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Damodarian's Valuation and Dividend Implied Equity Premium

first posted: 2024-03-25 03:47:36.398149

In the book On Valuation by Damodarian. Some normative models are used to define the equity premium and help with comparison accross companies and countries.

  • equity premium through dividend yield and dividend growth points to a long term premium of equity 3% over 10Y bonds, which is reasonnable
  • for cross companies comparison, the CAPM model is proposed, although this is not supported by data
  • for cross country comparison, a country premium is proposed, which is also not supported by data, unless the country premium is just the expected monetary debasement in that country relative to the USD

So one out of three formula appears to be useful. The book has a bias towards what can be taught rather than what has been tested to have predictive value.

Laer sections of the book focuses on analysing company cashflows and cashflow to equity. The argument made is that the value is that 0 is a pessimistic value for a company for Tencent or Amazon, so Damodarian makes the point for optimistically valuing the cashflows that the firm did not give back to the investor at 100% instead of 0% of their value. The truth is probably a value in between, but Damodarian works seems focused on models that are teachable, not necessarily on validating them with statistics.

Our article below focuses on statistical data relevant to the simpler dividend based valuation.

Dividends and Equity Premium

The gordon model is proposed to infer the equity premium from dividend yield:

$$ P = \frac{D}{r-g} = \frac{P r_d}{r-g} $$ Hence the relationship between the equity discount rate $y$ and the dividend yield $r_d$: $$ r = r_d + g$$

This calculation can be made on individual stocks or as an aggregate on an index such as SP500 whose dividend yield was published by SP until their website changed in september 2023.

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Equity Premium and CAPM

The equity premium is defined as the average equity return $\bar{r}$ over bond yields $y_0$. While $\bar{r} = \alpha + \beta (\bar{r} - y_0)$ is tautological for $\alpha=y_0, \beta=1$, the CAPM assumes that a statistical estimation $\alpha$ should give $y_0$, while the market should require a higher return for high $\beta$ stocks: $$ E(r) = y_0 + \beta (\bar{r} - y_0) $$

It is a well documented fact since 1972 that this relation does not hold and high $\beta$ stocks have a negative $\alpha$ (lower implied rate), and yet, valuation textbooks still suggest a formula based on $\beta$ for discounting future cashflows.

We show the graph of $r$ vs $\beta$ for the 500 top worldwide stocks:

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The equity dividend return $r=y_d+g$ has not been adjusted for dividend withholding tax although companies include Microsoft, Aramco, Novo Nordisk, Nestle and Toyota Motor.

Equity Premium and Foreign Country Risk

Damodarian suggests that an additional country risk premium $c_0$ be added to $r$: $$ r = y_0 + c_0 + \beta (\bar{r} - y_0)$$

or that it be integrated to $\beta$ if this is a country equity market premium: $$ r = y_0 + \beta (\bar{r} - y_0 + c_0)$$

or that a separate country risk multiplier be added, which depends on how much the company is linked to the country: $$ r = y_0 + \beta (\bar{r} - y_0) + \lambda c_0$$

We know that FX currency for most currencies in the world except the G10 include a strong devaluation trend. We use dividend growth measured in USD In the table below, there is then little in the way of consistently positive country premium.

For correctness, the return has been adjusted for the withholding tax $w$ of a Hong Kong investor $r = y_d (1-w) + g$. This tax depends on the investor location.

