## **Guide**

Looking back on the history of stock valuation development, the evolution of valuation methods is full of ups and downs. When Internet companies emerged, traditional valuation methods failed. In the face of new things, investors are inevitably stunned. The same problems have been encountered today.

## **Summary**

**The PTO investors urgently need a practical valuation method to assist investment judgment.** Although BTC has been born for only ten years, the pursuit of the valuation method is more urgent than ever. The general practitioners urgently need a practical valuation method to assist investment judgment and discover the growth potential and intrinsic value of the certificate. .

**The characteristics of the certificate valuation:** **new things, existing methods are difficult to apply directly.** In the face of the new thing of the certificate, the existing valuation methods are difficult to apply directly, or the applicability is too limited. **Complexity, the certificate has multiple asset attributes.** One of the main difficulties in the valuation of the certificate is the judgment of the asset attributes. The certificate has multiple attributes, and many valuation methods can only be applied to partial certificates. **In the early stages of development, there are still a lot of problems to be solved.** There are a large number of problems to be solved in the existing valuation methods, which need to be continuously improved in practice.

- 14 banks, 5 kinds of certificates: Fnality creates a missing link in the inter-bank blockchain system
- Viewpoint | Blockchain don't pass the pass?
- The blockchain industry is in trouble, where is the road to break?
- How to measure the value of Token from the cost?
- Getting started with blockchain | The phone or computer with the wallet installed is broken, is the currency gone?
- A brief history of the pass: a journey from the past to the future

**Classification of the method of valuation of the pass:** Like the stock valuation, the existing method of valuation can be divided into two categories: absolute valuation method and relative valuation method. According to the source of the method borrowed, it can be divided into reference stock valuation. According to the option type, it can be divided into securities type certificate valuation method, practical type certificate valuation method and payment type certificate valuation method.

**There are a large number of outstanding problems in the existing VAT valuation methods,** including: interpretative questions, applicability problems, lack of empirical support and valuation information basis. **The problem of the knowledge of the pass and the valuation method itself have led to the lack of valuation methods that are widely accepted by investors.** The existing valuation methods of the common certificates are proposed from different angles, which provide different ideas for the valuation of the certificates. However, at present, the asset attributes of the certificates are still unclear. On the other hand, the various valuation methods of the certificates still need to be Continuous improvement, so there is no valuation method widely recognized by investors.

The development of valuation methods is the process of constantly searching for historical references and evolving. Up to now, the valuation of the certificate has produced a series of methods such as cost pricing, option pricing, exchange equation, value reserve, and relative valuation. Although there are still many problems to be solved, the birth of the certificate is still short. The exploration of valuation is still in the early stage. **With the continuous improvement of the basic knowledge of the certificate and the continuous improvement of the valuation method, it is inevitable to find a reasonable method of valuation in the future.**

Risk warning: ETF progress is less than expected, quantum computer technology is advancing by leaps and bounds

## **table of Contents**

**1 The market urgently needs a reasonable method of valuation**

1.1 Crowdsale blowout and "bubble" burst

1.2 The battle for the value of the certificate

1.3 Urgent need for a reasonable valuation method

1.4 What is the difference between the valuation of the certificate?

**2 Existing method of valuation**

2.1 Cost Pricing Method

2.2 Option Pricing Method

2.3 Exchange equation method

2.3.1 Encrypted J Curve

2.3.2 Exchange equation method

2.4 Value reserve method

2.5 Relative valuation method

2.5.1 NVT ratio

2.5.2 PMR ratio

2.5.3 NVM ratio

2.5.4 NVTG ratio

2.6 Other valuation methods

**3 Summary and outlook**

## **text**

1 The **market urgently needs a reasonable method of valuation**

**1.1 Crowdsale blowout and "bubble" burst**

**2017 Crowdsale spurt growth.** In 2017, the global Crowdsale saw a spurt of growth, far exceeding the investment of VCs and enterprises. According to statistics, the number of Crowdsale in the world and the funds raised through Crowdsale in 2017 were 875 and 7.4 billion respectively, an increase of 2917% and 3160% respectively compared with 2016.

**Fraud and manipulation of the market.** In the process of barbaric growth in the market, due to lack of supervision, fraudulent manipulation is rampant. One hundred years ago, the “blue sky and hot air” securities turned into “air pass”. According to the Statis Group, 78% of the 2017 Crowdsale project is suspected of fraud, and only 15% are still trading.

