80 common and uncommon errors in company valuation 80 common and uncommon errors in company valuation Pablo Fernandez PricewaterhouseCoopers Professor of Corporate Finance IESE Business School. University of Navarra. Camino del Cerro del Aguila 3. 28023 Madrid, Spain. Telephone 34-91-357 08 09. Fax 34-91-357 29 13. e-mail: [email protected] edu ABSTRACT This paper contains a collection and classification of 80 errors seen in company valuations performed by financial analysts, investment banks and financial consultants.

The author had access to most of the valuations referred to in this paper in his capacity as a consultant in company acquisitions, sales and mergers , and arbitrage processes. Some of the errors are taken from published reports by financial analysts. We classify the errors in six main categories: 1) Errors in the discount rate calculation and concerning the riskiness of the company; 2) Errors when calculating or forecasting the expected cash flows; 3) Errors in the calculation of the residual value; 4) Inconsistencies and conceptual errors; 5) Errors when interpreting the valuation; and 6) Organizational errors.

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Keywords: valuation, company valuation, valuation errors JEL Classification: G12 , G31, M21 November 4, 2003 1 80 common and uncommon errors in company valuation This paper contains a classification of the 80 errors providing at least one example of each, taken from actual valuations. The sections of the paper are as follows: 1. Errors in the discount rate calculation and concerning the riskiness of the company 2. Errors when calculating or forecasting the expected cash flows 3. Errors in the calculation of the residual value 4. Inconsistencies and conceptual errors 5. Errors when interpreting the valuation 6.

Organizational errors Appendix 1. List of the 80 errors Appendix 2. A valuation containing multiple errors using an ad hoc method Bibliography 2 80 common and uncommon errors in company valuation 1. Errors in the discount rate calculation and concerning the riskiness of the company 1. A. Wrong risk-free rate used for the valuation 1. A. 1. Using the historical average of the risk-free rate as the actual risk-free rate. Example taken from a financial consultant: “The best estimate of the risk-free rate to use in the CAPM is the historical average of the US risk-free rate from 1928 until today. This is patently absurd. Any student who used an average historical rate from 1928 to 2001 in a university examination (not to mention in an MBA) would be failed on the spot. The risk-free rate is by definition the rate that can be obtained now (at the time when Ke is calculated) by buying risk-free government bonds now. Expectations and forecasts have little to do with the past, or with an average historical rate. 1. A. 2. Using the short-term government bond rate as the meaningful risk-free rate in a valuation.

Example taken from a financial consultant: “The best estimate of the risk-free rate to use in the CAPM is the return of 90-day US Treasury Bills. ” The correct way to calculate a company’s cost of capital is to use the rate (Yield or IRR) of long-term government bonds (using bonds of similar duration to that of the expected cash flows) at the time of calculating Ke. 1. B . Wrong beta used for the valuation 1. B. 1. Use the historical industry beta, or the average of the betas of similar companies, when the result goes against common sense. The example of this error comes from a report written by a financial consulting firm. The purpose of our study has been to make a professional estimate of the fair value at 31 December 2001 of the shares of INMOSEV, an unlisted real estate firm whose main business consists of buying land and building houses for resale. We have assumed a capital contribution by a third party in the amount of 30 million euros in the year 2002, with an estimated return on its investment of 20%; that is, 6 million euros. “Our study is based essentially on information provided to us by INMOSEV, consisting of historical data and assumptions and hypotheses about estimated future income over the next 11 years.

Table 1. Main magnitudes of the INMOSEV valuation Ku Ke Present value of ECF ? u ? L 0 -30,000 0 0 0 0 0 5,631 6,401 7,184 7,963 20,501 0. 27 0. 27 0. 27 0. 27 0. 27 0. 27 0. 27 0. 27 0. 27 0. 27 0. 27 0. 27 6. 22% 6. 22% 6. 22% 6. 22% 6. 22% 6. 22% 6. 22% 6. 22% 6. 22% 6. 22% 6. 22% 6. 22% 0. 45 0. 42 0. 5 0. 52 0. 53 0. 57 0. 59 0. 56 0. 54 0. 52 0. 49 7. 04% 6. 91% 7. 26% 7. 35% 7. 37% 7. 55% 7. 67% 7. 54% 7. 43% 7. 32% 7. 23% Sum 0 -28,026 0 0 0 0 0 3,437 3,633 3,796 3,920 9,412 152,913 149,085 Equity cash flow (ECF) 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012

Present value of cash flows from 2013 onward From this total we must deduct the margin that the new shareholder who contributes the 30 million euros will earn on the deal (we estimate a figure of around 6 million). —————————————————————————————————Table 1 shows the equity cash flows that have been used in this study. Th main assumptions e and estimates made in applying the valuation method mentioned above are as follows: Growth rate of the equity cash flows after 2012 = 1%. 3 80 common and uncommon errors in company valuation Discount rate.

The cost of equity corresponds to the return on long-term risk-free assets, plus the market risk premium, multiplied by a coefficient called beta Return on Spanish 15 -year government bonds (risk-free return) = 5. 00% Market risk premium = 4. 50% (Source: BNP Paribas, SCH) Unlevered beta (? u) = 0. 27. Average of the unlevered betas of listed companies in Spain (see Table 2) Levered beta (? L) according to INMOSEV’s (average) capital structure = 0. 50 The average cost of equity is 7. 25%. Consequently, the value of INMOSEV’s shares at 31 December 2001 is on the order of approximately 143. 09 million euros. ” Table 2.

Betas of listed real estate firms in Spain Vallehermoso Levered beta Unlevered beta Source: SCH. 0. 49 0. 29 Colonial 0. 12 0. 11 Metrovacesa 0. 38 0. 27 Bami 0. 67 0. 39 Urbis 0. 42 0. 28 average 0. 42 0. 27 Error. The resulting unlevered beta (0. 27) is so small that it makes no sense to use it to value any company, let alone an unlisted one. Also, these betas (and any others that might have been used) are arbitrary, as Table 3 shows. If we calculate the betas of the five companies on 31 December 2001 using daily and monthly data and different periods, we can obtain average unlevered betas ranging anywhere from 0 to 0. 5. Obviously, a valuation that depends on such a shifting and unreliable . 22 variable is contrary to all common sense and prudence. Table 3. Betas calculated at December 31, 2001, with respect to the Madrid Stock Exchange General Index, using daily and monthly data for different periods prior to 31/12/2001 Period Data Daily 5 years Monthly Daily 4 years Monthly Daily 3 years monthly Daily 2 years Monthly Daily 1 year Monthly Daily 6 months Monthly Maximum Minimum Vallehermoso 0. 70 0. 71 0. 67 0. 58 0. 60 0. 41 0. 42 0. 68 0. 37 0. 59 0. 1 0. 81 0. 81 0. 31 Beta at 31/12/2001 Colonial Metrovacesa 0. 46 0. 45 0. 41 0. 43 0. 31 0. 17 0. 15 0. 19 0. 28 0. 50 0. 18 0. 18 0. 41 0. 46 0. 23 0. 22 0. 72 0. 68 0. 72 0. 68 0. 15 0. 17 Bami 0. 67 1. 25 0. 63 0. 95 0. 51 0. 59 0. 27 0. 85 0. 19 0. 32 0. 09 0. 39 1. 25 0. 09 Urbis 0. 58 1. 00 0. 59 0. 80 0. 48 0. 42 0. 25 0. 67 0. 27 0. 78 0. 25 0. 80 1. 00 0. 25 Average 0. 60 0. 85 0. 58 0. 69 0. 48 0. 40 0. 26 0. 60 0. 24 0. 51 0. 22 0. 68 0. 85 0. 22 In the end, the shares were sold for 70. 4 million euros (instead of 143 million).

