Microsoft Excel LibreOffice Calc

Danaher Corp. (DHR)


Capital Asset Pricing Model (CAPM)

Difficulty: Intermediate

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


Rates of Return

Danaher Corp., monthly rates of return

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Danaher Corp. (DHR) Standard & Poor’s 500 (S&P 500)
t Date PriceDHR,t1 DividendDHR,t1 RDHR,t2 PriceS&P 500,t RS&P 500,t3
Jan 31, 2014 74.39 1,782.59
1. Feb 28, 2014 76.49 2.82% 1,859.45 4.31%
2. Mar 31, 2014 75.00 0.10 -1.82% 1,872.34 0.69%
3. Apr 30, 2014 73.38 -2.16% 1,883.95 0.62%
. . . . . . .
. . . . . . .
. . . . . . .
58. Nov 30, 2018 109.54 10.20% 2,760.17 1.79%
59. Dec 31, 2018 103.12 0.16 -5.71% 2,506.85 -9.18%
Average: 1.15% 0.63%
Standard Deviation: 4.26% 3.13%
Danaher Corp. (DHR) Standard & Poor’s 500 (S&P 500)
t Date PriceDHR,t1 DividendDHR,t1 RDHR,t2 PriceS&P 500,t RS&P 500,t3
Jan 31, 2014 74.39 1,782.59
1. Feb 28, 2014 76.49 2.82% 1,859.45 4.31%
2. Mar 31, 2014 75.00 0.10 -1.82% 1,872.34 0.69%
3. Apr 30, 2014 73.38 -2.16% 1,883.95 0.62%
4. May 31, 2014 78.43 6.88% 1,923.57 2.10%
5. Jun 30, 2014 78.73 0.10 0.51% 1,960.23 1.91%
6. Jul 31, 2014 73.88 -6.16% 1,930.67 -1.51%
7. Aug 31, 2014 76.61 3.70% 2,003.37 3.77%
8. Sep 30, 2014 75.98 0.10 -0.69% 1,972.29 -1.55%
9. Oct 31, 2014 80.40 5.82% 2,018.05 2.32%
10. Nov 30, 2014 83.56 3.93% 2,067.56 2.45%
11. Dec 31, 2014 85.71 0.10 2.69% 2,058.90 -0.42%
12. Jan 31, 2015 82.38 -3.89% 1,994.99 -3.10%
13. Feb 28, 2015 87.28 5.95% 2,104.50 5.49%
14. Mar 31, 2015 84.90 0.135 -2.57% 2,067.89 -1.74%
15. Apr 30, 2015 81.88 -3.56% 2,085.51 0.85%
16. May 31, 2015 86.32 5.42% 2,107.39 1.05%
17. Jun 30, 2015 85.59 0.135 -0.69% 2,063.11 -2.10%
18. Jul 31, 2015 91.56 6.98% 2,103.84 1.97%
19. Aug 31, 2015 87.02 -4.96% 1,972.18 -6.26%
20. Sep 30, 2015 85.21 0.135 -1.92% 1,920.03 -2.64%
21. Oct 31, 2015 93.31 9.51% 2,079.36 8.30%
22. Nov 30, 2015 96.39 3.30% 2,080.41 0.05%
23. Dec 31, 2015 92.88 0.135 -3.50% 2,043.94 -1.75%
24. Jan 31, 2016 86.65 -6.71% 1,940.24 -5.07%
25. Feb 29, 2016 89.27 3.02% 1,932.23 -0.41%
26. Mar 31, 2016 94.86 0.16 6.44% 2,059.74 6.60%
27. Apr 30, 2016 96.75 1.99% 2,065.30 0.27%
28. May 31, 2016 98.36 1.66% 2,096.95 1.53%
29. Jun 30, 2016 101.00 0.16 2.85% 2,098.86 0.09%
30. Jul 31, 2016 81.44 24.56 4.95% 2,173.60 3.56%
31. Aug 31, 2016 81.41 -0.04% 2,170.95 -0.12%
32. Sep 30, 2016 78.39 0.125 -3.56% 2,168.27 -0.12%
33. Oct 31, 2016 78.55 0.20% 2,126.15 -1.94%
34. Nov 30, 2016 78.17 -0.48% 2,198.81 3.42%
35. Dec 31, 2016 77.84 0.125 -0.26% 2,238.83 1.82%
36. Jan 31, 2017 83.92 7.81% 2,278.87 1.79%
37. Feb 28, 2017 85.55 1.94% 2,363.64 3.72%
38. Mar 31, 2017 85.53 0.14 0.14% 2,362.72 -0.04%
39. Apr 30, 2017 83.33 -2.57% 2,384.20 0.91%
40. May 31, 2017 84.94 1.93% 2,411.80 1.16%
41. Jun 30, 2017 84.39 0.14 -0.48% 2,423.41 0.48%
42. Jul 31, 2017 81.49 -3.44% 2,470.30 1.93%
43. Aug 31, 2017 83.42 2.37% 2,471.65 0.05%
44. Sep 30, 2017 85.78 0.14 3.00% 2,519.36 1.93%
45. Oct 31, 2017 92.27 7.57% 2,575.26 2.22%
46. Nov 30, 2017 94.36 2.27% 2,647.58 2.81%
47. Dec 31, 2017 92.82 0.14 -1.48% 2,673.61 0.98%
48. Jan 31, 2018 101.28 9.11% 2,823.81 5.62%
49. Feb 28, 2018 97.78 -3.46% 2,713.83 -3.89%
50. Mar 31, 2018 97.91 0.16 0.30% 2,640.87 -2.69%
51. Apr 30, 2018 100.32 2.46% 2,648.05 0.27%
52. May 31, 2018 99.28 -1.04% 2,705.27 2.16%
53. Jun 30, 2018 98.68 0.16 -0.44% 2,718.37 0.48%
54. Jul 31, 2018 102.58 3.95% 2,816.29 3.60%
55. Aug 31, 2018 103.54 0.94% 2,901.52 3.03%
56. Sep 30, 2018 108.66 0.16 5.10% 2,913.98 0.43%
57. Oct 31, 2018 99.40 -8.52% 2,711.74 -6.94%
58. Nov 30, 2018 109.54 10.20% 2,760.17 1.79%
59. Dec 31, 2018 103.12 0.16 -5.71% 2,506.85 -9.18%
Average: 1.15% 0.63%
Standard Deviation: 4.26% 3.13%

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1 Data in USD $ per share of common stock, adjusted for splits and stock dividends.

2 Rate of return on common stock of DHR 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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VarianceDHR 18.16
VarianceS&P 500 9.77
CovarianceDHR, S&P 500 9.73
Correlation CoefficientDHR, S&P 5001 0.73
βDHR2 1.00
αDHR3 0.52

Calculations

1 CovarianceDHR, S&P 500 ÷ (Standard DeviationDHR × Standard DeviationS&P 500)
= 9.73 ÷ (4.26 × 3.13)

2 CovarianceDHR, S&P 500 ÷ VarianceS&P 500
= 9.73 ÷ 9.77

3 AverageDHR – βDHR × AverageS&P 500
= 1.151.00 × 0.63


Expected Rate of Return

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Assumptions
Rate of return on LT Treasury Composite1 RF 2.87%
Expected rate of return on market portfolio2 E(RM) 11.96%
Systematic risk (β) of Danaher Corp.’s common stock βDHR 1.00
Expected rate of return on Danaher Corp.’s common stock3 E(RDHR) 11.93%

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).

Calculations

2 See Details »

3 E(RDHR) = RF + βDHR [E(RM) – RF]
= 2.87% + 1.00 [11.96%2.87%]
= 11.93%