Cash Accounting, Accrual Accounting, and Discounted Cash Flow Valuation

By Penman, S.H.

Edited by Paul Ducham


Many investment texts focus on the dividend discount model in their valuation chapter. At first sight, the model is very appealing. Dividends are the cash flows that shareholders get from the firm, so value should be based on expected dividends. In valuing bonds we forecast the cash flows from the bond, so, in valuing stocks, why not forecast the cash flows from stocks? The dividend discount model is stated as follows:

Value of equity = Present value of expected dividends (4.1)

value of equity

(The ellipsis in the formula indicates that dividends must be forecast indefinitely into the future, for years 5, 6, and so on.) The model instructs us to forecast dividends and to convert the forecasts to a value by discounting them at one plus the equity cost of capital, ρE. One might forecast varying discount rates for future periods but for the moment we will treat the discount rate as a constant. The dividend discount model is a straight application of the bond valuation model to valuing equity. That model works for a terminal investment. Will it work for a going-concern investment under the practical criteria?
     Well, going concerns are expected to pay out dividends for many (infinite?) periods in the future. Clearly, forecasting for infinite periods is a problem. How would we proceed by forecasting (realistically) for a finite period, say 10 years? For a finite horizon forecast of T years, we might be able to predict the dividends to Year T but we are left with a problem: The payoff for T years includes the terminal price, PT, as well as the dividends, so we also need to forecast PT, the price at which we might sell at the forecast horizon. Forecasting just the dividends would be like forecasting the coupon payments on a bond and forgetting the bond repayment. This last component, the terminal payoff, is also called the terminal value. So we have the problem of calculating a terminal value such that

Value of equity= Present value of expected dividends to time T + Present value of expected terminal value at T (4.2)


You can see that this model is technically correct, for it is simply the present value of all the payoffs from the investment that are laid out in Figure 3.3. The problem is that one of those payoffs is the price that the share will be worth T years ahead, PT. This is awkward, to say the least: The value of the share at time zero is determined by its expected value in the future, but it is the value we are trying to assess. To break the circularity, we must investigate fundamentals that determine value.
     A method often suggested is to assume that the dividend at the forecast horizon will be the same forever afterward. Thus

Equity (4.3)

The terminal value here (in the bracketed term) is the value of a perpetuity, calculated by capitalizing the forecasted dividend at T + 1 at the cost of capital. This terminal value is then discounted to present value.

This perpetuity assumption is a bold one. We are guessing. How do we know the firm will maintain a constant payout? If there is less than full payout of earnings, one would expect dividends to grow as the retained funds earn more in the firm. This idea can be accommodated in a terminal value calculation that incorporates growth:

Equity (4.4)

where g is 1 plus a forecasted growth rate.1 The terminal value here is the value of a perpetuity with growth. If the constant growth starts in the first period, the entire series collapses to V0E = d1/(ρE – g), which is sometimes referred to as the constant growth model. See Box 4.1.
     What would we do, however, for a firm that might be expected to have zero payout for a very long time in the future? For a firm that has exceptionally high payout that can’t be maintained? What if payout comes in stock repurchases (that typically don’t affect shareholder value) rather than dividends?

        The truth of the matter is that dividend payout over the foreseeable future doesn’t mean much. Some firms pay a lot of dividends, others none.A firm that is very profitable and worth a lot can have zero payout and a firmthat is marginally profitable can have high payout, at least in the short run. Dividends usually are not necessarily tied to value creation. Indeed, firms can borrow to pay dividends, and this has nothing to do with their investing and operating activities where value is created. Dividends are distributions of value, not the creation of value.
       Dividends are not relevant to value. To be practical we have to forecast over finite horizons. To do so, the dividend discount model (equation 4.2) requires us to forecast dividends up to a forecast horizon plus the terminal price. But payoffs (dividends plus the terminal price) are insensitive to the dividend component: If you expect a stock to pay you more dividends, it will pay off a lower terminal price; if the firm pays out cash, the price will drop by this amount to reflect that value has left the firm. Any change in dividends will be exactly offset by a price change such that, in present value terms, the net effect is zero. In other words, paying dividends is a zero-NPV activity. That’s dividend irrelevance! Dividends do not create value. If dividends are irrelevant, we are left with the task of forecasting the terminal price, but it is price that we are after. Box 4.2 summarizes the advantages and disadvantages of the dividend discount model.
         This leaves us with the so-called dividend conundrum: Equity value is based on future dividends, but forecasting dividends over a finite horizon does not give an indication of value. The dividend discount model fails the first criterion for a practical analysis. We have to forecast something else that is tied to the value creation. The model fails the second criterion—validation—also. Dividends can be observed after the fact, so a dividend forecast can be validated for its accuracy. But a change in a dividend from a forecast may not be related to value at all, just a change in payout policy, so ex-post dividends cannot validate a valuation.