Crowdsale "bubble" burst. The slow landing of many projects and the rampant fraudulent manipulation caused the market to fall short. The superimposed funds were diverted from the main circulation certificate, negative news shocks and market sentiment fluctuations. The market fell and the “bubble” burst.

**1.2 The battle for the value of the certificate**

Historical lessons, the complete logic of basic analytical methods in stock investment, and the successful practice of a number of value investors have long made the concept of price investment and the concepts of “intrinsic value” and “security margin” deeply rooted in the hearts of the people. Therefore, since the birth of BTC, there have been such questions lingering in people's minds: Is the certificate worthwhile? If so, what is its value? How to evaluate it?

The debate over the value of the pass has never stopped. Passport investors are often labeled as speculative. When Buffett first talked about BTC in 2014, he called it "Stay away from it. It's amirage, basically.", and the bursting of the bubble further aggravated people's doubts. .

**If the certificate has no value, the discussion on valuation has lost its necessity.** For the question of the value of the certificate, it is necessary to make the following points:

**First of all, the pass is not equal to** **the fraudulent manipulation** **of Crowdsale** **.** In the fraudulent manipulation phenomenon of Crowdsale, the certificate is only a tool. Just like the "blue sky and hot air" securities existed many years ago, "air pass" has no more special features.

**Second, the existence of a bubble does not mean that there is no value.** Bubbles are widespread in the economy. Any asset may have bubbles, such as the South China Sea bubble, the Tulip Bubble, the Internet bubble, and the real estate bubble. But the value of stocks or real estate cannot be denied because of the existence of bubbles. The bubble is only the price when the price deviates from the value. Economic phenomenon.

**Once again, more and more applications and innovations have emerged.** The first important application of the certificate is BTC – a secure, verifiable and non-tamperable and efficient electronic payment method that helps reduce costs such as reconciliation and dispute resolution. Crowdsale and STO (securities-based issuance) can be used as a start-up. Corporate financing channels, blindly suspected and denied, stem from fear of the unknown.

**Finally, the certificate was incorporated into regulation and gained more and more recognition.** The certificate began to be more linked to legitimate applications. According to the DEA (United States Drug Enforcement Administration) data, only 10% of the current BTC transaction volume is related to illegal activities, and 90% is used for legal transactions. Governments of various countries (regions) have incorporated the certificate into the regulation and defined the certificate as a crypto asset. The certificate embraced the regulation also has a feasible solution like the STO/ETF (transactional open index fund). Mainstream institutions are increasingly recognizing that CME (Chicago Mercantile Exchange, Chicago Mercantile Exchange) has launched BTC futures.

**1.3 Urgent need for a reasonable valuation method**

Although BTC has been born for only ten years, the pursuit of the valuation method is more urgent than ever. The general practitioners urgently need a practical valuation method to assist investment judgment and discover the growth potential and intrinsic value of the certificate. .

**1.4 What is the difference between the valuation of the certificate?**

**New things, existing methods are difficult to apply directly.** In the face of the new thing of the certificate, the existing valuation methods have failed without exception. The valuation problems experienced by Internet companies in the past were once again staged in the general market. The development of valuation methods is a process of constantly looking for references from history. Just as stocks were first born, people found a reference to bonds and used bond valuation methods to value stocks. Now, people try to estimate them again. The value method is applied to the certificate, but it turns out that the existing valuation method is difficult to apply directly, or the applicability is too limited.

**Complexity, the certificate has multiple asset attributes.** One of the main difficulties in the valuation of the certificate is the judgment of asset attributes. The certificate has multiple attributes such as currency attributes, equity attributes and property rights attributes, but there are significant differences compared with each type of assets, which leads to many existing valuation methods can only be applied to partial certificates.

Note: Classification of the SEC and FINMA. The SEC divides the certificate into Security tokens, Utility tokens and Cryptocurrencies, and the classification and SEC of the FINMA (Swiss Financial Market Supervisory Authority). Similarly, the pass is divided into Asset tokens, Utility tokens, and Payment tokens.

**In the early stages of development, there are still a lot of problems to be solved.** Investors have not yet reached a consensus on the valuation of the certificate. Although a variety of valuation methods have been proposed, there are a large number of problems to be solved in the existing valuation methods, which need to be continuously improved in practice.

