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Valuation of Common Stocks and Bonds

Valuation of Common Stocks and Bonds. How to apply the PV concept. Today’s plan. Review what we have learned in the last lecture Valuing stocks Some terms about stocks Valuing stocks using dividends Valuing stocks using earnings Valuing stocks using free cash flows.

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Valuation of Common Stocks and Bonds

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  1. Valuation of Common Stocks and Bonds How to apply the PV concept FIN 819: lecture 3

  2. Today’s plan • Review what we have learned in the last lecture • Valuing stocks • Some terms about stocks • Valuing stocks using dividends • Valuing stocks using earnings • Valuing stocks using free cash flows FIN 819: lecture 3

  3. Today’s plan (Continue) • Bond valuation and the term-structure of interest rates • Terminology about bonds • The valuation of bonds • The term structure of interest rates • Use duration to measure the volatility of the bond price FIN 819: lecture 3

  4. What have we learned in the last lecture? • Payback rule • Shortcomings • IRR rule • Shortcomings • Free-cash flow calculation FIN 819: lecture 3

  5. Some specific questions in the calculation of cash flows • Include all incidental effects • Do not forget working capital requirements • Forget sunk costs • Include opportunity costs • Be careful about inflation • Depreciation • Financing FIN 819: lecture 3

  6. Free cash flows calculation • Free cash flows = cash flows from operations + cash flows from the change in working capital + cash flows from capital investment and disposal FIN 819: lecture 3

  7. Calculating cash flows from operations • Method 1 • Cash flows from operations =revenue –cost (cash expenses) – tax payment • Methods 2 • Cash flows from operations = accounting profit + depreciation • Method 3 • Cash flows from operations =(revenue –cost)*(1-tax rate) + depreciation *tax rate FIN 819: lecture 4

  8. A summary example 2 • Now we can apply what we have learned about how to calculate cash flows to the IM&C’s Guano Project (in the textbook), whose information is given in the following slide. FIN 819: lecture 4

  9. IM&C’s Guano Project Revised projections ($1000s) reflecting inflation FIN 819: lecture 4

  10. IM&C’s Guano Project Cash flow analysis ($1000s) FIN 819: lecture 4

  11. IM&C’s Guano Project • NPV using nominal cash flows FIN 819: lecture 4

  12. New formula • In chapter 4, it is argued that FCF=earnings –net investment Net investment = total investment - depreciation • Do you agree with this formula? Why? FIN 819: lecture 4

  13. Example • A project costs $2,000 and is expected to last 2 years, producing cash income of $1,500 and $500 respectively. The cost of the project can be depreciated at $1,000 per year. If the tax rate is 50%, what are the free cash flows? FIN 819: lecture 4

  14. One more question • Mr. Pool is now 40 years old and plans to invest some fraction of his current annual income of $40,000 in an account with an annual real interest rate of 5%, starting next year until he retires at the age of 70 to accumulate $500,000 in real terms. If the real growth rate of his income is 2%, what fraction of his income must be invested? FIN 819: lecture 4

  15. Some terms about stocks Book Value – The value of the stocks 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. FIN 819: lecture 4

  16. Some terms about stocks 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. Dividend yield – Dividends per share over the price of per share FIN 819: lecture 4

  17. Example • IBM has a trading price of $70 per share. Its annual earnings per share is $5. Its annual dividend per share is $3.5. What are the P/E and the dividend yield? • P/E=70/5=14 • Dividend yield=3.5/70 or 5% FIN 819: lecture 4

  18. Valuing Common Stocks using dividends (first approach) Dividend Discount Model - Computation of today’s stock price which states that share value equals the present value of all expected future dividends plus the selling price of the stock. H - Time horizon for your investment. FIN 819: lecture 4

  19. Example • George has bought one IBM share in the beginning of this year and decides to hold this share until next year. The expected dividend this year is $10 per share and the stock is expected to sell at $110 per share in the end of the year. If the cost of the capital is 10%, what is the current stock price? FIN 819: lecture 4

  20. Solution • P0=(110+10)/(1+0.1)=$109.1 FIN 819: lecture 4

  21. Valuing common stocks using dividends 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? FIN 819: lecture 4

  22. Solution FIN 819: lecture 4

  23. Valuing common stocks using dividends If we forecast no growth, and plan to hold out stock indefinitely, we will then value the stock as the PV of a PERPETUITY. Assumes all earnings are paid to shareholders. FIN 819: lecture 4

  24. Example • Suppose that a stock is going to pay a dividend of $3 every year forever. If the discount rate is 10%, what is the stock price for the following cases: • (a) you invest and hold it forever? • (b) you invest and hold it for two years? • (c) you invest and hold it for 20 years? FIN 819: lecture 4

  25. Solution • (a) P0=3/0.1=$30 • (b)P0=PV (annuity) + PV( the stock price at year 2) = 3/1.1 + 3/1.12+(3/0.1)/1.12 = 3/0.1=$30 (c) P0=PV (annuity of 20 years) + PV (the stock price at the year of 20) =$30 FIN 819: lecture 4

