Capital Asset Pricing Model (CAPM)
Capital asset pricing model (CAPM) indicates what should be the expected or required rate of return on risky assets like Time Warner Inc. common stock.
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- Common-Size Income Statement
- Common-Size Balance Sheet: Liabilities and Stockholders’ Equity
- Analysis of Reportable Segments
- Price to FCFE (P/FCFE)
- Present Value of Free Cash Flow to Equity (FCFE)
- Net Profit Margin since 2005
- Return on Equity (ROE) since 2005
- Current Ratio since 2005
- Debt to Equity since 2005
- Aggregate Accruals
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Rates of Return
Time Warner Inc., monthly rates of return
| Time Warner Inc. (TWX) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PriceTWX,t1 | DividendTWX,t1 | RTWX,t2 | PriceS&P 500,t | RS&P 500,t3 |
| Jan 31, 2013 | ||||||
| 1. | Feb 28, 2013 | |||||
| 2. | Mar 31, 2013 | |||||
| 3. | Apr 30, 2013 | |||||
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | Nov 30, 2017 | |||||
| 59. | Dec 31, 2017 | |||||
| Average (R): | ||||||
| Standard deviation: | ||||||
| Time Warner Inc. (TWX) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PriceTWX,t1 | DividendTWX,t1 | RTWX,t2 | PriceS&P 500,t | RS&P 500,t3 |
