Operating income is defined to be revenues less operating expenses and should be before financial expenses (interest expenses, for example) and capital expenses (which create benefits over multiple periods). Specify at least two items that currently affect operating income that fail this definitional test and explain what you would do to adjust for their effects.
The two items that most directly contradict this definition of operating income are operating leases and R&D expenses, both of which are categorized as operating expenses. Operating leases are financial expenses and R&D expenses are capital expenses. To correct the operating income, we have to do the following:
§ Take the present value of operating lease commitments, using the pre-tax cost of debt of the firm as the discount rate, and treat the present value as debt. The operating income has to be adjusted by adding back the operating lease expense and subtracting out the depreciation created by the operating leases.
§ Specify the number of years before R&D can be expected to generate commercial products, collect R&D expenses from the past for that many years and then amortize them; straight line usually works. The remaining unamortized R&D from prior years can be considered the book value of the R&D asset, and operating income has to be adjusted by adding back the R&D expense from the current year and subtracting out the R&D amortization for the current year.
§ Operating income can be volatile both as a result of the normal ebb and flow of business and as a result of accounting transactions (one time income and expenses). Should you smooth or normalize operating income and if so how do you do it?
§ If you plan to base your future operating income on current operating income, it stands to reason that you want to remove any items that are transitional (one time charges or income) or cancel out over time (exchange rate or pension fund gains or losses). It is a tougher call as to whether you should smooth out operating income by using the average income over time. For some firms, such as commodity companies, it clearly makes sense given the ups and downs in commodity prices over time. For other firms, especially those that are facing long term structural or operating problems, you should not replace current depressed earnings with an average earnings over time. Instead, you should recognize that the earnings improvement, if it occurs, will happen gradually over time and reflect that in your valuation by a gradual improvement in operating margins.
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§ In computing the tax on the operating income, there are three choices that you can use - effective tax rate (about 29% for the average US company in 2003), marginal tax rate (35-40% for most US companies) and actual taxes paid.
a. Which one would you choose?
§ a. Which one should you choose?
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§ Let's start with what you cannot use - the actual taxes paid. Why not? The actual taxes paid will reflect the fact that you save on taxes when you make interest payments. The problem, however, is that you have already counted the tax benefits in your cost of capital (by using the after-tax cost of debt) and increasing your cashflow for the same reason would be double counting.
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§ It boils down to a choice between effective and marginal tax rates. The effective tax rate is lower than the marginal tax rate for a number of reasons but one reason is that companies defer paying taxes. Since this is a tax saving, there is nothing wrong with using the effective tax rate in computing the after-tax operating income for last year and even for the next few years. If you use it forever, though, you are assuming that you can defer taxes in perpetuity and that is a dangerous assumption. The best compromise is to use effective tax rates for the early forecast years and move towards a marginal tax rate in the later years.
§ b. What happens if you are a multinational and are in several countries with very different tax rates?
§ While some would push for an average tax rate, weighted by the income in each country, I think it makes far more sense to use the marginal tax rate of the country the company is domiciled in as a floor. After all, income earned in countries with lower tax rates than the domestic tax rate eventually has to be repatriated back to the domicile at which point it will be taxed. It is a tougher call for countries with higher marginal tax rates than the domestic tax rate. Here, it does make sense to use a weighted average.
§ What happens if you are reporting an operating loss?
§ In the year of the operating loss, the tax rate used in computing the after-tax operating income and the after-tax rate cost of debt should be zero. As you project the earnings into future years and they turn positive, you first have to cover your net operating losses from prior years, during which period your tax rate will still be zero. When you use up your net operating losses, your tax rate will converge on the marginal tax rate.
§ Many companies grow through acquisitions, some of which they pay for with cash and some with stock. In computing capital expenditures, should you include any of the acquisitions, only acquisitions funded with cash or all acquisitions?
§ The basic rule is both simple and logical. If you want to count the growth from acquisitions in your top line earnings, you have to consider the acquisitions, whether they be paid for with cash or stock, as part of your cap ex. If you do not do this, you will be giving companies that grow through acquisitions the equivalent of a free lunch - growth without cost. The argument that stock based acquisitions do not affect cashflows is an absurd one, since all you are doing is skipping a step. If you had issued that same stock to the market and used the cash to fund the acquisitions, it would have been a cash acquisition.