This is the figure obtained by discounting the flows shown in Table 1 at 9. 8% (rather than at 7. 26%). 1. B. 2 . Us ing the historical beta of the company when the result goes against common sense. Historical betas change dramatically, as is shown in Campa and Fernandez (2004). These authors calculate the betas of 3,813 companies on each day of December 2001 and January 2002, using 60 monthly returns, and report that the maximum beta of a company was, on the average, 15. 7 times its minimum beta. The median of the maximum beta divided by the minimum beta was 3. 07.

The median of the percentage daily change (in absolute value) of the betas was 20%, and the median of the percentage (in absolute value) of the betas was 43%. Table 3 of this paper and Damodaran (2001, page 72) also show that the calculated betas change dramatically and depend very much on the period used to estimate them. 1. B. 3. Assuming that the beta calculated from historica l data captures the country risk. Interpretation of the beta of a foreign company listed on the stock market in the USA, t aken from an investment bank: “The question is: Does the beta calculated on the basis of the company’s share price in New 80 common and uncommon errors in company valuation York capture the different premiums for each risk? Our answer is yes, because just as the beta captures changes in the economy and the effect of leverage, it must necessarily absorb the country risk. ” There are various ways of including a company’s country risk component in the CAPM formula. The most common is to use the spread between the long-term dollar treasury bonds of the country in which the firm operates and long-term U. S. Treasury bonds. 1. B. 4. Using the wrong formulae to lever and unlever the beta.

Fernandez (2002, page 506) shows six different formulae for levering and unlevering the beta. Only one of them is correct, as shown in Fernandez (2004): the correct relationship between the levered beta (? L) and the unlevered beta (? u) is: ? L = ? u + (? u – ? d) D (1 – T) / E. The other wrong relationships are: Damodaran (1994): ? L = ? u + ? u D (1 – T) / E Practitioners: ? L = ? u + ? u D / E Harris -Pringle (1985), Ruback (1995 and 2002): ? L = ? u + (? u – ? d) D / E. Myers (1974): ? L = ? u + (? u – ? d) (D – VTS) / E.

Miles-Ezzell (1980): ? L = ? u + (? u – ? d) (D / E) [1 – T Kd / (1+Kd)] 1. B. 5. Arguing that the best estimation of the beta of an emerging market company is the company’s beta with respect to the S&P 500. “The best way to estimate t e beta of an emerging economy h company with a U. S. stock market listing is through a regression of the return of the share on the return of a U. S. stock market index. ” No, because it is well known (we have plenty of data to confirm this) that companies that are rarely traded have absurdly low calculated betas.

Scholes and Williams (1977), for example, warned of this problem and suggested a method for partly getting around it. There is also the problem of the instability of betas that have been estimated by regression: they are very unstable and depend very much on the data used to calculate them. Simply using a share’s historical beta without analyzing the share and the company’s future prospects is very risky, as historical betas are unstable and depend, in almost all companies, on what data we use (daily, weekly, monthly… ). 1. B. 6. When valuing an acquisition, us ing the beta of the acquiring company.

From an analyst’s report: “As the target company is much smaller than the bidder, the Target Comp any will have almost no influence on the resulting capital structure and the riskiness of the resulting company. Therefore, the relevant beta and the relevant capital structure for the valuation of the Target Company are those of the acquiring company. ” Wrong, the relevant risk is the risk of the acquired assets. If this were not the case, a Government bond would have a different value for every company. 1. C. Wrong market risk premium used for the valuation 1. C. 1.

The required market risk premium is equal to the historical equity risk premium. Table 4 shows that the historical U. S. equity risk premium changes considerably depending on the interval used to calculate it. The required market risk premium (the one used in valuation to determine the required return to equity) is an expectation and has little to do with history. Table 4. Historical equity risk premium in the U. S . Average Annual Returns of Arithmetic Average 1928-1953 1928-1999 1928-2002 1962-2002 1992-2002 Stocks 9. 46% 12. 68% 11. 60% 11. 19% 10. 73% T-Bills 1. 03% 3. 92% 3. 93% 6. 03% 4. 40% T-Bonds 2. 6% 5. 05% 5. 35% 7. 53% 8. 58% Equity Risk Premium Stocks – T -Bills Stocks – T -Bonds 8. 44% 8. 76% 7. 67% 5. 17% 6. 32% Risk Premium 6. 51% 7. 63% 6. 25% 3. 66% 2. 15% Average Annual Returns of 5 80 common and uncommon errors in company valuation Geometric Average 1928-1953 1928-1999 1928-2002 1962-2002 1992-2002 Stocks 6. 49% 10. 76% 9. 62% 9. 90% 9. 09% T-Bills 1. 02% 3. 87% 3. 89% 5. 99% 4. 40% T-Bonds 2. 92% 4. 79% 5. 09% 7. 14% 8. 14% Stocks – T -Bills Stocks – T -Bonds 5. 47% 6. 89% 5. 73% 3. 90% 4. 69% 3. 57% 5. 96% 4. 53% 2. 76% 0. 95% 1. C. 2. The required market risk premium is equal to zero.

This argument typically follows the arguments of Mehra and Prescott (1985) and Mehra (2003) , who say that “stocks and bonds pay off in approximately the same states of nature or economic scenarios, and hence, they should command approximately the same rate of return. ” Siegel (1998 and 1999) interprets Table 4 by saying: “although it may seem that stocks have more risk than long-term Treasury bonds, this is not true. The safest longterm investment (from the viewpoint of preserving the investor’s purchasing power) has been stocks, not Treasury bonds. ” 1. D. Wrong calculation of WACC 1. D. 1. Wrong definition of WACC.

An example: Valuation, dated April 2001, of an edible oil company in Ukraine, provided by a leading European investment bank. “The weighted average cost of capital (WACC) is defined as: WACC = Rf + ? u (Rm – Rf), (1) where: Rf = risk-free rate; ? u = unlevered beta; Rm = market risk rate. ” The WACC calculated for the Ukrainian company was 14. 6% and the expected free cash flows (in real terms, which means, excluding inflation) for the Ukrainian company were: (Million euros) FCF 2001 3. 7 2002 14. 7 2003 11. 9 2004 -3. 0 2005 12. 9 2006 12. 9 2007 12. 6 2008 12. 6 2009 12. 6 The reported enterprise value in December 2000 was 71 million euros.

This result comes from adding the present value of the 2001-2009 FCFs (45. 6) discounted at the 14. 6% plus the present value of the residual value calculated with the FCF of 2009 assuming no growth (25. 3). In fact, (1) is not at all the definition of the WACC. It is the definition of the required return to assets, also known as the cost of unlevered equity (Ku). We also must interpret the term (Rm – Rf) as the expected risk premium. The correct formula for the WACC is: WACC = [D / (D+E)] Kd (1– T) + [E / (D+E)] Ke (2) where: Ke = Ku + (D / E) (1-T) (Ku – Kd) (3) Kd = Cost of debt.

