Whither cask flow? Whence value? Chapter II

Abstract

Why would anyone pay a price in excess of 60 times the sales per share for a corporate stock? If there were earnings at a net margin of 10%, this would equate to a price earnings ratio of 600: but there are no earnings! What is being valued here?

The answer, as we will see, is a growth option. When growth options are present in an investment, traditional models of valuation, such as the ple model, are passed up in favor of others. These more accurately measure the value of a growth option in economic environment characterized by a high degree of uncertainty. While uncertainty, represented by volatility in future outcomes, leads to lower prices in the traditional models, it leads to higher prices in others, such as option valuation models. Option models explain more of the behavior observed in markets where the future is less certain yet asset prices are high. This article will review two types of valuation models and show how each can be used in a dynamic economic environment. It will close by discussing why it is important for credit managers to have an understanding of these different approaches to valuation.

Uncertainty and Intangibles

In the first article in this series, we reviewed a traditional discounted cash flow (DCF) model of valuation. We then looked at what can be done to account for the impact of changes in capital structure and the cost of capital on the valuation result. We found that it is important to carefully account for these changes in order to accurately measure value. Even so, we assumed that the net cash flows and the costs of capital, were reasonably predictable. In an environment of high yet uncertain growth opportunities, this will not be the case. Rather, we know that there will be tremendous cash flows to earn, but we are unsure of the exact structure of the business model and final outcome. This is particularly true when it comes to firms in the "tech" and ".com" markets, yet it also extends to firms operating with a heavier concentration of intangible assets.

Intangible assets pose a challenge to valuation for two reasons. From a book value perspective, the difficulty is due to the lack of a transaction such as that which accompanies the purchase of a tangible asset. Pricing an intangible asset is further complicated by the fact that it is difficult to measure its capacity, and therefore, the cash flows it will generate. A striking example of this is the SABRE reservation system owned by AMR Corporation. Unlike an aircraft, that can, fly only one route at a time with a limited number of people on board, the SABRE system can be used by a virtually unlimited number of people at the same time. Hence, whereas the annual revenue producing capacity of a jet aircraft is finite and easy to estimate, the cash flow generated by SABRE is much more difficult to identify. The value of this cash flow would certainly not be reflected in the historical cost to develop the system itself.1

AMR eventually valued the SABRE system by creating a transaction in which 18% of the shares in a SABRE subsidiary were sold on the open market. Evidence of the importance of this intangible is found in the fact that AMR's ownership share in SABRE comprises almost 50% of the value of AMR itself. Other companies have created similar transactions, such as AT&T issuing a "tracking stock" indexed to its wireless business.

The main reason for the actions of firms like AMR and AT&T is that the traditional valuation models no longer work when companies make substantial investments in assets that represent substantial growth opportunities. This problem is compounded when the extent of the growth opportunity is uncertain, but it is known that there will be substantial growth in the market for the product or service. In the case of SABRE, growth is limited only to the number of people wanting to access the system. In the case of AT&T, it is well understood that wireless will expand tremendously in the future, it only remains to be seen as to whose product and business model will be most successful in that market.

In cases such as these, the presence of volatility in uncertain outcomes actually increases the value of an investment. Value is further enhanced when the investment itself can be implemented in stages. This is the case where substantial amounts of research and development (R&D) are involved. R&D can be viewed as an option on a future investment project. A relatively limited amount of money is invested in R&D at the front end of a project. At the end of each stage of the R&D project, a decision is made as to whether to proceed further with the project, consider other applications, or abandon the idea altogether. Proceeding to the next stage usually involves the expenditure of additional funds, which can be viewed as the price to exercise the option to move ahead. The presence of volatility as well as the "option" structure of many investments has led to the broadened use of option pricing models in the valuation of real and financial assets.

Before getting to the use of option and other models, however, we will establish some guidelines for choosing a valuation technique.

Objectives and Guidelines for Choosing Valuation Models

When choosing a model to apply in valuing an asset, whether it be as small as the purchase of a piece of equipment or as large as the purchase of an entire subsidiary, it is important to consider several important factors. First, is to identify the source of value generation. The source may be an assembly line type of production facility or it may be an R&D project. If you are valuing an entire corporate entity, it is important to identify exactly what are the critical value generators within that entity. Is its strength in the area of scale economies of production? Is its strength in the area of retailing? Where does the retailing take place, a physical store location or on the internet? Are the company's assets primarily tangible or intangible?

