Chapter 1

How do you keep bias out of your valuation?

            The honest answer is that you cannot. No matter how hard you try, bias will find its way into your valuations, but these are a few things that you can keep do to minimize its impact:

1. Do not get too close to the management of the firm that you are trying to value.

2. Do not take strong positions on a company before you value it ­ if you state that you think a company is a good value prior to valuing it, you are going to find a way to make it undervalued.

3. Never throw out an estimated value for a company before you commence the valuation.

4. Try to be as honest as you can about your biases and see if you can compensate for them.

What is the cost of having more detail in valuations?

            More detail impresses clients and those who look at your valuations, but it has two costs:

1. You have to provide the inputs for the additional detail. Since your time is constrained, this will take your attention away from the more important inputs.

2. The details can be overwhelming when you look at the big picture. It is often very difficult to isolate the variables that matter when a valuation is extremely detailed.

Chapter 2

Is there an easy way to tell if a cashflow is an equity cashflow or a firm cashflow?

            There is an easy way. Since equity cashflows are after debt payments, check to see whether your cashflow is before or after interest and principal payments. If it is after, you have an equity cashflow. If it is before, it is a firm cashflow. Another short cut that works is to look at the starting point for the cashflow estimation. If the cashflow estimation begins with net income, it is probably an equity cashflow. If the cashflow begins with operating income or EBIT, it is probably a firm cashflow.

What is the difference, if any, between discounted cashflow and asset based valuation?

            In discounted cashflows, you estimated the expected cashflows on the assets of a firm, and discount them to the present to estimate value. In asset based valuation, you make a list of the assets that a firm owns, obtain estimated market values for these assets and aggregate them. Though the latter seems easier, it is, in fact, a subset of the former. To estimate the value of an asset, you ultimately have to consider its cashflow generating potential and discount it.

Chapter 3

How different are accounting rules in different countries?

            Though we tend to overemphasize the differences across countries, accounting rules across countries are more similar than different. In fact, as you see globabilization in investing, you see convergence in accounting standards. The differences that remain tend to be around specific areas ­ leases, reserves and R&D.

How do you do valuation when you do not trust the accounting statements?

            Much as I like to beat up on accountants and how they are responsible for all that is wrong with the world, I have to admit that much of the information that we use comes from accountants. If you do not trust accounting statements, valuation becomes very difficult to do. You can try to compensate for the obvious biases ­ use a lower operating income than the one reported, for instance ­ but the resulting value will be extremely noisy.

Chapter 4

Why is the marginal investor assumed to be diversified?

            There are two reasons. The theoretical one is that diversification is the rational thing to do and in a rational world, investors will end up being diversified. The pragmatic one is that a significant proportion of the stock in most publicly traded firms is held by institutions (which tend to be diversified) and these institutions also account for the bulk of the trading on these stocks.

How do I estimate historical standard deviations and variances?

            We generally use historical data to estimate standard deviations and variances. You can use daily, weekly or monthly data to obtain the values. Note that they measure the variance in the past and that we tend to assume that they are good measures of expected future variances.

How about correlations and covariances?

            Correlations and covariances are also estimated using historical data. While the estimation is not difficult to do, correlations and covariances are notoriously unstable and the problems of backward looking versus forward looking estimates is exacerbated.

Chapter 5

How do I make sure that the inputs to the Black-Scholes model are consistent?

            The simplest way to keep inputs consistent is to annualize them. For variances, this takes the form of multiplying a monthly variance by 12 or a weekly variance by 52.  Riskfree rates (such as T.Bill rates and T.Bond rates)  are usually already annualized.

Will the Black-Scholes and Binomial models give me different values and why?

            The Black-Scholes is a special case of the binomial model and in a world with continuous price changes (and log normal distributions for these changes), the values from the two models will converge. More generally, when price changes are not continuous and do not converge on non-normality, the Binomial model will give you a more precise estimate of value. In addition, it is easier to consider the possibility of early exercise in the Binomial model.

Chapter 6

How do my views on market efficiency affect how I approach valuation?

            To begin with, if you believed that markets were efficient, you would work hard to ensure that the value from your model converges on the market price (which is the best estimate of value in an efficient market). If you believe that markets are inefficient, you will

1. focus your energy on valuing assets in markets which you believe are most likely to have inefficiencies.

