Stock Analysis on Net

Cummins Inc. (NYSE:CMI)

This company has been moved to the archive! The financial data has not been updated since May 2, 2024.

Capital Asset Pricing Model (CAPM)

Microsoft Excel

Rates of Return

Cummins Inc., monthly rates of return

Microsoft Excel
Cummins Inc. (CMI) Standard & Poor’s 500 (S&P 500)
t Date PriceCMI,t1 DividendCMI,t1 RCMI,t2 PriceS&P 500,t RS&P 500,t3
Jan 31, 2019 $147.11 2,704.10
1. Feb 28, 2019 $154.09 $1.14 5.52% 2,784.49 2.97%
2. Mar 31, 2019 $157.87 2.45% 2,834.40 1.79%
3. Apr 30, 2019 $166.29 5.33% 2,945.83 3.93%
. . . . . . .
. . . . . . .
. . . . . . .
58. Nov 30, 2023 $224.16 $1.68 4.41% 4,567.80 8.92%
59. Dec 31, 2023 $239.57 6.87% 4,769.83 4.42%
Average (R): 1.36% 1.11%
Standard deviation: 7.89% 5.31%
Cummins Inc. (CMI) Standard & Poor’s 500 (S&P 500)
t Date PriceCMI,t1 DividendCMI,t1 RCMI,t2 PriceS&P 500,t RS&P 500,t3
Jan 31, 2019 $147.11 2,704.10
1. Feb 28, 2019 $154.09 $1.14 5.52% 2,784.49 2.97%
2. Mar 31, 2019 $157.87 2.45% 2,834.40 1.79%
3. Apr 30, 2019 $166.29 5.33% 2,945.83 3.93%
4. May 31, 2019 $150.76 $1.14 -8.65% 2,752.06 -6.58%
5. Jun 30, 2019 $171.34 13.65% 2,941.76 6.89%
6. Jul 31, 2019 $164.00 -4.28% 2,980.38 1.31%
7. Aug 31, 2019 $149.27 $1.311 -8.18% 2,926.46 -1.81%
8. Sep 30, 2019 $162.67 8.98% 2,976.74 1.72%
9. Oct 31, 2019 $172.48 6.03% 3,037.56 2.04%
10. Nov 30, 2019 $182.86 $1.311 6.78% 3,140.98 3.40%
11. Dec 31, 2019 $178.96 -2.13% 3,230.78 2.86%
12. Jan 31, 2020 $159.97 -10.61% 3,225.52 -0.16%
13. Feb 29, 2020 $151.29 $1.311 -4.61% 2,954.22 -8.41%
14. Mar 31, 2020 $135.32 -10.56% 2,584.59 -12.51%
15. Apr 30, 2020 $163.50 20.82% 2,912.43 12.68%
16. May 31, 2020 $169.60 $1.311 4.53% 3,044.31 4.53%
17. Jun 30, 2020 $173.26 2.16% 3,100.29 1.84%
18. Jul 31, 2020 $193.26 11.54% 3,271.12 5.51%
19. Aug 31, 2020 $207.25 $1.311 7.92% 3,500.31 7.01%
20. Sep 30, 2020 $211.16 1.89% 3,363.00 -3.92%
21. Oct 31, 2020 $219.89 4.13% 3,269.96 -2.77%
22. Nov 30, 2020 $231.17 $1.35 5.74% 3,621.63 10.75%
23. Dec 31, 2020 $227.10 -1.76% 3,756.07 3.71%
24. Jan 31, 2021 $234.42 3.22% 3,714.24 -1.11%
25. Feb 28, 2021 $253.20 $1.35 8.59% 3,811.15 2.61%
26. Mar 31, 2021 $259.11 2.33% 3,972.89 4.24%
27. Apr 30, 2021 $252.04 -2.73% 4,181.17 5.24%
28. May 31, 2021 $257.28 $1.35 2.61% 4,204.11 0.55%
29. Jun 30, 2021 $243.81 -5.24% 4,297.50 2.22%
30. Jul 31, 2021 $232.10 -4.80% 4,395.26 2.27%
31. Aug 31, 2021 $235.98 $1.45 2.30% 4,522.68 2.90%
32. Sep 30, 2021 $224.56 -4.84% 4,307.54 -4.76%
33. Oct 31, 2021 $239.84 6.80% 4,605.38 6.91%
34. Nov 30, 2021 $209.75 $1.45 -11.94% 4,567.00 -0.83%
35. Dec 31, 2021 $218.14 4.00% 4,766.18 4.36%
36. Jan 31, 2022 $220.88 1.26% 4,515.55 -5.26%
37. Feb 28, 2022 $204.12 $1.45 -6.93% 4,373.94 -3.14%
38. Mar 31, 2022 $205.11 0.49% 4,530.41 3.58%
39. Apr 30, 2022 $189.19 -7.76% 4,131.93 -8.80%
40. May 31, 2022 $209.12 $1.45 11.30% 4,132.15 0.01%
41. Jun 30, 2022 $193.53 -7.46% 3,785.38 -8.39%
42. Jul 31, 2022 $221.31 14.35% 4,130.29 9.11%
43. Aug 31, 2022 $215.37 $1.57 -1.97% 3,955.00 -4.24%
44. Sep 30, 2022 $203.51 -5.51% 3,585.62 -9.34%
45. Oct 31, 2022 $244.51 20.15% 3,871.98 7.99%
46. Nov 30, 2022 $251.16 $1.57 3.36% 4,080.11 5.38%
47. Dec 31, 2022 $242.29 -3.53% 3,839.50 -5.90%
48. Jan 31, 2023 $249.54 2.99% 4,076.60 6.18%
49. Feb 28, 2023 $243.08 $1.57 -1.96% 3,970.15 -2.61%
50. Mar 31, 2023 $238.88 -1.73% 4,109.31 3.51%
51. Apr 30, 2023 $235.04 -1.61% 4,169.48 1.46%
52. May 31, 2023 $204.41 $1.57 -12.36% 4,179.83 0.25%
53. Jun 30, 2023 $245.16 19.94% 4,376.86 4.71%
54. Jul 31, 2023 $260.80 6.38% 4,588.96 4.85%
55. Aug 31, 2023 $230.04 $1.68 -11.15% 4,507.66 -1.77%
56. Sep 30, 2023 $228.46 -0.69% 4,288.05 -4.87%
57. Oct 31, 2023 $216.30 -5.32% 4,193.80 -2.20%
58. Nov 30, 2023 $224.16 $1.68 4.41% 4,567.80 8.92%
59. Dec 31, 2023 $239.57 6.87% 4,769.83 4.42%
Average (R): 1.36% 1.11%
Standard deviation: 7.89% 5.31%