Once the principle source (or sources) of value generation are identified, then it becomes important to match your choice of a valuation model to the environmental conditions that best represent that source. For example, if value generation comes in the form of a stable and fairly predictable cash flow resulting from production and sales in a predictable market, a discounted cash flow model of valuation may be appropriate. If, on the other hand, the source of value is a growth option that may be exercised following the results of an R&D project, an option model is more appropriate for arriving at an investment value.

When calculating the actual value, it is then important to link your analysis to actual market valuation activity as much as possible. For example, suppose you are valuing a professional services firm that relies on intangible assets and human capital to generate its revenues and profits. A preferable model in this environment is most likely a multiplier model, where valuation is based upon comparing your firm to a number of firms for which valuation transactions have actually taken place in the market. As we will see, the comparison model has its roots in traditional valuation theory, but its dependence on actual market trading data allows you to reduce your reliance on estimates, which is the final factor to be considered in developing a model of valuation. While it is clear that in any valuation situation estimates must be made, the fewer you make the better off you will be, particularly when there is good market trading activity available for comparison purposes.

Comparison Multiplier Models

Comparison multiplier models begin with traditional theory that assumes value to be generated by a string of discounted cash flows, as follows:

Value = Sigma^sub i^ (NCF^sub i^) / (I + k)^sup i^ , [1]

where NCF^sub i^ is the net cash flow for period i, k is a risk-adjusted cost of capital, and Sigma is the summation notation. When valuing a going concern, it is assumed that the net cash

flow will be perpetual. In the case of a perpetual cash flow that grows at a constant rate, call it g, the equation reduces to the following:

Value = NCF^sub 1^ / (k - g), [2]

where NCF^sub 1^ is the net cash flow for the first year in the perpetual string, k and g are the discount and growth rates respectively. This type of model is also referred to as a capitalization model, where (k - g) is a capitalization rate.2

Virtually any economic measure of performance can be capitalized to determine value. For example, the most popular of these types of capitalization models is the price/earnings model. This model begins with the fact that the source of value to equity investors is corporate earnings, which means that the model in equation [2] can be reexpressed as:

Value = alpha(eps)/ (k - g), [3a]

where eps are the earnings per share and alpha is a multiplier.3 If we assume then that market prices accurately reflect intrinsic value, then we have,

Price = alpha(eps)/ (k - g). [3b]

If we divide both sides of equation [3b] by earnings per share, we end up with the earnings capitalization factor, or p/e ratio:

price/earnings = alpha / (k -g) [4]

The p/e model is a popular model for pricing equity investments, and is frequently used to estimate the value of IPO's where there is no historical valuation data available for the issuing corporation, but it is possible to make comparisons to other publicly traded companies.

The entire basis for using such comparison multiplier or capitalization models is that there are relationships between value and different measures of economic performance that are going to be similar for companies of similar structure and behavior. When applying such a model, it is important to establish a benchmark for comparison, and then make adjustments to equate the benchmark to the characteristics of the target company being valued. Once adjustments are made, it is then possible to identify a comparison multiplier to apply to the economic performance measure of the target firm. We'll take a look at an example of this further below. Before that, however, it is important to point out that comparison models are not limited to the use of earnings as a measure of economic performance. In many cases other economic performance measures may be used and even be preferred to earnings.

To illustrate the breadth of multipliers available, we will again take a look at the p/e model, but in an expanded form, whereby earnings are broken out into several components, as follows:

Earnings = Sales * pi^sub gross^ * pi^sub operating^ * pi^sub net^ [5]

Equation [5] shows how earnings are actually a product of sales and several levels of profit factors. The factors in equation [5], shown as pi, represent gross, operating, and net profit margins.4 When we substitute equation [5] back into the p/e capitalization model (equation [3b], we get the following result:

Price = alpha( Sales * pi^sub gross^ * pi^sub operating^ * pi^sub net^)/ (k - g) [6]

Equation [61 shows that value can be a related to a number of different factors. For example, in cases of valuing personal and/or professional services firms, price/sales ratios are commonly used. There are two primary reasons for this. First, many of these firms are privately held and operated by owners who desire to minimize taxes by rolling as many expenses back through the company as possible. In these cases, earnings are not necessarily the best measure of economic performance. Second, there may be economies to scale to be generated by the merger of two of these types of firm, and the net profit margin may be sensitive to changes in cost structure that such a merger would bring about. In valuing such firms, therefore, measures of performance other than earnings are employed. A price-to-sales ratio, for example, captures the following information:

Price/Sales = alpha( pi^sub gross^ * pi^sub operating^ * pi^sub net^)/ (k - g). [7]

When applying comparison multiplier models, the following steps should be followed:

1.Identify and describe the source of value.

2. Determine what methods are most commonly used to value these assets in a market environment (i.e., which multipliers are commonly used).

