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  1. Investments BSC III Winter Semester 2010 Lahore School of Economics

  2. Investments Chap 10 Common Stock Valuation

  3. Common Stock Valuation Learning Objectives • Common Stock Valuation • Dividend Growth model • Zero Growth • Constant Growth • Multiple growth model • Intrinsic Value & Market price • Relative Valuation Techniques (P/E,P/S,P/S) • Components of Required Return

  4. Capital Market Securities • Fixed Income (Bonds) • Treasuries • Corporates • Equities • Preferred Stock • Common Stock

  5. Common Stock It is an equity ownership in a corporation, initially issued to raise capital Points to keep in mind! • C/F’s are NOT known in advance • Life of stocks is forever – no maturity • Difficult to observe required rate of return for discounting

  6. Common stock valuation The two approaches to valuing common stock using fundamental security analysis are: • Discounted Cash flow techniques • Relative valuation techniques

  7. Common stock valuation The two approaches to valuing common stocks using fundamental security analysis are: • Discounted Cash flow techniques Attempts to estimate the value of a stock today using a present value analysis. • Relative valuation techniques A stock is valued relative to other stocks based on the basis of ratios. Key difference!

  8. Discounted Cash Flow Techniques The estimated value of a security is equal to the discounted value (Present Value) of the future stream of cash flows that an investor expects to receive from the security: Estimated Value of any security= V0 V0= Expected Cash Flows/(1 + K)t Where: K is the appropriated Discount Rate

  9. Discounted Cash Flow Techniques To use Discounted Cash flow Model, an investor must: • Estimate the amount & timing of future stream of Cash flows. • Estimate an appropriate Discount Rate • Use these two components in PV Model to estimate the value of the security, which is then compared to the current Market Price of the security.

  10. Discounted Cash Flow Techniques Two different approaches to the cash flows & discount rates can be used in the valuation of stocks: • Value the Equity of the Firm, using the required rate of Return to shareholders. • Value the entire firm using the Weighted Average Cost of Capital (WACC).

  11. Discounted Cash Flow Techniques How to come up with the Price of a Stock? Assumptions: • Assume a dividend the stock will pay. • Assume a selling price at the end of 1 year. • Come up with a required rate of return.

  12. Discounted Cash Flow Techniques - Example Example: Stock selling price after 1 year is $70 Stock dividend will be $10 Investors require 25% return PV= 80/(1.25) =$64

  13. Discounted Cash Flow Techniques - Example Example: Stock selling price after 1 year is $70 Stock dividend will be $10 Investors require 25% return PV= 80/(1.25) =$64 • Or, • Po=(D1+P1)/(1+k)

  14. Discounted Cash Flow Techniques P1 at t1, could also be found the same way by assuming year 2 price & dividend: P1=(D2+P2) / (1+K)

  15. Discounted Cash Flow Techniques Substituting P1 in Po equation: Po= (D1+(D2+P2)/(1+K))/ (1+K) =[D1/(1+K)1]+ [D2/(1+K)2]+[P2/(1+K)2]

  16. Dividend Discount Model Formula: Po=E [Dn/ (1+K)n] Present Value of all future dividends as a general valuation framework!

  17. Dividend Discount Model • Investors must value a stream of dividends that may be paid forever, since common stock has no maturity value. • The dividend Stream is uncertain: • There is no specified number of dividends, if in fact any are paid at all. • Dividends are Expected to grow in most cases.

  18. Dividend Discount Models – Special cases Growth Rate Cases for the DDM: • The Zero Growth rate Case • The Constant Growth rate Case • The Multiple Growth rate Case

  19. The Zero Growth Rate Model Zero-growth: A Dividend Stream resulting from Fixed dollar Dividend equal to the current Dividend, Do. So, Value of the stock is a Present value of a Perpetuity! Po=D/K

  20. The Zero Growth rate model- Example A company pays a dividend of $2 per share, which is not expected to change. Required return is 20%.What’s the price per share today?