country divyield divgrowth count mktcap wht r
0 United States 0.013882 0.062972 4842 4.552017e+13 0.3 0.072689
1 China 0.026602 0.083033 2533 9.527179e+12 0.1 0.106975
2 Japan 0.020218 0.008545 3872 6.225274e+12 0.15 0.02573
3 United Kingdom 0.032981 0.001114 826 5.181922e+12 0.0 0.034095
4 India 0.008942 0.022857 1523 4.456707e+12 0.05 0.031352
5 France 0.024787 0.044636 568 3.457746e+12 0.25 0.063226
6 Saudi Arabia 0.031152 0.048900 229 2.968482e+12 0.05 0.078495
7 Canada 0.022856 0.063289 1996 2.758667e+12 0.15 0.082717
8 Switzerland 0.026171 0.033391 229 2.724169e+12 0.35 0.050403
9 Germany 0.022942 0.033720 481 2.449960e+12 0.1 0.054368
10 Taiwan 0.031188 0.127480 969 2.369955e+12 0.21 0.152118
11 Australia 0.037399 0.042232 1796 1.898344e+12 0.3 0.068412
12 South Korea 0.015098 0.108507 807 1.887738e+12 0.15 0.121341
13 Hong Kong 0.019335 0.057582 1405 1.667610e+12 0.0 0.076917
14 Brazil 0.053900 0.011873 406 1.644365e+12 0.0 0.065774
15 Netherlands 0.014413 0.168435 95 1.574975e+12 0.0 0.182848
16 Ireland 0.013935 0.064182 58 1.154320e+12 0.0 0.078118
17 Sweden 0.019094 0.035461 647 1.045870e+12 0.3 0.048826
18 Denmark 0.014932 0.087391 159 9.717430e+11 0.275 0.098217
19 Spain 0.031525 0.009748 139 8.120395e+11 0.19 0.035284
20 Italy 0.028483 0.053912 375 8.119027e+11 0.1 0.079546
21 Indonesia 0.026866 -0.139784 874 7.087751e+11 0.1 -0.115604
22 Mexico 0.035903 0.109782 125 6.665680e+11 0.0 0.145686
23 Belgium 0.025691 -0.030855 86 5.510959e+11 0.15 -0.009017
24 Singapore 0.037972 0.043640 393 5.165128e+11 0.0 0.081611
25 Thailand 0.038464 0.023244 884 4.822688e+11 0.1 0.057862
26 Turkey 0.012009 0.012782 533 4.325922e+11 0.1 0.02359
27 Norway 0.021681 -0.111988 199 4.004372e+11 0.25 -0.095727
28 Malaysia 0.029048 0.007387 758 3.889432e+11 0.0 0.036435
29 Russia 0.053867 0.089574 86 3.867150e+11 0.15 0.135361
30 Israel 0.014221 0.057931 462 3.604961e+11 0.22 0.069024
31 South Africa 0.029489 0.014682 224 3.330064e+11 0.2 0.038273
32 Finland 0.026097 0.046477 98 2.911277e+11 0.1 0.069965
33 Luxembourg 0.012189 0.085743 55 2.533710e+11 0.1 0.096712
34 Vietnam 0.017380 0.024177 337 2.087371e+11 0.1 0.039819
35 Bermuda 0.023175 0.050781 57 2.073252e+11 0.0 0.073956
36 Poland 0.026415 0.144183 307 1.845841e+11 0.19 0.165579
37 Chile 0.023100 0.051612 163 1.805444e+11 0.35 0.066627
38 Austria 0.028145 0.083437 73 1.723833e+11 0.1 0.108767
39 Qatar 0.036076 0.021138 51 1.627576e+11 0.0 0.057214
40 Kuwait 0.030238 0.070329 144 1.382336e+11 0.05 0.099055
41 Colombia 0.050836 0.054003 23 9.796259e+10 0.35 0.087047
42 Uruguay 0.000678 NaN 4 9.665977e+10 0.07 NaN
43 Greece 0.024061 0.006618 150 9.222828e+10 0.05 0.029476
44 Argentina 0.005102 1.293891 77 8.726615e+10 0.35 1.297207
45 New Zealand 0.022350 0.015250 55 8.014322e+10 0.15 0.034248