3.Identify a set of assets (e.g., companies) for which market transactions exist to serve as a benchmark.

4. Develop a proxy multiplier for the target by making adjustments to the multiplier observed for the benchmark sample.

5. Measure the economic performance variable for the target and apply the multiplier to determine value.

Example of a Valuation using a Comparison Multiplier Communication Dynamics is a public relations (PR) firm operating a large urban region, whose most recent annual revenues are $1.90MM. The firm has tangible assets of $350,000, consisting of office equipment and supplies and some capitalized leases. Its net worth, however, is -$400,000, due in part to its status as a "Subchapter S" company. The company has been operated by its original owner for 30 years. A plan is in place to transfer ownership and control to her daughter, who has been the Vice President of the firm for several years. What is this firm worth?

Finding data regarding valuation of PR firms is difficult because most firms are small, privately held entities. Further research reveals, however, that while individual transaction data is difficult to gather, the merger and acquisition market is very active. Additionally, there are several studies available that report on this M&A activity. This research shows that value is measured by applying a multiplier to both revenues and "pretax adjusted operating income." The latter value is determined by replacing the owner/operator salary with a salary that is more consistent with what non-owner executives earn on the open market.5 The median multipliers applied to transactions in the most recent year are 7.0 for operating income, and 1.0 for revenues. Using these as a starting point, it is possible to develop a valuation multiplier for Communication Dynamics.

To develop the specific multiplier for Communication Dynamics, it is necessary to modify the benchmarks to account for factors such as size, regional strength, capital structure (the debt/equity mix), sensitivity of revenues and earnings to major clients, degree of specialized knowledge, management strength and others. Examination reveals that Communication Dynamics is about average when it comes to the size and capital structure of firms involved in the benchmark transactions. Factors that would lead to the upward revision of the benchmark multipliers are: the quality of its long term performance; capabilities of its management and human resource talent; its strong regional reputation; continued prospects for success given the transition plan; general stability of its client base, and the depth of its media contacts (the most important of the intangible assets owned by a PR firm). On the downside, the multiplier should be reduced due to account for the fact that revenues and earnings may be sensitive to a dependence on several major clients (i.e., the largest five clients provide 80% of the revenues). Losing one or two major clients could have a substantial impact on revenues and earnings if they are not quickly replaced. Given the factors evaluated above, it is reasonable to conclude that an operating income multiplier of 7.0 to 9.0 would apply to a transaction in which Communication Dynamics were sold.

The next step is to measure the economic performance variable. In this case, the pre-tax adjusted operating income is measured by replacing the owner/operator salaries with a an alternative fair-market-determined executive salary. Using the most current year's income statements arrives at an estimate of $218,000. If we multiply the pre-tax adjusted operating income by 7.0 and 9.0, we arrive at a value range of $1.53MM to $1.96MM respectively. The upper bound of $1.96 MM is consistent with a factor of 1.0 times revenues, which is the other approach used to value market transactions.

In applying this method here, it is important to note that we have matched our valuation model to the environment by using the same techniques used to value open market transactions. As such, our valuation is also linked directly to market activity as we rely on the results of actual transaction data in determining the benchmark multiplier. Further, by using the most recent year of actual income statement data in our calculations, we have avoided the need to estimate cash flows into the future. 6 Hence, the resulting valuation is a reasonable measure of what the company would sell for in an open market transaction.

Option Pricing Models

Valuing a firm like Communication Dynamics was made easier by the presence of a history of financial performance data contained in the income statements. There were identifiable revenues and earnings on which to base a measure of economic cash flow. In many cases, however, particularly in the new "tech" and "internet" markets, there is often a paucity of such data. In spite of this, observed market values are often very high. What is being valued here are not cash flows, but growth opportunities that represent future cash flows.

Traditional cash flow and capitalization models include risk-adjusted discount factors that reduce value in the presence of expected future volatility. In the case of growth opportunities, however, expected future volatility is actually a source of value rather than a source of risk. In order to capture the positive effects of expected future volatility, it is necessary to use a model in which value is a positive function of such volatility. Here is where option models are well-matched to the environment.

