1. Analyzing Determinants of Multiples
2. The Average of Median May Not Always Be Applicable
The key driver of a good Relative Valuation is how comparable the firms are with the subject firm. The varying degrees of comparability would determine what is the appropriate percentile to apply to the subject firm.
If the companies are very comparable, the average or median may be appropriate. But, if the discrepancies are wider, then the subject firm may require a higher or lower multiple than the average or median.
How do we determine where the subject firm falls? We can compare the risk, growth, and profitability of the comparable companies with the subject firm.
We can also look at where the subject firm's multiple falls relative to peers say over the last 5 or 10 years.
All else equal, we would expect that riskier firms will have a lower multiple, lower growth firms will have a lower multiple, less profitable firms will have a lower multiple.
In other words, we would expect investors to pay less for these firms.
However, the ultimate determination of what the appropriate multiple is may be subjective. Alternatively, we can use the regression analysis that we will discuss next.
3. Regression-Based Approach
An alternative way to arrive at the appropriate valuation multiple based on fundamentals is to use regression analysis. Different valuation multiples have different determinants. For example, P/B ratios are often regressed on Return on Equity and P/E Ratios on 5-Year EPS growth. You can also do the regression using multiple independent variables. For example, P/E Ratio on 5-Year EPS Growth, Beta, and Payout Ratio.
Since we let the results of the regression determine the appropriate multiple for the subject firm, this approach is a little less subjective than the approach in the prior slide.
4. Example Using P/B vs. ROE
Suppose we are trying to value a midcap financial firm. We then determined that the set of comparable companies are members of the S&P 400 Midcap index that are in the Financials Sector. To extract the Financial Firms, we use the subset() command as we show in the first two lines of the R code.
Next, we calculate the ROE and P/B ratio. Note that to make sure any non-meaningful numbers, such as negative BVPS do not make it to our final dataset, we use the ifelse() command to set negative BVPS observations into NA. That way, we can remove such observations easily using the complete dot cases() argument.
5. Example Using P/B vs. ROE
The plot of the P/B to ROE is shown here. The red line is the regression line based on all the observations in the data. This confirms that the higher the ROE or profitability, the higher the P/B Ratio. Also, what is remarkable is the strength of the relationship as proxied by a high R-squared of 0.8462. The R-squared is a measure of how well our model fits the data. The closer to 1 the R-squared, the better the model's fit.
6. Example Using P/B vs. ROE
The equation of the line can be extracted from the regression. The intercept term is stored in the variable "a" and the slope coefficient is stored in the variable "b".
7. Implied Price
Now, assuming an ROE of 10% for our subject firm, the implied price-to-book ratio is around 2.
Then, assuming a BVPS of $30 for our subject firm, we find an implied price of $62. This yields a lower value than the $81 using the average P/B ratio. This suggests that the subject firm may be operating below the average of the peers.
8. Let's practice!
Let's practice.