Stock Analysis on Net

Accenture PLC (NYSE:ACN)

Capital Asset Pricing Model (CAPM)

Microsoft Excel

Rates of Return

Accenture PLC, monthly rates of return

Microsoft Excel
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, 2017 $135.07 2,519.36
1. Oct 31, 2017 $142.36 $1.33 6.38% 2,575.26 2.22%
2. Nov 30, 2017 $148.01 3.97% 2,647.58 2.81%
3. Dec 31, 2017 $153.09 3.43% 2,673.61 0.98%
. . . . . . .
. . . . . . .
. . . . . . .
70. Jul 31, 2023 $316.35 $1.12 2.88% 4,588.96 4.85%
71. Aug 31, 2023 $323.77 2.35% 4,507.66 -1.77%
Average (R): 1.63% 0.95%
Standard deviation: 7.17% 5.08%
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, 2017 $135.07 2,519.36
1. Oct 31, 2017 $142.36 $1.33 6.38% 2,575.26 2.22%
2. Nov 30, 2017 $148.01 3.97% 2,647.58 2.81%
3. Dec 31, 2017 $153.09 3.43% 2,673.61 0.98%
4. Jan 31, 2018 $160.70 4.97% 2,823.81 5.62%
5. Feb 28, 2018 $161.01 0.19% 2,713.83 -3.89%
6. Mar 31, 2018 $153.50 -4.66% 2,640.87 -2.69%
7. Apr 30, 2018 $151.20 $1.33 -0.63% 2,648.05 0.27%
8. May 31, 2018 $155.74 3.00% 2,705.27 2.16%
9. Jun 30, 2018 $163.59 5.04% 2,718.37 0.48%
10. Jul 31, 2018 $159.33 -2.60% 2,816.29 3.60%
11. Aug 31, 2018 $169.07 6.11% 2,901.52 3.03%
12. Sep 30, 2018 $170.20 0.67% 2,913.98 0.43%
13. Oct 31, 2018 $157.62 $1.46 -6.53% 2,711.74 -6.94%
14. Nov 30, 2018 $164.52 4.38% 2,760.17 1.79%
15. Dec 31, 2018 $141.01 -14.29% 2,506.85 -9.18%
16. Jan 31, 2019 $153.55 8.89% 2,704.10 7.87%
17. Feb 28, 2019 $161.38 5.10% 2,784.49 2.97%
18. Mar 31, 2019 $176.02 9.07% 2,834.40 1.79%
19. Apr 30, 2019 $182.67 $1.46 4.61% 2,945.83 3.93%
20. May 31, 2019 $178.07 -2.52% 2,752.06 -6.58%
21. Jun 30, 2019 $184.77 3.76% 2,941.76 6.89%
22. Jul 31, 2019 $192.58 4.23% 2,980.38 1.31%
23. Aug 31, 2019 $198.17 2.90% 2,926.46 -1.81%
24. Sep 30, 2019 $192.35 -2.94% 2,976.74 1.72%
25. Oct 31, 2019 $185.42 $0.80 -3.19% 3,037.56 2.04%
26. Nov 30, 2019 $201.16 8.49% 3,140.98 3.40%
27. Dec 31, 2019 $210.57 4.68% 3,230.78 2.86%
28. Jan 31, 2020 $205.21 $0.80 -2.17% 3,225.52 -0.16%
29. Feb 29, 2020 $180.59 -12.00% 2,954.22 -8.41%
30. Mar 31, 2020 $163.26 -9.60% 2,584.59 -12.51%
31. Apr 30, 2020 $185.19 $0.80 13.92% 2,912.43 12.68%
32. May 31, 2020 $201.62 8.87% 3,044.31 4.53%
33. Jun 30, 2020 $214.72 6.50% 3,100.29 1.84%
34. Jul 31, 2020 $224.78 $0.80 5.06% 3,271.12 5.51%
35. Aug 31, 2020 $239.93 6.74% 3,500.31 7.01%
36. Sep 30, 2020 $225.99 -5.81% 3,363.00 -3.92%
37. Oct 31, 2020 $216.91 $0.88 -3.63% 3,269.96 -2.77%
38. Nov 30, 2020 $249.09 14.84% 3,621.63 10.75%
39. Dec 31, 2020 $261.21 4.87% 3,756.07 3.71%
40. Jan 31, 2021 $241.92 $0.88 -7.05% 3,714.24 -1.11%
41. Feb 28, 2021 $250.90 3.71% 3,811.15 2.61%
42. Mar 31, 2021 $276.25 10.10% 3,972.89 4.24%
43. Apr 30, 2021 $289.97 $0.88 5.29% 4,181.17 5.24%
44. May 31, 2021 $282.16 -2.69% 4,204.11 0.55%
45. Jun 30, 2021 $294.79 4.48% 4,297.50 2.22%
46. Jul 31, 2021 $317.68 $0.88 8.06% 4,395.26 2.27%
47. Aug 31, 2021 $336.56 5.94% 4,522.68 2.90%
48. Sep 30, 2021 $319.92 -4.94% 4,307.54 -4.76%
49. Oct 31, 2021 $358.79 $0.97 12.45% 4,605.38 6.91%
50. Nov 30, 2021 $357.40 -0.39% 4,567.00 -0.83%
51. Dec 31, 2021 $414.55 15.99% 4,766.18 4.36%
52. Jan 31, 2022 $353.58 $0.97 -14.47% 4,515.55 -5.26%
53. Feb 28, 2022 $316.02 -10.62% 4,373.94 -3.14%
54. Mar 31, 2022 $337.23 6.71% 4,530.41 3.58%
55. Apr 30, 2022 $300.36 $0.97 -10.65% 4,131.93 -8.80%
56. May 31, 2022 $298.46 -0.63% 4,132.15 0.01%
57. Jun 30, 2022 $277.65 -6.97% 3,785.38 -8.39%
58. Jul 31, 2022 $306.26 $0.97 10.65% 4,130.29 9.11%
59. Aug 31, 2022 $288.46 -5.81% 3,955.00 -4.24%
60. Sep 30, 2022 $257.30 -10.80% 3,585.62 -9.34%
61. Oct 31, 2022 $283.90 $1.12 10.77% 3,871.98 7.99%
62. Nov 30, 2022 $300.93 6.00% 4,080.11 5.38%
63. Dec 31, 2022 $266.84 -11.33% 3,839.50 -5.90%
64. Jan 31, 2023 $279.05 $1.12 5.00% 4,076.60 6.18%
65. Feb 28, 2023 $265.55 -4.84% 3,970.15 -2.61%
66. Mar 31, 2023 $285.81 7.63% 4,109.31 3.51%
67. Apr 30, 2023 $280.29 $1.12 -1.54% 4,169.48 1.46%
68. May 31, 2023 $305.92 9.14% 4,179.83 0.25%
69. Jun 30, 2023 $308.58 0.87% 4,376.86 4.71%
70. Jul 31, 2023 $316.35 $1.12 2.88% 4,588.96 4.85%
71. Aug 31, 2023 $323.77 2.35% 4,507.66 -1.77%
Average (R): 1.63% 0.95%
Standard deviation: 7.17% 5.08%