The failure of the dividend discount model is remedied by looking inside the firm to the features that do create value—the investing and operating activities. Discounted cash flow analysis does just that.

Box 4.1

Dividend Discount Analysis 4.2


Easy concept:   Dividends are what shareholders get, so forecast them.

Predictability:  Dividends are usually fairly stable in the short run so dividends are easy to forecast (in the short run).


Relevance:   Dividend payout is not related to value, at least in the short run; dividend forecasts ignore the capital gain component of payoffs.

Forecast horizons:   Typically requires forecasts for long periods.


When payout is permanently tied to the value generation in the firm. For example, when a firm has a fixed payout ratio (dividends/earnings).


One can conclude that Coke is worth $40.67 per share because it can generate considerable cash flows. But now look at Exhibit 4.2 where cash flows are given for General Electric for the same five years. GE earned one of the highest stock returns of all U.S. companies from 1993–2004, yet its free cash flows are negative for all years except 2003.
      Suppose you were thinking of buying GE in 1999. Suppose also that, again with perfect foresight, you knew then what GE’s cash flows were going to be and had sought to apply a DCF valuation. Well, the free cash flows are negative in all but one year and their present value is negative! The last cash flow in 2004 is also negative, so it can’t be capitalized to yield a continuing value. And if, in 2004, you had looked back on the free cash flows GE had produced, you surely would not have concluded that they indicate the value added to the stock price.
        Exhibit 4.2 also gives the cash flows for Starbucks, the ubiquitous coffee chain, for 1996–2000. Starbucks has been quite successful, with coffee shops in so many countries that it has become a worldwide name. During the years 1996–2000, the firm's stock price more than doubled. Yet the free cash flows are consistently negative. Again, if you were standing at the beginning of 1996 and were given these (future) cash flows and asked to value the firm, you would have a great deal of trouble. As the free cash flows are negative up to 2000, your continuing value would have to be more than 100 percent of the value, yet you have no idea how to calculate it. Any calculation would be highly speculative. See Box 4.3.
       Why does DCF valuation not work for these firms? The short answer is that free cash flow does not measure value added from operations. Cash flow from operations is value flowing into the firm from selling products but it is reduced by cash investment. If a firm invests more cash in operations than it takes in from operations, its free cash flow is negative. And even if investment is positive NPV (it adds value), free cash flow is reduced. Investment is treated as a “bad” rather than a “good.” Of course, the return to investments will come later in cash flow from operations, but the more investing the firm does for a longer period in the future, the longer the forecasting horizon has to be to capture these cash inflows. GE has continually found new investment opportunities so its investment has been greater than its cash inflow. Starbucks, a growing firm, is continually opening more stores and that investment gives it negative free cash flow even though the investments are made to add value. Many growth firms—that generate a lot of value—have negative free cash flows.
       How can a firm double its stock price while generating negative cash flows? Well, free cash flow is not really a measure about adding value in operations. It confuses investments (and the value they create) with the payoffs from investments, so it is partly an investment or a liquidation concept. A firm decreases its free cash flow by investing and increases it by liquidating or reducing its investments. But a firm is worth more if it invests profitably, not less. If an analyst forecasts low or negative free cash flow for the next few years, would we take this as a lack of success in operations? GE’s positive free cash flow in 2003 might have been seen as bad news because it resulted mostly from a decrease in investment. Indeed, Coke’s increasing cash flows in 2003 and 2004 in Exhibit 4.1 result partly from a decrease in investment. Decreasing investment means lower future cash flows, calling into question the 5 percent growth rate used in Coke’s continuing value calculation.
       Free cash flow would be a measure of value from operations if cash receipts were matched in the same period with the cash investments that generated them. Then we would have value received less value surrendered to gain it. But in DCF analysis, cash receipts from investments are recognized in periods after the investment is made, and this can force us to forecast over long horizons to capture value. DCF analysis violates the matching principle.
       A solution to the GE and Starbucks valuation problem is to have a very long forecast horizon. But this offends the first criterion of practical analysis. It requires too much speculation about the long run. It is the long run that we are very uncertain about. See Box 4.3.

