I have already written once about the reliability of commonly used P/E and P/BV multipliers... but the questions and comments sent to us encourage us to address the issue again...

The indicators (multipliers) used in the comparative approach to business valuation are divided into two groups: equity multipliers and invested capital multipliers.

Invested capital multipliers are indicators where both the numerator and denominator refer to the invested capital. Examples are the popular MVIC / EBIT and MVIC / EBITDA multipliers, where MVIC (Market Value of Invested Capital) is defined as Capitalization + Bank Debt – Cash (in extension, this expression is additionally increased by Non-Operating Liabilities and decreased by Non-Operating Assets other than Cash), EBIT is operating profit, and EBITDA is operating profit plus depreciation.

Similarly, equity multipliers are those where both the numerator and denominator refer to equity. The most popular indicators of this type are P/E (Price/Profit) and P/BV (Price/Book Value), where P is Price (i.e. Capitalization), E is Earnings (i.e. Net Profit), BV is Book Value (by default - equity).

And that's right... equity multipliers are much more popular than invested capital multipliers. The problem is that equity multipliers are strongly dependent on the financing structure (i.e. the debt/equity ratio) and, consequently, are unreliable. Unreliable, i.e. uncertain, unreliable, unreliable and unreliable…

Let's illustrate my point with an example.

Company A is a public company and its shares are listed on the stock exchange. The share capital of A is 10 million PLN and includes 1 million shares with a nominal value of 10 PLN each. As at December 31, 20X0, apart from the share capital, other equity items totaled 40 PLN million. A's bank debt as at December 31, 20X0 was 100 million PLN and its cash was zero. Selected items of the profit and loss account are presented below (data in million PLN). For simplicity, a "round" income tax rate of 20% was adopted.

- earnings before deducting interest and taxes (EBIT) - 25 million PLN

- Financial costs (bank interest rate 5%) - 5 million PLN

- Gross profit - 20 million PLN

- Income tax (20%) - 4 million PLN

- Net profit - 16 million PLN

- The stock exchange (market) price of 1 share A as of January 31, 20X1 was 150 PLN.

What are the P/E, P/BV, EV/EBIT and EV/BVIC ratios at given values?

- P (Price) = number of shares x share price = 1 million x 150 = 150 million PLN

- E (Earnings) – net profit = 16 million PLN

- BV (Book Value) – book value of equity = 10 + 40 = 50 million PLN

- MVIC – fair market value of invested capital = market capitalization (P) + bank debt – cash = 150 + 100 – 0 = 250 million PLN

- EBIT (Earnings Before Interest and Taxes) – operating profit = 25 million PLN

- BVIC (Book Value of Invested Capital) – book value of invested capital = book value of equity + bank debt – cash = 50 (equity) + 100 (debt) - 0 = 150 million PLN

Calculating the multipliers is simple:

- P/E = 150/16 = 9.38

- P/BV = 150/50 = 3

- EV/EBIT = 250/25 = 10

- EV/BVIC = 250/150 = 1.67

On February 1, 20X1, A changes the structure of financing its operating activities - it wants to repay the entire bank debt by issuing new shares: it increases equity by 100 million PLN by issuing 666,667 shares with an issue price of 150 PLN each (the issue price is consistent with the stock exchange price) and repays the debt in full bank debt 100 million PLN (the difference of 50 PLN between the cash raised from the issue of shares and the repaid bank debt is ignored: 666,667 x 150 – 100,000,000 = 50 PLN). What are the P/E, P/BV, EV/EBIT and EV/BVIC ratios now after the change in the financing structure?

- P (Price) = number of shares x share price = (1,000,000 + 666,667) 1.666667 million x 150 = 250 million PLN (we have 0.666667 million new issue shares)

- E (Earnings) - net profit = 16 million PLN (unchanged)

- BV (Book Value) – book value of equity = 50 + 100 = 150 million PLN (50 million PLN is the value of equity before the increase; 100 million PLN is the value of the increase in equity)

- EV (Enterprise Value) - fair market value of invested capital = market capitalization (P) + bank debt - cash = 1.666667 million x 150 + 0 - 0 = 250 million PLN (after changing the structure we already have 1,666,667 shares and zero debt; i.e. the final value remains unchanged but the structure is different)