  21. Discounted Cash Flow Techniques – Zero Growth - Example A company pays a dividend of $2 per share, which is not expected to change. Required return is 20%.What’s the price per share today? Po = Do/ k = 2/0.2 = 10

  22. The Constant Growth Rate Model The constant Growth rate Case for the DDM reflects a dividend stream that is expected to grow at a constant rate g, forever. Which implies: If dividend just paid is Do, then the next D1 is: D1 = Do*(1+g) Dividend for period 2, D2: D2= D1*(1+g) =[Do*(1+g)]* (1+g) = Do*(1+g)2

  23. The Constant Growth Rate Model Stock Price with constant growth dividends: Po=Do*(1+g)/(K-g) OR P0=D1/(K – g)

  24. Dividend Discount Model - Assumptions • Dividend paying stock • Required Return by investors is greater than the Growth Rate of Dividends. • Dividends will grow at a constant Rate forever.

  25. The Constant Growth Rate Model - example Suppose Do = 2.30, K=13%, g=5%.What’s the price per share?

  26. The Constant Growth Rate Model - example Suppose Do = 2.30, K=13%, g=5%.What’s the price per share? P0 = D1/(k – g) = 2.3 *(1.05)/(0.13 - 0.05) = 2.415 / 0.8 = 30.19

  27. The Constant Growth Rate Model Constant Growth Model can be used to find thestock price at any pointin time! Find the Dividend for that year. Grow it at (1+g) Divide by K-g

  28. The Constant Growth Rate Model - example Suppose Do = 2.30, K=13%, g=5%.What’s the price per share in 5 years? Hint: P5= D6/ (K – g)

  29. The Constant Growth Rate Model - example Suppose Do = 2.30, K=13%, g=5%.What’s the price per share in 5 years? P5= D6/ (K – g) =[2.3 *(1.05)^5]/ (0.13-0.05) = [2.935x(1.05)]/ 0.8 = 3.0822 / .08 =38.53

  30. The Constant Growth Rate Model - example Suppose Company XYZ’s next dividend will be $4. Required return is 16%. Dividend increases by 6% every year, forever. What’s the price per share today? & in 4 years?

  31. The Constant Growth Rate Model - example Suppose Company XYZ’s next dividend will be $4. Required return is 16%. Dividend increases by 6% every year, forever. What’s the price per share today? P0 = D1 /(k – g) =4/(.16-.06) =4/.1 =$40

  32. The Constant Growth Rate Model - example Suppose Company XYZ’s next dividend will be $4. Required return is 16%. Dividend increases by 6% every year, forever. Price in 4 years? P4= D5/ (k – g) D5=D1* (1+g)4 =4(1.06)4 = 5.05 P4=5.05/0.1 =50.50

  33. Investments BSC/BBA III Winter Semester 2010 Lahore School of Economics

  34. Investments Chap 10 Common Stock Valuation

  35. Common Stock Valuation Learning Objectives • Common Stock Valuation • Dividend Growth model • Zero Growth • Constant Growth • Multiple growth model • Intrinsic Value & Market price • Relative Valuation Techniques (P/E,P/S,P/S) • Components of Required Return

  36. Dividend discount models -Multiple Growth Rate Case For many companies, it is inappropriate to assume that dividends will grow at a constant rate as Firms typically go through life cycles. P0 =PV of Expected Future Cash flows

  37. Dividend discount models -Multiple Growth Rate Case For many companies, it is inappropriate to assume that dividends will grow at a constant rate as Firms typically go through life cycles. P0 =PV of Expected Future Cash flows P0=PV of Dividends during the non Constant period PLUS PV of Dividends during the constant Growth Period

  38. Multiple Growth Rate Case To findValue of Stock with Non Constant Growth, we go through the followingthree steps: • Find thePV of Dividendsduring the period of Non Constant Growth. • Find thePV of Stock at the end of Non Constant Growthperiod at which point it has become a constant growth Stock, and discount the price back to the present. • Add these two componentsto find the intrinsic Value of the Stock.