§ If you are willing to ignore the growth from acquisitions, you can ignore acquisitions in your cap ex, but your resulting value can be different. To the extent that you systematically underpay or overpay on acquisitions, you will under or over estimate value by ignoring them. Only with fair value acquisitions will ignoring them give you the same value.
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§ Depreciation and amortization includes a number of different items. Some of them are tax deductible (like conventional depreciation on assets) but some are not (like amortization of goodwill). In computing depreciation, should you include all depreciation and amortization or only tax-deductible depreciation and amortization?
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§ It is only tax deductible depreciation and amortization that affects your cash flows. Consequently, you should compute the operating income after tax deductible depreciation and add back only the tax deductible depreciation. For example, assume that you have EBITDA of 500 million, tax deductible depreciation of $ 100 million and non-tax deductible amortization of 50 million. You should use operating income of 400 million (500 less 100) to compute your after tax operating income and then add back only the tax deductible depreciation. What, you may wonder, is the harm in using all depreciation since you add it back anyway? If you subtract out 150 from the EBITDA to get an operating income of 350 million, compute the taxes on 350 million and then add back the entire depreciation and amortization back, you will give the non-tax deductible amortization a tax benefit.
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§ If you had a choice, you would much rather based you cashflow estimates on the income and depreciation reported in the tax books than in the reporting books. When companies use different depreciation methods in their tax and reporting books, and you have access only to the latter, your cashflow estimates will be skewed by your use of the reported (rather than the tax) depreciation
§ The conventional accounting definition of working capital is current assets minus current liabilities and includes cash and marketable securities in current assets and short term debt in current liabilities.
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§ a. Should you consider all cash, operating cash or no cash at all when you compute working capital?
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§ The entire reason we consider working capital when computing cash flows is because investments in working capital are considered wasting assets that don't earn a fair rate of return. Thus, money invested in inventory is wasted because inventory sits on your shelves and does not earn a return. Until a few decades ago, the same could be said of cash that would be invested in a checking account. Today, cash at most reasonably run publicly traded firms is invested in commercial paper or treasury bills, earning a low but a fair rate of return (given the lack of risk in these investments). Hence, cash is no longer a wasting asset at most firms and should not be considered part of working capital.
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§ There should be no distinction drawn between operating and non-operating cash for purposes of this analysis. Even if a company needs cash for its operations (a retail firm like Walmart has to maintain large cash balances), if that cash is invested in financial assets like commercial paper, it should not be considered part of working capital because it isnot a wasting asset.
§ Should you consider short term debt as part of current liabilities?
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§ All interest bearing debt, whether short term or long term, should be considered part of debt for computing cost of capital. Consequently, short term should not be considered part of current liabilities to compute working capital. Supplier credit, accounts payable and accrued items (salaries, taxes etc), should be considered as part of current liabilities.
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§ Most of us have seen the equations for sustainable growth. In particular, the growth in earnings per share = (1 - payout ratio) * Return on equity.
a. Can you use the same equation to compute growth in operating income?
b. Under what assumptions will this sustainable growth rate also be equal to your expected growth rate?
c. Increasing the amount you reinvest back into the business (reduce the payout ratio or increase the reinvestment rate) will increase the growth rate for any company that is prfitable. Will it also increase value? Can you use the same equation to compute growth in operating income?
§ No. When computing growth in operating income, the equation is slightly different: Expected growth in operating income = {(Cap ex - Depreciation + Change in non-cash Working capital)/ After-tax Operating Income}* Return on capital
Return on capital = After-tax Operating Income/ (Book value of debt + Book value of equity)
You have to be consistent. When talking about firm value, every input has to be stated in terms of firm value. Thus, in the above equation the retention ratio (which measures reinvestment as a percent of equity income) is replaced by the reinvestment rate (which measures reinvestment as a percent of after-tax operating income) and the return on equity (which is the net income divided by book equity) is replaced by the return on capital (which measures the total return to all investment).
b. Under what assumptions will this sustainable growth rate also be equal to your expected growth rate?
These equations hold only if the return on equity and capital on existing assets remain unchanged over time. If the return on equity or capital is expected to change over time, there will be a second component to the expected growth rate equation. For instance, assume that your return on capital this year is 10% and that you expect it to improve to 12% next year on exiting assets and that you plan to reinvest 50% of your operating income back next year into new projects on which you expect to make 12%.
