This blog covers the general topic of financial markets.

# Elements of Fundamental Valuation

first posted: 2024-01-17 06:17:53.862775

## Fundamental Formula

We use the fundamental valuation $P_f$ based on the discounted future value at $T$ and the value of dividends received between now and $T$:

\begin{eqnarray} P_f &=& f m R_0 \frac{e^{-r T}}{y} + f_d m R_0 \frac{1- e^{-r T}}{r} \\ r &=& y-g+d+d\ln(cpi) \end{eqnarray}

• $g$ is the revenue growth, $d$ the share dilution, $y=5\%$ the discount yield, $T=7.5$ the dividend, growth and dilution horizon
• $r$ is the growth adjusted yield,
• $m$ income margin,
• $f_d$ div payout ratio net of applicable country withholding tax
• $f = f_d - d P_0$ is the dividend and buyback yield, $P_0$ the market price,
• $R_0$ the revenue,
• $f,f_d$ are highly dependent on governance, "paid ratio" uses current payout ratios "income ratio" assumes $f=f_d=30\%$

A 5% return after tax above cpi may sound very ambitious, but this is what triumph of the optimist is claiming as total return before tax for the 20th century, and 19th century landlords were able to get that.

## Distribution of Values:

Last 3 Years (source: Yahoo Finance), we show quantiles and market cap weighted quantiles from 12.5% to 87.5%:

c p12 p25 p37 p50 p62 p75 p87 wp12 wp25 wp37 wp50 wp62 wp75 wp87
0 ratio 0 0 0 0 0 1.10% 28.60% 0 0 1.20% 9.82% 30.06% 78.71% 2.05
1 incratio 0 0 0 14.90% 34.27% 62.72% 1.29 2.86% 8.27% 22.17% 36.31% 50.42% 75.05% 82.13%
2 dlncpi 4.94% 5.51% 5.51% 5.51% 5.55% 5.61% 5.61% 5.51% 5.51% 5.51% 5.56% 5.56% 5.56% 5.61%
3 growth -6.05% 0.17% 3.36% 6.19% 9.42% 14.01% 24.03% 1.62% 4.33% 6.20% 8.44% 10.57% 13.89% 18.72%
4 assetgrowth -4.44% 0.52% 3.71% 6.73% 10.37% 16.22% 30.25% 0.27% 3.33% 5.78% 8.67% 10.43% 14.27% 24.00%
5 dlnfx 0 0.11% 0.82% 1.31% 2.52% 3.66% 8.05% 0 0 0 0 0.73% 1.07% 3.07%
6 dilution -0.65% -0.01% 0 0.07% 0.89% 3.44% 9.37% -2.20% -1.04% -0.48% -0.00% 0.13% 0.97% 3.44%
7 r -28.25% -13.78% -7.47% -2.92% 1.14% 6.65% 18.54% -10.57% -5.24% -1.98% -0.69% 2.85% 8.62% 12.15%
8 rstd 6.03% 9.37% 12.55% 17.69% 24.42% 35.59% 61.08% 5.06% 6.62% 7.46% 10.44% 11.62% 16.19% 22.56%
9 wht 0 10.00% 10.00% 15.00% 15.00% 25.00% 30.00% 10.00% 10.00% 15.00% 30.00% 30.00% 30.00% 30.00%
10 margin 0 0 1.64% 3.92% 6.55% 10.73% 20.37% 2.11% 5.13% 8.20% 12.13% 17.48% 23.59% 32.72%
11 smargin -36.81% -10.16% -2.79% 0.69% 2.94% 5.93% 12.07% -3.97% 1.66% 4.31% 7.59% 12.13% 18.27% 26.21%
12 f 0 0 0 0 0 1.17% 26.68% 0 0 0 7.01% 31.49% 51.41% 77.31%
13 fd 0 0 0 0 0 0 0 0 0 0 0 8.21% 26.83% 44.15%

In the above, growth and asset growth are given in local currency, and and be adjusted by dlnfx and dlncpi to get real USD.

### Long Term Accounting Data

Last 40 years (source ROIC)

c p12 p25 p37 p50 p62 p75 p87 wp12 wp25 wp37 wp50 wp62 wp75 wp87
0 paidratio 0 0.63% 5.37% 11.49% 19.72% 35.02% 92.69% 1.24% 6.30% 12.24% 18.37% 26.93% 41.34% 80.04%
1 incratio 0 35.24% 99.22% 1.55 2.29 3.75 10.2 47.71% 90.09% 1.23 1.69 2.29 3.56 7.76
2 dlnmktcap -46.83% -22.24% -7.96% 3.57% 15.33% 30.03% 54.89% -23.26% -8.16% 2.04% 10.61% 19.42% 29.54% 45.38%
3 dlncpi 0.75% 1.49% 1.89% 2.09% 2.51% 3.02% 6.25% 1.35% 1.49% 1.89% 2.09% 2.51% 3.33% 6.25%
4 growth -17.66% -6.22% 0.15% 5.23% 10.54% 17.69% 31.50% -8.52% -1.07% 3.35% 7.12% 11.47% 17.40% 27.63%
5 agrowth -13.39% -4.71% 0.39% 4.62% 9.19% 15.40% 27.74% -4.67% 0.17% 3.49% 6.62% 10.23% 15.09% 24.33%
6 dilution -1.53% -0.07% 0 0.05% 0.84% 4.23% 15.30% -2.89% -1.21% -0.26% 0 0.21% 1.12% 4.87%
7 r -31.30% -16.72% -9.41% -3.91% 1.27% 7.74% 20.10% -17.60% -9.32% -4.23% -0.49% 3.39% 8.11% 17.52%
8 wht 0 10.00% 15.00% 15.00% 21.00% 30.00% 30.00% 0 10.00% 15.00% 25.00% 30.00% 30.00% 30.00%
9 margin -14.07% 0.45% 2.46% 4.51% 7.16% 11.52% 21.49% 2.11% 5.14% 7.93% 11.08% 15.61% 21.22% 30.03%
10 opmargin -10.30% 1.42% 4.96% 8.15% 12.00% 18.07% 31.29% 4.63% 9.52% 13.24% 18.12% 24.05% 31.03% 42.89%
11 finmargin -43.40% -7.86% -1.13% 1.15% 3.14% 6.30% 13.81% -16.58% -2.53% 1.39% 4.11% 7.56% 12.08% 21.09%
12 shmargin -24.29% -2.39% 0 0.51% 1.42% 3.29% 8.42% -8.23% 0 1.51% 3.24% 5.69% 9.38% 15.52%
13 divmargin 0 0 0 0 0.44% 1.32% 3.82% 0 0 0 0 0.70% 2.44% 6.16%