D = Value of debt. E = Value of equity. T = effective corporate tax rate The valuation of the Ukrainian company used a (wrongly defined) “WACC” of 14. 6%. But 14. 6% was the Ku, not the WACC. The 71 million euros was the value of the unlevered equity, not the enterprise value. On December 2000, the Ukrainian company ’s debt was 33. 7 million euros and the nominal cost of debt was 6. 49%. The correct WACC for the Ukrainian company should have been1: Ke = Ku + (D / E) (1-T) (Ku – Kd)= 14. 6 + (33. 7/48. 63) (1-0. 3)(14. 6-6. 49) = 18. 53% WACC = [D / (D+E)] Kd (1– T) + [E / (D+E)] Ke = 0. 09 x 6. 49 (1-0. 30) + 0. 591 x 18. 53 = 12. 81% Enterprise value = E+D = PV(FCF;12. 81%) = 82. 33 m illion euros 1. D. 2. The debt to equity ratio used to calculate the WACC is different than the debt to equity ratio resulting from the valuation. An example is the valuation of a broadcasting company performed by an investment bank (see T able 5), which discounted the expected FCFs at the WACC (10%) and assumed a constant growth of 2% after 2008. The valuation provided lines 1 to 7, and stated that the WACC was 1 The (D/E) ratios must be calculated using the values obtained in the valuation. 80 common and uncommon errors in company valuation calculated assuming a constant Ke of 13. 3% (line 5) and a constant Kd of 9% (line 6). The WACC was calculated using market values (the equity market value on the valuation date was 1,490 million and the debt value 1,184 million) and the statutory corporate tax rate of 35%. The valuation also included the equity value at the end of 2002 (3,033; line 8) and the debt value at the end of 2002 (1,184; line 10). Table 6 provides the main results of the valuation according to the investment bank. Errors a. Wrong calculation of the WACC.

To calculate the WACC, we need to know the evolution of the equity value and the debt value. We calculate the equity value based on the equity value provided for 2002. The formula that relates the equity value in one year to the equity value in the previous year is E t = Et- 1 (1+Ket ) – ECFt. To calculate the debt value, we may use the formula for the increase of debt, shown in line 9. The increase of debt may be calculated if we know the ECF, the FCF, the interest and the effective tax rate. Given line 9, it is easy to fill line 10. Line 11 shows the debt ratio according to the valuation, which decreases with time.

If we calculate the WACC using lines 4, 5, 6, 8 and 10, we get line 12. The calculated WACC is higher than the WACC assumed and used by the valuer. Another way of showing the inconsistency of the WACC is to calculate the implicit Ke in a WACC of 10% using lines 4, 6, 8 and 10. This is shown in line 13. If we are using a WACC of 10%, Ke should be much lower than 13. 3%. b. The capital structure of 2008 is not valid for calculating the residual value because in order to calculate the present value of the FCF growing at 2% using a single rate, a constant debt to equity ratio is needed. Table 5.

Valuation of a broadcasting company performed by an investment bank Data provided by the investment bank in italics 2002 1 2 3 4 5 6 7 8 9 10 11 FCF ECF Interest expenses Effective tax rate Ke Kd WACC used in the valuation Equity value (E) ? D = ECF – FCF + Int (1-T ) Debt value (D) D/(D+E) 3,033 1,184 28. 1% 2003 -290 0 107 0. 0% 13. 3% 9. 0% 10. 0% 3,436 397 1,581 31. 5% 2004 -102 0 142 0. 0% 13. 3% 9. 0% 10. 0% 3,893 244 1,825 31. 9% 2005 250 0 164 0. 0% 13. 3% 9. 0% 10. 0% 4,410 -86 1,739 28. 3% 2006 354 0 157 0. 0% 13. 3% 9. 0% 10. 0% 4,997 -197 1,542 23. 6% 2007 459 34 139 12. 0% 13. 3% 9. 0% 10. 0% 5,627 -303 1,239 18. % 2008 496 35 112 35. 0% 13. 3% 9. 0% 10. 0% 6,341 -389 850 11. 8% 12 WACC using lines 4,5,6,8,10 13 Implicit Ke in a WACC of 10% 12. 09% 11. 95% 11. 93% 12. 08% 12. 03% 11. 96% 10. 39% 10. 46% 10. 47% 10. 39% 10. 64% 10. 91% Table 6. Valuation using the wrong WACC of 10% Present value in 2002 using a WACC of 10% Present value in 2002 of the free cash flows 2003-2008 Present val ue in 2002 of the residual value (g=2%) Sum Minus debt Equity value 647 3,570 4,217 -1,184 3,033 To perform a correct valuation, assuming a constant WACC from 2009 on, we must recalculate Table 5. Tables 7 and 8 contain the valuation correcting the WACC.

To assume a constant WACC from 2009 on, the debt must also increase by 2% per year (see line 9, 2009). This implies that the ECF (line 2) in 2009 is much higher than the ECF in 2008. 7 80 common and uncommon errors in company valuation Simply by correcting the error in the WACC, the equity value is reduced from 3,033 to 2,014 (a 33. 6% reduction). Table 7. Valuation calculating the WACC correctly 1 2 3 4 5 6 8 9 10 11 12 2002 2003 2004 2005 2006 2007 2008 2009 FCF -290 -102 250 354 459 496 505. 9 ECF 0 0 0 0 34 35 473. 2 Interest expenses 107 142 164 157 139 112 76. 5 Effective tax rate 0. 0% 0. 0% 0. 0% 0. 0% 12. 0% 35. % 35. 0% Ke 13. 3% 13. 3% 13. 3% 13. 3% 13. 3% 13. 3% 13. 3% Kd 9. 0% 9. 0% 9. 0% 9. 0% 9. 0% 9. 0% 9. 0% Equity value (E) 2,014 2,282 2,586 2,930 3,320 3,727 4,187 4,271 ? D = ECF – FCF + Int (1-T ) 397 244 -86 -197 -303 -389 17 Debt value (D) 1,184 1,581 1,825 1,739 1,542 1,239 850 867 D/(D+E) 37. 0% 40. 9% 41. 4% 37. 2% 31. 7% 25. 0% 16. 9% 16. 9% WACC calculated with 4,5,6,8,10 11. 71% 11. 54% 11. 52% 11. 70% 11. 59% 11. 44% 12. 04% Table 8. Valuation using the corrected WACC from T able 6 Present value in 2002 using the WACC calculated in T able 6 Present value in 2002 of the free cash flows 2003-2008 Present value in 002 of the residual value (g=2%) Sum Minus debt Equity value 588 2,610 3,198 -1,184 2,014 1. D. 3. Using discount rates lower than the risk-free rate. An example is error 3 in Appendix 2. Ke and Ku are always higher than the risk-free rate. WACC may be lower than the risk-free rate only for investments with extremely low risk. An example of that may be found in Ruback (1986). 1. D. 4 . Using the statutory tax rate, instead of the effective tax rate of the levered company. There are many valuations in which the tax rate used to calculate the WACC is the statutory tax rate (normally arguing that the correct tax rate is the marginal tax rate).

However this is wrong. The correct tax rate to use for calculating the WACC for valuing a company is the effective tax rate of the levered company in every year. 1. D. 5. Valuing all the different businesses of a diversified company using the same WACC (same leverage and same Ke). 1. D. 6. Considering that WACC / (1-T) is a reasonable return for the company’s stakeholders. Some countries as sume that a reasonable return a telephone company’s assets is WACC / (1-T). Obviously, this is not correct. It could only be valid for no n-growing perpetuities and if the return on assets was calculated before taxes. 1. D. 7 .

U sing the wrong formula for the WACC when the value of debt (D) is not equal to its book value (N). Fernandez (2002, page 416) shows that the expression for the WACC when the value of debt (D) is not equal to its book value (N) is WACC = (E Ke + D Kd – N r T) / (E + D). Kd is the required return to debt and r is the cost of debt. 1. D. 8 . Calculat ing the WACC assuming a capital structure and deducting the current debt from the enterprise value. This error appears in a valuation by an investment bank. Current debt was 125, enterprise value was 2180, and the debt to equity ratio used to calculate the WACC was 50%.