Box 4.4 summarizes the advantages and disadvantages of DCF analysis.

DCF Valuation and Speculation 4.3

Valuation is a matter of disciplining speculation about the future. In choosing a valuation technology, two of the fundamentalist’s tenets come into play: Don’t mix what you know with speculation and Anchor a valuation on what you know rather than on speculation. A method that puts less weight on speculation is to be preferred, and methods that admit speculation are to be shunned. We know more about the present and the near future than about the long run, so methods that give weight to what we observe at present and what we forecast for the near future are preferred to those that rely on speculation about the long run. To slightly misapply Keynes’s famous saying, in the long run we are all dead. This consideration is behind the criterion that a good valuation technology is one that yields a valuation with finite-horizon forecasts, and the shorter the horizon the better. Going concerns continue into the long run, of course, so some speculation about the long run is inevitable. But, if a valuation rides on speculation about the long run—about which we know little—we have a speculative, uncertain valuation indeed.
      Discounted cash flow valuation lends itself to speculation. The General Electric and Starbucks cases in Exhibit 4.2 are good examples. An analyst trying to value GE in 1999 may have a reasonably good feel for likely free cash flows in the near future, 2000 and 2001, but that would do her little good. Indeed, if she forecast the cash flows over the five years, 2000–2004 with some confidence, that would do little good. These cash flows are negative, so she is forced to forecast (speculate!) about free cash flows that may turn positive many years in the future. In 2010, 2015, 2020? These cash flows are hard to predict; they are very uncertain. In the long run we are all dead. The same can be said for Starbucks. A banker or analyst trying to justify a valuation might like the method, of course, for it is tolerant to plugging in any numbers, but a serious investor does not want to rely on such speculation.
      Speculation about the long run is contained in the continuing value calculation. So another way of invoking our principles is to say that a valuation is less satisfactory the more weight it places on the continuing value calculation. You can see with GE and Starbucks that, because cash flows up to the forecast horizon are negative, a continuing value calculation drawn at the forecast horizon would be more than 100 percent of the valuation. A valuation weighted toward forecasts for the near term is preferable, for we are more certain about the near term than the long run. But GE’s and Starbucks’s near term cash flows do not lend themselves to a valuation.

Discounted Cash Flow Analysis 4.4


Easy concept: Cash flows are “real” and easy to think about; they are not affected by accounting rules.

Familiarity: Cash flow valuation is a straightforward application of familiar present value techniques.


Suspect Free cash flow does not measure value concept: added in the short run; value gained is not matched with value given up. Investment is treated as a loss of value. Free cash flow is partly a liquidation
concept; firms increase free cash flow by cutting back on investments.

Forecast Typically, long forecast horizons are required
horizons: to recognize cash inflows from investments, particularly when investments are growing.Continuing values have a high weight in the valuation.
Not aligned with Analysts forecast earnings, not free what people cash flow. forecast:

When the investment pattern produces positive constant free cash flow or free cash flow growing at a constant rate; a “cash cow” business.
     DCF is useful when equity investments are terminal or the investor needs to “cash out,” as in leverage buyout situations and private equity investment where debt must be paid down or investors must be paid out within a certain Time Frame, so the ability to generate cash is important.

Exhibit 4.1

Exhibit 4.2


The cash flow statement under IFRS is similar to the U.S. statement, with a few exceptions:

1. Under IFRS, firms can classify dividends paid and received as either operating or financing activity. If a firm chooses to classify dividends paid as an operating activity, the analyst must transfer it to the financing section: Dividends paid are a distribution of cash from operations to shareholders, not cash used up in operations. But dividends received are appropriately operating items if they are dividends from investing in other businesses as part of the business plan.

2. Firms can classify interest paid and received as either operating or financing activity. If classified as an operating activity, the analyst must adjust cash from operations for the net interest (after tax), as in the United States (Box 4.5).

3. Taxes paid are in cash from operations (as in the United States), unless they can be specifically identifiable with a financing or investing activity. Purchases and sales of interest-bearing securities are classified as cash investing activities, as in the United States, so the same adjustment to cash investment must be made ( and Box 4.5).

