A User's Guide to Understanding the Discounted Future Benefits (Cash Flow) Valuation Methods
INTRODUCTION
We often give presentations to law firms on issues pertaining to business appraisal and investment banking. During a recent presentation to the tax and corporate departments of a Memphis law firm, I was asked about DCF. This question sparked the idea for the content of this issue because discounted future benefits valuation methods, often called discounted cash flow methods, are at once, theoretically sound, fairly straightforward in terms of concept, widely used, and widely misunderstood.
[**Reader Clue Number 1. I’ve tried to minimize the technical elements in this discussion to focus on a few key areas of judgment that are important for users of valuation reports and for appraisers. And I’ve tried to keep the length to a minimum. Nevertheless, the subject is an important one. If, as you begin to read this issue, you find that your tolerance for "the technical" is running low or your patience with length has reached its limits, print this newsletter and file it or bookmark our website so you can easily retrieve it. This issue of the E-Law newsletter will be important for you the next time you or one of your associates needs to understand a discounted cash flow valuation method.**]
DISCOUNTED FUTURE BENEFITS DEFINED
Discounted future benefits is a method used to determine the net present value of future income flows. The most frequently used variation of the discounted future benefits family is called discounted cash flow (DCF). Discounted future benefits is the flip side of the concept of compound interest. We learn in school that a dollar invested "at interest" will grow over time, and that a dollar regularly (or periodically) invested at interest will grow even faster. Normally, then, we begin with the investment and determine or estimate what it will be worth at some point in the future.
With discounted future benefits, we begin with the future stream of benefits and ask what is the PRESENT VALUE of that stream of benefits. In order to answer the question, we must discount the expected future benefits to the present at an appropriate discount rate.
OVERVIEW OF DISCOUNTED FUTURE BENEFITS
In essence, the discounted future benefits methodology requires just three basic elements.
TYPES OF DISCOUNTED FUTURE BENEFITS METHODS
Appraisers use two different sub-methods of the DFB method, equity methods (DCF or DNI, which project measures of earnings available to the equity holders of a business) and total capital measures (DFNCF or DFNI, which project earnings available to the equity and debt holders, i.e., to the total capital of the enterprise).
EQUITY METHODS
DISCOUNTED (NET) CASH FLOW (DCF). This is the basic DCF method. Net cash flow is forecasted into the future and is generally defined as:
Some appraisers attribute great weight and importance to the DCF method, suggesting that the method is theoretically more rigorous than, for example, a direct capitalization of earnings method. But the DCF method is not inherently better or worse than other valuation methods. As you will see below, appraisers must use common sense, informed judgment and reasonableness in the utilization of the DCF method as with any other valuation method.
DISCOUNTED NET INCOME (DNI). The net income of a business is projected into the future.
With either the DCF or DNI methods, which measure cash flows available to equity owners of a business, an appropriate equity discount rate should be used. There is a debate among appraisers regarding whether a discount rate developed using the Capital Asset Pricing Model is applicable to net income or net cash flow. I have generally taken the position that the Adjusted Capital Asset Pricing Model, which is the basic build-up method used by most appraisers, yields discount rates applicable to the net income of a business, although other writers have disagreed with me. [See Mercer, "The Adjusted Capital Asset Pricing Model for Developing Capitalization Rates ...", BUSINESS VALUATION REVIEW, Vol. 8, No. 4, December, 1989, pp. 147-156. See also "Exhibit 8-2, The Adjusted Capital Asset Pricing Model," found in Mercer, QUANTIFYING MARKETABILITY DISCOUNTS (Memphis's Peabody Publishing, LP: 1997), pp. 260-267. This book is available from the publisher by calling 1-800-769-0967.]
I tend to use the basic build-up equity discount rate to discount net income, although I have, in some circumstances, used it to capitalize net cash flow. As a result of wrestling with this issue, I wrote what has become a widely cited article that develops a method for estimating any differences between net income and net cash flow discount rates. The article indicated that the difference between a net income and a net cash flow discount rate may not be, for many closely held business situations, as great as many appraisers think. [Mercer, "Adjusting Capitalization Rates for the Difference Between Net Income and Net Free Cash Flow," BUSINESS VALUATION REVIEW, Vol. 11, No. 4, December, 1992, pp. 201-207.]
For the reasons cited in the 1989 and 1992 articles, I believe that the ACAPM discount rate is generally applicable to the net income of a business. While appraisers may differ in opinions, there are two practical considerations that can mitigate differences in DFB valuations relative to this issue.
DEBT FREE NET CASH FLOW (DFNCF). This method is analogous to the DCF method, except that Earnings Before Interest and Taxes (EBIT) is generally fully taxed (to put the subject enterprise on a "debt-free" basis). Debt free net cash flow is then projected for the finite forecast period.
DEBT FREE NET INCOME (DFNI). Again, the analyst goes to the EBIT line on the income statement (before debt service) and taxes operating earnings to place the income statement on a debt-free basis.
With either of the total capital (debt-free) methods, the appropriate discount rate is the Weighted Average Cost of Capital (WACC). Appraisers make an assumption about the portion of equity and debt in the capital structure of a business and then weight the costs of equity (the equity discount rate) and of debt (the after-tax cost of borrowings) to develop a WACC. One common mistake is to weight debt and equity on a book value basis, when WACC should be determined based on market value weightings.