This is wrong because the outstanding and forecasted debt should be used to calculate the WACC. The equity value of a firm is given by the difference between the firm value and the outstanding debt, where the firm value is calculated using the WACC, and the WACC is calculated using the outstanding (market value of) debt. Alternatively, if the firm starts with its current debt and moves towards another round of financing, then a variable WACC (different for each year) should be used, and the current debt should be deducted from the enterprise value. 8 0 common and uncommon errors in company valuation 1. D. 9 . Calculat ing the WACC using book values of debt and equity. This is quite a common error. The appropriate values of debt and equity are the ones resulting from the valuation. 1. E. Wrong calculation of the value of tax shields 1. E. 1. Discounting the tax shield using the cost of debt or the required return to unlevered equity. Many valuers assume, following Ruback (1995 and 2002), that the value of tax shields (VTS) is the present value of tax shields (D Kd T) discounted at the required return to unlevered equity (Ku).

There are also many valuers who assume, following Damodaran (1994), that the value of tax shields (VTS) is the present value of tax shields discounted at the cost of debt (Kd). Fernandez (2004) proves that both expressions are incorrect and that the value of tax shields is the present value of D Ku T discounted at the required return to unlevered equity (Ku): VTS = PV[D Ku T; Ku] 1. E. 2. Odd or ad-hoc formulae. Fernandez (2002, page 506) shows different expressions for calculating the value of tax shields that are frequently used and that are supported by some papers in the financial literature.

However, Fernandez (2004) proves that the value of tax shields is the present value of D Ku T discounted at the required return to unlevered equity (Ku): VTS = PV[D Ku T; Ku]. Some incorrect formulae for calculating the value of tax shields are: Harris -Pringle (1985) and Ruback (1995, 2002): PV[Ku; D T Kd ] Myers (1974): PV[Kd; D T Kd ] Damodaran (1994): PV[Ku; DTKu – D (Kd- R F) (1 -T)] Practitioners: PV[Ku; DTKd – D(Kd- R F)] Miles-Ezzell (1980): PV[Ku; D T Kd] (1+Ku)/ (1+Kd) 1. F. Wrong treatment of country risk 1. F. 1.

Not considering the country risk, arguing that it is diversifiable. Example taken from a regulat or: “It is not correct to include the country risk of an emerging country because from the perspective of global investors only systematic risk matters, and country -specific events will be uncorrelated with global market movements. Therefore, country-specific events will be unsystematic risk, totally uncorrelated with global market movements. ” According to this view, the required return to equity will be the same for a US diversified portfolio as for a Bolivian diversified portfolio. . F. 2. Assuming that a disaster in an emerging market will increase the calculated beta, in relation to the S&P 500, of the country’s companies. Example taken from a financial consulting firm: “The occurrence of any dramatic systemic event (devaluation, end of convertibility, capital transfer controls, threats to democratic stability) that significantly raises the country risk will lead automatically to a substantial increase in the estimated beta, in relation to the S&P500, of the companies that operate in that country. ” No.

That is why, when valuing companies in emerging countries, we use the country risk, because the beta no longer captures all the above-mentioned risks: devaluation, end of convertibility, capital transfer controls, threats to democratic stability… Also, if ADRs have low liquidity (if they are traded only a few times each day and are unlikely to be traded exactly at the close of each session, which is when analysts usually take prices for calculating betas), then the calculated beta will tend towards zero, owing to the non-synchronous trading effect, which is perfectly described by Scholes and Williams (1977). . F. 3. Assuming that an agreement with a government agency eliminates country risk. Example taken from an investment bank: “If a government grants a company a monopoly of a particular market, with agreements that guarantee legal and tax stability and economic equilibrium, then there is no country risk (such as devaluation, end of convertibility, capital transfer control s, threats to democratic stability). ” No. The risks of devaluation, end of convertibility, capital transfer controls, threats to democratic stability, etc. remain. No government can eliminate its own risk.

That is to say, the shares of a company that operates in a country cannot have less risk than the government bonds of that country. A company’s shares would have exactly the same risk as the country’s government bonds only if the 9 80 common and uncommon errors in company valuation government were to guarantee and fix future dividends for shareholders. However, that does not usually happen. 1. F. 4. Assume that the beta provided by Market Guide with the Bloomberg adjustment incorporates the illiquidity risk and the small cap premium.

Example taken from an investment bank: “The Market Guide beta c aptures the distorting effects of the share’s low liquidity and the small size of the firm through the so-called Bloomberg adjustment formula. ” No. The so-called “Bloomberg adjustment formula” is simply an arbitrary adjustment to make the calculated betas converge towards 1. The arbitrary adjustment consists of multiplying the calculated beta by 0. 67 and adding 0. 33. Adj. Beta = 0. 67 * raw beta + 0. 33. It must be stressed that this adjustment is completely arbitrary. . G. Includ ing an illiquidity, small-cap, or specific premium when it is not appropriate. Examples are errors 1 and 2 in section 12. 2. Errors when calculating or forecasting the expected cash flows 2. A. Wrong definition of the cash flows 2. A. 1. Forgetting the increase of working capital requirements when calculating cash flows. An example is error 1 in Appendix 2 . 2. A. 2. Considering an increase in the company’s cash position or financial investments as an equity cash flow.

Examples of this error may be found in many valuations; and also in Damodaran (2001, page 211), who argues that “when valuing a firm, you should add the value of cash balances and nearcash investments to the value of operating assets. ” In several valuations of Internet com panies, the analysts calculate the present values of expected cash flows and add the company ’s cash, even though it is well known that the company is not going to distribute it in the foreseeable future. It is wrong to add all the cash because: 1.

The company needs some cash to continue its operations, and 2. The company is not expected to distribute the cash immediately It will be correct to add the cash only if: – The interest received on the cash were equal to the interest paid on the debt, or – The cash is due be distributed immediately, or – The cost of debt used to calculate the WACC was the weighted average of the cost of debt and the interest received on the cash holdings. In this case, the debt used to calculate the debt to equity ratio must be debt minus cash.

Increases in cash must then be included in “Investments in working capital. ” The value of the excess cash (cash above and beyond the minimum cash needed to continue operations) is lower than its book value if the interest received on the cash is lower than the interest paid on the debt. The company increases its value by distributing excess cash to the shareholders or by using it to reduce its debt, rather than keeping it. 2. A. 3. Errors in the calculation of the taxes that affect the FCF. Using the taxes paid (in $ amount) by the levered company.

Some valuers use the statutory tax rate, or a tax rate other than the tax rate of the levered company , to calculate the FCF. Fernandez (2002, page 501) claims that the correct tax rate for calculating the FCF is the tax rate of the levered company. 2. A. 4. Expected equity cash flows are not equal to expected dividends plus other payments to shareholders (share repurchases…). In several valuation reports, the valuer computes the present value of positive equity cash flows in years when the company will not distribute anything to shareholders.

Also, Stowe, Robinson, Pinto, and McLeavey (2002) say that “Generally, Equity Cash Flow and dividends will differ. Equity Cash Flow recognizes value as the cash flow available to stockholders even if it is not paid out. ” Obviously, that is not correct, unless we assume that the amounts not paid out are reinvested and obtain a return equal to Ke (the required return to equity). 10 80 common and uncommon errors in company valuation 2. A. 5. Considering net income as a cash flow.

Fernandez (2002, page 178) points out that net income is equal to the equity cash flow only in a no-growth perpetuity (a constant P&L and constant balance sheet company). 2. A. 6. Considering net income plus depreciation as a cash flow. Example taken from a valuation performed by an institution: “The sum of the net income plus depreciation is the rent (cash flow) generated by the company. ” Then, the valuer concluded that the equity value was the net present value of this “rent”. 2. B . Errors when valuing seasonal companies 2. B. 1.