A call option is actually a contract that gives the owner the right, but not the obligation, to buy an asset at a predetermined price (referred to as the exercise price). This can be done either at (in the case of a European option) or up to (in the case of an American option) a particular point in time (referred to as the expiration date. A contract that gives the owner the right to sell an asset under the same conditions is known as a put option. The diagram labeled Figure I, shows the expected payoff on the ownership of a call option. As can be seen, the payoff is positively related to future volatility. After paying a price (P) for the option when it is purchased, the option is not exercised unless the value of the underlying asset exceeds the exercise price (X). For example, if you owned a call option to buy shares of Microsoft at $70 per share at the time of expiration of the contract, you would exercise that option if the price of Microsoft exceeded $70 per share on that date. As can be seen in the diagram, if the value of the asset ends up being below the exercise price, the option goes unexercised, and the investor loses only the amount originally paid for the option (P). Hence, the downside loss is truncated. On the upside, however, the potential gain is limited only by the increase in the underlying asset value. Here, the potential gain is unbounded and therefore a positive function of future volatility. The greater the volatility, the greater the chance of a high rate of return.

As mentioned earlier, an R&D project can be viewed as an analogy to the option diagram above. First, a company invests an amount of money ($P) in an R&D project. At some point in the future (analogous to the expiration of the option), the results of the R&D project will be reviewed to determine whether or not to continue with the project. In order to continue, a certain amount of additional funds would be required for investment (analogous to the exercise price, X, of the option). The project will be continued (the option exercised) if the value of the underlying asset (project continuation) exceeds the additional cost of investment (exercise price). Hence, higher R&D project valuations are associated with greater expected future volatility in the resulting product markets.

It is important to note here that the value of a call option is positively related to several factors, including the term to expiration (t), the risk free rate of interest (r), and the volatility of the underlying asset (sigma). This provides the answers to several interesting questions.

The positive relationship between call option value and term to expiration explains why long term growth options are more highly valued, even in cases where there is limited information regarding the exact look of the potential outcomes of those investment opportunities, as in the case of the Internet market. Further, the direct relationship between option value and interest rates explains why the stock markets seemed to be unresponsive to some of the Fed.'s interest rate increases in late 1999. These rate increases may have made investments representing long-term growth options look more attractive. Finally, where there is more expected volatility there is greater value. This explains why investments that would be heavily discounted by the more traditional valuation models due to high risk are actually some of the most highly valued investments on the markets today. To see this more clearly, let's consider an example of how the option model may be applied to valuing an R&D company.

Example of an Option Pricing Model Application

A small biotechnology company has initiated an R&D study that will require expenditures of $3.0MM made in equal amounts of $1.0MM per year for the next three years. At the end of that time, the company will make a decision on whether to move into the commercialization stage or abandon the product idea. Commercialization will require an additional investment of $8.0MM, and is expected to yield sales of $3.5MM in the first year of operation. Investors require at least a 20% return on investment. What is this company worth?

To determine the equity value here requires three steps. First, it is necessary to calculate the discounted value of the R&D expenditures over the next three years. Next, it is necessary to make an estimate of the underlying asset value to be used in the optionpricing model. In this case, the underlying asset is the commercial product that results from the R&D project. If this is a single product firm, as we'll assume for the purpose of simplicity, the value of the firm will be based on sales and profits generated by that product. To estimate this value, a comparison multiplier approach can be applied to the anticipated sales of the company, as we'll see below. Once we have estimated the value of the underlying asset, we then calculate the option value using an option pricing formula, in this case the Black-Scholes model. In applying the model, the investment cost necessary to commercialize the product, $8.0MM, becomes the exercise price of the option. The term to maturity of the option is the three years to the end of the R&D investigation. The risk free rate is the treasury bill rate, assumed to be 5.0%. We'll discuss the measure of volatility further below.

In order to estimate the underlying asset value of the product, it is necessary to determine the price/sales ratios of companies who produce and sell similar products in similar markets (which process was described earlier in the article). Our research indicates that comparable firms trade at price/sales ratios of 4.5 times. Applying this to the anticipated sales of $3.5MM results in a value estimate of $15.75MM. Since this is an estimate of the value of the firm three years from now, we discount it back by 20% over the three years to estimate the underlying asset value today:

Underlying Asset Value = ($3.5MM*4.5)/(1.20)3 = $9.12MM [101

As a measure of volatility, we can use the standard deviation of the returns to the equities in the sample of firms used to benchmark the value of the underlying asset. For the purposes of the example, we'll assume it to be 45%.7 Once this value is determined, we can use the option model to estimate the value of the R&D project itself The inputs we need- to- fill- the -model- shown -in equation [8]are as follows:

A = Underlying asset value = $9.12MM

X = Exercise price = future investment cost = $B.OMM

r = Treasury bill rate = 5.0%

sigma = Volatility = standard deviation of benchmark returns = 45%

t = term to expiration of the R&D project = 3 yrs.

Inputting the above values into the Black-Scholes formula (Equations [8a]-[8c]) yields a result of $3.687MM 8. This represents the value of the R&D project itself. As can be seen, it is the value of the option of investing in the commercialization of the R&D product three years from now. The net value of the project would be obtained by subtracting the present value of the R&D expenditures ($2.106MM) from the option value, arriving at a result of $1.581 MM.

