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The harmonic average takes an average of the reciprocals and then takes the reciprocal of the average
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Is a P/E of 8 or 547 the correct average for purposes of computing the firm's value The conventional average (the P/E of 8) tends to weight extreme values higher than is appropriate For example, assume there are 3 comparable firms, 2 with P/Es of 10 and 1 with a P/E of 100 The conventional average P/E is 40
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It is not obvious that 40 is the correct measure The example could be more extreme by having the P/E of the third firm 10,000 (as might occur if earnings were unusually low for the observed year) The average P/E is
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PRIVATE EQUITY
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The 1499 P/E multiplier would seem to be more useful for valuation purposes than the 3,340 P/E multiplier
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Multipliers: Theoretical Basis
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The use of the average P/E of comparable firms has the complexities of determining firms that are actually comparable and computing the average P/E An alternative approach is to compute a theoretical target P/E based on the firm's economic characteristics We will consider three different multipliers, all of which will be used to compute the value of the stock M0 applied to after-tax earnings: M0(E) M1 applied to earnings before interest and taxes: M1(EBIT) M2 applied to earnings before interest, taxes, depreciation, and amortization: M2(EBITDA)
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Determination of M0 Let P be the value now of a share of common stock Then by definition of M0:
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P = M0E
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14 ________________________________________________________PRIVATE EQUITY
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Remember the above example assumes zero debt With outstanding debt the formulation becomes more complex The above multipliers cannot be applied to a different firm with a different cost of equity and a different growth rate The multipliers were computed based on specific information, and other information will lead to different multipliers Since all the above measures are based on objective measures of earnings, EBIT and EBITDA, they appear to be objective, but in fact all the calculations have a significant subjective input However, the appearance of objectivity makes them popular methods of valuation Since all the methods are implicitly assuming future benefits, it is sensible to also compute the present value of these benefits
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MEASURES OF PRESENT VALUE __________
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We consider six different present value calculations that are actually all equivalent, thus are actually one method: 1 Present value of future dividends for perpetuity 2 Present value of discretionary (free) cash flows
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16 _________________________________________________ PRIVATE EQUITY
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3 Present value of future earnings minus the present value of new investments 4 Present value of an earnings perpetuity plus the present value of growth opportunities (PVGO) 5 Present value of dividends for n years plus present value of the firm's value at time n 6 Present value of economic incomes For the infinite life situation with the firm earning $65 and paying $39 of dividends, a 12 cost of equity and a 02 growth rate, the value is:
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The firm is retaining 4 of earnings and has a growth rate of 02 This implies that incremental investments earn 05 Since 05 is less than the cost of equity, the undertaking of the growth opportunities actually reduces value Instead of assuming one growth rate for perpetuity one could assume a series of changing growth rates The calculations and formulations are more complex, but the logic is perfectly consistent with the infinite life and one growth rate model
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Reinvestment Rate Greater than the Cost of Equity
Now assume all facts are the same except the firm earns 15 on new investments and has a 06 growth rate (4 of earnings are retained)
= $650
Finite Life Models
18 ________________________________________________________PRIVATE EQUITY
For simplification assume there are no taxes Assume the four balance sheets are as shown in Table 21 The economic incomes for the three years are as shown in Table 22 PV (10) = -$18,154 (PV of economic incomes) PV of residual value = 66,555(110)-3 = 50,000 PV of terminal book value = 73,000(110)-3 = 54,846 The firm's value is: V0 = book value + PV of incomes + PV of residual value - PV of terminal book value V0 = 100,000 18,154 + 50,000 - 54,846 = $77,000 The present values of the economic incomes plus the initial book value plus the present value of the residual value minus the present value of the terminal book value is equal to the firm's value at time 0 The amount is also equal to the present value of the cash flows