Wrong treatment of seasonal working capital requirements. Fernandez (2003) provides a valuation of a company in which the seasonality is due to purchases of raw materials: the equity value of this company calculated using annual data without making the necessary adjustments understates the true value by 45% if the valuation is done at the end of December, and overstates the true value by 38% if the valuation is done at the end of November. The error due to adjusting only by using average debt and average working capital requirements ranges from –17. 9% to 8. %. 2. B. 2. Wrong treatment of inventories that are cash equivalents. Fernandez (2003) shows that when inventories are a liquid commodity such as grain or seeds, it is not correct to consider all of them as working capital requirements. Excess inventories financed with debt are equivalent to a set of futures contracts: not considering them as such leads us to undervalue the company. 2. B. 3 . Wrong treatment of seasonal debt. Fernandez (2003) shows that the error due to using annual data instead of monthly data when there is seasonal debt is enormous.

It also shows that adjusting by using average debt reduces the error, but the error is still considerable. 2. C. Errors due to not projecting the balance sheets 2. C. 1. Forgetting balance sheet accounts that affect the cash flows. In a balance sheet, WCR + NFA = D + Ebv, where WCR = Working Capital Requirements; NFA = Net Fixed Assets; D = Book value of debt; Ebv = Book value of equity. It also holds that ? WCR + ? NFA = ? D + ? Ebv. Many valuations are wrong because the valuer did not project the balance sheet s, and the increase in assets ( ? WCR + ?

NFA, which appear in the cash flow calculation) does not match the assumed increase in debt plus the assumed increase in the book value of equity. 2. C. 2. Considering an asset revaluation as a cash flow. In countries with high inflation, companies are permitted to revalue their fixed assets (and their net worth). But this is merely an accounting appreciation, not a cash outflow (although the fixed assets increase) nor a cash inflow (although the net worth increases). 2. C. 3. Interest payments are not equal to debt times cost of debt. In several valuations, this simple relationship did not hold. . D. Exaggerated optimism when forecasting the cash flows. Two examples are error 5 in Appendix 2 and the following lines extracted from a valuation report about Enron Corp. , produced by a recognized investment bank on July 12, 2001, when the share price was $49. “We view Enron as one of the best companies in the economy. There are still several misconceptions about Enron that mask the company’s strong fundamentals. We therefore hosted an investor conference call on June 27 to clarify Enron’s growth prospects and answer investors’ questions. We expect Enron shares to rebound sharply in the com ing months. We believe that Enron shares have found their lows and will recover significantly as investor confidence in the company returns and as misconceptions about Enron dissipate. We strongly reiterate our Buy rating on the stock with a $68 price target over the next 12 months. “Enron is a world-class company, in our view. We view Enron as one of the best companies in the economy, let alone among our group of diversified natural gas companies. We are confident in 11 80 common and uncommon errors in company valuation he company’s ability to grow earnings 25% annually for the next five to ten years, despite its already large base. We believe that Enron investors have the unique opportunity to invest in a high growth company with improving fundamentals. “We strongly reiterate our Buy rating on the stock with a $68 price target over the next 12 months. Enron earning model, 1994-2005E. US$ millions except per- share data 1994 1995 1996 1997 1998 1999 2000 2001E 2002E 2003E 2004E 2005E Net income 438 504 568 88 686 827 896 1,563 1,939 2,536 3,348 4,376 Adjust ed EPS 0. 3 0. 91 0. 91 0. 87 1. 00 1. 18 1. 47 1. 85 2. 25 2. 75 3. 52 4. 47 Dividends per share 0. 38 0. 41 0. 43 0. 46 0. 48 0. 50 0. 50 0. 50 0. 50 0. 50 0. 50 0. 50 Book value per share 5. 15 5. 65 6. 64 9. 27 9. 95 12. 28 13. 94 15. 47 17. 99 21. 02 24. 79 29. 47 “We recently rais ed our 2001 EPS estimate $0. 05 to $1. 85 and established a well-aboveconsensus 2002 estimate of $2. 25. We are confident in the company’s ability to grow earnings 25% annually for the next five to ten years, despite its already large base. It is well known what happened to Enron’s share price after the date of this report. 3. Errors in the calculation of the residual value 3. A. Inconsistent cash flow used to calculate the value of a perpetuity. An example is the valuation of a manufacturing company performed by a financial consulting firm (see Table 9), which shows a valuation performed by discounting expected free cash flows at the WACC rate of 12%. Lines 1 to 5 contain the calculation of the free cash flows. NOPAT (Net Operating Profit after Taxes) does not include interest expenses.

The residual value in 2007 is calculated assuming a residual growth of 2. 5%: Residual value in 2007 = 12,699 = 1,177 x 1. 025 / (0. 12 – 0. 025). The enterprise value (line 9) is the sum of the present value of the free cash flows 2003-2007 (line 7) plus the present value of the terminal value (line 8). Adding cash (line 10) and subtracting debt value (line 11), the financial consulting firm calculates the equity value (line 12) as $6. 561 million. It sounds all right , but the valuation contains two errors. Table 9.

Valuation of a manufacturing company performed by a financial consulting firm $million 2003 2004 2005 2006 2007 Net Operating Profit After Taxes 500 522 533 574 616 Depreciation 1,125 1,197 1,270 1,306 1,342 Capital expenditures Investment in working capital Free cash flow -1,445 203 383 -722 -450 547 -722 -314 767 -361 -399 1,120 -361 -420 1,177 12,699 line 1 2 3 4 5 6 Residual value in 2007 (WACC 12% and residual growth 2. 5%) Present value in 2002 of free cash flows (WACC =12%) 7 8 9 10 11 12 2003-2007 Residual value in 2007 Total EV (Enterprise Value) Plus cash Minus debt Equity value ,704 7,206 9,909 280 -3,628 6,561 Errors 1. It is inconsistent to use the FCF of 2007 to calculate the residual value. The reason for this is that in 2007 the forecasted capital expenditures (361) are smaller than the forecasted depreciation (1342). It is wrong to assume that this will happen in the future indefinitely: net fixed assets would be negative in 2010! 12 80 common and uncommon errors in company valuation The normative 2007 FCF used to calculate the residual value should be $196 million (assuming capital expenditures equal to depreciation) or less (if we assume that the net fixed assets also grow at 2. %). Correcting this error in the valuation, Table 3 shows that the equity value is reduced to $556 million (instead of $6,561 million). Table 10. Valuation of the manufacturing company in Table 9 adjusti ng the normative free cash flow and the residual value Normative 2007 FCF 6 7 8 9 10 11 12 Residual value in 2007 Present value in 2002 of free cash flows: 2003-2007 Residual value in 2007 Total EV (Enterprise Value) Plus cash Minus debt Equity value 2,704 1,200 3,904 280 -3,628 556 196 2,115 =196 x 1. 025 / (0. 12 – 0. 025)

Of course, in a given year or in several years, capital expenditures may be lower than depreciation, but it is not consistent to take this as the normative cash flow for calculat ing the residual value as a growing perpetuity. 3. B. The debt to equity ratio used to calculate the WACC for discounting the perpetuity is different than the debt to equity ratio resulting from the valuation. This error is commonly made in many valuations and is also found in the valuation in section 1. D. 2. 3. C. U sing ad hoc formulas that have no economic meaning. An example is error 4 in Appendix 2. 3. D.

