Microsoft Excel LibreOffice Calc

Accenture PLC (ACN)


Capital Asset Pricing Model (CAPM)

Medium level of difficulty

Capital asset pricing model (CAPM) indicates what should be the expected or required rate of return on risky assets like Accenture PLC’s common stock.


Rates of Return

Accenture PLC, monthly rates of return

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Accenture PLC (ACN) Standard & Poor’s 500 (S&P 500)
t Date PriceACN,t1 DividendACN,t1 RACN,t2 PriceS&P 500,t RS&P 500,t3
Sep 30, 2013 73.64 1,681.55
1. Oct 31, 2013 73.50 0.93 1.07% 1,756.54 4.46%
2. Nov 30, 2013 77.47 5.40% 1,805.81 2.80%
3. Dec 31, 2013 82.22 6.13% 1,848.36 2.36%
. . . . . . .
. . . . . . .
. . . . . . .
64. Jan 31, 2019 153.55 8.89% 2,704.10 7.87%
65. Feb 28, 2019 161.38 5.10% 2,784.49 2.97%
Average: 1.51% 0.83%
Standard deviation: 4.76% 3.22%
Accenture PLC (ACN) Standard & Poor’s 500 (S&P 500)
t Date PriceACN,t1 DividendACN,t1 RACN,t2 PriceS&P 500,t RS&P 500,t3
Sep 30, 2013 73.64 1,681.55
1. Oct 31, 2013 73.50 0.93 1.07% 1,756.54 4.46%
2. Nov 30, 2013 77.47 5.40% 1,805.81 2.80%
3. Dec 31, 2013 82.22 6.13% 1,848.36 2.36%
4. Jan 31, 2014 79.88 -2.85% 1,782.59 -3.56%
5. Feb 28, 2014 83.35 4.34% 1,859.45 4.31%
6. Mar 31, 2014 79.72 -4.36% 1,872.34 0.69%
7. Apr 30, 2014 80.22 0.93 1.79% 1,883.95 0.62%
8. May 31, 2014 81.45 1.53% 1,923.57 2.10%
9. Jun 30, 2014 80.84 -0.75% 1,960.23 1.91%
10. Jul 31, 2014 79.28 -1.93% 1,930.67 -1.51%
11. Aug 31, 2014 81.06 2.25% 2,003.37 3.77%
12. Sep 30, 2014 81.32 0.32% 1,972.29 -1.55%
13. Oct 31, 2014 81.12 1.02 1.01% 2,018.05 2.32%
14. Nov 30, 2014 86.33 6.42% 2,067.56 2.45%
15. Dec 31, 2014 89.31 3.45% 2,058.90 -0.42%
16. Jan 31, 2015 84.03 -5.91% 1,994.99 -3.10%
17. Feb 28, 2015 90.03 7.14% 2,104.50 5.49%
18. Mar 31, 2015 93.69 4.07% 2,067.89 -1.74%
19. Apr 30, 2015 92.65 1.02 -0.02% 2,085.51 0.85%
20. May 31, 2015 96.04 3.66% 2,107.39 1.05%
21. Jun 30, 2015 96.78 0.77% 2,063.11 -2.10%
22. Jul 31, 2015 103.11 6.54% 2,103.84 1.97%
23. Aug 31, 2015 94.27 -8.57% 1,972.18 -6.26%
24. Sep 30, 2015 98.26 4.23% 1,920.03 -2.64%
25. Oct 31, 2015 107.20 1.10 10.22% 2,079.36 8.30%
26. Nov 30, 2015 107.22 0.02% 2,080.41 0.05%
27. Dec 31, 2015 104.50 -2.54% 2,043.94 -1.75%
28. Jan 31, 2016 105.54 1.00% 1,940.24 -5.07%
29. Feb 29, 2016 100.26 -5.00% 1,932.23 -0.41%
30. Mar 31, 2016 115.40 15.10% 2,059.74 6.60%
31. Apr 30, 2016 112.92 1.10 -1.20% 2,065.30 0.27%
32. May 31, 2016 118.97 5.36% 2,096.95 1.53%
33. Jun 30, 2016 113.29 -4.77% 2,098.86 0.09%
34. Jul 31, 2016 112.81 -0.42% 2,173.60 3.56%
35. Aug 31, 2016 115.00 1.94% 2,170.95 -0.12%
36. Sep 30, 2016 122.17 6.23% 2,168.27 -0.12%
37. Oct 31, 2016 116.24 1.21 -3.86% 2,126.15 -1.94%
38. Nov 30, 2016 119.43 2.74% 2,198.81 3.42%
39. Dec 31, 2016 117.13 -1.93% 2,238.83 1.82%
40. Jan 31, 2017 113.87 -2.78% 2,278.87 1.79%
41. Feb 28, 2017 122.50 7.58% 2,363.64 3.72%
42. Mar 31, 2017 119.88 -2.14% 2,362.72 -0.04%
43. Apr 30, 2017 121.30 1.21 2.19% 2,384.20 0.91%
44. May 31, 2017 124.47 2.61% 2,411.80 1.16%
45. Jun 30, 2017 123.68 -0.63% 2,423.41 0.48%
46. Jul 31, 2017 128.82 4.16% 2,470.30 1.93%
47. Aug 31, 2017 130.76 1.51% 2,471.65 0.05%
48. Sep 30, 2017 135.07 3.30% 2,519.36 1.93%
49. Oct 31, 2017 142.36 1.33 6.38% 2,575.26 2.22%
50. Nov 30, 2017 148.01 3.97% 2,647.58 2.81%
51. Dec 31, 2017 153.09 3.43% 2,673.61 0.98%
52. Jan 31, 2018 160.70 4.97% 2,823.81 5.62%
53. Feb 28, 2018 161.01 0.19% 2,713.83 -3.89%
54. Mar 31, 2018 153.50 -4.66% 2,640.87 -2.69%
55. Apr 30, 2018 151.20 1.33 -0.63% 2,648.05 0.27%
56. May 31, 2018 155.74 3.00% 2,705.27 2.16%
57. Jun 30, 2018 163.59 5.04% 2,718.37 0.48%
58. Jul 31, 2018 159.33 -2.60% 2,816.29 3.60%
59. Aug 31, 2018 169.07 6.11% 2,901.52 3.03%
60. Sep 30, 2018 170.20 0.67% 2,913.98 0.43%
61. Oct 31, 2018 157.62 1.46 -6.53% 2,711.74 -6.94%
62. Nov 30, 2018 164.52 4.38% 2,760.17 1.79%
63. Dec 31, 2018 141.01 -14.29% 2,506.85 -9.18%
64. Jan 31, 2019 153.55 8.89% 2,704.10 7.87%
65. Feb 28, 2019 161.38 5.10% 2,784.49 2.97%
Average: 1.51% 0.83%
Standard deviation: 4.76% 3.22%

