Stocks&bonds2214 1
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Stocks&bonds2214 1 Stocks&bonds2214 1 Presentation Transcript

  • 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.
  • 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
  • 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
  • Topics Covered  How To Value Common Stock  Capitalization Rates  Stock Prices and EPS
  • 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.
  • 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.
  • 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
  • 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
  • Valuing Common StocksThe formula can be broken into two parts. Dividend Yield + Capital Appreciation Div1 P − P0Expected Return = r = + 1 P0 P0
  • 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 )
  • 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?
  • 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
  • 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
  • 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:
  • 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
  • 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
  • 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.
  • 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.
  • 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
  • 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.
  • 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
  • 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.
  • 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
  • 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
  • Where does g come from? It come from retained earnings which are reinvested at the cost of capital. This increases subsequent earnings and dividends.
  • 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.
  • 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
  • g is a sustainable growth level Sustainable Growth Rate - Steady rate at which a firm can grow: plowback ratio X return on equity
  • 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
  • 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.
  • 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
  • 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%
  • 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
  • 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?
  • 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
  • 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
  • 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).
  • Valuing Common StocksNet Present Value of Growth Opportunities (PVGO) - Net present value of a firm’s future investments.
  • Value of a share with growth EPS1 P0 = + PVGO r AND P 1 PVGO = + E r EPS1
  • 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
  • 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%
  • 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.
  • ∞ 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
  • 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
  • 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
  • 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
  •  NPV of the project is NPV = − 100 + 20 = 100 0.1
  • 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
  • ∞ 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
  • 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