U sing arithmetic averages instead of geometric averages to assess growth. An example is given in Table 11, which shows the past evolution of the EBITDA of a manufacturing company operating in a mature industry. The investment bank that performed the valuation used this table as a justification for a forecasted average annual increase of EBITDA of 6%. It is obvious that the geometric average is a much better indicator of average growth in the past. Table 11. Arithmetic vs. geometric growth EBITDA Annual growth Arithmetic average 1995-2002 Geometric average 1995-2002 1995 127 6. 0% 2. 1% 1996 132 3. % 1997 149 12. 9% 1998 91 -38. 9% 1999 2000 150 132 64. 8% -12. 0% 2001 146 10. 6% 2002 147 0. 7% 3. E. Calculating the residual value using the wrong formula. When the residual value is calculated as a growing perpetuity, the correct formula is RV = CFt+1 / (K – g). RVt is the residual value in year t. t CFt+1 is the cash flow of the following year. K is the appropriate discount rate, and g is the expected growth of the cash flows. But many valuations use the following incorrect formulae: RVt = CFt / (K – g). RVt = CF t+1 (1+g) / (K – g). 4. Inconsistencies and conceptual errors 4. A.

Conceptual errors about the free cash flow and the equity cash flow 4. A. 1. Considering the cash in the company as an equity cash flow when the company is not going to distribute it. An example of this was given in section 1. 13 80 common and uncommon errors in company valuation 4. A. 2 . Using real cash flows and nominal discount rates , or viceversa. An example is the valuation in section 1. D. 1. , which also has another error: the projected FCF are given in real terms, that is, excluding inflation (which is why free cash flows are constant fr om 2007-2009), while Ku (14. 6%) is calculated in nominal terms, that is, including inflation.

For a correct valuation, the cash flows and the discount rate used must be consist ent. This means that: • Cash flows in real terms must be discounted with real discount rates, and • Cash flows in nominal terms must be discounted with nominal discount rates. The correct way is either to increase cash flows by inflation or to deduct inflation from nominal discount rates. In fact, for real (constant) cash flows, such as those used in this valuation, we must use real WACC and real Ku: Real WACC = (1+Nominal WACC) /(1+ expected inflation) – 1 Real Ku = (1+Nominal Ku) /(1+ expected inflation) – 1 4. A. 3 .

The free cash flow and the equity cash flow do not satisfy ECF = FCF + ? D – Int (1-T). This equation represents the relationship between the equity cash flow and the free cash flow. It may be found in Fernandez (2002, pages 42 and 401). In many valuation reports, given the FCF, the debt increase (? D), the interest payments (Int), and the effective tax rate (T), the calculated ECF bears no relation at all to the company’s expected equity cash flows (dividends plus share repurchases). 4. B . Errors when using multiples 4. B. 1. Using the average of multiples extracted from transactions executed over a very long period of time.

An investment bank produced this valuation in January 2003. “Table 12 shows the multiples of recent transactions. We use the median of these multiples (6. 8), as the median eliminates extremes. ” Table 12. Transaction multiples in the oil business Acquirer/Target Bunge/Cereol Cargill/Cerestar Land O’Lakes/Purina Mills Primor Inversiones/Mavesa Corn Product International/Arcancia CPC Eridania Beghin-Say/American Maize products Date November 2002 October 2001 June 2001 January 2001 October 1998 February 1995 Average Median EV/EBITDA 6. x 12. 1x 4. 0x 7. 5x 7. 3x 5. 5x 7. 1x 6. 8x EV/EBIT 9. 6x na 8. 2x 10. 3x na 8. 3x 9. 1x 9. 0x Errors 1. The multiples come from a very long period of time: from February 1995 to November 2002. 2. Dispersion of the multiples. The EV/EBITDA ranges between 4 and 12. 1. Why should 6. 8 (the median) be a reasonable multiple? 4. B. 2 . Using the average of transactions multiples that have a wide dispersion. An example is Table 12. 4. B. 3. U sing multiples in a way that is inconsistent with their definition.

An example is Table 13, which shows a valuation performed by a well known investment bank using the price-earnings ratio. Table 13. Valuation using the price-earnings ratio. 1 2 3 4 5 Expected net income of next year Valuation using PER Assumed PER PER x net income Plus: excess cash Minus: Financial debt 28. 6 $ millions Minimum Maximum 9. 0 10. 0 257. 4 286. 0 93. 1 93. 1 115. 6 115. 6 14 80 common and uncommon errors in company valuation 6 7 Minus: Retirement commitments Equity value 34. 5 200. 4 34. 5 229. 0 Error.

The Price-earnings ratio is equal to the equity value divided by net income. It is not correct to deduct the debt (line 5). The correct equity value (according to the assumptions) should be 115. 6 million higher than line 7. A dding the excess cash (line 4) is correct in this case because the buyer planned to distribute the excess cash immediately to the shareholders. 4. B. 4 . U sing a multiple from an extraordinary transaction. An example is the following valuation performed by a consulting firm for an arbitrage. Table 14 shows the balance sheets and P&L of Telecosin. Table 14.

Balance sheets and P&L of Telecosin, 1995-2000 (thousand euros) (Thousand euros) Sales Net income Dividends Cash and banks Accounts receivable Inventories Net fixed assets T OTAL ASSETS Short-term financial debt Trade creditors Other creditors Long-term bank debt Shareholders’ equity T OTAL LIABILITIES Employees at 31 December 1995 336 15 0 33 119 0 59 212 0 100 47 0 64 212 11 1996 768 8 0 13 201 73 53 340 0 233 36 0 72 340 15 1997 1,009 11 0 53 211 20 50 334 2 102 146 0 83 334 21 1998 1,848 98 0 426 635 42 158 1,261 2 212 340 405 301 1,261 41 1999 2,746 156 0 421 779 150 235 1,586 0 204 558 367 457 1,586 51 2000 6,815 87 0 82 3,372 141 804 4,400 1,124 1,619 798 314 545 4,400 101 “The legitimacy of the comparable transactions method is based on the fact that financial analysts working for merchant banks, consulting firms and financial companies for valuing companies like Telecosin widely and predominantly use this method and the revenue parameter. “In September last year a group of investors consisting of Dresdner Kleinwort Benson, MCH and Sibec acquired 20% of the company IP Systems for 3. 6 million euros. This implies that 100% of the company was valued at 18 million euros. “IP Systems has many features in common with Telecosin, making it a suitable point of comparison for determining the value of Telecosin.

There are, however, two differences in Telecosin’s favor that need to be mentioned: long experience in the market (which implies more consolidated goodwill and greater recognition by customers), and a significantly larger workforce. The following table offers a comparison of the two companies: IP SYSTEMS 0. 9 million euros (1 month) 10. 4 million euros 63 people 1999 Telecosin 2. 75 million euros 6. 81 million euros 110 people 1994 Turnover 99 Turnover 2000 Workforce Founded in In 1999 IP Systems had a turnover of 0. 9 million euros. However, the company had only started trading in November. If we extrapolate this turnover to the year as a whole, we get an annual 15 0 common and uncommon errors in company valuation turnover of 5. 4 million. Therefore, the growth in IP System’s turnover in the period 1999-2000 is 90%, lower than that of Telecosin in the same period (146%). The IP Systems investors valued the company with reference to the sales figure for the current year (2000), using a sales multiple of 1. 7. If this same multiple (1. 7) is applied to Telecosin’s minimum forecasted sales for 2001 (16. 8 million euros), the value of the shares of the company in December 2000 is 28. 6 million. Decision of the Court of Arbitration “A party has presented a valuation based on what is known as the comparable transactions method.

Some securities firms and investment banks used this method for a period of approximately two years (betwee n 1998 and 2000). There was a clear reason for using it: it was impossible to explain the exorbitant prices paid for many new economy firms using the methods in general use up until then. The comparable transactions method never had any theoretical underpinnings. And certainly, after the summer or autumn of 2000 it was totally discredited. This method is therefore not worth considering. “We are left, therefore, with the discounted cash flow method, which is the most widely accepted method of firm valuation, and the one that the Panel of Arbitrators considers most appropriate in this case. We value the shares of Telecosin at 2. 4 million euros. ” 4. B. 5 .