Box 4.5


For DCF analysis we need forecasts of free cash flow that will be reported in the cash flow statement in the future. However, developing such forecasts without first forecasting sales and earnings is difficult. These are accrual numbers, so forecasts of free cash flow are made by converting earnings forecasts into forecasts of cash flows from operations, then deducting anticipated investment in operations. The difference between earnings (net income) and cash from operations is due to income statement accruals, the noncash items in net income, and these accruals are indicated by the difference between net income and cash from operations in the cash flow statement. The accruals in Nike’s 2010 statement total $1,257.5 million. Deducting these accruals from net income—and making the adjustment for after-tax interest—produces cash flow from operations. Box 4.6 shows you how to convert Nike’s earnings to cash flow from operations and, with a deduction for new investments in operations, to free cash flow.
       Forecasting future accruals is not all that easy. People resort to shortcuts by forecasting earnings before interest and taxes (ebit), deducting taxes that apply to ebit, then making the accrual adjustment by adding back depreciation and amortization (in the cash flow statement) plus the change in working capital items involved in operations. This is only an approximation, and somewhat cumbersome. The common method that starts with ebit is demonstrated for Nike in Box 4.6.
       We must ask whether the exercise of converting earnings forecasts to cash flows is a useful one, particularly if we end up with the negative free cash flows we saw for General Electric and Starbucks in Exhibit 4.2. Can we value a firm from earnings forecasts rather than cash flow forecasts and save ourselves the work in making the conversion? The answer is yes. Indeed we will now show that taking the accruals out of earnings can actually introduce more complications to the valuation task and produce a more speculative valuation.

Box 4.6


These are of two types, revenue accruals and expense accruals.
Revenues are recorded when value is received from sales of products. To measure this value inflow, revenue accruals recognize value increases that are not cash flows and subtract cash inflows that are not value increases. The most common revenue accruals are receivables: A sale on credit is considered an increase in value even though cash has not been received. Correspondingly, cash received in advance of a sale is not included in revenue because value is not deemed to have been added: The recognition of value is deferred (as deferred or unearned revenue) until such time as the goods are shipped and the sale is completed.
     Expense accruals recognize value given up in generating revenue that is not a cash flow. Cash payments are modified by accruals by recognizing amounts incurred in generating revenues but not yet paid and amounts paid in the past for generating revenues in the current period. Pension expense is an example of an expense incurred in generating revenue that will not be paid until later. Wages payable is another example. A prepaid wage for work in the future is an example of cash paid for expenses in advance. Depreciation arises from cash flows in the past for investments in plant. Plants wear out. Depreciation is that part of the cost of the investment that is deemed to be used up in producing the revenue of the current period. Income tax expense, includes taxes due for the period but not paid and cost of goods sold excludes cash paid for production of merchandise that has not yet been sold.
       Accruals for a period are reported as the difference between net income and cash flow from operations in the statement of cash flows. We saw in Box 4.6 that Nike had $1,257.5 million in accruals in 2010.
       Accruals change the timing for recognizing value in the financial statements from when cash flows occur. Recognizing a receivable as revenue or recognizing an increase in a pension obligation as expense recognizes value ahead of the future cash flow; recognizing deferred revenue or depreciation recognizes value later than cash flow. In all cases, the concept is to match value inflows and outflows to get a measure of value added in selling products in the market.Timing is important to our first criterion for practical valuation analysis, a reasonably short forecast horizon. You readily see how recognizing a pension expense 30 years before the cash flow at Retirement is going to shorten the forecast horizon.We will now see how deferring recognition until after a cash flow also will shorten the forecast horizon.


The performance measure in DCF analysis is free cash flow, not cash flow from operations. Free cash flow is cash generated from operations after cash investments, C – I, and we saw that investments are troublesome in the DCF calculation because they are treated as decreases in value. But investments are made to generate value; they lose value only later as the assets are used up in operations (as depreciation). The value lost in operations occurs after the cash flow. The earnings calculation recognizes this. Effectively, earnings adds investment back to the free cash flow to correct the error in free cash flow as a measure of value added:

Earnings = Free cash flow − Net cash interest + Investments + Accruals  (4.11)