2 **Existing method of valuation**

Like the stock valuation, the existing valuation method can be divided into two categories: absolute valuation method and relative valuation method. The absolute valuation method includes exchange equation method, cost pricing method, option pricing method and value. The reserve method, etc., the relative valuation method multiples include NVT ratio, PMR ratio, NVM ratio and NVTG ratio; according to the source of the method borrowed, it can be divided into reference stock valuation, borrowing option pricing and others; Securities-based certificate valuation method, practical-type certificate valuation method and payment-based certificate valuation method.

**2.1 Cost Pricing Method**

The cost pricing method is proposed by Adam Hayes for BTC. The theoretical basis is that the marginal cost of BTC mining should be equal to the marginal benefit. The rational miner will only mine if it is profitable. If the marginal cost of mining exceeds the marginal income, the miner The resources will be redeployed to remove power from the network.

The basic idea of the cost pricing method is to divide the mining cost per day (Eday) of the miner by the number of BTCs (BTC/day*) digging every day to obtain the mining cost P* of the unit BTC:

P*=Eday/(BTC/day*)

Eday=(ρ/1000)($/kWh×WperGH/s×hrday)

Where ρ is the power of the miners, $/kWh is the unit price of electricity, WperGH/s is the energy efficiency of the hardware, and hrsday is the number of hours of the day.

Where β is the block reward (currently 12.5), δ is the block difficulty, and sechr is the number of seconds in an hour.

The price price calculated based on the mining cost and the number of BTCs can be used to set the floor price for BTC. Hayes used this method to empirically test BTC and found that 92% of BTC price changes can be explained by the cost pricing model and passed the Granger test.

Despite the empirical research support, the model still has a series of problems to be solved. First, the model does not take into account the problem of centralization of computing power. Hayes' model is based on the completely competitive market hypothesis, but the current BTC mining market is more similar to the oligopoly market. According to BTC.com data, the top five mining pools account for The ratio is about 60% (December 12, 2018). Second, the model ignores some factors that may have a significant impact on BTC prices. In terms of revenue, the model only considers block rewards, not considering transaction costs, and transaction costs are not negligible compared to block rewards. In terms of cost, the model only considers the cost of mining electricity. Finally, this method has yet to be validated for the effectiveness of the pass of the PoW consensus mechanism other than BTC and the adoption of a common mechanism other than the PoW consensus.

**2.2 Option Pricing Method**

The option pricing method treats the pass as a call option for the actual utility value that the crypto asset may provide, and then uses the option pricing formula to calculate the intrinsic value of the pass.

The traditional Black-Scholes equation is as follows:

Where V is the option price, V is a function of the stock price S and time t, r is the risk-free rate, and σ is the volatility of the stock price. In the valuation of the certificate, V is defined as the price of the encrypted asset, S is the actual utility value of the encrypted asset in the certificate economy, r is the risk-free rate, and σ is the volatility of S.

The option pricing method provides a new idea for the valuation of the certificate. The problem is that S, σ, K and T are unknown, and there is no clear description about the influencing factors of S and how S affects V.

**2.3 Exchange equation method**

**2.3.1 Encrypted J Curve**

The J curve originates from private equity investment, and the encrypted J curve is proposed by Chris Burniske. According to the model, the pass price consists of two parts:

(1) CUV (Current Utility Value, current utility value);

(2) DEUV (Discounted Expected Utility Value).

Their contribution to the price of the certificate will change over time.

According to the J-curve model, the initial CUV of the project has not yet been formed. The price of the certificate is mainly dominated by DEUV. The early investors are optimistic about the prospect of the project, which will lead to the growth of DEUV and the first peak; but as the investor's enthusiasm declines or the project encounters difficulties DEUV will be compressed and the price will drop; as the project matures, CUV and DEUV will grow in parallel, and the evolution will form a J curve.

The above process will occur cyclically, and the J curve will be composed of multiple micro J curves, and the peak appearing in front is insignificant compared to the later stage.

**2.3.2 Exchange equation method**

**(1** **) INET** **model**

The earliest use of the exchange equation for the pass valuation is Chris Burniske, which is based on the J curve and is used to calculate the current utility of the CIS economy and the expected future utility.