Using ad hoc valuation multiples that conflict with common sense. An example is the valuation of Terra’s shares performed by a Euro-American bank in April 2000 (see Table 15), when Terra’s share price was 73. 8 euros. As the valuation given by Table 15 is 104 euros per share, the bank advised its customers to buy Terra shares. Table 15. Valuati on of Terra performed by a Euro-American bank on 7 April 2000 EV (enterprise Price per Million shares Capitalization Net debt value) share ($) ($ million) AOL Yahoo! Lycos [email protected] Go Networks NBC Interactive About. com The Go2Net Ask Jeeves LookSmart Juno Infospace GoTo. com Earthink TheGlobe. com 65. 0 158. 61,5 30,0 19,0 38,5 65,0 71,4 59,0 38,0 13,8 65,5 43,0 18,0 5,0 2,282 526 110 352 165 32 17 31 35 88 39 217 49 138 30 148,315 83,184 6,760 10,559 3,133 1,223 1,075 2,182 2,062 3,340 531 14,186 2,107 2,489 152 281,298 -1,472 -1,208 -618 302 349 259 -176 214 -166 -97 -89 -89 -104 -206 -52 -3,153 146,843 81,976 6,142 10,861 3,482 1,482 899 2,396 1,896 3,243 442 14,097 2,003 2,283 100 278,145 273 1,019 32,328 Adjusted EV per capita (US$) [3] 542 509 237 286 Million Terra market inhabitants share (%) [4] 39 30 338 407 [5] 30% 5% 25% 23% Sum of the 15 largest information hubs in USA No. inhabitants (million) EV per capita (US$) GNP per capita in the US (US$) GNP per GNP per capita capita (US$) vs.

USA (%) Spain Hispanic America Latin America Average [1] 17,207 16,164 7,513 9,080 [2] 53% 50% 23% 28% Value [6] 6,345 764 20,008 27,117 -525 27,642 Value of Terra ($ million) Net debt ($ million) Implicit capitalization ($ million) 16 80 common and uncommon errors in company valuation Million shares: 280 Dollar/euro exchange rate: 0. 94875 Price per share (euros) 104 The valuation is based on the 15 largest Internet companies in the U. S. A. The first column gives the price per share, the second column the number of shares outstanding, and the third column the companies’ capitalization in million dollars. When the net debt is added to the capitalization, what the bank calls enterprise value (EV) is obtained.

Thus, the sum of the enterprise values of the 15 largest Internet companies in USA was 278. 145 billion dollars. The Euro American bank’s analyst then divided this quantity by the number of inhabitants in the U. S. , which he estimated to be 273 million, obtaining the EV per capita in the U. S. : 1,019 dollars. At the bottom of Table 15, the analyst divided Terra’s market into 3 geographical areas: Spain, Hispanic America ( U. S. citizens who are Spanish speakers) and Latin America. Column [1] shows the gross national product per capita in each of the three geographical areas, and column [2] shows the percentage they represent with respect to the gross national product per capita in USA ($32,328).

Column [3] is the result obtained by multiplying the EV per capita in the U. S. (1,019 dollars) by the ratio between the gross national product per capita in each of the three geographical areas and the U. S. gross national product per capita (column [2]). He then multiplied column [3] by the number of inhabitants in each geographical area (column [4]) and by Terra’s estimated market share in each of these markets (column [5]), to obtain Terra’s value in each of these geographical areas (column [6]). Adding the three amounts in column [6], he arrived at the value for Terra: 27. 117 billion dollars. After subtracting the net debt from this amount, he obtained Terra’s implicit capitalization: 27. 642 billion dollars.

By dividing this quantity by the number of Terra shares (280 million) and by the euro exchange rate, the analyst obtained the value of the Terra share: 104 euros per share. Doesn’t this valuation seem surprising to the reader? We suggest another way of getting the figure of 104 dollars per share: The value of the Terra share is twice the age of Manolo Gomez’s mother-in-law, who is 52. We chose Manolo because he lives near Terra’s corporate headquarters. Of course, this valuation is absurd, but it has as much rigor as that given in Table 15. As the saying goes, “the blind man dreamt he saw, and he dreamt what he wanted to see”. 2 Terra traded at 11 euros at the end of 2000, at 9 euros at the end of 2001, and was trading between 4 and 5. euros in the first six months of 2003. 4. C. Time inconsistencies 4. C. 1. Assume that the equity value wi l be constant in the future. Example taken from an analyst’s l valuation report: “As we do not know the evolution of the equity value of the company, a good approximation is to assume that the equity value will remain constant in the following five years. ” That is not correct. Fernandez (2002, pages 401 and 497) shows that the relationship between the equity value of different years is: E = Et-1 (1+Ket) – ECFt. Note that the equity value is constant (Et = t E t-1) only if ECFt = E t-1 K et . That only happens in no-growth perpetuities. 4. C. 2.

The Equity value or the Enterprise Value does not satisfy the time consistency formulae. Fernandez (2002, page 401) shows that the relationship between the enterprise value of different years is: Et+Dt = (E t-1+D t-1) (1+WACCt) – FCFt. 4. D. Other conceptual errors 4. D. 1 . Not considering cash flows resulting from future investments. Oleina Holding, a leading edible oil company in the Ukraine, with strong volume and brand recognition also in Russia. The company was operating almost at full capacity and had plans to invest in a new plant in Russia. Example taken from an investment bank: “From a methodological viewpoint, if this project had to be taken into account, its net present value should be assumed to be nil.

The most reasonable approach would be to assume that the investment is expected to deliver a return that is equal to financial market expectations, which implies a net present value equal to zero. ” 2 Other valuations of Internet companies using esoteric multiples may be seen in Fernandez (2002), chapter 12. 17 80 common and uncommon errors in company valuation Example taken from a business school professor, acting as expert witness in an arbitrage : “By taking into account a future Russian plant project in the valuation, the seller of the shares would benefit from the profits generated by this new project without incurring the related risks, as he would anyway not take part in the future investment. ” 4. D. 2.

Considering that a change in economic conditions invalidates signed contracts. A European bank bou ght a securities company on February 16, 2001. The European bank bought 80% of the shares and gave the current owners a put on the remaining 20% of the shares with an exercise price of 54 million euros (same per share price as the transaction). The current owners tried to exercise the put in May 2002, but the European bank refused, arguing that: “As, due to specific extraordinary circumstances, the situation of the financial markets and of the world economy in May 2002 was very much worse than on 16 February 2001, we have no obligation to accept the exercise of the put at the agreed exercise price.

The unforeseen recession was aggravated by the shock of 11 September 2001, which had both short and medium-term effects, insofar as stock market behavior over the following twelve months was unfavorable and highly volatile. ” The European bank had a new valuation of the shares of the securities company on May 2002 that argued that the price of the shares that fallen 86. 3% since February 2001. Contracts a signed to be fulfilled. On top of that, there are no grounds for the claim that re stock market volatility increased significantly after 11 September 2001. By March 2002 the volatility of the main American indexes was similar to what it had been before September 11. Consequently, the effect of September 11 did not cause a permanent increase in volatility. The effect of September 11 on prices was also short-lived.

