2.Market value of a voucher book  
Now I will present my subjective estimate of the market value of a voucher book. Apart from the above mentioned value set by the options of investment funds a number of other estimates of the value of the privatized property per one voucher book appeared in recent months. Almost all these estimates were calculated by dividing the total expected book value of the property privatized in the first wave of voucher privatization by the expected number of owners of voucher books. With the rising number of registered people the estimates of the property per one voucher book gradually declined from the original 130 thousand Kcs to mere 30 thousand Kcs. My approach is quite different. It is based on the estimate of the present, i.e. discounted value of future property which an average citizen will acquire for his or her voucher book. The book value of the privatized property does appear in my formula as well but it has a minor role compared to the other parameters. Despite this fact it is interesting that one of the resulting numbers, namely the "riskfree" value is not too far from the estimates based on the book value. The estimate of the market value of a voucher book must be logically based on the estimate of the expected present value of future property acquired by one owner in the process of privatization. The term "present value" means that the future value of the property must be discounted, i.e. decreased by the real interest. Thus e.g. at the 5 per cent interest rate 100 Kcs received one year from today has now the present value of only 100/1.05 = 95.24 Kcs. The reason is that 95.24 Kcs deposited today at the bank at 5 percent interest will in a year’s time increase its value to 100 Kcs. The term "expected value" is used here in two related meanings. First, expectation means here the necessity to anticipate uncertain future and, secondly, it means a mathematical expectation or a mean in the crosssectional sense. The voucher book provides its owner with the right to purchase shares of any enterprise, therefore its value must be equal to the value of an average portfolio of such shares.  
In calculating the expected present value of future property it is of a great importance to determine the correct discount factor. If we used in discounting a low interest rate which is normally paid on saving deposits or Treasury bills we would implicitly assume that the property to be distributed by privatization entails only minimum risk. That would be a mistake. Shares are very risky securities and in this case the risk is especially high because of the lack of reliable information for forecasting the future changes. Thus the hypothetical market value of the voucher book must be equal to the expected "riskfree" value reduced by a relatively high risk premium. The "riskfree" value of the property per one voucher book will be calculated bellow by discounting with the "low risk" interest rate. It does not represent any real market value of the voucher book and its sole purpose is to demonstrate the size of the risk premium. The estimate of the true market value of the voucher book will be calculated by discounting with the real interest rate increased by the annual rate of risk premium.  
I will divide my estimate into two parts: the first one will be the discounted expected flow of dividends in the period 19922001, the second will be the present value of property by the end of 2001. I assume that the full transformation to market economy will take almost ten years and in the course of this period the economic decline will gradually come to an end and then the economy will start to grow again. Therefore it can be expected that dividends will be very low at the beginning and that they will grow only very slowly. The dividend rate used in my calculations is further diminished because certain number of joint stock companies will very likely go bankrupt and thus the nominal value of the "voucher equity " will gradually decrease. For the sake of simplification I have, however, left the nominal value constant in the estimated formula. I also anticipate that by the end of 2001 Czechoslovakia will reach approximately two thirds of the present economic level of Western Europe. For my calculation I will use the following formulae:  
 
It is quite simple to estimate A and N. Today we already know quite reliably the number of registered voucher books is a little more than 8.5 million. We also know, that the Government has committed at least 260 mil. Kcs of property for the first wave of voucher privatization and that at present it tries to overfulfill this commitment. It is much harder to estimate B, i.e. the market value of the equity per one voucher book at the end of 2001. Because we know the number of registered voucher books we need to estimate the total value of equity which will by owned in 2001 by owners of these books. We shall estimate this value as a proportion of the total equity which we shall again estimate as a proportion of the total national net worth in 2001. To estimate national net worth we shall multiply the expected gross national product of 2001 by the capitaloutput ratio. To estimate the total GNP in the year 2001 we need two facts: gross national product per capita at 1992 dollar prices and the present exchange rate of the Cz. crown with regard to US dollar. In this case the purchasing power parity exchange rate is relevant. Thus we can write the estimate of B in the following manner
 
The meaning of formula (3) is as follows: xy is per capita GNP in the year 2001 but at 1992 prices in Kcs, xyN is total GNP of 2001 at 1992 prices in Kcs, xyNk is total national net worth of 2001, xyNke is the total value of all equity in 2001 and thus xyNkem is the estimated value of the equity owned by the participants of the first wave of voucher privatization. As none of the quantities occurring in the formulae (1), (2) and (3) is exactly known I will consider them random variables and with the exception of the dividend rate I will assume that they have normal distribution of probabilities. In this case I will formulate my own subjective distribution of probabilities by determining expected value (mean) and standard deviation. Because we know that 95 percent of normal distribution is concentrated in the interval of +/ two standard deviations from the mean it is the same as to determine the upper and lower limit of the interval within which the estimated quantity will lie with 95 per cent probability. In case of the dividend I shall simply determine subjectively the expected upper and lower limits taking into account that the mean is in the middle of this interval.  
PARAMETERS OF NORMALLY DISTRIBUTED QUANTITIES
 