  26. Valuing Common Stocks Gordon Growth Model: A version of the dividend growth model in which dividends grow at a constant rate (Gordon Growth Model). Stocks can be valued as a perpetuity with a growth rate, if you want to hold this stock forever, that is FIN 819: lecture 4

  27. Example • Suppose that a stock is going to pay a dividend of $3 next year. Dividends grow at a growth rate of 3%. If the discount rate is 10%, what is the stock price for the following cases: • (a) you buy and hold it forever? • (b) you buy and hold it for two years? • (c) you buy and hold it for 20 years? FIN 819: lecture 4

  28. Solution • (a) P0=3/(0.1-0.03)=$42.86 • (b)P0=PV (annuity) + PV( the stock price at year 2) = 3/1.1 + 3*1.03/1.12+(3*1.032/(0.1- 0.03))/1.12 = 3/(0.1-0.03)=$42.86 (c) P0=PV (annuity of 20 years) + PV (the stock price at the year of 20) =$42.86 FIN 819: lecture 4

  29. Capitalization rate 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. FIN 819: lecture 4

  30. Example 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? FIN 819: lecture 4

  31. Solution According to the formula, FIN 819: lecture 4

  32. Capitalization rate The formula for the capitalization rate can be broken into two parts. Capital. Rate = Dividend Yield + Capital Appreciation FIN 819: lecture 4

  33. Using dividends models to derive the capitalization rate Capitalization Rate can be estimated using the perpetuity formula, given minor algebraic manipulation. FIN 819: lecture 4

  34. Valuing Common Stocks Example- If a stock is selling for $100 in the stock market, the cost of capital is 12% and the next year dividend is $3, what might the market be assuming about the growth in dividends? FIN 819: lecture 4

  35. Some terms about dividend growth rates • 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 dividends Plowback Ratio - Fraction of earnings retained by the firm. FIN 819: lecture 4

  36. Deriving the dividend growth rate g Growth can be derived from applying the return on equity to the percentage of earnings plowed back into operations. g = return on equity X plowback ratio FIN 819: lecture 4

  37. 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 plow 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? FIN 819: lecture 4

  38. Solution • Without growth • With growth FIN 819: lecture 4

  39. Example (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 Present Value of Growth Opportunities (PVGO). FIN 819: lecture 4

  40. Valuing common stocks using earnings • We often use earnings to value stocks as • What is the relationship between this formula and the dividend growth formula? FIN 819: lecture 4

  41. Example • Firm A has a market capitalization rate of 15%. The earnings are expected to be $8.33 per share next year. The plowback ratio is 0.4 and ROE is 25%. Every investment in year i is to yield a simple perpetuity starting in year (i+1) with each cash flow equal to total investment times ROE. All the investments have the same capitalization rate. • (a) Using the formula P=ESP1/r + PVGO to calculate the stock price • (b) If ROE is increased, what will happen to the stock price? Why? • (c) Use the dividend model to calculate the stock price? • (d) What have you found? • (e) Think about why you have this kind of result? FIN 819: lecture 4

  42. Simple Solution (a) g=10%, EPS1/r=8.33/0.15=$55.56 PVGO=NPV1/(r-g)=2.22/(0.15- 0.1)=$44.44, P=$100 (b) The price will be increased (c) P=Div1/(r-g)=5/(0.15-0.1)=$100 FIN 819: lecture 4

  43. Valuing common stocks using FCF (free cash flows) The value of a business or stock is usually computed as the discounted value of FCF out to a valuation horizon (H). • The horizon value is sometimes called the terminal value . FIN 819: lecture 4

  44. FCF and PV PV (free cash flows) PV (horizon value) FIN 819: lecture 4

  45. FCF and PV • Free Cash Flows (FCF) should be the theoretical basis for all PV calculations. • FCF is a more accurate measurement of PV than either Div or EPS. • The market price does not always reflect the PV of FCF. • When valuing a business for purchase, always use FCF. FIN 819: lecture 4

  46. FCF and PV Example Given the cash flows for Concatenator Manufacturing Division, calculate the PV of near term cash flows, PV (horizon value), and the total value of the firm. r=10% and g= 6% FIN 819: lecture 4

  47. FCF and PV Solution FIN 819: lecture 4

  48. FCF and PV FIN 819: lecture 4

  49. How to estimate the horizon value? • It is very difficult to forecast or estimate the horizon value. There are several ideas that may be used to estimate the horizon value. • Competition • Constant growth rate FIN 819: lecture 4

  50. Another example Imagine Corporation has just paid a dividend of $0.40 per share. The dividends are expected to grow at 30% per year for the next two years and at 5% per year thereafter. If the required rate of return in the stock is 15% (APR), calculate the current stock price. FIN 819: lecture 4

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