Expected growth next year = (.50) (.12) + (.12-.10)/.12 = 26%
You can decompose this growth into 2 parts - growth from new investments (6%) and growth from more efficient use of existing investments (20%). The problem with depending upon the latter is that it is a finite source of growth. At some point in time, your assets will be optimally utilized and you will no longer be able to extract additional growth. That is why you cannot count on the latter in perpetual growth (terminal value).
c. Increasing the amount you reinvest back into the business (reduce the payout ratio or increase the reinvestment rate) will increase the growth rate for any company that is prfitable. Will it also increase value?
No. It depends upon whether the return on capital (equity) is greater that the cost of capital (equity). If the return on capital is less than the cost of capital, increasing the reinvestment rate will increase growth but reduce value. If it is equal, increasing reinvestment will not affect value. It is growth with excess returns that is the source of value
How long can high growth last?
Answer
Now let's consider the big enchilada - terminal value - at the end of the high growth phase. There are three ways in which terminal value can be estimated - liquidation value for the assets, a multiple of earnings or revenues in the terminal year or by assuming that cashflows grow at a constant rate forever after your terminal year.
Since it is not growth that creates value but excess returns, this question can really be framed as: "How long will excess returns continue?" Since excess returns are conditioned on the existence of barriers of entry, the larger and more sustainable the barriers to entry in a business, the longer the high growth/excess return period can last. There are other pragmatic considerations. As firms get larger and acquire larger market shares, there is a limit on how much longer they can continue to grow at rates higher than the economy. Hence, a firm might find its growth tapering off even before the excess returns go to zero.
How do you decide which approach to use to estimate terminal value?
Of the three approaches, the one that is least defensible is the use of a multiple to estimate terminal value. Since this multiple comes from looking at how comparable companies trade in the market, it effectively converts the discounted cashflow valuation into a relative valuation. Liquidation value, which in practice often becomes equated with book value, and terminal value, which comes from assuming a stable growth rate forever, will converge if we assume that the firm makes no excess returns in perpetuity. If you do assume that a firm can make excess returns in perpetuity, liquidation value will generally yield a more conservative estimate of value than the stable growth model.
If you are valuing a private company where you are uncomfortable assuming that the firm will be a going concern forever, liquidation value is the more sensible choice. If you are valuing a publicly traded company with significant competitive advantages and potential excess returns, it is best to stick with a going concern assumption and value the firm assuming a constant growth rate forever.
Assuming that you use the perpetual growth model, can the stable growth rate be negative?
The only constraint on the stable growth rate is that it be less than the growth rate of the economy in which you operate. If you are working with nominal cashflows, this would be a nominal growth rate in the economy; with real growth rates, it would be a real growth rate for the economy. The growth rate can be 0% or negative. In fact, given what we know about firm life cycles where firms peak and then become smaller over time, you can argue that assuming a negative growth rate is more realistic than assuming that your firm will keep getting larger over time
What effect will increasing the growth rate in perpetuity have on terminal value?
One of the easiest ways to increase your value is to nudge up your stable growth rate towards your cost of capital. At first sight, therefore, it looks like increasing the stable growth rate will always increase terminal value. However, this is only true if you are internally inconsistent in your assumptions. If you estimate the reinvestment rate as a function of your expected growth and return on capital, you set up a trade off:
Reinvestment rate = Stable growth rate/ Return on capital
The trade off is as follows. If you increase the stable growth rate, the reinvestment rate will go up. Thus, while you gain from growth, you will lose in cashflows:
Terminal value = EBIT (1-t) (1 - Reinvestment rate)/ (Cost of capital -g)
In the special case where you assume that the return on capital is equal to your cost of capital, your gain from increasing growth will exactly be offset by the loss from having a higher reinvestment rate, nullifying the effect of growth. In that case, the terminal value will always be
Terminal value = EBIT (1-t) / Cost of capital
If you assume that the firm will earn more than its cost of capital in perpetuity, increasing growth will increase value. If you assume that it will earn less than its cost of capital in perpetuity, increasing growth will reduce terminal value.
Debt can be defined in many ways - total liabilities, total debt or long term debt. What would you include in debt?
The debt in the cost of capital is the debt used to fund the operations and investments of the firm. Using this rationale, it should include all interest bearing debt, short term as well as long term. Non-interest bearing liabilities such as accounts payable, supplier credit and accrued items should be incorporated into working capital and should not be counted as debt.
