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Valuation of Common Stocks and Bonds

Explore stock and bond valuation methods, cash flow calculations, and investment decision-making in financial lectures. Learn about earnings, dividends, free cash flows, and more.

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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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