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To the disappointment of many shareholders, Berkshire Hathaway (BRK.A)(BRK.B) doesn't pay a dividend, and Warren Buffett has frequently said that as long as he and his investment managers can add more than $1 of intrinsic value for each $1 of earnings retained, shareholders will be better off without dividends. Buffett also has said that in his opinion Berkshire Hathaway should trade at a lower earnings multiple if it paid a dividend.

Considering the continuing controversy in the investment community around the dividend issue, these statements probably haven't been understood. In this short article I will shed some light on the underlying math of Buffett's statements.

First of all, I'm in the camp of those who don't believe that Berkshire's book value per share is still a good proxy for intrinsic value per share. This is because Berkshire is not anymore mostly a stock investment vehicle but has become a conglomerate of operating businesses with a huge stock portfolio attached. Most operating businesses are best valued based on their earnings, not based on book value, and that's why Berkshire's value should be determined looking more closely at its operating earnings than at book value per share. I'm saying this because, as book value has lost some of his significance for evaluation purposes, the same applies to the return on equity ratio and Berkshire's GAAP-earnings understate Berkshire's true earning power.

However, for the sake of simplicity, in this article we will base our comparison of Berkshire and a hypothetical mid-cap insurance company mostly on book value related parameters.

This hypothetical insurance company has a book value of $50 per share and generates a return on equity of 15%, hence its EPS is $7.5. Differently from Berkshire, it pays out 80% of its earnings. With such a nice yield, it trades at 1.5 times book value, that is $75 per share or 10 times earnings.

So which returns can an investor expect for the next twenty years? The following table shows the math: Each year we add last year's retained earnings to last year's equity and calculate the new EPS (15% of equity) and dividend (80% of EPS).

Equity

EPS

Dividend

Stock price

2013

50.0

7.5

6.0

75

2014

51.5

7.7

6.2

77

2015

53.0

8.0

6.4

80

2016

54.6

8.2

6.6

82

2017

56.3

8.4

6.8

84

2018

58.0

8.7

7.0

87

2019

59.7

9.0

7.2

90

2020

61.5

9.2

7.4

92

2021

63.3

9.5

7.6

95

2022

65.2

9.8

7.8

98

2023

67.2

10.1

8.1

101

2024

69.2

10.4

8.3

104

2025

71.3

10.7

8.6

107

2026

73.4

11.0

8.8

110

2027

75.6

11.3

9.1

113

2028

77.9

11.7

9.3

117

2029

80.2

12.0

9.6

120

2030

82.6

12.4

9.9

124

2031

85.1

12.8

10.2

128

2032

87.7

13.2

10.5

132

2033

90.3

13.5

10.8

135

In twenty years an investor would have about doubled the initial investment and cashed in $172 of dividends. Presuming a rather generous return of 10% on the net dividends (after taxes of 30%) reinvested each year, the investor would have achieved the following:

Cumulative dividends after taxes + returns on dividends reinvested

Returns on reinvested dividends after taxes at 10%

2013

4.2

0.4

2014

8.9

0.9

2015

14.3

1.4

2016

20.3

2.0

2017

27.1

2.7

2018

34.7

3.5

2019

43.1

4.3

2020

52.6

5.3

2021

63.2

6.3

2022

75.0

7.5

2023

88.1

8.8

2024

102.8

10.3

2025

119.0

11.9

2026

137.1

13.7

2027

157.2

15.7

2028

179.4

17.9

2029

204.1

20.4

2030

231.4

23.1

2031

261.7

26.2

2032

295.3

29.5

2033

332.4

Thus, the total return on the initial investment of $75 (1.5 times book value and 10 times EPS) would be $332 plus the appreciation of the common stock owned, i.e. another $60, for a total gain of $392 or 523%.

This is of course a mid-cap insurance company that keeps its capital base rather small in order to stay lean and focused on high return opportunities.

Now let's see how Berkshire compares to this surely more than decent investment: We simply presume that Warren Buffett and his team will be able to grow book value per share at a rate of 9% per year. As I said above, this rate, having been achieved on average over the past (rather bad) decade, probably understates the growth rate of intrinsic value, hence we can consider it to be a conservative assumption. Furthermore, considering the official buyback limit of 1.2 times book value, we can presume that Warren Buffett himself sees conservatively calculated intrinsic value at least around 1.5 times book value.

So here's the math, conveniently based on $50 of equity, so it's easier to compare to the mid-cap above:

Equity

EPS

Stock price

2013

50.0

4.5

75

2014

54.5

4.9

82

2015

59.4

5.3

89

2016

64.8

5.8

97

2017

70.6

6.4

106

2018

76.9

6.9

115

2019

83.9

7.5

126

2020

91.4

8.2

137

2021

99.6

9.0

149

2022

108.6

9.8

163

2023

118.4

10.7

178

2024

129.0

11.6

194

2025

140.6

12.7

211

2026

153.3

13.8

230

2027

167.1

15.0

251

2028

182.1

16.4

273

2029

198.5

17.9

298

2030

216.4

19.5

325

2031

235.9

21.2

354

2032

257.1

23.1

386

2033

280.2

25.2

420

An investor who pays $75 for $50 of equity or 15 times earnings at the beginning will have achieved a return of $345 or 460% on his initial capital.

This not very different outcome makes clear that the higher earnings multiple paid in the case of Berkshire was totally justified and thus Buffett was right to state that Berkshire, if it paid a dividend, would deserve to trade at a lower multiple. In fact, the hypothetical mid-cap above, in spite of a far smaller size and a far higher return on equity ratio, does not provide much higher returns compared to Berkshire Hathaway. This is clearly because of the taxes associated with the dividends and the lack of compounding on the capital paid out to shareholders.

If you now factor in the much lower risk associated with an investment in Warren Buffett's company compared to a mid sized insurance business, I think it is safe to say that Berkshire Hathaway would be the better choice for most investors that don't really need a quarterly dividend check.

Hence, in my opinion Berkshire should continue to retain 100% of its earnings.

This conclusion is of course based on the assumption that Berkshire will be able to continue compounding its capital base at a rate of 9% per year for many years to come. This rate requires to double the present equity over the next 8 years or to add another $200 billion. It won't be possible without huge (and smart) acquisitions, but who would have thought about Berkshire buying a whole $40 billion railroad a dozen years ago, when the company had about $100 billion of equity? Personally I believe that Berkshire will certainly do a $100 billion acquisition a few years from now, and the day when it will start paying out dividends is still at least 10 years away.

Source: Should Berkshire Hathaway Finally Pay A Dividend?