2. pick a valuation approach that is consistent with what form of inefficiency you see in markets. For instance, if you believe that markets make mistakes and correct their mistakes over time, you would use discounted cashflow valuation approaches. If, on the other hand, you believe that markets are correct in the aggregate but make mistakes on individual assets, you are more likely to use relative valuation.

Chapter 7

Should I use the government bond rate of the country where my firm is located as my riskfree rate?

            No. The correct riskfree rate to use will depend upon what currency you choose for estimating the cashflows and not which country your company is incorporated in. Thus, if you value Nokia in dollars, you should use the U.S. treasury bond rate and not the Finnish government bond rate.

What if I have a firm with operations in different countires and cashflows in different currencies?

            You have two choices. The easier one is to convert all of the cashflows into one currency and value the company in that currency. The other is to value the operations in each country separately (in the currency of that country) and then aggregate the values (after converting into one currency) at the end. If you expect the mix of your geographical operations to change over time, the second approach is the better one.

What if the government bond rate of the currency (of my companyıs cashflows) includes default risk?
            You have two choices. First, you can try to strip the government bond rate of the default risk (check the chapter for details). Second, you can do your valuation in a different currency ­ say U.S. dollars or Euros.

When would I use the arithmetic average risk premium (as opposed to the geometric risk premium)?

            If you wanted to estimate a cost of equity for just the next period, there is good reason to go with arithmetic average risk premiums. If you are estimating a cost of equity for the long term, you should go with the geometric average.

Why is the historical premium so much higher than the implied premium in the United States?

            While some view this difference as a problem, I think it indicates the selection bias associated with picking the most successful equity market of the 20th century (the U.S. market) as our base for estimating risk premiums. Not surprisingly, the actual returns earned by this market exceeded what people expected to earn at the time that they made these investments?

Chapter 8

When can I use the regression beta as my estimate of beta in a valuation?

            I would say never, but that would make me sound doctrinaire. Perhaps, if you have a firm that has remained unchanged in terms of its business mix and financial leverage over the last 5 years and the regression yields a beta estimate with a very small standard errorŝ

When estimating bottom-up betas by looking at comparable firms, how should I define comparable firms?

            While some analysts define comparable firms as firms in the same business, I would use a broader definition. A comparable firm to me is one that is affected by the same broad business conditions as the company I am analyzing. Thus, I believe that investment banks represent a much better set of comparable firms when valuing a five-star restaurant in New York city, than a sample of restaurants that are publicly traded.

Should I adjust the beta for a firmıs size or other characteristics?

            In theory, there is no reason why you should not adjust betas for firm size or other characteristics. The adjustment should not be arbitrary, though. You can adjust betas for operating and financial leverage differences (as shown in the illustrations in the chapter) and even for market capitalization (using a cross-sectional regression).

Can I use the yield to maturity on a bond issued by the company as the cost of debt?

            You can, as long as the bond is liquid and has no special features embedded in it. For firms in distress, the yield to maturity will overstate the true cost of debt because it is based on promised cashflows (the coupons and face value of the bond), rather than expected cashflows (which should be much lower because of the bankruptcy risk).

If I have an actual rating, do I need to even estimate a synthetic rating?

            While it is convenient to have an actual rating for a firm, there might still be cases where you use a synthetic rating:

1. If different bonds issued by a company have different ratings

2. If the company has significant amounts of non-traded debt on its books. The rated bonds may be structured in such a way that they do not represent the default risk of the firm.

How can I build a more complete model for estimating ratings?

            To build a more complete model for estimating ratings, you need to begin by identifying a series of variables  that the ratings agencies use to estimate ratings. You can find a number of financial ratios that S&P uses to rate firms on its web site. You can add other observable variables to the mix and then examine the relationship between these variables and the actual ratings that you observe for firms. (Essentially, you are creating a composite credit score for a firm and relating credit scores to ratings)

Can I use book value of debt as a proxy for market value of debt?

            For healthy firms in markets where interest rates are stable, the book value of debt should be close to the market value of debt. If a firmıs default risk has changed or if interest rates have changed significantly since the firm issued its debt, you should estimate the market value of debt.

What should be in my market value of equity?

            The market value of equity should include the market value of all traded stock as well as the estimated market value of other equity claims on the firm such as warrants, conversion options in convertibles and management options. Estimating the former is simple but estimating the latter can be messy especially when you have non-traded options.