  39. Dividend discount models -Multiple Growth Rate Case Multiple Growth model Company grows at a certain high rate first, then slows down to grow at a constant sustainable rate.

  40. Dividend discount models -Multiple Growth Rate Case Multiple Growth model Company grows at a certain high rate first, then slows down to grow at a constant sustainable rate. Value=PV of dividends+PV of terminal price = E [Dt /(1+k)t]+{[Dn+1 /(k-g)]*[(1/1+k)n]}

  41. Multiple Growth Rate Case - Example The last dividend paid by Klein Company was $1.00. Klein’s growth rate is expected to be a constant 5 percent for 2 years, after which dividends are expected to grow at a rate of 10 percent forever. Klein’s required rate of return on equity (ks) is 12 percent. What is the current price of Klein’s common stock?

  42. Multiple Growth Rate Case - Example The last dividend paid by Klein Company was $1.00. Klein’s growth rate is expected to be a constant 5 percent for 2 years, after which dividends are expected to grow at a rate of 10 percent forever. Klein’s required rate of return on equity (ks) is 12 percent. What is the current price of Klein’s common stock?

  43. Multiple Growth Rate Case - Example The last dividend paid by Klein Company was $1.00. Klein’s growth rate is expected to be a constant 5 percent for 2 years, after which dividends are expected to grow at a rate of 10 percent forever. Klein’s required rate of return on equity (ks) is 12 percent. What is the current price of Klein’s common stock? Financial calculator solution: Enter in Cash register CF0 = 0, CF1 = 1.05, and CF2 = 61.74. Then, Enter I = 12, and press NPV to getNPV=P0= $50.16.

  44. Multiple Growth Rate Case - Example Your company paid a dividend of $2.00 last year. The growth rate is expected to be 4 percent for 1 year, 5 percent the next year, then 6 percent for the following year, and then the growth rate is expected to be a constant 7 percent thereafter. The required rate of return on equity (ks) is 10 percent.What is the current stock price?

  45. Multiple Growth Rate Case - Example Your company paid a dividend of $2.00 last year. The growth rate is expected to be 4 percent for 1 year, 5 percent the next year, then 6 percent for the following year, and then the growth rate is expected to be a constant 7 percent thereafter. The required rate of return on equity (ks) is 10 percent.What is the current stock price?

  46. Multiple Growth Rate Case - Example Your company paid a dividend of $2.00 last year. The growth rate is expected to be 4 percent for 1 year, 5 percent the next year, then 6 percent for the following year, and then the growth rate is expected to be a constant 7 percent thereafter. The required rate of return on equity (ks) is 10 percent.What is the current stock price? Financial calculator Solution: CF0= 0; CF1= 2.08; CF2= 2.1840; and CF3= 84.8848; I = 10; and press NPV to getNPV = P0 = $67.47.

  47. Intrinsic Value & Market Price If Intrinsic Value>Market Price=under-valued Intrinsic Value<Market Price= over-valued

  48. Assignment (7 Questions) Q1:A stock is expected to pay $0.45 dividend at the end of the year. The dividend is expected to grow at a constant rate of 4 percent a year, and the stock’s required rate of return is 11 percent.What is the expected price of the stock 10 years from today?

  49. Q#2 A stock that currently trades for $40 per share is expected to pay a year-end dividend of $2 per share. The dividend is expected to grow at a constant rate over time. The stock has a required rate of return of 11%. What is the stock’s expected price seven years from today?

  50. Q#3 Motor Homes Inc. (MHI) is presently in a stage of abnormally high growth because of a surge in the demand for motor homes. The company expects earnings and dividends to grow at a rate of 20 percent for the next 4 years, after which time there will be no growth (g = 0) in earnings and dividends. The company’s last dividend was $1.50. MHI’s required return on stock is 18%. What should be the current common stock price?