| Jan 31, 2013 | ||||||
| 1. | Feb 28, 2013 | |||||
| 2. | Mar 31, 2013 | |||||
| 3. | Apr 30, 2013 | |||||
| 4. | May 31, 2013 | |||||
| 5. | Jun 30, 2013 | |||||
| 6. | Jul 31, 2013 | |||||
| 7. | Aug 31, 2013 | |||||
| 8. | Sep 30, 2013 | |||||
| 9. | Oct 31, 2013 | |||||
| 10. | Nov 30, 2013 | |||||
| 11. | Dec 31, 2013 | |||||
| 12. | Jan 31, 2014 | |||||
| 13. | Feb 28, 2014 | |||||
| 14. | Mar 31, 2014 | |||||
| 15. | Apr 30, 2014 | |||||
| 16. | May 31, 2014 | |||||
| 17. | Jun 30, 2014 | |||||
| 18. | Jul 31, 2014 | |||||
| 19. | Aug 31, 2014 | |||||
| 20. | Sep 30, 2014 | |||||
| 21. | Oct 31, 2014 | |||||
| 22. | Nov 30, 2014 | |||||
| 23. | Dec 31, 2014 | |||||
| 24. | Jan 31, 2015 | |||||
| 25. | Feb 28, 2015 | |||||
| 26. | Mar 31, 2015 | |||||
| 27. | Apr 30, 2015 | |||||
| 28. | May 31, 2015 | |||||
| 29. | Jun 30, 2015 | |||||
| 30. | Jul 31, 2015 | |||||
| 31. | Aug 31, 2015 | |||||
| 32. | Sep 30, 2015 | |||||
| 33. | Oct 31, 2015 | |||||
| 34. | Nov 30, 2015 | |||||
| 35. | Dec 31, 2015 | |||||
| 36. | Jan 31, 2016 | |||||
| 37. | Feb 29, 2016 | |||||
| 38. | Mar 31, 2016 | |||||
| 39. | Apr 30, 2016 | |||||
| 40. | May 31, 2016 | |||||
| 41. | Jun 30, 2016 | |||||
| 42. | Jul 31, 2016 | |||||
| 43. | Aug 31, 2016 | |||||
| 44. | Sep 30, 2016 | |||||
| 45. | Oct 31, 2016 | |||||
| 46. | Nov 30, 2016 | |||||
| 47. | Dec 31, 2016 | |||||
| 48. | Jan 31, 2017 | |||||
| 49. | Feb 28, 2017 | |||||
| 50. | Mar 31, 2017 | |||||
| 51. | Apr 30, 2017 | |||||
| 52. | May 31, 2017 | |||||
| 53. | Jun 30, 2017 | |||||
| 54. | Jul 31, 2017 | |||||
| 55. | Aug 31, 2017 | |||||
| 56. | Sep 30, 2017 | |||||
| 57. | Oct 31, 2017 | |||||
| 58. | Nov 30, 2017 | |||||
| 59. | Dec 31, 2017 | |||||
| Average (R): | ||||||
| Standard deviation: | ||||||
Show all
1 Data in US$ per share of common stock, adjusted for splits and stock dividends.
2 Rate of return on common stock of TWX during period t
3 Rate of return on S&P 500 (the market portfolio proxy) during period t
Variance and Covariance
Time Warner Inc., calculation of variance and covariance of returns
| t | Date | RTWX,t | RS&P 500,t | (RTWX,t–RTWX)2 | (RS&P 500,t–RS&P 500)2 | (RTWX,t–RTWX)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | Feb 28, 2013 | |||||
| 2. | Mar 31, 2013 | |||||
| 3. | Apr 30, 2013 | |||||
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | Nov 30, 2017 | |||||
| 59. | Dec 31, 2017 | |||||
| Total (Σ): | ||||||
| t | Date | RTWX,t | RS&P 500,t | (RTWX,t–RTWX)2 | (RS&P 500,t–RS&P 500)2 | (RTWX,t–RTWX)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | Feb 28, 2013 | |||||
| 2. | Mar 31, 2013 | |||||
| 3. | Apr 30, 2013 | |||||
| 4. | May 31, 2013 | |||||
| 5. | Jun 30, 2013 | |||||
| 6. | Jul 31, 2013 | |||||
| 7. | Aug 31, 2013 | |||||
| 8. | Sep 30, 2013 | |||||
| 9. | Oct 31, 2013 | |||||
| 10. | Nov 30, 2013 | |||||
| 11. | Dec 31, 2013 | |||||
| 12. | Jan 31, 2014 | |||||
| 13. | Feb 28, 2014 | |||||
| 14. | Mar 31, 2014 | |||||
| 15. | Apr 30, 2014 | |||||
| 16. | May 31, 2014 | |||||
| 17. | Jun 30, 2014 | |||||
| 18. | Jul 31, 2014 | |||||
| 19. | Aug 31, 2014 | |||||
| 20. | Sep 30, 2014 | |||||
| 21. | Oct 31, 2014 | |||||
| 22. | Nov 30, 2014 | |||||
| 23. | Dec 31, 2014 | |||||
| 24. | Jan 31, 2015 | |||||
| 25. | Feb 28, 2015 | |||||
| 26. | Mar 31, 2015 | |||||
| 27. | Apr 30, 2015 | |||||
| 28. | May 31, 2015 | |||||
| 29. | Jun 30, 2015 | |||||
| 30. | Jul 31, 2015 | |||||
| 31. | Aug 31, 2015 | |||||
| 32. | Sep 30, 2015 | |||||
| 33. | Oct 31, 2015 | |||||
| 34. | Nov 30, 2015 | |||||
| 35. | Dec 31, 2015 | |||||
| 36. | Jan 31, 2016 | |||||
| 37. | Feb 29, 2016 | |||||
| 38. | Mar 31, 2016 | |||||
| 39. | Apr 30, 2016 | |||||
| 40. | May 31, 2016 | |||||
| 41. | Jun 30, 2016 | |||||
| 42. | Jul 31, 2016 | |||||
| 43. | Aug 31, 2016 | |||||
| 44. | Sep 30, 2016 | |||||
| 45. | Oct 31, 2016 | |||||
| 46. | Nov 30, 2016 | |||||
| 47. | Dec 31, 2016 | |||||
| 48. | Jan 31, 2017 | |||||
| 49. | Feb 28, 2017 | |||||
| 50. | Mar 31, 2017 | |||||
| 51. | Apr 30, 2017 | |||||
| 52. | May 31, 2017 | |||||
| 53. | Jun 30, 2017 | |||||
| 54. | Jul 31, 2017 | |||||
| 55. | Aug 31, 2017 | |||||
| 56. | Sep 30, 2017 | |||||
| 57. | Oct 31, 2017 | |||||
| 58. | Nov 30, 2017 | |||||
| 59. | Dec 31, 2017 | |||||
| Total (Σ): | ||||||
Show all
VarianceTWX = Σ(RTWX,t–RTWX)2 ÷ (59 – 1)
= ÷ (59 – 1)
=
VarianceS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= ÷ (59 – 1)
=
CovarianceTWX, S&P 500 = Σ(RTWX,t–RTWX)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= ÷ (59 – 1)
=
Systematic Risk (β) Estimation
| VarianceTWX | |
| VarianceS&P 500 | |
| CovarianceTWX, S&P 500 | |
| Correlation coefficientTWX, S&P 5001 | |
| βTWX2 | |
| αTWX3 |
Calculations
1 Correlation coefficientTWX, S&P 500
= CovarianceTWX, S&P 500 ÷ (Standard deviationTWX × Standard deviationS&P 500)
= ÷ ( × )
=
2 βTWX
= CovarianceTWX, S&P 500 ÷ VarianceS&P 500
= ÷
=
3 αTWX
= AverageTWX – βTWX × AverageS&P 500
= – ×
=
Expected Rate of Return
| Assumptions | ||
| Rate of return on LT Treasury Composite1 | RF | |
| Expected rate of return on market portfolio2 | E(RM) | |
| Systematic risk (β) of Time Warner Inc. common stock | βTWX | |
| Expected rate of return on Time Warner Inc. common stock3 | E(RTWX) | |
1 Unweighted average of bid yields on all outstanding fixed-coupon U.S. Treasury bonds neither due or callable in less than 10 years (risk-free rate of return proxy).
3 E(RTWX) = RF + βTWX [E(RM) – RF]
= + [ – ]
=