Chapter 9

How do you know if a one-time charge or income is truly one time?

            This is a tough call. All firms claim that their one-time charges are truly one-time but you have to look at three factors:

1. History: If a firm has one-time charges that show up year after year, it is very likely that this is part of an ongoing process.

2. Management credibility: Managers are asking you to trust them when they claim one-time losses. If a management team has a history of being open with markets, I would give them the benefit of the doubt. With secretive management teams, I would begin with the presumption that they are not telling me the truth.

3. Details: Firms that are mysterious about the sources of losses or gains, labeling them with generic terms such as restructuring charges should be viewed more skeptically than firms that provide detailed information.

Chapter 10

When would you include cash in working capital to compute cash flows?

            Two conditions need to be met for cash to be considered as part of working capital:

1. The cash should be needed for operations

2. The cash must be earning a below-market rate return. Note that a low return by itself is not a sufficient condition, since riskless investments should have low returns.

What marginal tax rate do you use when you have a firm that operates in multiple countries (with different tax rates)?

            The conservative rule is the following. If the tax rate in the foreign holdings is less than the domestic tax rate, you should use the domestic tax rate, on the assumption that the income will eventually be taxed in the home country. If the tax rate in the foreign holdings is higher than the domestic tax rate, you should apply this tax rate to the income from those holdings.

What will happen to value if you ignore acquisitions when estimating capital expenditures?

            The answer will depend upon two factors. The first is whether the acquisitions are value destroying, value neutral or value creating. This judgment can be made by comparing what you pay on the acquisition to what you receive in cashflows from the acquisition. Value neutral acquisitions have no effect on value and can be safely ignored. Value creating and value destroying acquisitions that you foresee in the future should be built into your valuation. The second thing to consider is whether there is a disconnect between your growth rate estimate and you assumptions about acquisitions. For instance, if you use a historical growth rate which is high because a company has made acquisitions in the past as your expected future growth rate and you ignore acquisitions, you will overstate the value of the firm.

Chapter 11

Why might analyst estimates of growth deviate from the fundamental growth rate?

            The charitable conclusion would be that analysts have information that leads them to believe that the future of the firm will be different from the past (reinvestment rates and returns on capital). The other possibility, however, is that growth rates are sometimes driven by hype and fed by over-optimistic managers with grandiose plans.

Can you use historical, analyst and fundamental growth rates in the same valuation?

            You can, but it is generally not a good idea. You are often making different and sometimes contradictory assumptions with each growth rate and it is difficult to bring them all into one calculation. You are often better off using a fundamental growth rate but adjusting the fundamentals to reflect the information in analyst and historical growth rates.

Can the fundamental growth rate be negative?

            Yes. If your firm has a negative reinvestment rate ­ it is withdrawing cash from the business ­ and you expect it to continue to maintain a negative reinvestment rate, and if your return on capital is stable ­ your existing assets are not expected to become more efficient ­ you can have a negative fundamental growth rate.

Chapter 12

Can I use a growth rate higher than the growth rate of the economy as my stable growth rate if my firm is a well-managed firm or if it has other stellar qualities?

            No. You can, however, allow the firm to have a higher return on capital in stable growth that will reduce its reinvestment needs and increase the terminal value.

When would you use liquidation value instead of terminal value?

            Liquidation value is more appropriate when you are considering an asset or business with a finite life. Terminal value is more appropriate when you are considering an asset with a very long life or a business with an infinite life. Thus, liquidation value may be better suited to a small private business or a real estate venture whereas terminal value may be more appropriate for valuing a healthy publicly traded firms.

How do you estimate terminal multiples from fundamentals?

            See the chapters on multiples. A discounted cashflow model with a little algebra will yield you the equations for all of the multiples.          

Chapter 13

Can you value stocks that do not pay dividends with the dividend discount model?

            Yes. Note that you will have to set a payout ratio in stable growth to reflect the lower growth. All of the value will then come from the terminal value but this should not be surprising for a high growth firm that pays no dividends.

How do you allow for stock buybacks in the dividend discount models?

            You can treat them as lumpy dividends that get paid out at irregular intervals. You should average the buybacks across time and compute a modified dividend payout ratio based upon the consolidate value (of dividends and average buybacks).

