) t DIV1 Div2 DIV3 DiV4 P0 = + + + + ..... (1 + r) (1 + r) (1 + r) (1 + r) 1 2 3 4 DIV1 Div2 DiV4P0 = + + ... + (1 + r) (1 + r) 1 2 r(1 + r)3 100 100 120P0 = + + ... + (1 + r) (1 + r) 1 2 r(1 + r)3
- 50. 4 to 1 2 3 infinity Divs 100 100 0 120 PV of Divsfrom year 4 atyear 3. 1200 DiscountValue Factor 1.1 1.21 1.331 1075.13 PV 90.91 82.64 901.58

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