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 ACN during period t

3 Rate of return on S&P 500 (the market portfolio proxy) during period t


Systematic Risk (β) Estimation

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VarianceACN 22.67
VarianceS&P 500 10.34
CovarianceACN, S&P 500 11.25
Correlation coefficientACN, S&P 5001 0.74
βACN2 1.09
αACN3 0.60

Calculations

1 Correlation coefficientACN, S&P 500
= CovarianceACN, S&P 500 ÷ (Standard deviationACN × Standard deviationS&P 500)
= 11.25 ÷ (4.76 × 3.22)

2 βACN
= CovarianceACN, S&P 500 ÷ VarianceS&P 500
= 11.25 ÷ 10.34

3 αACN
= AverageACN – βACN × AverageS&P 500
= 1.511.09 × 0.83


Expected Rate of Return

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Assumptions
Rate of return on LT Treasury Composite1 RF 2.22%
Expected rate of return on market portfolio2 E(RM) 11.53%
Systematic risk (β) of Accenture PLC’s common stock βACN 1.09
 
Expected rate of return on Accenture PLC’s common stock3 E(RACN) 12.36%

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).

2 See details »

3 E(RACN) = RF + βACN [E(RM) – RF]
= 2.22% + 1.09 [11.53%2.22%]
= 12.36%