Table 16 shows what a short time the effect of September 11 on the S&P 500, the NASDAQ and oth world stock market indexes er lasted. It is quite clear that the effect of September 11 did not lead to a permanent increase in volatility or a permanent decrease in prices. Consequently, it cannot be true to say that the market risk has increased as a result of September 11. Table 16. Effect of September 11, 2001 on four stock indexes: S&P 500, NASDAQ , EURO STOXX 50, and FTSE 100 S&P 500 NASDA EURO Q STOXX 50 FTSE 100 10/09/01 11/09/01 12/09/01 13/09/01 14/09/01 17/09/01 18/09/01 19/09/01 20/09/01 1092. 5 1092. 5 1092. 5 1092. 5 1092. 5 1038. 8 1032. 7 1016. 1 984. 5 1695. 4 1695. 4 1695. 4 1695. 4 1695. 4 1579. 6 1555. 1527. 8 1470. 9 3440. 7 3220. 3 3260. 9 3293. 8 3091. 2 3205. 0 3189. 9 3105. 1 2967. 9 5033. 7 4746. 0 4882. 1 4943. 6 4755. 8 4898. 9 4848. 7 4721. 7 4556. 9 4433. 7 5153. 1 5164. 9 5067. 3 5082. 6 5188. 7 September 11, 2001 21/09/01 965. 8 1423. 2 2877. 7 10/10/01 1081. 0 1626. 3 3468. 3 11/10/01 1097. 4 1701. 5 3510. 6 15/10/01 1090. 0 1696. 3 3393. 6 16/10/01 1097. 5 1722. 1 3455. 3 26/10/01 1104. 6 1769. 0 3611. 9 Source: Thomson Financial DataStream. Lowest level after September 11 Eurostoxx higher than on September 10 FTSE 100 higher than on September 10 NASDAQ higher than on September 10 S&P 500 higher than on September 10 4. D. 3.

Considering that the value of debt is equal to its book value, when they are different. A common assumption in valuations is to consider that the value of debt (D) is equal to its book value (N). However, there are circumstances in which this assumption is not reasonable. For example, if a company has long-term fixed rate debt and interest rates have increased (decreased), the debt value (D) will be lower (higher) than its book value (N). 4. D. 4. Not using the correct formulae when the value of debt (D) is not equal to its book value (N). Fernandez (2002, page 416) shows that the expression for the WACC, when the value of debt (D) is not equal to its book value (N), is WACC = (E Ke + D Kd – N r T) / (E + D).

Kd is the required return to debt and r is the cost of debt. 18 80 common and uncommon errors in company valuation 4. D. 5. Including the value of real options that have no economic meaning. An example: Table 17 contains the net present value calculation of a project for a new plant in Brazil for a supplier of automotive interior systems to most of the major car assemblers. Initial outlays amounted to nearly $38 million. The project involved supplying components for 500,000 cars the first year and 850,000 cars the following years. The net present value of the project (given the cost of the new plant and the expected free cash flows), using a WACC of 14. 95%, is negative: -$ 7. 98 million. Table 17.

Net present value calculation of a project for a new plant in Brazil. WACC = 14. 95% ($ million) in nominal term s FCF NPV 0 -37. 9 -7. 98 1 3. 5 2 12. 6 3 10. 7 4 8. 5 5 Salvage value 7. 1 3. 8 However, the valuer argued that the owner of the plant had additional options that were not included in the net present value calculation: – Options that came from obtaining further supply contracts in the future during the life of the plant (growth options, valued as three European options with strike prices of $5. 6, $0. 4 and $0. 085 million). – Option to renew initial supply contracts at their expiration date (prolongation option, valued as a European option with strike price of $42. 7 million).

The salvage value of the project was neither the value of its contract renewal nor the liquidation price of its assets, but the higher of the two. – Flexibility options: possibility of adapting project costs to the evolution of sales . – Abandonment option: possibility of abandoning the investment prior to the end of its life (valued as an American put option on the future cash flows stream with strike price equal to its salvage value and maturity equal to the project’s life). Valuing the options and the project together, the valuer said that the expanded net present value (value of the plant taking into consideration the real options embedded in the investment) was as shown in T able 18.

The valuer concluded: “Considering the real options together displays a significant positive expanded NPV for different assumptions about the future evolution of the state variable (number of cars produced and assembled in Brazil), and therefore validates the optimality of the investment decision. ” Table 18. Expanded net present value of a project for a new plant in Brazil, as a function of the drift rate and of the volatility Volatility 7% 0% Drift rate 7% 15% 2. 4 7. 5 15. 2 13% 2. 5 7. 6 15. 2 20% 2. 8 7. 2 13. 6 Volatility is the standard deviation of the number of cars that are produced and assembled in Brazil. Drift rate means the expected growth of the number of cars that are produced and assembled in Brazil. Questions to the reader: Do the options belong to the company?

Do you think that the specification of the options (which depend almost exclusively on the number of cars produced and assembled in Brazil) is a good description of them? Would you advise the company to invest in the project? 4. D. 6. Forget ting to include the value of non-operating assets. Example taken from a valuation report: “We do not consider in our valuation the value of the shares that the company has in a traded telephone company because this investment is totally unrelated to the company’s industrial and commercial activities. ” The value of a company’s shares is the present value of the expected equity cash flows plus the current value of the non-operating assets. 4. D. 7. Inconsistencies between discount rates and expected inflation.

In a valuation report, the WACC (in nominal terms) used was 5. 4% and the expected inflation rate used to forecast the free cash flows was 6%. 4. D. 8. Valuing a holding company assuming permanent losses (without tax savings) in some companies and permanent profits in others. In a valuation report performed by an investment bank of a holding company that had two subsidiaries, the equity value of one subsidiary was put at $81 million, and the equity value of the other, at -$33. 9. The taxes of the latter were forecasted as zero because the company was assumed to have permanent losses. 19 80 common and uncommon errors in company valuation 4. D. 9. Wrong concept of the optimal capital structure.

Example taken from a valuation report: “The optimal capital structure is that that maximizes the enterprise value (debt value plus equity value). In the context of the Adjusted Present Value, the enterprise value is equal to the value of the unlevered company plus the present value of tax shields. Since the value of the unlevered company is constant and unrelated to leverage, the optimal capital structure is the one that maximizes the present value of tax shields. ” More about the optimal capital structure may be found in chapter 18 of Fernandez (2002). 4. D. 10. In mature companies, assuming projected cash flows that are much higher than historical cash flows without any good reason. An example is error 5 in Appendix 2. 4. D. 11. Assumptions about future sales, margins, etc. hat are inconsistent with the economic environment, the industry outlook, or competitive analysis. Example taken from a valuation performed by a financial consultant of a platform company: “The following table presents the two extreme scenarios of the evolution of the sales of the company. 2001 2. 7 2. 7 2002 3. 5 3. 4 2003 4. 2 4. 1 2004 5. 1 4. 9 2005 6. 2 5. 7 2006 7. 4 6. 8 2007 9. 0 8. 0 2008 10. 5 9. 2 2009 12. 1 10. 5 2010 13. 6 11. 6 2011 15. 0 12. 5 Optimistic Pessimistic The expected inflation is 2%. ” 4. D. 12. Consider ing that the ROE is the return to shareholders in non-traded companies. This is a fairly common and quite mistaken assumption.

If ROE is a good approximation of the return to the shareholders of non-traded companies, it should be also a good approximation for traded companies. The following table shows that the ROE of General Electric has little to do with the return to its shareholders. General Electric Shareholder return ROE 1992 1993 1994 1995 1996 1997 1998 1999 14% 26% 1% 44% 40% 51% 42% 53% 21% 18% 18% 23% 24% 25% 25% 26% 2000 2001 -5% -15% 27% 27% 2002 average -37% 16% 26% 24% 4. D. 13. Considering that the ROA is the return of the debt and equityholders. Following the same argument as in the previous point, the ROA has little to do with the return to the shareholders.

The ROA (NOPAT / (Ebv +D)) is an accounting ratio, while return is som

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