As more information becomes available regarding the prospects for successfully exercising the growth option inherent in the R&D project, it will be revalued, at first using another option model. As more reliable information regarding the project cash flows becomes available, revaluation may take place using either a hybrid model that combines option and discounted cash flow valuation, or a discounted cash flow or capitalization model itself The current value of the growth option ($3.687MM) measures the value of waiting for additional information regarding the outcome of this project.9 As further information is revealed, the decision to remain invested or to abandon the project will be reconsidered.

The Valuation Arc

Choice of an appropriate valuation model can be considered as a function of degrees of information and uncertainty. As can be seen in the diagram labeled Figure II, where there is little information and lots of volatility, pricing becomes an exercise in valuing a growth option. Following the dashed line, as additional information becomes available, we can move into the realm of combining option and various discounted cash flow models. As information increases and volatility decreases, discounted cash flow models themselves become more suitable for valuation purposes. In the tech and internet markets, we should expect to see a shift from a high volatility/low information environment to one in which there is more information, resulting in at least some degree of re-valuation of investments. In such cases, we may witness large changes in market prices as new information regarding the value of exercising growth options becomes available. The March 2000 "correction" observed in the market for Proctor & Gamble stock may have been just such a revision.10

Importance to Credit Managers

An obvious question raised by this discussion is: why do credit managers, who are fundamentally asset-based lenders, need to know about this? The answer is understood in the knowledge that an increasing number of firms are relying on intangible assets and growth options to generate firm value. In a business environment that emphasizes the importance of developing long term relationships with customers, a credit manager needs to be in a position to understand the sources and measures of long term value in its customers. In such an environment, credit decisions may be increasingly based on an assessment of the customers ability to raise additional funds in the capital markets to finance their growth opportunities. Knowledge and understanding of comparison multiplier and option pricing models will enhance a credit manager's abilities to properly assess the long-term viability of a customer, and therefore, help identify customers with which his/her company should develop relationships. This will be a key to the survival of credit-extending companies in the uncertain yet lucrative future.

1 For a detailed discussion of this case as well as the problem of valuing intangibles, see the interview with Baruch Lev in Fast Company, January-February 2000, pgs. 216-224

2 Capitalization rates are defined as a discount rate less a growth rate. While (k - g) is the actual capitalization rate, the term is also often used to describe its inverse 1 / (k - g) which is more correctly referred to as a capitalization factor.

3 The exact form of this multiplier is undefined. Intuitively it should capture the relationship between cash flow and earnings. If a is a dividend payout ratio, this model becomes Value = d / (k - g), which finance students will recognize as the Gordon growth model.

4 As the equation is written, only pi^sub gross^ represents an actual profit margin. The factor pi^sub operating^ is a multiplier that will convert gross profit into operating profit, and Tnet one that turns operating profits into net profits.

5 This is done to adjust for the fact that the salary taken by an owner/operator includes both executive compensation and a return on equity investment. Therefore, owner/operator salaries exceed what would be paid to a non-owner executive to run the company.

6 It is very important to note, however, that the capitalization model we've used to value the cash flows essentially reduces to a discount factor and a growth estimate. Therefore, an implicit forecast of growth has been made, it just does not rely on point estimates of cash flows.

7 The most common method of estimating this value is to measure the standard deviation in the recent historical returns of stocks included in the benchmark sample. In this case, the benchmark sample would include other biotech firms selling similar products. This sample is chosen because our target firm's behavior and the accompanying valuation by the market will be similar.

8 The value for d^sub 1^ is 0.7495. For d^sub 2^ it is -0.0299. The associated probabilities for d^sub 1^ and d^sub 2^ under the standard normal distribution are 0.7732 and 0.4881 respectively. A spreadsheet to calculate the BlackScholes option value is available from the author at sisberg@ubmail.ubalt.edu

9 An excellent and complete treatment of this material can be obtained in the book Real Options: Managing Strategic Investment in an Uncertain World, by Martha Amram & Nalin Kulatilaka, Harvard Business School Press, 1999.

10 See "Whither Cash Flow? Where Value? Chapter II," Credit & Financial Management Review, First Quarter 2000.

Steven C. Isberg, Ph.D. is currently serving as Credit Research Fellow at the Credit Research Foundation. He is also Associate Professor of Finance at the Robert G. Herrick School of Business, University of Baltimore. He has developed a professional expertise in the area of valuation, where his experiences include teaching both university and professional development courses, consulting and serving as an expert witness in a number of litigation proceedings.

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