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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 CMI during period t

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


Variance and Covariance

Cummins Inc., calculation of variance and covariance of returns

Microsoft Excel
t Date RCMI,t RS&P 500,t (RCMI,tRCMI)2 (RS&P 500,tRS&P 500)2 (RCMI,tRCMI)×(RS&P 500,tRS&P 500)
1. Feb 28, 2019 5.52% 2.97% 17.26 3.49 7.76
2. Mar 31, 2019 2.45% 1.79% 1.18 0.47 0.75
3. Apr 30, 2019 5.33% 3.93% 15.75 7.98 11.21
. . . . . . .
. . . . . . .
. . . . . . .
58. Nov 30, 2023 4.41% 8.92% 9.28 61.03 23.79
59. Dec 31, 2023 6.87% 4.42% 30.36 11.00 18.28
Total (Σ): 3,606.22 1,634.30 1,651.43
t Date RCMI,t RS&P 500,t (RCMI,tRCMI)2 (RS&P 500,tRS&P 500)2 (RCMI,tRCMI)×(RS&P 500,tRS&P 500)
1. Feb 28, 2019 5.52% 2.97% 17.26 3.49 7.76
2. Mar 31, 2019 2.45% 1.79% 1.18 0.47 0.75
3. Apr 30, 2019 5.33% 3.93% 15.75 7.98 11.21
4. May 31, 2019 -8.65% -6.58% 100.37 59.04 76.98
5. Jun 30, 2019 13.65% 6.89% 150.95 33.49 71.10
6. Jul 31, 2019 -4.28% 1.31% 31.91 0.04 -1.17
7. Aug 31, 2019 -8.18% -1.81% 91.15 8.50 27.83
8. Sep 30, 2019 8.98% 1.72% 57.95 0.37 4.66
9. Oct 31, 2019 6.03% 2.04% 21.77 0.88 4.37
10. Nov 30, 2019 6.78% 3.40% 29.30 5.28 12.44
11. Dec 31, 2019 -2.13% 2.86% 12.23 3.07 -6.13
12. Jan 31, 2020 -10.61% -0.16% 143.43 1.61 15.19
13. Feb 29, 2020 -4.61% -8.41% 35.66 90.57 56.83
14. Mar 31, 2020 -10.56% -12.51% 142.10 185.44 162.33
15. Apr 30, 2020 20.82% 12.68% 378.69 134.06 225.32
16. May 31, 2020 4.53% 4.53% 10.04 11.71 10.84
17. Jun 30, 2020 2.16% 1.84% 0.63 0.54 0.58
18. Jul 31, 2020 11.54% 5.51% 103.60 19.40 44.83
19. Aug 31, 2020 7.92% 7.01% 42.93 34.82 38.66
20. Sep 30, 2020 1.89% -3.92% 0.27 25.29 -2.62
21. Oct 31, 2020 4.13% -2.77% 7.67 15.00 -10.72
22. Nov 30, 2020 5.74% 10.75% 19.17 93.10 42.25
23. Dec 31, 2020 -1.76% 3.71% 9.77 6.79 -8.15
24. Jan 31, 2021 3.22% -1.11% 3.45 4.93 -4.12
25. Feb 28, 2021 8.59% 2.61% 52.16 2.26 10.86
26. Mar 31, 2021 2.33% 4.24% 0.94 9.85 3.04
27. Apr 30, 2021 -2.73% 5.24% 16.76 17.11 -16.93
28. May 31, 2021 2.61% 0.55% 1.56 0.31 -0.70
29. Jun 30, 2021 -5.24% 2.22% 43.57 1.24 -7.36
30. Jul 31, 2021 -4.80% 2.27% 38.04 1.37 -7.21
31. Aug 31, 2021 2.30% 2.90% 0.87 3.22 1.67
32. Sep 30, 2021 -4.84% -4.76% 38.49 34.37 36.37
33. Oct 31, 2021 6.80% 6.91% 29.59 33.74 31.60
34. Nov 30, 2021 -11.94% -0.83% 177.05 3.76 25.80
35. Dec 31, 2021 4.00% 4.36% 6.94 10.60 8.58