To the extent that firms fund their operations with off-balance sheet debt, you should try to incorporate these borrowings as well into debt. While this may be difficult to do when firms are deceitful, you can, at the minimum, bring the present value of operating lease commitments into your debt.
One final comment, Analysts are often tempted to include more items in debt, assuming that this is the conservative thing to do. In reality, defining debt much more broadly will increase the debt ratio and reduce the cost of capital. This, in turn, will increase value and not decrease it.
Why do we use market value weights to come up with a cost of capital instead of book value weights
While we can present pragmatic arguments for using market value - that market value weights will always be positive whereas book equity can turn negative or that the costs of equity and debt represent current costs and the values used for each should be a current market value as well - the real reason is a little deeper. Every discounted cashflow valuation is ultimately a hypothetical acquisition valuation, where we buy all of the debt and the equity in the firm and acquire the business. Since we have to pay market values when we buy debt and equity, we should market values to compute the weights.
The use of market value weights to compute cost of capital does create a problem of circular reasoning. The cost of capital, after all, is used to estimate the values of debt and equity that will generally be different from the market value weights used in the first place. If we use the hypothetical acquisition argument, this is not a problem. We will buy at the prevailing market values of debt and equity, even though our estimated values are different. If we want to restore consistency to the valuation, we can use our estimated values of debt and equity to compute the cost of capital and iterate to a solution. This is a good idea when valuing private businesses or initial public offerings, where there is no market value to begin with.
In private businesses, neither debt nor equity is traded. In most publicly traded firms, equity has a market value but a significant portion (or often all) of the debt is not publicly traded.
a. How do you get market value of debt when all or even some of your firm's debt is bank debt and not publicly traded? How would you compute an updated cost of debt for an unrated company with bank debt?
b. How do you get a market value of equity for a private business?
a. How do you get market value of debt when all or even some of your firm's debt is bank debt and not publicly traded? How would you compute an updated cost of debt for an unrated company with bank debt?
The questions are related. After all, we rely on traded bonds or bond ratings to come up with an updated cost of debt. To estimate the cost of debt for an unrated company, we would estimate a synthetic rating based upon the company's financial ratios. In its simplest form, you can estimate a synthetic rating for a firm based upon its interest coverage ratio. By estimating a default spread based upon this synthetic rating and adding it to the riskfree rate, you can estimate an updated pre-tax cost of debt for this firm.
While many analysts assume that book debt is equal to market debt to get over the fact that most debt is not traded, there is a reasonable approximation that you can use to estimate market value of debt. Consider the book debt to be the equivalent of a coupon bond, with the book value of the debt representing face value, the interest payments comprising the coupon and the weighted average maturity of the debt representing the maturity of the bond. Using the pre-tax cost of debt from the synthetic rating as the interest rate, you can compute the market value of this bond.
b. How do you get a market value of equity for a private business?
You can do it in one of two ways. One is to use a multiple of earnings or book value, based upon what publicly traded firms in the business trade at, to get an estimate of market value of equity. The second is to use the iterative process, where you use your estimated values of debt and equity to compute the weights in the cost of capital. The one thing you should avoid doing is using book value weights.
Can the weights change from year to year in computing the cost of capital?
Not only can the weights on debt and equity change, but so can the other components - cost of equity, cost of debt and tax rate. In fact, you should expect the cost of capital to change for most firms, and especially so for young firms or firms in transition. Generally, firms that are young and risky have high costs of equity and debt, little or no debt and high costs of capital. As you expect these firms to grow and mature over time, you would expect the costs of equity and debt to come down, the debt ratio to increase and the cost of capital to decline.
The practical question that you will face is in coming up with these target debt ratios and costs of funding. There are two solutions. One is to look at industry averages, especially the averages for mature firms in the business for all of these components. The other is to compute the optimal debt ratio (with all the components) for your firm.
In conventional practice, firms are often valued with a constant debt ratio and cost of capital over time. This is why there is much debate about whether one should use actual debt ratio weights or target weights, with many analysts arguing for the latter. Either extreme will be incorrect, with the former leading to too low a value for young and risky firms and the latter to too high a value (since you are assuming that the firm will do tomorrow what it cannot really do for another 5 or 10 years). The best compromise is to start with the actual debt ratio and move to your target debt ratio over time.