How does the personal taxation of dividends affect the value of a share?

            At the investor level, dividends often get taxed at a different rate than capital gains. Generally speaking, you should avoid bringing personal taxes into stock valuation because the discount rate will also then have to be adjusted for personal taxes. Instead, you should value the stock, ignoring personal taxes, but bring in the personal tax issue when making your final portfolio judgments. In other words, if you have a high tax rate on dividends you should avoid stocks with high dividend yields.

Chapter 14

Why do firms not pay out their free cashflow to equity as dividends?

            Managers sometimes choose not to pay out their FCFE as dividends (or stock buybacks) because

1. FCFE are volatile and dividends are smoothed. In good years, firms will hold back some of their FCFE to cover dividends in bad years.

2. Managers like to accumulate cash to  fund acquisitions or grand strategic plans (often with questionable value to stockholders)

What is the link between corporate governance and the use of FCFE models?

            In markets with weak corporate governance, managers often hold back on returning cash to stockholders. Thus, the dividend discount model risks missing the cash build up that occurs in these companies. In markets with strong corporate governance, there is much greater pressure to return cash to stockholders and FCFE tend towards dividends and stock buybacks.

Chapter 15

What is the key difference between the cost of capital and APV approaches?

            There are two key differences. The first is in how the approaches deal with bankruptcy. In the cost of capital approach, you adjust the discount rate (cost of equity and debt) for the bankruptcy risk ­ using a higher cost of equity and debt. In the APV approach, you estimate the cost of bankruptcy separately by estimating the probability of bankruptcy and multiplying by an estimated cost (stated as percent of firm value). The second is that the cost of capital approach looks at keeping the debt ratio fixed and examines the effect on value. The adjusted present value approach looks at the costs and benefits of a fixed dollar debt.

When is it more appropriate to use the APV approach to value firms?

            The APV approach requires two key inputs ­ the probability of bankruptcy and the cost of bankruptcy (as a percent of firm value). For companies where you can estimate both inputs, the APV approach is a more flexible approach for dealing with distress and bankruptcy. If, on the other hand, you cannot get these values, the APV approach devolves into one where debt always increases value.

Chapter 16

How do you value holdings of private companies?

            The optimal solution would be to obtain the information on the private companyıs operations and to value the company. Absent that, you have to settle for less information-intensive approaches. One simple approach is to take the book value of the holdings in the private company (or companies) and multiply by the price to book ratio at which publicly traded firms in the business trade at. You could use alternate multiples (price earnings or price to sales) if you have information on the private company.

What do you do about minority interests?

            Minority interests represent the share of the equity in a consolidated holding that does not belong to your firm. Optimally, you would like to value the subsidiary and take the share that does not belong to you and treat it as the true minority interest. This would then be subtracted out from the value of the consolidated company to get to the value of equity.

How is the valuation of executive stock options different from the valuation of other options?

            Executive stock options differ from standard options in three ways. First, executive options cannot be exercised until they are vested ­ employees have to work a certain number of years before exercising options. Second, firms have to come up with the shares to cover executive option exercises. This can cause stock dilution. Third, managers control many of the levers affecting the stock price. The potential for conflicts of interest and game playing are much greater.

Chapter 17

Do you make fewer assumptions when you use multiples than when you do discounted cashflow valuation?

            No. Embedded in every multiple are the same assumptions that you make when you do discounted cashflow valuation. The key difference is that the assumptions often remain implied rather than becoming explicit.

Chapter 18

How do outstanding options affect PE ratio comparisons?

            If a company has a disproportionately large number of options outstanding, and you use primary earnings per share to compute PE, the PE should be lower for this firm than for its peer group. The reason is simple. The option overhang will lower the market capitalization for the firm. If you wanted to adjust for this, there are two things you can do. The easier (and less precise) way is to use diluted earnings per share. Since this will be lower for firms with large option issues, this may correct for the bias. The better way to adjust for options is to value them and to add them to the market capitalization and then dividing by net income.

Should you look at earnings before or after extraordinary items?

            Assuming that extraordinary items are truly extraordinary, you should look at earnings before extraordinary items. The problem is that firms sometimes categorize normal expenses as extraordinary, taking advantage of the leeway that they are often given in the accounting standards.

Where do rules of thumb (say 8 times EBITDA) come from?