Because accrual accounting places investment in the balance sheet as assets, it does not affect income. Accrual accounting then recognizes decreases in those assets in subsequent periods in the form of depreciation accruals (and other amortizations) as assets lose value in generating revenue. Box 4.7 explains the differences between cash flow and earnings, with a demonstration for Nike. Note that investments are really accruals also, so accruals plus investment is sometimes referred to as total accruals.
       To appreciate the full details of how accrual accounting works, you must grasp a good deal of detail. Here we have seen only a broad outline of how the accounting works to measure value flows.
       The outline of earnings measurement here nominally describes how the accounting works, and our expression for earnings above looks like a good way to measure value added. But there is no guarantee that a particular set of accounting rules—U.S. GAAP or international accounting standards, for example—achieves the ideal. Yes, depreciation nominally matches value lost to value gained, but whether this is achieved depends on how the depreciation is actually measured. This is true for all accruals. Cash flows are objective, but the accruals depend on accounting rules, and these rules may not be good ones. Indeed, in the case of depreciation, firms can choose from different methods. Many accruals involve estimates, which offer a potential for error. Accruals can be manipulated to some degree. R&D expenditures are expensed in the income statement even though they are investments. These observations suggest that the value-added measure, net income, may be mismeasured, so a valuation technique based on forecasting earnings must accommodate this mismeasurement. Indeed, one rationale for DCF analysis is that the accounting is so suspect that one must subtract or “back out” the accruals from income statements to get to the “real cash flows.” We have seen in this chapter that this induces problems, however.

Accounting Clinic II

Accounting Clinic II, on the book’s Web site, lays out in more detail how accrual accounting works and contrasts accrual accounting with cash accounting. After going through this clinic you will understand how and when revenues are recorded and why cash received from customers is not the same as revenues recorded under accrual accounting. You also will understand how accrual accounting records expenses. You will see how the matching principle—to measure value added—is applied through the rules of accrual accounting. You also will recognize those cases where GAAP violates the principle of good matching. And you will appreciate how accrual accounting affects not only the income statement but also the balance sheet.

Box 4.7


The investments (which are not placed in the income statement) are there—inventories, land, buildings, equipment, and intangible assets. But the statement also has accruals. Shareholders’ equity is assets minus liabilities, so one cannot affect the shareholders’ equity through earnings without affecting assets and liabilities also. Thus, as earnings add to shareholders’ equity, they also add to assets minus liabilities. Credit sales, recognized as a revenue accrual on Nike’s income statement, produce receivables on the balance sheet and estimates of bad debts and sales returns reduce net receivables. Inventories are costs incurred ahead of matching against revenue in the future. Nike’s property, plant, and equipment are investments whose costs will later be matched against revenues as the assets are used up in producing those revenues. On the liability side, Nike’s accrued liabilities and accounts payable are accruals. Accrued marketing and promotion costs, for example, are costs incurred in generating revenue but not yet paid for.
       Indeed all balance sheet items, apart from cash, securities that absorb excess cash, and debt and equity financing items, result from either investment or accruals. To modify free cash flow according to the accounting relation (equation 4.11), investments and accruals are put in the balance sheet.
        Box 4.8 gives some examples of specific accruals and how they affect both the income statement and the balance sheet.
      The investments and accruals in the balance sheet take on a meaning of their own, either as assets or liabilities. An asset is something that will generate future benefits. Accounts receivable are assets because they are cash to be received from customers in the future. Inventories are assets because they can generate sales and ultimately cash in the future. A liability is an obligation to give up value in the future. Accrued compensation, for example, is a liability to pay wages; a pension liability, an obligation to pay pension benefits. Property, plant, and equipment are assets from investment but subtracting accumulated depreciation recognizes that some of the ability to generate future cash has been given up in earning revenues to date. So net assets (assets minus liabilities) are anticipated value that comes from investment but also anticipated value that is recognized by accruals.
       To close, go back to the cash flows for General Electric and Starbucks in Exhibit 4.2. We saw there that valuating these firms on the basis of their negative free cash flows was hopeless. The exhibit also gives the earnings for these firms. We understand now that these earnings differ from the free cash flows because of the accruals and investments recognized by accrual accounting. In contrast to the free cash flows, the earnings are positive and indeed growing at a fairly regular rate. Earnings look like a better basis for valuing a firm than cash flows.
        Some versions of DCF valuation handle the free cash flow problem by dividing investment into “maintenance capital expenditure” and “growth investment.” Maintenance capital expenditure is investment to maintain operations at their current level—replacing existing assets, for example—whereas growth investment is investment to enlarge operations. This is really a form of accrual accounting where maintenance capital expenditure is a measure of depreciation, expensed immediately in the income statement, with growth investment placed on the balance sheet. So it is a question of whether this is good accrual accounting. Distinguishing the two types of investment is quite difficult in practice where firms are dynamically changing their business, Dropping Products and adding new ones, investing in new locations, Outsourcing, and so on, never really having the same business. Maintenance capital expenditure is an elusive notion requiring too much judgment for the fundamental investor. Note further, that practitioners of this type of (modified) DCF valuation make the mistake of not depreciating the growth investment that is implicitly placed on the balance sheet, so it is never charged against cash flows.

box 4.8