- EBIT (Earnings Before Interest and Taxes) – operating profit = 25 million PLN (unchanged)

- BVIC (Book Value of Invested Capital) – book value of invested capital = book value of equity + bank debt – cash = 150 (new book value of equity) + 0 (debt has been repaid) – 0 = 150 PLN million (i.e. final unchanged but different structure)

- P/E = 250/16 = 15.63 (change)

- P/BV = 250/150 = 1.67 (change)

- EV/EBIT = 250/25 = 10 (unchanged)

- EV/BVIC = 250/150 = 1.67 (unchanged)

There was a change in the financing structure and, as a result:

- P/E and P/BV multipliers have changed very significantly (an increase from 9.38 to 15.63 and a decrease from 3 to 1.67, respectively)

- EV/EBIT and EV/BVIC multiples have not changed at all.

With respect to the P/E multiple, it could be argued that historical net profit (E) would have changed in a hypothetical situation of no bank debt over the full year 20X0. Interest costs (financial costs) related to bank debt A in 20X0 amounted to 5 million PLN and the adopted income tax rate is 20% - the lack of bank debt costs would mean an increase in net profit by 4 million PLN (5 x (1-20%)). In such a situation, the adjusted net profit would amount to 16 + 4 = 20 million PLN, and the adjusted P/E multiplier = 250/20 = 12.5 - but this multiplier would still change significantly compared to the initial value of 9.38.

The conclusions are obvious - the mere technical change in the debt/equity financing structure may lead to very significant changes in the value of P/E and P/BV multipliers, so these multipliers should not be used to estimate the value of enterprises and companies in a comparative approach. The situation is different with the MVIC/EBIT and MVIC/BVIC ratios, which are generally not dependent on the financing structure - so they can be used in a comparative approach to company valuation.

Theoretical question: should the MVIC financing structure remain the same if the financing structure changes?

The majority (rather) of theoreticians and practitioners claim that no - the value of invested capital should be based on the appropriate - optimal financing structure for a given sector/type of operating activity. Consequently, any deviations of the actual debt/equity structure from this optimal structure should not affect the value. The increased share of debt, on the one hand, leads to tax savings, but on the other hand, it increases financial risk and ultimately increases the cost of capital. Conversely, a smaller share of debt financing reduces tax savings, but also reduces financial risk, which in turn translates into a lower cost of capital.

A smaller (rather) part of specialists believes that because a change in the financing structure leads to a change in income tax (different tax shield), the financial flows available jointly to shareholders and bank debt also change - ultimately, the value of MVIC should also change. In our case, financial costs are reduced from 5 million PLN per year to zero, which, given the adopted income tax rate of 20%, results in an increase in tax by 1 million PLN. Assuming roughly the cost of capital at 10% (and the end-period discounting convention), such an increase in tax leads to a decrease in value by 10 PLN million (1/10%). This means that the total invested capital would decrease from PLN 250 million to 240 million PLN - a decrease of 4%. Since in the end we only have equity capital, such a reduction should reduce the share price by 4%, i.e. from 150 PLN to 144 PLN. In such a situation, to replace the debt worth 100 million PLN, it would be necessary to issue 694,444 shares with an issue price of 144 PLN. How would multipliers be shaped in such a situation?

- P/E = 240/20 = 12.00 (still a very significant change compared to the initial value of 9.38)

- P/BV = 240/150 = 1.60 (still a very significant change versus the initial value of 3.00)

- EV/EBIT = 240/25 = 9.60 (small change versus initial value of 10.00)

- EV/BVIC = 240/150 = 1.60 (small change versus baseline 1.67)

To sum up, even assuming that a change in the financing structure (through a change in the tax shield) may lead to a change in the fair market value of invested capital, jumps in the values of P/E and P/BV ratios still remain very large, while EV/EBIT and EV/BVIC multipliers change slightly. This clearly proves the lack of reliability of P/E and P/BV multipliers.

Personally, I am a supporter of the thesis that changing the debt/equity financing structure does not affect (even slightly) MVIC.

Basic question - why is P/E and P/BV so popular in the comparative approach to company valuation? One main reason comes to mind - simplicity and ease of calculations. Unfortunately, such simplicity and ease do not always lead to the right results...