The exchange equation is derived from monetary economics and was proposed by Irving Fisher:

M*V=P*Q

Among them, M is the money supply, V is the money circulation speed, P is the price level, Q is the actual goods labor output, and P*Q is the GDP (Gross Domestic Product).

In the valuation of the certificate, these variables are given corresponding meanings, M is the value of the legal currency, V is the circulation speed of the certificate, P is not the price of the certificate, but the price of the encrypted asset in the certificate economy, Q is The number of encrypted assets. The different models of the exchange equation method have slightly different definitions of the above variables, but they are basically the same.

According to the exchange equation, M = PQ / V can be obtained naturally, and if P, Q and V can be obtained, M can be obtained naturally.

Burniske has created a certificate called INET that can share bandwidth through a decentralized virtual private network (VPN). P is determined by the market. In order to obtain Q, it is necessary to estimate the market size and the penetration rate of INET. Finally, it is necessary to estimate the circulation speed V.

Burniske estimates V's approach to split the 2016 BTC's integrated circulation rate into "strict investment" circulation speed V1 and "transaction medium" circulation speed V2, where "strict investment" refers to buying or holding BTC and in this year There is no sale, so the corresponding V1 is 0. "Transaction medium" means that BTC has been sent to other addresses in one year.

BTC integrated circulation speed = "strict investment" BTC% × V1 + "transaction medium" BTC% × V2 = "transaction medium" BTC quantity % × V2

According to Coinbase data, 46% of Coinbase users in 2016 used BTC as a “transaction medium”, from which V2 was calculated to be 14. Since the INET economy has commodities, its pass rate should be faster than BTC, which is only a currency, so it is assumed to be 20. At this point, the current utility value can be calculated.

According to the J-curve model, the current price consists of the current utility value and the discounted expected utility value. The next step is to calculate the expected utility value and discount it, thus involving the estimation of the expected utility value and the choice of the discount rate.

This method has a series of problems to be solved, such as the determination of the circulation speed. On the one hand, the circulation speed will change with time, on the other hand, it is worth discussing the circulation speed as completely unrelated to PQ. In addition, the model does not consider transaction costs and payment methods, and does not distinguish between currency demand and commodity demand.

**(2** **) VOLT** **model**

The model was proposed by Alex Evans and improved on the basis of the INET model, which uses the Baumol-Tolbin model to separate funding needs from commodity needs.

Evans has created a certificate called VOLT that allows it to buy electricity at prices below the retail price.

The relevant variables are defined as follows: Assume that the user consumes evenly throughout the year, Y is the annual VOLT cost of the user plan, R is the expected return of the value storage asset, C is the transaction cost of transferring the asset from the value storage asset to the VOLT, and N is the VOLT user. The number of transfers completed each year.

Therefore, the user pays the transaction cost of C*N every year, and the average VOLT balance held each year is Y/2N. The return that the user holds VOLT every year is R*Y/2N. Therefore, the user chooses N, depending on Y. R and C in order to minimize their total cost function: R*Y/2N + C*N. According to this, when the total cost is the smallest

Re-substituting the cost-minarized N value into the average currency balance formula (Y/2N) yields the VOLT demand function:

Also in this model, the correlation coefficient between speed and PQ is no longer zero. On the basis of the above improvements, the value of the VOLT certificate can be estimated in a manner similar to the INET model.

**2.4 Value reserve method**

The value reserve method starts from the certificate as a value reserve. The idea is to estimate the market share of various types of reserve assets that can be occupied by the certificate, and then estimate the price of the certificate, which is very similar to the exchange equation method. For example, according to Howmuch.net, the total value of global gold in 2018 is about 7.8 trillion US dollars, and the upper limit of BTC is 21 million. If BTC can occupy 10% of the gold market, the valuation of BTC is about 37,000 US dollars.

Of course, the above example is too simplistic, because only the gold market is considered, and it can be further extended to other markets. Since the number of BTCs is ultimately constant, considering that more markets will further increase the reserve value of BTC.

This method is too simple, has many problems, and has only limited reference value. First of all, it is difficult to obtain the market size, and it is easy to be influenced by subjective judgments. It can be arbitrarily large. Secondly, it is difficult to judge the value change due to lack of value drivers.