As it has been stated above, today we have got the best information on quantities A (book value of equity) and D (number of registered voucher books) and therefore their probability distribution may be determined with a relatively small variance. The population size in 2001 N may also be relatively reliably forecasted from demographic statistics. For the estimates of other quantities we have got much less information and therefore their subjective probability distribution will have much greater variance. I have based the estimate of GNP per capita of 2001 on the following consideration: it is neither very likely that the Czechoslovak economy would not improve at all or even fall below the present level of approximately 5 thousand dollars per capital nor is it probable that it will reach the present West European level of approximately 15 thousand dollars per capita already in 2001. Therefore I can state with about 95 percent probability that in the year 2001 GNP per capita will range in the interval from 5 thousand to 15 thousand dollars. It follows that the expected value is 10 thousand and the standard deviations is 2.5 thousand dollars. It should be pointed out that this is entirely my subjective estimate. Some people may consider the level of 10 thousand dollars too optimistic for the year 2001, others may find it too pessimistic. I do not claim that this level will be actually achieved. I allow for a relatively wide margin of possible outcomes but consider extremes values as less probable than the values closer to the center. After all anybody disapproving of my subjective assumption may put down his own and repeat the whole calculation.  
One of presently controversial problems is the estimate of purchasing power parity exchangerate. Without any claim to accuracy my subjective estimate is that this rate ranges with 95 percent probability between 10 and 20 Kcs per dollar. Capitaloutput ratio and the proportion of equity in national net worth were taken approximately from the US data. From the national net worth one needs to subtract the value of residential housing and governmental facilities (administration, army, educational system, health service etc.) to get the value of the property of commercial enterprises out of which a little over one half is usually financed by loans and the rest by equity. My very approximate estimate is that the equity will in Czechoslovakia form about one third of national net worth. Parameter m is determined approximately from the fact that the book value of firms privatized by vouchers in the first wave amounts approximately to one quarter of the book value of the total capital of all state enterprises. Apart from that I took into account that the quality of enterprises privatized by vouchers was on average lower than of those privatized by direct sale, that a number of these enterprises would be most likely closed within few years after privatization and that some part of the capital in the year 2001 would be created from new savings and import of capital from abroad. Finally it remains to estimate the discount factors, i.e. the real interest rate r and the annual rate of the risk premium d. Taking the experience of the USA economy and Western Europe in account I have chosen with 95 percent probability the intervals between 2 and 6 percent for the interest rate and between 6.5 and 10.5 percent for the risk premium.  
In case of the average rate of dividend in 1992 I assumed that it would be uniformly distributed in the interval from 0 to 2 percent. I also assumed that in the following years both the upper and lower limit of the uniform distribution would increase by 0.5 percent per year and as a result of this the interval in the year 2001 would be from 4.5 to 6.5 percent. Because the analytical derivation of the probability distribution of quantities V and P is quite complex I have chosen the method of numerical simulations. From the random sample of the size 250 thousand I got the following results: EXPECTED PRESENT VALUE OF PROPERTY PER ONE VOUCHER BOOK
 
DISTRIBUTION OF PROBABILITIES OF THE PRESENT VALUE
 
The "risk free" expected present value of privatized property per one voucher book, i.e. the value before the deduction of the risk premium amounts according to my subjective estimate to 28.6 thousand Kcs, which is only slightly less than the expected book value per one voucher book. According to my subjective probability distribution the risk that this value would fall below 10 thousand or even 15 thousand Kcs is not too high. Because these were the most frequently issued guarantees by investment funds, it might seem that the danger of the "run on funds" is remote. This conclusion would be, however, true only if the privatized property was riskfree. The estimated risk premium makes up almost precisely one half of the "riskfree" value and, consequently, the estimated expected market value of one voucher book is only slightly over 14 thousand Kcs. Thus the amounts disbursed by the State to citizens through vouchers is not 28.6 but only 14 thousand Kcs. The probability that the market value would fall below 10 thousand Kcs is 8.44 percent which is still relatively small. The probability that it would fall below 15 thousand Kcs is, however, enormous.  
Those privatization funds which will cleverly invest during the iterations of the first wave of privatization may acquire property with the value exceeding guarantees issued by them. Funds such as the Harvard Fund which issued guarantees for 10 thousand Kcs only do not seem to be exposed to tremendous risk. However, the funds which have issued much higher guarantees may very easily find themselves in an extremely difficult situation. If these funds would want to keep their commitments they may be forced to sell some of the shares acquired by privatization. By that they may depress the market value of the average portfolio far below 15 thousand and maybe even bellow 10 thousand Kcs and thus unleash a general "run on funds". The collapse of financial markets is not a farfetched possibility. The government should be aware of it and should take measures to prevent the potential crash of privatization funds. 



