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Topic 8 Business Valuation II Solutions to Tutorial Questions

1. Please refer to the supplied spreadsheet “bvt8data.xls” containing recent financial and comparable data for Google as of late 2010. (a) Perform a qualitative evaluation of whether Google is overvalued, fairly valued or undervalued relative to its peers. (Hint: Compare Google’s multiples to the median for its peers as well as Google’s measures of profitability to the median profitability of the peers.) Solution: In this case it is straightforward to note that Google is trading at a medium PE value (relative to the four peer companies) and has the highest expected growth rate of future earnings per share. This points towards an undervaluation. The PB and PS values for Google are the highest (relative to the four peers) but also we note that Google has the highest ROE and NPM so perhaps these high PB and PS value are justified based on Google’s economic fundamentals. (b) Perform a quantitative evaluation of whether Google is overvalued, fairly valued or undervalued relative to its peers using an adjusted PE ratio which controls for variation in future expected earnings growth. In order to do this I suggest you regress the twelve months trailing PE ratio on a constant/intercept and the future expected five-year earnings growth rate. Solution: Regressing the peers’ PE ratios on the expected growth rates we find that P E = 4.79 + 1.42 × g. The slope (1.42) is statistically significant (t Stat greater than 2) and has the expected sign (higher g should lead to greater current PE). We ignore the lack of statistical significant of the intercept and include it in the equation for the sake of completeness. Inputting Google’s g into the equation we find that the regression-adjusted PE ratio for Google is 4.79+1.42 × 29.72 = 46.85. Multiplying the latter by Google’s current EPS (provided as $20.41) we find that Google’s intrinsic value per share is equal to 46.85 × $20.41 = $956.27. Comparing this to the stock price ($564.19) we conclude that on the basis of this regression-adjusted PE ratio, the market is greatly undervaluing shares in Google. (c) Perform a quantitative evaluation of whether Google is overvalued, fairly valued or undervalued relative to its peers using an adjusted P/B ratio which controls for variation in their historical return on equity (ROE). To do this you should regress the P/B ratio on a constant and the trailing twelve months ROE. Solution: Eye-balling the data we note that SOHU has the highest value of ROE among the four comparable firms. Hence, this gives us a reason to exclude it from the regression because it appears to be an outlier. Regressing the PB ratios of the remaining three comparable companies on their respective ROE values we find that P B = 0.27+0.30 × ROE. Both coefficients are statistically significant. Also, the sign of the slope (0.30) conforms with economic intuition, i.e., greater profitability should lead to larger PB values. Inputting Google’s ROE into this equation we find that Google’s regressionadjusted PB ratio is equal to 0.27 + 0.30 × 20.30 = 6.30. Multiplying the latter by the book value of equity per share (provided as $113.29) we find Google’s intrinsic value of equity per share as 6.30 × $113.29 = $714.02 per share. Comparing this to the 1