In the above, growth and asset growth are measured in USD.

## Fundamental Ratio per Year: The Triumph of the Optimists

If one makes the optimistic assumption that all net income will eventually be paid to the stockholders, we get fundamental valuations that are above 1. If we more skeptically only look at actual dividends and buybacks, the ratio is most often below one, even during the great financial crisis.

If optimists are being vindicated, it is not because the owners of stock are being rewarded with actual cash payments of dividends and buybacks, or is it because the market has a very optimistic valuation compared to the fundamentals?

## Return Table: with Compounding Effect

Below is the annual compounded return (geometric average) of the mean return (arithmetic average) by quantile.

quantile q1 q2 q3 q4 q5 q6 q7 q8 q9 q10
0 paidratio 18.66% 15.75% 16.56% 11.67% 13.84% 33.29% 14.55% 15.23% 17.97% 21.50%
1 dlnadjprice 22.40% 15.09% 16.10% 15.37% 15.52% 33.88% 15.44% 16.11% 17.86% 18.07%
2 incratio 17.24% 16.30% 12.84% 12.86% 33.71% 14.17% 14.52% 16.28% 19.17% 20.37%
3 r 20.08% 16.32% 16.12% 14.95% 34.47% 14.51% 15.06% 16.49% 17.37% 18.11%
4 dilution 20.99% 15.75% 16.01% 33.83% 20.52% 16.81% 16.19% 17.18% 14.92% 15.06%
5 growth 21.21% 16.36% 15.94% 17.06% 31.64% 16.31% 15.59% 16.44% 17.08% 16.39%
6 divmargin 20.55% 34.80% 20.05% 17.56% 18.05% 18.81% 18.12% 16.35% 15.28% 13.48%
7 shmargin 11.31% 14.32% 18.22% 23.18% 20.60% 16.64% 33.84% 15.47% 13.93% 17.22%
8 opmargin 16.93% 18.55% 16.59% 16.48% 17.54% 18.13% 38.32% 16.55% 16.82% 18.31%
9 margin 21.02% 19.16% 19.03% 15.05% 18.12% 32.14% 18.00% 16.43% 16.29% 18.08%
10 agrowth 28.46% 17.18% 13.48% 16.22% 33.51% 17.32% 15.53% 15.75% 15.09% 14.94%
11 dlnadjprice5 33.86% 18.57% 12.24% 35.32% 13.70% 13.15% 13.31% 12.89% 14.04% 10.54%
12 growth5 21.36% 15.96% 16.35% 34.04% 16.30% 16.40% 15.82% 12.79% 14.59% 19.13%
13 shmargin5 13.58% 16.09% 17.25% 18.08% 15.89% 16.25% 37.27% 16.34% 15.90% 14.51%
14 opmargin5 19.19% 20.23% 18.71% 16.73% 15.71% 15.58% 39.15% 14.51% 14.61% 14.86%
15 margin5 22.08% 22.05% 18.48% 17.00% 15.71% 15.44% 33.76% 15.20% 13.10% 12.93%
16 agrowth5 25.89% 20.11% 16.54% 35.64% 16.82% 12.19% 15.38% 16.60% 14.63% 13.19%

In the above, growth and asset growth are computed in USD, and need be adjusted by dlncpi only to get real dollar growth.

## Previous Total Return Next 5 Year Total Return

These values are unadjusted for survivorship bias we observe that it is best not to invest in top performing decile of previous year, and that mild underperformance in last 5 year is rewarded in the next 5Y.

## Fundamental Price and Next 5 Year Total Return

Using actual paid value of $f$ and $f_d$, or full net income and assuming $f=1$. We don't see much predictive value for the fundamental value formula, but we see bad performance of the lowest deciles of value stocks.

## Effect of Margin

We show performance by operating margin, net margin, shareholder yield (div+buyback) margin and div margin, we see that operating and net margin lowest 2 quantiles are associated with underperformance, shareholder yield margin takes into account share dilution and the lowest 3 deciles need to be avoided.

## Effect of Dilution

This is the clearest effect of all: we see that increasing dilution has negative effect on stocks total return accross all deciles.

## Revenue Growth Asset Growth

We see that growth and asset growth outliers (top and bottom decile) need to be avoided.

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