Valuation of unquoted sharesNational Accounts : Market Value : V

Listed companies : VL = Market Capitalization

Unlisted companies : VUL : ? PtBFpF

VFV UL

L

L

ULUL .

1ˆ

This estimation cannot in general be subjected to empirical validation

LIFI (financial links survey)

1. a direct valuation of unlisted shares

2. an improvement of the indirect estimation

• Which listed companies can be compared to unlisted companies ?

• Which premium, p, to apply ?

F : own funds p : premium (liquidity and profitability) PtB : Price to Book

. VABIL: value of the stake recorded on the balance sheet (source LIFI)

. TxC: rate of control given by this particular link (source LIFI)

Validation of valuation by LIFI

TxC

VABILV

nn

Construction of the sample• Files of financial liaisons from 1994 to 1999

• Detection of the year of acquisition

• acquisition value market value elimination of the newly created companies

Estimation possible for 16,000 listed and unlisted companies in the field (non financial firms)For listed companies this valuation is an unbiased estimator of the capitalization

First results

Figure 1

PtB according to size (in MF)

0,5

1,0

1,5

2,0

0 - 1 1 - 10 10 - 100 100 - 1,000

1,000 - 10,000

10,001+

All

Unlisted FV

PtB

PtB : Price to Book F : own funds

• PtB is decreasing with size (profitability)

• PtB is higher for listed companies U – curve

Extension to all non-financial unlisted companies…

Cluster constructed on the basis of three criteria– Sum of fixed assets

– Share of capital assets

– Profitability

… leads to an average PtB of 1.56 in 1999

The PtB applied in national accounts ranks from 1.33 in 1995 to 3.04 in 1999, a year of high market capitalization

2 – Liquidity premiumWhich kind of listed companies ?

In 1999 (in € billions)

TYPE Number Equity capital

Result Market capitalisation

PtB PER Profitability %

CAC 40 32 226 20 884 3.92 43.4 9.0 SBF 120 60 50 6 141 2.85 22.4 12.7 SBF 250 96 27 2 71 2.62 31.5 8.3 P & S 300 24 2 35 1.47 17.9 8.2 Others 184 3 0 11 3.78 41.6 9.1 TOTAL 672 329 31 1,143 3.47 36.7 9.5

P&S : listed companies on the Primary and Secondary markets that do not figure in the SBF indices

1

1,5

2

2,5

3

3,5

4

1996 1997 1998 1999 2000 2001

Pri

ce T

o B

oo

k

CAC40

SBF120

SBF250

P & S

PtB of P&S listed companies :

• closer to that of the unlisted

• less volatility than other listed

P&S listed companies

P&S : listed companies on the Primary and Secondary markets that do not figure in the SBF indices

P&S companies have an average PtB close to that of unlisted companies but this is purely coincidental because of two opposite factors :• listed companies are bigger and profitability decreases with size• premium liquidity

0 1 2 3 4 5 6 7 8

10 to 20 MF 20 to 50 MF 50 to 100 MF

100 MF to 1 BF

> 1 BF

Unlisted P & S SBF250 SBF120 CAC40 Others

Companies with share of capital assets in total fixed assets <10%. PER’ = V/EBE REB=EBE/K

Own funds bracket

0,00

2,00

4,00

6,00

8,00

10,00

12,00

1 2 3 4 5 6 7 8 9 10

Asset brackets

a ra

tios

and

PE

R

00,1

0,20,3

0,40,50,6

0,70,8

0,91

Pro

fitab

ility A

PER'

REB

The Price Earning Ratio (PER)

)(11

Pr pfdV

PER Pr : Profit

d : discount rate

p : liquidity premium

96979899 Pr2*Pr3*Pr4*Pr*10

V

PER

Profit : Bottom line (Résultat net comptable) in consolidated accounts

Theorically : anticipated profits

Practically : weighted average of past profits

Computation of the profits

Pr : ProfitBL : Bottom line

i

n

iimm TxDIVBLBL *)(Pr1

This computed consolidated result is an unbiased estimator of the published consolidated result

134 listed companies with no foreign affiliate

Weighted Average Pr

0

5

10

15

20

<0 10 30 50 70 90 110

130

150

170

190

210

230

100*(Computed Profit/consolidated accounts)

0

4

8

12

16

<0 10 30 50 70 90 110

130

150

170

190

210

230

>25

0

100 * (Individual Accounts/Consolidated Accounts)

Own funds

Bottom Line

DIV : DividendsTx : Rate of financial control

From : INSEE & COFISEM, 484 non financial listed companies, year = 1999

Profits in the individual accounts of the parent company ignore the reinvested profits of the subsidiaries

Results

PER for unlisted companies is, controlled for other variables, 4 points below the PER for P&S

This leads, for a PER of 16, to a liquidity premium of about 25% (4/16 = 25%)