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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


Variance and Covariance

Accenture PLC, calculation of variance and covariance of returns

Microsoft Excel
t Date RACN,t RS&P 500,t (RACN,tRACN)2 (RS&P 500,tRS&P 500)2 (RACN,tRACN)×(RS&P 500,tRS&P 500)
1. Oct 31, 2017 6.38% 2.22% 22.63 1.61 6.03
2. Nov 30, 2017 3.97% 2.81% 5.49 3.45 4.35
3. Dec 31, 2017 3.43% 0.98% 3.26 0.00 0.06
. . . . . . .
. . . . . . .
. . . . . . .
70. Jul 31, 2023 2.88% 4.85% 1.58 15.17 4.89
71. Aug 31, 2023 2.35% -1.77% 0.52 7.41 -1.96
Total (Σ): 3,595.64 1,807.09 2,179.01
t Date RACN,t RS&P 500,t (RACN,tRACN)2 (RS&P 500,tRS&P 500)2 (RACN,tRACN)×(RS&P 500,tRS&P 500)
1. Oct 31, 2017 6.38% 2.22% 22.63 1.61 6.03
2. Nov 30, 2017 3.97% 2.81% 5.49 3.45 4.35
3. Dec 31, 2017 3.43% 0.98% 3.26 0.00 0.06
4. Jan 31, 2018 4.97% 5.62% 11.19 21.78 15.61
5. Feb 28, 2018 0.19% -3.89% 2.05 23.48 6.94
6. Mar 31, 2018 -4.66% -2.69% 39.56 13.25 22.89
7. Apr 30, 2018 -0.63% 0.27% 5.10 0.46 1.53
8. May 31, 2018 3.00% 2.16% 1.90 1.46 1.67
9. Jun 30, 2018 5.04% 0.48% 11.66 0.22 -1.59
10. Jul 31, 2018 -2.60% 3.60% 17.89 7.03 -11.21
11. Aug 31, 2018 6.11% 3.03% 20.14 4.31 9.31
12. Sep 30, 2018 0.67% 0.43% 0.92 0.27 0.50
13. Oct 31, 2018 -6.53% -6.94% 66.57 62.28 64.38
14. Nov 30, 2018 4.38% 1.79% 7.58 0.70 2.30
15. Dec 31, 2018 -14.29% -9.18% 253.30 102.59 161.20
16. Jan 31, 2019 8.89% 7.87% 52.82 47.85 50.27
17. Feb 28, 2019 5.10% 2.97% 12.07 4.09 7.02
18. Mar 31, 2019 9.07% 1.79% 55.45 0.71 6.26
19. Apr 30, 2019 4.61% 3.93% 8.89 8.88 8.89
20. May 31, 2019 -2.52% -6.58% 17.17 56.68 31.20
21. Jun 30, 2019 3.76% 6.89% 4.57 35.31 12.70
22. Jul 31, 2019 4.23% 1.31% 6.77 0.13 0.94
23. Aug 31, 2019 2.90% -1.81% 1.63 7.62 -3.53
24. Sep 30, 2019 -2.94% 1.72% 20.81 0.59 -3.50
25. Oct 31, 2019 -3.19% 2.04% 23.16 1.19 -5.26
26. Nov 30, 2019 8.49% 3.40% 47.11 6.02 16.84
27. Dec 31, 2019 4.68% 2.86% 9.32 3.64 5.82
28. Jan 31, 2020 -2.17% -0.16% 14.37 1.24 4.22
29. Feb 29, 2020 -12.00% -8.41% 185.58 87.65 127.54