            The rules usually evolve rationally. For instance, the value to EBITDA multiple developed during the heyday of the leveraged buyout movement. Given the leverage in the deal, the types of companies being acquired and interest rates in the 1980s, deal makers concluded that they needed to pay less than 8 times EBITDA to be able to service their debt payments. The problem is that these rules outlive the rule makers and the original connections get lost.

Chapter 19

How do stock buybacks affect price to book ratios?

            Stock buybacks reduce the book equity disproportionately. This is because most firms trade at above book value, and it is the market value of what they buy back that is taken out of book equity. Consequently, price to book ratios increase after stock buybacks.

When do price to book ratios and value to book ratios convey the most information?

            Book multiples convey the most information when book value means something. That is why price to book ratios work well for financial service firms, where the assets are financial assets and are marked to market. They tend to work less well for technology firms where the most valuable assets (research assets) are often off the books.

Chapter 20

What is the argument for using sector-specific multiples?

            Sector specific multiples allow us to tie value to something that is critical (and unique) to a sector. For instance, you could estimate the value of an oil company as a function of the barrels of oil it has in its reserves or the value of cable company in terms of the number of subscribers. It also allows us to tie value to strategic analysis. For instance, a cable analyst who has developed a good model for forecasting how many subscribers will be picked up by a cable company can relate this statistic back to value.

When do sector-specific multiples work best?

            When the units used to compute the multiple are homogeneous. A good example would be subscribers to internet service provider, if all subscribers subscribe to the same service and pay roughly the same amount. If the units become less homogeneous ­ you have DSL, cable modem and phone service subscribers for instance, and different companies have different mixes of subscribers, value per subscriber loses its advantage.

Chapter 21

How do you factor in regulatory constraints and rules into the value of a bank or financial service firm?

            While some analysts consider this a source of risk and build it into the discount rate, it is far easier to bring the effect into cashflows and expected growth rates. This is especially true if you estimate growth from fundamentals. Changes in regulatory policy will affect the expected return on equity and retention ratio and through these, the expected growth rate.

How does the quality of a bank's loans get reflected in its value?

            In a perfect world, it should be already be reflected in the provisions that banks set aside for bad loans. Banks with poorer quality loans should set aside more of their net income for bad loans and report lower income. In reality, though, you may have to adjust the provisions for future bad loans yourself for the quality of loans. In particular, you may need to adjust the provision upwards for banks with poorer quality loans and reduce their net income. This is based on the assumption that you can observe the quality of a bankıs loans.

Chapter 22

How do you assess the probability of bankruptcy?

            There are at least three ways. First, you can use the bond rating of the company to estimate a cumulative probability that the firm will go bankrupt by looking at the empirical evidence on distress for bonds in each ratings class. For example, a BBB rated bond historically has had a 15% cumulative chance of defaulting over the following 10 years. Second, you can use the existing bond price to back out the probability that is being assigned to bankruptcy. To do this, set up the following equation:

where p= Probability of bankruptcy

The third way to estimate the probability of bankruptcy is to do a probit, a statistical technique that allows us to estimate the probability of bankruptcy.

How do you adjust value for the probability of bankruptcy?

            Work through your discounted cashflow valuation, as if the firm will become a going concern. Then, estimate how much the firmıs assets can be sold for in the event of distress. The value of the firm then can be written as:

Value of firm = DCF value (1 ­ Probability of bankruptcy) + Distress sale value (Probability of bankruptcy)

How do you estimate distress sale value?

            First, focus only on assets in place (and not on expected growth). Second, look at what other distressed firms in the business are receiving on their assets. It is simplest to consider distress proceeds as a percent of book value.

Chapter 23

How do you estimate revenue growth in future years for a young firm with no history?

            The simplest way to estimate revenue growth is to work backwards. In other words, begin with the total market size that the firm is aiming at and the market share that you think it will achieve and use that as expected revenues when the firm matures (say 10 years from now). You can then work towards estimating revenues in earlier years, keeping in mind both infrastructure and capital constraints.

How do you consider the possibility that a young firm may not survive?

            You can assess a probability of distress by looking at the cash that the firm has on hand, its access to capital and its  operating cash needs. Firms with small cash balances, no access to capital and substantial operating cash needs are obviously most at risk.

Chapter 24

How can a private business owner maximize the value of the business for sale?