There are a number of different risk and return models in finance used to compute the cost of equity but they all assume that the marginal investor is well diversified. If you use these models to estimate costs of equity for private or closely held firms, are you likely to under or over estimate the cost of equity? How would you fix the bias?
When you use conventional risk and return models (such as the CAPM, APM and multi-factor models) to estimate costs of equity for a private firm, you will tend to under estimate the risk in the firm. This is because these models look at only the portion of the risk that is not diversifiable and assume that the remaining risk will be diversified away. To the extent that private business owners or the investors in closely held firms are not diversified, they will be cognizant of all risk (and not just the market risk). In fact, if you know how much of the risk in the firm is market risk, you can compute a modified beta for the CAPM:
Total Beta = Market Beta/ Correlation between stock and the market
For a private business, both the market beta and the correlation will have to come from looking at publicly traded firms in the same business. For example, assume that you have to estimate the cost of equity for a private software firm. If the average market beta of software firms is 1.20 and only 25% of the risk in software firms is from the market (correlation with the market), the total beta for the software firm will be:
Total beta = 1.20/ .25 = 4.80
This total beta can be used to come up with a much higher cost of equity for a private business. As the owner of the private firm diversifies (either by taking his firm into other business or by withdrawing some of his or her wealth out of the business and investing in an index fund or a pension fund), the total beta will decrease.
Multinationals now operate and trade in different markets and different currencies. Which riskfree rate should you use to value a company (Nestle, for instance)?
You can value any company in any currency. The riskfree rate that you use will reflect the currency you decided to do the valuation in. For instance, you would use the U.S. treasury bond rate as your riskfree rate if you were valuing Nestle in U.S. dollars. If you decided to value Nestle in Swiss francs, you would use the 10-year Swiss franc government bond rate. If you shift to a Euro valuation of Nestle, your riskfree rate has to be a Euro riskfree rate. Since a dozen different European governments issue 10-year Euro bonds, you should go with the bond with the lowest interest rate since it is likely to be closest to being riskfree.
Extending this concept, your valuation should not be a function of which currency you decide to do the valuation in; a company should not go from being over valued in one currency to under valued in another currency at the same point in time. For this proposition to hold, though, your forecasts of future exchange rates (which you will need to convert your cashflows into a base currency) have to be consistent with your interest rate assumptions. Put simply, valuation will be invariant to currency choices only if you assume purchasing power parity.
Most analysts estimate risk premiums by looking at historical data in the United States. What are the perils of historical premiums?
The obvious problem is that historical prremiums are backward looking when what you really want is the premium for the future. There are also three measurement problems:
· Historical risk premiums come with large standard errors. Even with 75 years of data on stock and bond returns, which we can get for the United States, the standard errors remain high (about 2.5%). The problem becomes worse in emerging markets with less data. If you go further back in time (to 1871, for example), you run the risk of getting a risk premium that means very little at the current time.
· If you decide to use historical data in the United States because you have a long and easily accessible history, you run into a problem of selection bias. After all, the U.S, market was the most successful market of the twentieth century; as a consequence, the premium you get will be too high as a forward-looking estimate. A more reasonable estimate would require you to look across a number of different equity markets over the twentieth century and compute an average premium over the markets.
· Markets are priced based upon investor assessments of how risky stocks are and how much of a premium they should charge for investing in stocks. In bullish times, stock prices rise as investors become more optimistic about the future and reduce their required risk premiums. As stock prices rise and deliver high positive returns, historical risk premiums go up. In other words, historical risk premiums rise just as investor's expected risk premiums decrease.
There is an alternative to historical premiums. Based upon how stocks are priced collectively (looking at a broad equity index) and the expected cashflows you would get from buying these stocks (dividends, for instance), you can back out the risk premium that investors are demanding. This risk premium is called an implied equity risk premium.The historical risk premium form 1928-2002 in the United States was 4.53%. The implied equity risk premium declined to 2% at the height of the bull market in 1999 and has averaged about 4% over the last 40 years.
Increasingly, we are called upon to value companies in emerging markets in Asia and Latin America and we have to estimate risk premiums there.
a. Should there be an additional country risk premium for investing in a Brazilian or a Chinese company?
b. If yes, how would you go about estimating it?
c. Once you estimate the country risk premium, should the same premium be added on for all companies in that country? If you don't think so, how would you go about estimating a company's exposure to country risk?