30. Mar 31, 2020 -9.60% -12.51% 125.92 181.25 151.08
31. Apr 30, 2020 13.92% 12.68% 151.22 137.67 144.29
32. May 31, 2020 8.87% 4.53% 52.51 12.80 25.92
33. Jun 30, 2020 6.50% 1.84% 23.74 0.79 4.32
34. Jul 31, 2020 5.06% 5.51% 11.78 20.78 15.65
35. Aug 31, 2020 6.74% 7.01% 26.16 36.67 30.97
36. Sep 30, 2020 -5.81% -3.92% 55.28 23.76 36.24
37. Oct 31, 2020 -3.63% -2.77% 27.60 13.82 19.53
38. Nov 30, 2020 14.84% 10.75% 174.51 96.11 129.51
39. Dec 31, 2020 4.87% 3.71% 10.50 7.62 8.95
40. Jan 31, 2021 -7.05% -1.11% 75.23 4.26 17.91
41. Feb 28, 2021 3.71% 2.61% 4.35 2.75 3.46
42. Mar 31, 2021 10.10% 4.24% 71.88 10.84 27.92
43. Apr 30, 2021 5.29% 5.24% 13.39 18.42 15.71
44. May 31, 2021 -2.69% 0.55% 18.65 0.16 1.74
45. Jun 30, 2021 4.48% 2.22% 8.13 1.61 3.62
46. Jul 31, 2021 8.06% 2.27% 41.45 1.75 8.52
47. Aug 31, 2021 5.94% 2.90% 18.64 3.79 8.41
48. Sep 30, 2021 -4.94% -4.76% 43.16 32.58 37.50
49. Oct 31, 2021 12.45% 6.91% 117.24 35.56 64.57
50. Nov 30, 2021 -0.39% -0.83% 4.05 3.18 3.59
51. Dec 31, 2021 15.99% 4.36% 206.36 11.63 48.99
52. Jan 31, 2022 -14.47% -5.26% 259.17 38.56 99.97
53. Feb 28, 2022 -10.62% -3.14% 150.02 16.71 50.06
54. Mar 31, 2022 6.71% 3.58% 25.87 6.90 13.36
55. Apr 30, 2022 -10.65% -8.80% 150.57 95.00 119.60
56. May 31, 2022 -0.63% 0.01% 5.10 0.89 2.14
57. Jun 30, 2022 -6.97% -8.39% 73.92 87.29 80.33
58. Jul 31, 2022 10.65% 9.11% 81.51 66.59 73.68
59. Aug 31, 2022 -5.81% -4.24% 55.31 26.99 38.64
60. Sep 30, 2022 -10.80% -9.34% 154.44 105.90 127.89
61. Oct 31, 2022 10.77% 7.99% 83.69 49.49 64.36
62. Nov 30, 2022 6.00% 5.38% 19.13 19.57 19.35
63. Dec 31, 2022 -11.33% -5.90% 167.79 46.90 88.71
64. Jan 31, 2023 5.00% 6.18% 11.36 27.29 17.61
65. Feb 28, 2023 -4.84% -2.61% 41.77 12.69 23.02
66. Mar 31, 2023 7.63% 3.51% 36.05 6.52 15.33
67. Apr 30, 2023 -1.54% 1.46% 10.02 0.26 -1.62
68. May 31, 2023 9.14% 0.25% 56.53 0.49 -5.28
69. Jun 30, 2023 0.87% 4.71% 0.57 14.16 -2.84
70. Jul 31, 2023 2.88% 4.85% 1.58 15.17 4.89
71. Aug 31, 2023 2.35% -1.77% 0.52 7.41 -1.96
Total (Σ): 3,595.64 1,807.09 2,179.01

