VALUING UNLISTED SHARES



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Valuing unlisted shares :

The contribution of the INSEE Financial Links Survey

Note: this text is an abridged version of a study that will soon be available in the form of a working document on the INSEE’s website or from the author.

Summary

Most estimates of the aggregate value of unlisted shares are done by applying to unlisted companies, the ratios which are calculated for listed companies. The aim is to obtain, in line with national accounting principles, a market value. However, the implicit assumption of equality between the ratios [pic] between listed and unlisted companies cannot usually be validated empirically due to the lack of data on the market value of unlisted companies that could be exploited statistically. The market value used for listed companies is the stock market capitalisation. The ‘book figure’ is either profit -- as measured by a price earning/ratio (PER) -- or the book value of equity -- a Price-to-Book Ratio.

The INSEE Financial Links (LIFI) Survey provides information, which up to now has not been exploited, on the value of a participation as shown in a parent company’s balance sheet. Dividing this value by the size of the upstream company’s holding in the downstream company[1] gives a valuation of the downstream company.

After validating the source, a direct estimate can be made of the value of unlisted shares. For France, this would lead to reduce notably the current estimate of unlisted shares in the national accounts.

Secondly, the valuation of unlisted companies is compared with that for different kind of listed companies. It is necessary to do this for the sake of comparability with other countries that do not have sources equivalent to the INSEE financial links survey. For these countries, it is still necessary to apply to unlisted shares a ratio computed for listed companies, but this study makes it possible to improve the method by determining which sub--population of listed companies is the closest, in terms of value, to unlisted companies, and what liquidity premium should be applied when using ratios for listed companies to value unlisted shares.

Valuing unlisted shares

Valuing unlisted shares using the INSEE financial links survey

The INSEE financial links (LIFI) survey is an annual survey that has been carried out amongst companies every year since 1979. The sample used for this study was constructed from the surveys relating to the period 1994-1999. After checking for consistency and identifying the year of acquisition of a participation, we have [pic] and we define[pic]with :

➢ Vn: Value of the enterprise in year n

➢ VABIL: Balance sheet value of the participation (source INSEE survey),

➢ TxC: rate of control given by this financial link[2] (source INSEE survey ),

➢ FP: equity (source Système unifié des statistiques d’entreprise (SUSE),

➢ PtB: Price to Book Ratio.

It is necessary to check that these values are indeed market values and not merely the accounting transcription of intra-group transactions. Of the various criteria used to detect such transactions, only that which leads one to suspect that activities have been externalised (newly created companies) is really conclusive. Newly created enterprises are characterised by a PtB ratio that is often equal to 1 and are excluded from the sample.

The PtB ratios obtained are very dispersed.

The factors with the biggest impact on the PtB ratio are (see graphs in annex):

• The size of the enterprise in terms of equity: the PtB ratio is much higher for the smallest enterprises

• Whether the company is listed: for a given size, listed companies are worth more.

• The dividends/equity ratio

Other factors such as the sector of activity or the year of acquisition have little or no impact on the PtB ratio for unlisted companies.

Validation by comparison with the stock market capitalisation for listed companies

When the market value obtained for an enterprise via the survey of financial links is compared with its stock market capitalisation, no systematic bias is observed (Table 1). The dispersion of estimated value /capitalisation is fairly high but it narrows and becomes more symmetrical if we restrict the analysis to cases in which there is no reason to have doubts about the year of acquisition (COACQ = 1[3]). On the other hand, correcting of temporal lags - the stock market capitalisation is that at 31 December while the transaction detected via the survey may have taken place in January just as easily as in December - by taking the average market capitalisation at 31 December of year n-1 and at 31 December of year n has little impact and shifts the distribution by only 0.1 point to the right.

Table 1

Distribution of the ratio : estimated value/ capitalisation

|Scope |Number |Capitalisation at |Q1 |Med |Q3 |DISP* |

|Total |487 |31/12/n |0.55 |0.97 |1.23 |0.70 |

| |378 |Average n, n-1 |0.65 |1.03 |1.30 |0.63 |

| |378 |31/12/n |0.55 |0.96 |1.23 |0.71 |

| | | | | | | |

|Restricted |310 |31/12/n |0.71 |1.00 |1.23 |0.52 |

|(COACQ=1) |239 |Average n, n-1 |0.81 |1.09 |1.30 |0.45 |

| |239 |31/12/n |0.73 |1.00 |1.23 |0.50 |

Source: INSEE (estimate via survey of financial links) and COFISEM (stock market capitalisation)

* : (Q3-Q1)/med

Extension to all unlisted financial companies

The difficulty involved in extrapolating the ratio to all companies stems from the distribution of PtB ratios observed in the sample. For this reason, it is preferable use the median, which is more robust than the average, in the descriptive part. As an average ratio per stratum needs to be calculated for the extrapolation, it is necessary to use a more robust ratio than the PtB ratio. The market value of the enterprise/book value of the fixed assets is better than the PtB ratio used in Part A.