            You can try to get a publicly traded firm interested in your business. Even better, if you can two publicly traded firms interested in your business, you can get them to compete and claim the surplus. To prepare for this, though, you have to consider shifting to more transparent accounting systems well before you plan to sell and professionalize the firm. In other words, you have to make the firm less dependent upon you (as a key person) and more self-standing.

Chapter 25

How should the value of synergy be apportioned between the bidder and target firms?

            Generally speaking, as a bidding firm, you do not want to pay for the portions of the synergy that come from your strengths ­ your lower cost of debt, your distribution system, for example. In practice, thought, whether you can pull this off depends upon whether you get into a bidding war for the target firm. In a bidding war, you substantially increase the probability that the target firm will end up with the bulk of the synergy.

Chapter 26

How do you factor the effect of rent control into the value of a building?

            If you are doing a discounted cashflow valuation, it will show up in the expected cashflows ­ presumably they will be lower because of rent control. If you are valuing a property based upon how similar properties are priced, you have to adjust the estimated value if your building is subject to rent control and the other buildings are not.

How do you value vacant land?

            You can value it purely as a speculative investment and estimate the value that you think the land will have in 5 or 10 years and discount this value back to the present. Alternatively, you can consider it an option ­ an option to develop the land and value it as such.

Chapter 27

What is the difference between valuing cash-flow generating assets and collectibles?

            A collectibleıs value comes entirely from perception. Thus, value is truly in the eye of the beholder and a collectible with substantial value can lose it if perception changes. The other is that a collectibleıs value comes from its scarcity. A sudden increase in the supply will reduce its value. In contract, a cash flow generating asset has an intrinsic value based upon its cashflows.

How do you reduce the impact of the "key person" in a valuation?

            Value the business twice, once with the key person in place and once without. The difference between the two values is the value of the key person.

Chapter 28

Why, if a patent is an option, will firms ever exercise the option (develop the patent)?

            Once a patent becomes viable, there is a cost to not exercising. You give up one year of protection from competition and the cashflows you would have generated during that year. This cost will increase as the number of years of protection that you have remaining decreases.

When would you use option pricing to value a firm with patents?

            This approach works best for firms that derive the bulk of their value from a patent or patents and do not have a portfolio of commercially developed products that generate substantial cashflows for the firm.

Chapter 29

When does it make sense to add a premium for the option to expand?

            It makes the most sense when the firm has the exclusive right to expand and can use its competitive power to generate large excess returns. It makes far less sense as the exclusivity fades.

How does financial flexibility affect how much firms borrow and how much cash they hold?

            Firms that value financial flexibility highly (because they have restricted access to capital and superior and unpredictable investment needs) will remain underlevered. By borrowing to full capacity they give up financial flexibility.

Chapter 30

What are the implications of viewing equity as an option for vulture investing?

            Vulture investors hold portfolios of deep out-of the money options. Such portfolios have the following characteristics:

1. Many investments in the portfolio will end up worthless but the winners will make huge returns.

2. They are worth most when the underlying assets (the firms) are volatile

3. You need to be an activist investor to be a successful vulture investor, since there are conflicts of interest within each of these firms between inside stockholders and outside stockholders, inside bondholders and outside bondholdersŝ.

What are the implications of viewing equity as an option for lenders to firms?

            Take an active role in the management of the firm. You need to have veto power over investment, financing and dividend decisions. If you do not protect your interests, you will be taken to the cleaners.

Chapter 31

Is there a "best way" to restructure?

            No. Each firm is different and its problems require a different response. Some firms need short term cost cutting and others need long term strategic repositioning. You need to understand a firmıs problems before you devise the restructuring solution for that firm.

Chapter 32

Under what conditions will your estimate of firm value be the same using both EVA and DCF approaches?

            To get the same value, you will need to estimate growth from fundamentals in the DCF model. In other words, your growth rate has to be determined by the return on capital and reinvestment rate. The same return on capital needs to be used to come up wth the EVA.

Chapter 35

Is there a way to blend discounted cashflow and relative valuation?

            Yes. In a discounted cashflow model, you can use industry averages for fundamentals (such as return on capital and reinvestment rate) and the implied equity risk premium to bring in elements of the market into your valuation. In relative valuation, you can consider all of the fundamentals that should matter for that multiple and expand your sample of comparable firms to include the entire market.