46 Cayman Islands 0.008813 0.086408 63 7.437165e+10 0.0 0.095221
47 Kazakhstan 5.770967 0.500639 23 6.604369e+10 0.15 5.405961
48 Egypt 0.034592 0.095803 107 5.351686e+10 0.1 0.126936
49 Macau 0.012093 0.070620 16 3.723540e+10 0.0 0.082713
50 Peru 0.018947 0.127478 5 2.124148e+10 0.05 0.145478
51 Czech Republic 0.080742 0.114490 2 1.888434e+10 0.05 0.191195
52 Hungary 0.026897 0.076654 7 1.881912e+10 0.0 0.103551
53 United Arab Emirates 0.006051 NaN 10 1.672457e+10 0.0 NaN
54 Pakistan 0.054592 0.043361 44 1.672302e+10 0.1 0.092494
55 CuraƧao 0.032810 -0.029051 2 1.135348e+10 0.0 0.003759
56 Philippines 0.000000 NaN 2 1.080448e+10 0.25 NaN
57 Jersey 0.029850 0.374507 19 1.070466e+10 0.0 0.404357
58 Guernsey 0.021304 0.000277 17 1.032459e+10 0.0 0.021581
59 Monaco 0.027281 -0.024298 7 9.972276e+09 0.0 0.002983
60 Cyprus 0.034446 NaN 15 9.071393e+09 0.0 NaN
61 Morocco 0.000000 NaN 1 8.722357e+09 0.15 NaN
62 Lithuania 0.032841 -0.004305 27 6.735860e+09 0.15 0.023609
63 Iceland 0.000876 NaN 3 6.432646e+09 0.22 NaN
64 Malta 0.002760 0.202286 10 5.704080e+09 0.0 0.205046
65 Panama 0.030591 -0.039770 2 5.030780e+09 0.2 -0.015298
66 Korea 0.059375 0.048367 2 4.226763e+09 0.15 0.098836
67 Liechtenstein 0.033438 NaN 2 3.125880e+09 0.0 NaN
68 Mauritius 0.027886 0.306922 11 2.655469e+09 0.0 0.334808
69 Georgia 0.093977 NaN 2 2.517544e+09 0.05 NaN
70 Portugal 0.059703 -0.014311 2 2.160375e+09 0.1 0.039422
71 Isle of Man 0.029794 -0.100601 3 1.912501e+09 0.0 -0.070808
72 Cambodia 0.004732 NaN 1 1.741099e+09 0.14 NaN
73 Bahamas 0.004161 NaN 3 1.587848e+09 0.0 NaN
74 Mongolia 0.000000 NaN 3 1.432329e+09 0.2 NaN
75 Nigeria 0.082395 NaN 2 1.174157e+09 0.1 NaN
76 Bahrain 0.115303 NaN 3 1.121561e+09 0.0 NaN
77 Costa Rica 0.000000 NaN 1 1.071350e+09 0.15 NaN
78 Ukraine 0.005447 NaN 3 8.553552e+08 0.15 NaN
79 Gibraltar 0.017322 NaN 2 7.961045e+08 0.0 NaN
80 Gabon 0.118473 0.058544 1 7.681614e+08 0.2 0.153323
81 Barbados 0.027512 0.362677 1 6.496557e+08 0.05 0.388814
82 Papua New Guinea 0.066818 0.054186 3 5.708338e+08 0.15 0.110981
83 Jordan 0.013339 NaN 1 5.506400e+08 0.1 NaN
84 British Virgin Islands 0.014644 NaN 9 4.173784e+08 0.0 NaN
85 Zambia 0.590843 NaN 1 2.515148e+08 0.2 NaN
86 Macedonia 0.038683 NaN 2 2.413775e+08 0.1 NaN
87 Greenland 0.040325 NaN 1 1.756165e+08 0.44 NaN
88 Botswana 0.000000 NaN 1 6.230961e+07 0.1 NaN
89 Estonia 0.000000 NaN 4 2.918222e+07 0.0 NaN
90 Namibia 0.000000 NaN 1 2.340950e+07 0.2 NaN
91 Dominican Republic 0.000000 NaN 1 2.113918e+07 0.1 NaN
92 Kenya 0.000000 NaN 1 1.240714e+07 0.05 NaN
93 Liberia 0.000000 NaN 1 4.660614e+06 0.15 NaN
94 Bulgaria 0.000000 NaN 1 3.344554e+06 0.05 NaN
95 Zimbabwe 0.013590 NaN 1 3.326523e+06 0.15 NaN
96 French Guiana 0.000000 NaN 1 7.554022e+05 0.25 NaN
97 Martinique 0.042074 NaN 1 6.478878e+05 0.25 NaN