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VarianceACN = Σ(RACN,tRACN)2 ÷ (71 – 1)
= 3,595.64 ÷ (71 – 1)
= 51.37

VarianceS&P 500 = Σ(RS&P 500,tRS&P 500)2 ÷ (71 – 1)
= 1,807.09 ÷ (71 – 1)
= 25.82

CovarianceACN, S&P 500 = Σ(RACN,tRACN)×(RS&P 500,tRS&P 500) ÷ (71 – 1)
= 2,179.01 ÷ (71 – 1)
= 31.13


Systematic Risk (β) Estimation

Microsoft Excel
VarianceACN 51.37
VarianceS&P 500 25.82
CovarianceACN, S&P 500 31.13
Correlation coefficientACN, S&P 5001 0.85
βACN2 1.21
αACN3 0.48%

Calculations

1 Correlation coefficientACN, S&P 500
= CovarianceACN, S&P 500 ÷ (Standard deviationACN × Standard deviationS&P 500)
= 31.13 ÷ (7.17% × 5.08%)
= 0.85

2 βACN
= CovarianceACN, S&P 500 ÷ VarianceS&P 500
= 31.13 ÷ 25.82
= 1.21

3 αACN
= AverageACN – βACN × AverageS&P 500
= 1.63%1.21 × 0.95%
= 0.48%


Expected Rate of Return

Microsoft Excel
Assumptions
Rate of return on LT Treasury Composite1 RF 4.42%
Expected rate of return on market portfolio2 E(RM) 13.60%
Systematic risk (β) of Accenture PLC common stock βACN 1.21
 
Expected rate of return on Accenture PLC common stock3 E(RACN) 15.49%

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]
= 4.42% + 1.21 [13.60%4.42%]
= 15.49%