The scope is that of non-financial companies subject to the régime du bénéfice réel normal (standard tax regime based on actual profits), excluding listed companies, private limited liability companies (SARL) and natural persons, i.e. 210 000 enterprises in 1999 with a total equity of FF 4 700 billion [4].

The average PtB/equity ratio thus estimated is, after extrapolation, 1.56, i.e. less than half the PtB ratio for unlisted companies in the 1999 National Accounts. However, 1999 is a special year, in which the value of listed shares is exceptionnally high. The average reduction coefficient to be applied to the period 1994-1999 is approximately 25%.

The average market capitalisation/equity ratio should rely on the value of listed companies that are relevant to the non listed ones and take into account a liquidity premium.

Note: this part was initially compiled on the basis of a sample of listed companies input manually for the period 1994 - 1999. It was then elaborated using a database of listed companies and their stock market capitalisation. This database comprised only companies that were still listed in 2002,which introduces a selection bias for any longitudinal study, and gives the market capitalisation only from 1996, whereas the accounting data go back as far as 1992. Another source of bias lies in using the fact of belonging to an index(CAC40, SBF) to segment listed companies. It refers to the company’s situation in 2002 whereas the accounting data used relate to 1999. It was nevertheless used in so far as it was possible and the main conclusions seem robust at least for the period under consideration (1994 - 2001). This stems from the fact that the average stock market capitalisation/ equity ratio currently used in national accounts is in fact determined by the market capitalisation of the biggest companies (those in the CAC40) whereas that of smaller listed companies (those in the first or second market not included in the SBF250 index) is closer to that of unlisted companies, and that the average ratio constructed for these companies is much less volatile.

The multiplier coefficient of 1.56 - to be applied to the book equity of unlisted companies - proposed in part 1 would lead to a revision -which, if it were to be adopted, would raise the question of comparability with the accounts of European countries which, like France, currently apply to unlisted companies a Price to Book Ratio derived from listed companies. As these countries generally do not have tools equivalent to the INSEE survey on financial links which would allow unlisted shares to be valued directly, it would be useful to propose another ratio constructed from listed companies - from which a liquidity premium could possibly be deducted, as is already done in Germany - which would be better suited to unlisted companies. This study does not claim to offer a definitive solution to the problem but only to show why the ratio currently used is ill-adapted, and to propose another ratio which is surely not the optimal one but probably better.

The PtB ratio of companies which do not belong to an index is closer to that of unlisted companies…

In 2000, as in 1999, the average PtB ratio of listed non-financial companies (NFC) (respectively 2.89 and 3.47) was that of the 33 NFC in the CAC40 (3.15 and 3.92) and the 65 in the SBF120 (2.63 and 2.85) whereas the majority of NFC in the first and second market do not belong to either of these indices (nor to the SBF250 either) and had an average PtB ratio that was both lower and less volatile (1.38 and 1.47). These differences between companies are confirmed on the period 1994-2001.

The characteristics of listed companies in the first and second market which are not in the SBF indices - lower average PtB ratio with very small annual variations - are similar to the result obtained for unlisted non-financial companies. These are probably the listed companies that are the least different from unlisted companies.

but this proximity is the result of two differences operating in opposing directions

There is still a difference in terms of liquidity premium between unlisted companies and first and second-market companies as the diagram below shows. This difference is offset by the decrease in the PtB ratio stemming from the lower profitability with size. As first and second-market companies are on average bigger than unlisted companies, their average PtB ratio is affected negatively by this size effect.

PtB ratio in 1999 (y-axis) by size (equity) and type of company

Source: COFISEM (for stock market capitalisation), INSEE (SUSE, for equity - company accounts)

Estimating the liquidity premium directly- procedure

In financial theory, the value of an enterprise is the discounted sum of future flows of dividends, which can be taken, as a preliminary approximation within the theoretical framework of Modigliani and Miller where the distribution of dividends is neutral, to be the discounted present value of flows of profits. The PER (Price Earning Ratio), the ratio of market value to profits, is thus theoretically more satisfactory than the PtB ratio. But profits, besides their greater volatility than the book value of equity, are much more sensitive to the problem of consolidation: while in individual company accounts, the balance sheet of parent companies shows the value of financial assets, at least as at the time of their acquisition, profits show up only in the form of dividends, and the reinvested profits of subsidiaries are ignored. This point is illustrated by the diagram below.

Comparison between group consolidated accounts and parent company accounts

Source: INSEE (individual company accounts) and COFISEM (consolidated accounts). 484 financial companies, 1999 accounts.