**2.5 Relative valuation method**

**2.5.1 NVT ratio**

Willy Woo proposed the MTV Ratio (Market Cap to Transaction Value) in February 2017. In May 2017, Chris Burniske proposed a similar NVT Ratio (Network Value to Transactions Ratio):

NVT=28MA(DailyNV/Daily TV)

28MA refers to the 28-day moving average (14 days forward and 14 days back) to smooth the noise. TV (Transaction Volume) refers to the number of transactions on the chain, excluding the number of exchange transactions.

The basic idea of this method is that the transaction value on the BTC chain is highly correlated with the network value (as shown in the figure below), so the ratio should be in a relatively stable interval at most times, and the higher NVT ratio represents the network value higher than the flow. The actual transaction value of the network indicates that the market is optimistic about the future potential of the certificate.

The NVT ratio helps to determine if there is a bubble. When the NVT ratio is outside the normal area, it indicates that the trading activity cannot continue to maintain the network value, and price correction may occur in the future.

Compared with the network value, the NVT ratio trend shows obvious hysteresis, as shown in the green area above, so the indicator is not predictive, and its descriptiveness is also poor, as shown in the orange area above. The NVT ratio trend is opposite to the network value trend. In addition, whether this method can be applied to other passes except BTC remains to be verified, and most of the short-lived certificates do not have enough data for NVT Ratio analysis.

Based on the original NVT ratio, Dmitry Kalichki made improvements to propose a new NVT calculation method NVTnew (also known as NVT Signal, NVT signal).

The original NVT ratio uses a 28-day moving average (14 days forward and 14 days back), but there may be some problems with this smoothing method, such as 28 days may not be enough, relying on future data to develop predictive indicators There may be problems, and whether you want to smooth the overall ratio or just need to smooth the denominator.

After different attempts, Dmitry Kalichki's empirical conclusion is that the daily network value divided by the 90-day moving average of the trading volume is the optimal solution. The NVT signal is defined as follows:

NVT Signal=NV/90MA(Daily TV)

Using the NVT signal, it is also possible to judge the overbought and oversold area, with 150 or more being the overbought area and 45 or less being the oversold area.

Further by adding a trend line, the NVT signal can be used to determine the bottom position. For example, when the market is in the top area, by adding a trend line, once the price effectively falls below the trend line, the future probability will continue to decline, and a similar method can be used to determine the bottom position.

The NVT ratio provides a good idea for the valuation of the certificate, but its shortcomings are also obvious. First, NVT only considers the chain transaction, but for many passes, the exchange transaction actually accounts for a larger proportion of the transaction volume; secondly, the accuracy of the daily transaction volume data is difficult to guarantee, different transaction volume The calculation method will obviously lead to different results; in the end, more trading volume may not be sufficient to prove the value of the certificate is higher. In the case of French currency, the trading volume of the US dollar is much higher than that of the Swiss franc, but the value of the Swiss franc is still higher than Dollar.

**2.5.2 PMR ratio**

The PMR Ratio (Priceto Metcalfe Ratio) is proposed by Clearblocks, which is based on Metcalfe's Law. Metcalfe's law was proposed by George Gilder in 1993. The content of a network is proportional to the square of the number of users connected to the network (the only connection between nodes in a network of n nodes is n(n-1)/ 2):

NV (Network Value)=C*n2

There are many variations of the original Metcalfe's law, such as:

Generalized Metcalfe's law: NV (generalized) = C * 1.5

Zipf's Law: NV(Zipf)=C*n*logn, also known as Odlyzko's Law

Sarnoff's Law: NV(Sarnoff)=C*n

Different PMR ratios can be obtained by dividing the network value of the pass or the pass price by a different Metcalf predictor, such as the PMR given by Clearblocks according to the generalized Metcalf law:

PMRClearblocks=ln(NV/30MAn1.5)

Where n is the DAA (Dailyactive address), and the PMR ratio obtained using other Metcalf predictions is similar in form. PMR accurately predicted three corrections of BTC price. From the results, when the PMR exceeded 1, the BTC price was revised. When the PMR was less than -1.25, the BTC price rebounded, and the ETH test obtained similar results.

Although PMR has certain advantages over NVT, it is not without limitations. It also does not consider chain trading. It is also difficult to objectively choose among various ratios based on different Metcalf predictions. The NVM ratio is positive. It is raised against this issue.