36. Jan 31, 2022 1.26% -5.26% 0.01 40.51 0.69
37. Feb 28, 2022 -6.93% -3.14% 68.83 17.99 35.19
38. Mar 31, 2022 0.49% 3.58% 0.77 6.11 -2.17
39. Apr 30, 2022 -7.76% -8.80% 83.29 98.04 90.37
40. May 31, 2022 11.30% 0.01% 98.72 1.21 -10.93
41. Jun 30, 2022 -7.46% -8.39% 77.79 90.21 83.77
42. Jul 31, 2022 14.35% 9.11% 168.73 64.09 103.99
43. Aug 31, 2022 -1.97% -4.24% 11.15 28.62 17.87
44. Sep 30, 2022 -5.51% -9.34% 47.22 109.11 71.78
45. Oct 31, 2022 20.15% 7.99% 352.75 47.34 129.23
46. Nov 30, 2022 3.36% 5.38% 3.99 18.23 8.53
47. Dec 31, 2022 -3.53% -5.90% 23.98 49.04 34.29
48. Jan 31, 2023 2.99% 6.18% 2.65 25.70 8.25
49. Feb 28, 2023 -1.96% -2.61% 11.05 13.82 12.36
50. Mar 31, 2023 -1.73% 3.51% 9.56 5.76 -7.42
51. Apr 30, 2023 -1.61% 1.46% 8.83 0.13 -1.07
52. May 31, 2023 -12.36% 0.25% 188.48 0.74 11.77
53. Jun 30, 2023 19.94% 4.71% 344.87 13.02 67.00
54. Jul 31, 2023 6.38% 4.85% 25.15 13.99 18.76
55. Aug 31, 2023 -11.15% -1.77% 156.63 8.28 36.01
56. Sep 30, 2023 -0.69% -4.87% 4.21 35.73 12.26
57. Oct 31, 2023 -5.32% -2.20% 44.72 10.92 22.09
58. Nov 30, 2023 4.41% 8.92% 9.28 61.03 23.79
59. Dec 31, 2023 6.87% 4.42% 30.36 11.00 18.28
Total (Σ): 3,606.22 1,634.30 1,651.43

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VarianceCMI = Σ(RCMI,tRCMI)2 ÷ (59 – 1)
= 3,606.22 ÷ (59 – 1)
= 62.18

VarianceS&P 500 = Σ(RS&P 500,tRS&P 500)2 ÷ (59 – 1)
= 1,634.30 ÷ (59 – 1)
= 28.18

CovarianceCMI, S&P 500 = Σ(RCMI,tRCMI)×(RS&P 500,tRS&P 500) ÷ (59 – 1)
= 1,651.43 ÷ (59 – 1)
= 28.47


Systematic Risk (β) Estimation

Microsoft Excel
VarianceCMI 62.18
VarianceS&P 500 28.18
CovarianceCMI, S&P 500 28.47
Correlation coefficientCMI, S&P 5001 0.68
βCMI2 1.01
αCMI3 0.25%

Calculations

1 Correlation coefficientCMI, S&P 500
= CovarianceCMI, S&P 500 ÷ (Standard deviationCMI × Standard deviationS&P 500)
= 28.47 ÷ (7.89% × 5.31%)
= 0.68

2 βCMI
= CovarianceCMI, S&P 500 ÷ VarianceS&P 500
= 28.47 ÷ 28.18
= 1.01

3 αCMI
= AverageCMI – βCMI × AverageS&P 500
= 1.36%1.01 × 1.11%
= 0.25%


Expected Rate of Return

Microsoft Excel
Assumptions
Rate of return on LT Treasury Composite1 RF 4.67%
Expected rate of return on market portfolio2 E(RM) 13.79%
Systematic risk (β) of Cummins Inc. common stock βCMI 1.01
 
Expected rate of return on Cummins Inc. common stock3 E(RCMI) 13.88%

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(RCMI) = RF + βCMI [E(RM) – RF]
= 4.67% + 1.01 [13.79%4.67%]
= 13.88%