As the INSEE has only individual company accounts for unlisted groups, up to now the PtB ratio has been preferred . But it is not possible to confine the estimate of a liquidity premium to a comparison of PtB ratios, for even in the absence of a liquidity premium, differences in financial profitability lead to a difference in the PtB ratio. Consolidated profits were therefore reconstructed from individual accounts. As the profits of the companies of a group cannot be summed (because of double counting of dividends), only non-distributed profits are imputed upstream, giving the following formula: [pic]

where :

➢ RN: net book result

➢ DIV: Dividends

➢ TxF: Rate of financial holding (computed by a specific algorithm from the financial links)

➢ C: consolidated

➢ T: head company (a consolidated net book result RNc was computed for all the companies with subsidiaries irrespective of whether they were the head company of a group)

➢ I = 1 to m: subsidiaries

This formula is applicable only to enterprises that do not have any foreign subsidiaries since the results of foreign subsidiaries are not known. On the other hand, the liquidity premium obtained can be applied to enterprises which are of comparable size to listed enterprises. The PER is calculated with a weighted of average of net book result (RNc) in the denominator, which gives more weight to recent results (if it were possible, the anticipated net book result for future periods should be used ) :

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Val is the market value of the enterprise. For unlisted companies, it is equivalent to the value estimated for 1999 from the INSEE survey of financial links. For listed companies, as the sample of first and second-market market companies obtained from the survey is insufficient, Val is the stock market capitalisation (there is no systematic bias between the two methods of valuation, cf. 1.2).

If we disregard the impact of differences in the profit growth rates - g - for listed and unlisted companies[5], the liquidity premium corresponds to the difference between the discount rates r for the two types of companies.

Estimating the liquidity premium directly - Results

The diagram below shows that in contrast with the net book result, the computed consolidated result is an unbiased estimator of the consolidated result published by listed companies.

Comparison between computed profits and published consolidated profits

( net result/share of group)

Source: INSEE and COFISEM. 134 listed companies that do not have any foreign subsidiaries

The liquidity premium appears clearly in the results of a multivariate analysis (not given here). The PER for first and second-market companies is 3 to 4 points higher than that of unlisted companies. This translates, for, a PER of the order of 16, into a discount of 25% (=4/16) for unlisted companies compared with first and second-market companies. Compared with listed index companies, the discount would be much bigger since the PER of the latter is 11 points higher than that of unlisted companies.

However, this is only an order of magnitude given the prior constructions that were necessary to obtain such a result. It would moreover be dangerous to apply this discount directly in terms of the PtB ratio since profitability enters into the equation when we move from the PtB ratio to the PER, and the smallest companies are the most profitable. We lack a point of comparison for unlisted companies with an equity of less than FF 50 million. In terms of equity, they account for only 20% of unlisted non-financial companies but their high value gives them a considerable impact on the average PtB ratio.

The following proposition can be put forward :

1) It is possible to estimate the value of unlisted companies with more than FF 50 million of equity from the PtB ratio for listed first and second-market companies by applying a discount of 25% (on the assumption that the profitability of first and second-market companies is of the same order as that of unlisted large companies).

2) For unlisted small companies (less than FF 50 million of equity, a threshold which can be converted into € 10 million), a premium can be added for their greater profitability compared with unlisted large companies. Extrapolating, this premium would be 33% on the value of unlisted large companies, which would amount to applying the PtB ratio for first and second-market companies to unlisted small companies.

3) Every year, a new average PtB ratio for first and second-market companies is available. In contrast, the premium and discount coefficients may be considered to be structural parameters that have to be revised every 5 years.

Annex

Diagram 2

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[1] As financial links also comprises minority holdings, it is preferable to speak in terms of ‘downstream company’ and ‘upstream company’ (that holds the stake) rather than of subsidiaries and parent companies.

[2] The rate is that relating to the specific holding and not the overall rate of control a company may have via a subsidiary. The latter may be higher if, in addition to the direct link, other subsidiaries of the parent company hold shares of the subsidiary in question (indirect links).

[3] COACQ=1 if, for an upstream company, the value of the total acquisitions of financial fixed assets - which are not limited to equity securities - is less than the sum of the acquisition values of year n - detected further to the previous step -, then one may have doubts about the year of acquisition. The acquisition probably took place before the link became apparent and the value of the enterprise is probably understated.

[4] Including enterprises that come under the régime du bénéfice réel simplifié would, in the field considered of non-financial companies excluding SARL and natural persons, add only FF300 million of equity.

[5] The strong external growth of groups renders the observed profit growth rate irrelevant. Moreover, it cannot be ruled out that an over-estimation of g contributed to the very high PER observed in 1999 for index companies.

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