market price ($564.19 per share) we determine that the market is paying too little for Google shares at least on the basis of the regression-adjusted PB ratio. (d) Perform a quantitative evaluation of whether Google is overvalued, fairly valued or undervalued relative to its peers using an adjusted P/S ratio which controls for variation in their net profit margins (NPM). This time you need to regress the P/S ratio on a constant and the net profit margin. Solution: Taking a look at the data, we note that AKAM has the highest PS ratio among the four comparable firms and, hence, we choose to treat it as an outlier. Regressing the PS ratios of the three remaining comparable firms on their respective net profit margins we find that P S = 3.21+0.03 ×NPM. Both coefficients are highly statistically significant and the sign of the slope conforms with out economic intuition, i.e., greater profitability after-tax should lead to larger PS values. Inputting the NPM for Google into the equation we find Google’s regression-adjusted PS ratio as 3.21+0.03 × 29.58 = 4.05. Given the revenue per share provided for Google ($74.33) we can find the intrinsic value per share for Google as 4.05 × $74.33 = $301.24. Comparing this intrinsic value per share to the market price ($564.19) we determine that on the basis of the regression-adjusted PS ratio, the market appears to be paying too much for Google shares and they might be overvalued. (e) What do you conclude based on all of your work above? Solution: Comparing our findings from our work above we conclude that there is a preponderance (i.e., ma jority) of evidence in favor of the market paying too little for Google shares. Luckily, the subsequent upward movement in the market price of shares in Google does indeed confirm ex post that Google shares were undervalued at the time. 2. Please refer to the supplied spreadsheet “bvt8data.xls” containing recent financial and comparable data for Apple as of late 2014. (a) Perform a qualitative evaluation of whether Apple is overvalued, fairly valued or undervalued relative to its peers. (Hint: Compare Apple’s multiples to the median for its peers as well as Apple’s measures of profitability to the median profitability of the peers.) Solution: One thing we can do here is to compare Apple’s current PE (13.52) to the median PE of the comparable firms (26.84). At the same time, we notice that Apple’s expected growth rate is almost 32% while the median growth rate for the comparable firm is less than 14%. Hence, on this basis (current PE) we can conclude that the market price is likely too low. (b) Perform a quantitative evaluation of whether Apple is overvalued, fairly valued or undervalued relative to its peers using an adjusted PE ratio which controls for variation in future expected earnings growth. In order to do this I suggest you regress the twelve months trailing PE ratio on a constant/intercept and the future expected five-year earnings growth rate. Solution: Here is our chance to show off our statistical skills. After some extensive data mining, I decided to use only HPQ, NTAP and DBD as comparable firms for Apple. The regression equation I obtained is P E = 10.5 + 1.39 × g with both coefficients highly statistically significant and the slope having the expected sign. Inputting the value of g for Apple we obtain Apple’s regression-adjusted PE ratio as 10.5+1.39× 16.4 = 33.4. The final step involves multiplying the latter by Apple’s EPS (provided as $7.02) to 2

obtain an intrinsic value of 33.4 × $7.02 = $234.40 which is lower than the market price ($94.93 per share). Hence, we conclude that on the basis of regression-adjusted PE ratio, Apple appears to be seriously undervalued. (c) Perform a quantitative evaluation of whether Apple is overvalued, fairly valued or undervalued relative to its peers using an adjusted P/B ratio which controls for variation in their historical return on equity (ROE). To do this you should regress the P/B ratio on a constant and the trailing twelve months ROE. Solution: In this case, following some data mining, I decided to use EMC, WDC, SNDK, NTAP, NCR, EFII and SMCI as comparable firms. The regression equation I obtained is P B = 1.24 + 8.56 × ROE. Both coefficients are statistically significant and the sign of the slope is as expected. Plugging Apple’s ROE into the equation we obtain the regression-adjusted PB ratio for Apple as 1.24 + 8.56 × 31.6 = 3.94. The final step involves multiplying the last value by Apple’s book value of equity per share (provided as $23.42) to obtain 3.94 × $23.42 = $92.34 which is very close to the market price ($94.93) though a tiny bit lower which can be interpreted as a minor overvaluation. (d) Perform a quantitative evaluation of whether Apple is overvalued, fairly valued or undervalued relative to its peers using an adjusted P/S ratio which controls for variation in their net profit margins (NPM). This time you need to regress the P/S ratio on a constant and the net profit margin. Solution: Finally, for this regression I chose to include HPQ, EMC, WDC, SNDK, NTAP, NCR, EFII, SMCI and QLGC as comparable firms. By regressing the PS ratios for the chosen firms against their net profit margins I found that P S = 0.132 +19.537 × NPM with a statistically significant slope having the “right” sign. Inputting Apple’s NPM into the equation we obtain a regression-adjusted PS ratio for Apple as follows P S = 0.132 + 19.537 × 21.67 = 4.366. Since Apple’s sales per share is provided as $32.40, the intrinsic value per share must be given by 4.366 × $32.40 = $141.46 which is quite a bit higher than the market price ($94.93) indicating that the market is paying too little for Apple shares and, hence, they appear undervalued on the basis of the regression-adjusted PS ratio. (e) What do you conclude based on all of your work above? Solution: Overall, there appears to be more evidence in favour of undervaluation (at least from the regression-adjusted current PE and PS ratios). The relatively minor undervaluation on the basis of the regression-adjusted PB ratio does to appear to be that big of a deal. Hence, we can safely conclude that on a relative valuation basis, shares in Apple appear to be undervalued. Luckily, the price subsequently increased justifying the analysis that we performed. Alternatively, we could have been right for the wrong reasons.

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