. Should there be an additional country risk premium for investing in a Brazilian or a Chinese company?
It is easy to make the argument that there is more risk in investing in China and Brazil than there is in investing in a developed market. It is much more difficult to show that this translates into an additional country risk premium. This is because the only risk that should affect the discount rate is non-diversifiable risk. If we assume that stocks in emerging markets are lightly correlated with each other and with developed markets, the risk in these markets should be diversifiable (by investors in companies, even if companies cannot do it themselves) and there should be no country risk premium. If, on the other hand, these markets are highly correlated with each other, there will be a country risk premium that reflects how sensitive that market is to global shocks.
Empirically, which view of the world is right? Two decades ago, when most investors had not discovered emerging markets, the argument that country risk could be diversified away had solid backing. Partly as a result of globalization (both in product and financial markets), the correlation between markets has steadily risen over time, making it imperative that we consider country risk explicitly.
b. If yes, how would you go about estimating it?
There are three approaches that are commonly used. One is to find a dollar or euro denominated bond issued by a country (such as the Brazilian dollar denominated C-Bond) and comparing the interest rate on this bond to the interest rate on a riskless bond in the same currency (such as the U.S. treasury bond). The resulting difference is called a country bond default spread and is added on to the mature market risk premium (from the United States). The second is to take the premium that you charge in the U.S. equity market and scale it by the relative volatility of the emerging market (volatility of the emerging market / volatility of the US market). Thus, if the Brazilian market is twice as volatile as the US market, you would double the risk premium used in the US. The third is a blended approach, where you multiply the country bond default spread by the relative volatility of the equity market in that country to the country bond (volatility of the equity market/ volatility of the country bond).
The country risk premium that you estimate should not be frozen over time. In other words, if you have a ten-year time horizon in your valuation, your country risk premium can and often should change over time reflecting your views of that country.
c. Once you estimate the country risk premium, should the same premium be added on for all companies in that country? If you don't think so, how would you go about estimating a company's exposure to country risk?
While it is the conventional practice to add the country risk premium as a constant to every company's cost of equity, it seems unfair. After all, some companies in an emerging market (especially those that get the bulk of their revenues from outside the emerging market) should be less exposed to country risk that others. One simple way of measuring a company's exposure to country risk is to look at the percent of revenues it derives from that market and scale it to what the average company in the market derives as revenues. This estimate (which we called lambda) can then be applied to the country-specific premium to estimate a cost of equity.
An alternate approach to discounted cashflow valuation is the adjusted present value approach, where you value the firm with no debt (unlevered firm) first and then consider the value effects of debt. What is the fundamental difference between the cost of capital approach and the APV approach and why might they give you different answers?
In the APV approach, the value of the firm is estimated keeping dollar debt fixed over time. The tax benefits are computed on this dollar debt and the expected bankruptcy cost is also based upon this dollar debt. In the cost of capital approach, the debt ratio of a firm is kept fixed over time. For firms that are growing over time, the cost of capital approach will tend to yield the higher estimate of value because it incorporates, into the current estimate of value, your estimates of tax benefits from future debt issues.
In practice, analysts who use APV add the expected tax benefits from debt to the unlevered firm value and all too often ignore expected bankruptcy costs (which are difficult to estimate). This valuation is incomplete since it counts in the benefits of debt but does not consider the costs.
Discounted cashflow valuations are usually based upon the assumption that your firm will survive as a going concern. If you are valuing a young firm or a distressed firm where there is a significant likelihood that the firm will not make it as a going concern, how do you reflect that in your valuation?
Discounted cashflow valuation is built on two fundamental assumptions. The first is that capital markets are open and always accessible; thus firms that need to raise fresh capital to cover cashflow needs do not have any trouble doing so. The other is that real asset markets are liquid. In other words, a company that ceases operations will still get the present value of the expected cashflows from its assets in a sale. In reality, capital markets sometimes shut down and distress sales are at discounted prices.
While adherents to DCF valuation will claim that the discount rates (costs of equity and capital) can be adjusted to reflect the likelihood and consequences of distress, discount rates are blunt instruments that are more suited for dealing with volatility risk (that earnings and cashflows will be volatile) than for truncation risk (i.e., that the firm will not be around in 3 years).