**2.5.3 NVM ratio**

The NVM ratio (Network Value to Metcalfe Ratio) is proposed by Dmitry Kalichki. Since the ratios based on different Metcalf predictions may overestimate or underestimate the network value, different ratios are used as the network. The upper and lower limits of the value can be obtained from the operating range of the actual network value, and the mean of the upper and lower limits is used as the valuation.

Upper Bound=a1+b1*30MAln(n2)

Lower Bound=a2+b2*30MAln(n*lnn)

The definition of NVM is as follows:

NVM=ln(NVactual)-ln(NVmetcalfe)=ln(NVactual/NVmetcalfe)

Further standardize NVM to get NVMnorm:

NVMnorm=NVM/(Upper Boun-Lower Bound)/2

When NVMnorm is close to -1, the network value is close to the lower limit, and 1 means that the upper limit has been reached.

**2.5.4 NVTG ratio**

The above ratios tend to yield contradictory results in the judgment of overvaluation or underestimation of the pass. NVT does not consider the added value that new users bring to the network, while NVM only considers the active address and does not consider the user actually on the network. The impact of spending. The NVTG ratio (Network Value / Transaction Value to Growth Ratio) draws on the PEG ratio (Price/Earnings to Growth Ratio) based on the NVT ratio, using the original Metcalf prediction value. The NVTG ratio is as follows:

NVTG=NV/90EMA(TV)/90EMA(2N)

**2.6 Other valuation methods**

In addition to the above methods, there are other attempts to apply the traditional valuation method to the pass, such as the DCF model (Discounted Cash Flow Model), which will still apply to the securities pass.

3 **Summary and outlook**

There are a large number of problems to be solved in the existing VAT valuation method. At present, the exploration of the valuation method of the certificate is still in the early stage, and there is no mature and systematic method of valuation. The problems of the existing valuation methods mainly include the following aspects:

Explanatory questions. Part of the valuation method is simply to apply the valuation method of other assets, and the ability to interpret the valuation of the certificate is limited. For example, the value reserve method is too simplistic, the valuation process involves a large number of assumptions and is highly susceptible to subjective judgments, so the conclusions drawn from this method have only limited reference value.

**Applicability issues.** Existing valuation methods are often proposed for one or a type of certificate, and whether it can be applied to other certificates is yet to be tested. For example, the cost pricing method is proposed for the BTC adopting the PoW consensus, but it is still to be verified whether other certificates that also adopt the PoW consensus and the pass that adopts other consensus mechanisms can be applied.

**Lack of empirical support.** Some of the existing valuation methods are still at the theoretical level, lacking empirical support. Whether it can be applied to the valuation of the certificate still needs further testing. The basic problem of valuation information is one of the main reasons for this phenomenon.

**Basis of valuation information.** Various valuation methods have their own information base. The current certification industry lacks supervision and there is no unified information disclosure specification. Therefore, the reliability of many data is difficult to guarantee or even difficult to obtain the data required for valuation, such as the transaction volume in the NVT ratio. The accuracy of the data and the determination of the circulation speed of the exchange equation method all have a significant impact on the valuation method.

**The problem of the knowledge of the pass and the valuation method itself have led to the lack of valuation methods that are widely accepted by investors.** The existing valuation methods of the common certificates are proposed from different angles, which provide different ideas for the valuation of the certificates. However, at present, the asset attributes of the certificates are still unclear. On the other hand, the various valuation methods of the certificates still need to be Continuous improvement, so there is no valuation method widely recognized by investors.

The development of valuation methods is the process of constantly searching for historical references and evolving. Up to now, the valuation of the certificate has produced a series of methods such as cost pricing, option pricing, exchange equation, value reserve, and relative valuation. Although there are still many problems to be solved, the birth of the certificate is still short. The exploration of valuation is still in the early stage. **With the continuous improvement of the basic knowledge of the certificate and the continuous improvement of the valuation method, it is inevitable to find a reasonable method of valuation in the future.**

**Note:**

For some reasons, some of the nouns in this article are not very accurate, such as: pass, digital pass, digital currency, currency, token, Crowdsale, etc. If you have any questions, you can call us to discuss.

General Information Institute × FENBUSHI DIGITAL

Text: Song Shuangjie, CFA; Tian Zhiyuan

Special Adviser: Shen Bo; Rin

**This article is original for the General Research Institute.** **Unauthorized reproduction is prohibited.**