A better way to deal with the risk of truncation would be to do the following. First, assume that your firm will be a going concern and do a discounted cash flow valuation of it. Second, assess the probability that your firm will not be a going concern; a good place to look would be the bond market if the company has bonds outstanding. Third, estimate the distress sale value of the assets in the event of bankruptcy. Finally, compute the expected value of the firm = probability of going concern * DCF value + probability of distress * distress sale value.
What have you not valued yet? (In other words, what do you need to add on to the present value?)
If you are valuing the firm (rather than equity), you began with operating income as your measure of earnings to get to cashflows. Therefore, you have not valued any assets whose earnings are not part of operating income. The first of these assets is cash and marketable securities - interest income from these holdings shows up below the operating income line. You have to add the value of cash and marketable securities to your operating asset value. The second is minority holdings in other companies. The income from these cross holdings is variously accounted for but is almost never part of operating income. If you wanted a complete valuation, you would have to value each of these subsidiary companies individually and take the share of each company that your company owns into consideration. If you have a majority holding in another company, you have a different problem since you are required to consolidate 100% of that company into your financials. If you want your valuation to hold up to scrutiny, it is best to remove the consolidated subsidiary from your financials, value the parent company first and then add the majority stake of the consolidated subsidiary to this value.
If you are valuing equity, using net income or earnings per share as your starting point, you have valued cash and cross holdings implicitly since the income from these holdings is part of net income. The problem, though, is that you have also implicitly assumed that the share of income generated by these assets (cash and cross holdings) will not change over time. This is a dangerous assumption. It is safer to remove the income from cash and cross holdings from your net income, value equity based upon this adjusted net income and then add on cash and your share of cross holdings at the end of the process.
What do you need to subtract from firm value to get to the value of equity?
You would need to subtract out the market value of anything that you considered debt for your cost of capital calculation. Thus, you should subtract out the market value of all interest bearing debt, short as well as long term, and the present value of operating leases and other off-balance sheet debt that you can identify. Why market rather than book value? Even if the book value of debt is substantially higher than market value, a discounted cash flow valuation is based upon a going concern assumption and going concerns pay the cashflows on debt as they come due (and the market value reflects the present value of these cashflows). An alternative is do a liquidation valuation of the assets of the firm and subtract out the book value of the debt outstanding.
If your firm has other potential obligations, this is the place to show them. For instance, a tobacco firm can be expected to lose at least some of the lawsuits that are pending against it. The expected value of the payout (as a result of losing the lawsuit) should be subtracted from firm value to get to equity value. For firms with under funded pension and health care plans, you should subtract out the extent of the underfunding to get to the value of equity.
It is common practice in valuation to add a premium for control this value or subtract out a discount (minority, marketability, private company etc.). Is this a reasonable practice?
If you do a valuation right, there should be no need to apply discounts and premiums for most items to the estimated value. Consider the widely applied private company discount in the valuation of publicly traded companies. The rationale is that discounted cashflow valuations assume that a firm is optimally managed and most firms are not. This is patently absurd since the analyst chooses the inputs that go into the discounted cashflow valuation. If a firm is poorly managed with a sub-optimal debt ratio and a low return on capital, the discounted cashflow valuation with these inputs will already reflect the poor management. Consider also the premium that is often applied for control. To value control, all you would need to do is re-value the firm with optimal management and the difference between this value and the status quo value should be the value of control.
Liquidity is a tougher problem. All investments are illiquid, but to varying degrees; for publicly traded firms, it takes the form of a bid-ask spread and for private firms it takes the form of a discount on estimated value. The key is to be discriminating. Not all private companies are equally illiquid. Applying a rule of thumb (25-30% is widely used) strikes us as inappropriate.
How do you get from the value of equity to the value of equity per share?
If the firm has issued no equity options (to management as compensation or the market in the form of convertibles or warrants), you can divide by the number of shares and you should have the value of equity per share. If the firm has issued equity, it is best to value these equity options as options (rather than at exercise value), to subtract the value of equity options from the overall value of equity and then divide by the actual number of shares outstanding. The practice of using diluted shares that many analysts use as an alternative is a blunt instrument for dealing with options since there is no way to discriminate between options that are in the money to differing degrees.
What about expected stock issues in the future? If you do your DCF valuation right, they should already be incorporated into your present value. After all, you make equity issues to either cover negative cashflows in the future (and the present value of these negative cashflows will reduce the value today) or to change your financing mix (in which case your cost of capital in future years will change as the debt ratio changes).