We have already identified four versions of the basic discounted future benefits methodology. An appraiser must decide which variation of DFB will be used and make decisions regarding the appropriate discount rate. So the conceptually simple discounted future benefits method is a bit more complex than it might at first seem.
THE PRACTICAL IMPACT OF DFB ASSUMPTIONS
To illustrate the importance of the assumptions in any discounted future benefits valuation, consider the following situation. Assume that we have found eight appraisers who agree on several assumptions with regard to a Discounted Net Income (DNI) valuation method:
The model assumptions noted above can generate eight possible combinations, and therefore, eight possible DNI values for the forecast upon which so much was apparently agreed upon by our eight appraisers. The remainder of this discussion will focus on the range of conclusions indicated by the low and high results under each assumption set.
The lowest value of the eight possibilities $13.3 million, is reached by the appraiser who selected the end of year convention, capitalized year five earnings for the terminal value, and discounted the terminal value to the present for a period of five years. The highest value, $15.2 million, is reached by the appraiser who selected the mid-year convention, capitalized year six earnings to develop the terminal value, and discounted the terminal value for a period of 4.5 years (the period of receipt of the last year’s earnings).
AFTER AGREEING ON SO MUCH, THE APPRAISERS HAVING THE LOWEST AND HIGHEST ANSWERS ARE $1.9 MILLION APART, OR 13%-14%, DEPENDING ON WHETHER THE DIFFERENCE IS MEASURED FROM THE HIGHER OR THE LOWER VALUE.
We commented on the terminal value assumption above. The present values of the eight terminal values calculated accounted for between 65% and 70% of the total discounted present value indications. So we see that the assumptions made regarding the terminal value are critical. This fact lends support to appraisers who sometimes eschew discounted future benefits methods in favor of single-period income capitalization methods.
We ran the model above with all assumptions remaining the same, except that the equity discount rate was raised to 20%. The low and high indications were reduced to $8.5 million and $9.8 million respectively by the use of the higher discount rate. However, the percentage differences rose to the range of 13% to nearly 16%. The present values of the terminal values accounted for between 52% and 59% of the total discounted present value indications.
Although we have used a discounted net income model above, the sensitivity of a discounted cash flow model to variations based on seemingly minor assumptions would be similar for similar levels of net cash flow.
DEBT-FREE METHODS INCREASE SENSITIVITY
We can use the same basic model to simulate the sensitivity of debt-free discounted future benefits methods. All the assumptions above remain the same, except that the WACC (Weighted Average Cost of Capital) is assumed to be 13.25%. This is consistent with a 15% equity discount rate, a pre-tax debt rate of 8% (after-tax cost of 4.8% assuming a 40% tax rate), and an 83%-17% weighting of equity and debt in the capital structure (in this case, based on an assumed agreed upon guideline company group on a market value basis).
We are assuming that we have a debt-free net income of $1.7 million. We further assume that the subject enterprise has $14.0 million of debt. These assumptions are made to assure that our debt-free model is reasonably comparable with the net income model above in terms of equity valuation.
The market values of total capital (debt and equity) under the eight sets of assumptions range from $27.6 million to $31.5 million, a dollar difference of $3.9 million, and a percentage difference between 12% and 14%, depending on whether the high or the low is used as the base. This seems consistent with the earlier modeling.
But we are attempting to value the equity of the enterprise. If we subtract the $14.0 million of debt from the indicated values of total capital, the range of equity values is between $13.6 million ($31.5 million - $14.0 million) and $17.5 million ($31.5 million - $14.0 million). The indicated dollar range of equity values for presumably the same company as discussed above is $3.9 million. But the percentage differences widen substantially, ranging from 22% to 29%, depending upon whether the higher or lower equity value is considered the base.
For another perspective on the importance of the terminal value assumption, consider that under our DFNI model, the present value of the terminal value accounts for between 83% and 85% of the total value indicated by the method ON A TOTAL CAPITAL BASIS. However, when the terminal value, which is based on total capital, is compared with the resulting value of EQUITY, the present value of the terminal value accounts for between 180% and 203% of the resulting equity indications. All I can say is, wow!
We haven’t discussed the issue capital structure. Had one of the appraisers used a 75%/25% equity/debt weighting, a seemingly small difference (which lowers the WACC to 12.45%), other assumptions being the same, her equity values would have been about 25% higher.
One writer concluded a chapter on WACC with the following sentence: "There is much controversy about the potential impact on the WACC as a result of altering the capital structure." [Pratt, Shannon P., COST OF CAPITAL: ESTIMATION AND APPLICATIONS, (New York: John Wiley & Sons, 1998), p. 53] What understatement! And the quoted writer did not discuss the impact of the other issues raised in this newsletter.
LESSONS TO BE LEARNED
(Reprinted from Mercer Capital's E-Law Newsletter 99-01, January 8, 1999)
We often give presentations to law firms on issues pertaining to business appraisal and investment banking. During a recent presentation to the tax and corporate departments of a Memphis law firm, I was asked about DCF. This question sparked the idea for the content of this issue because discounted future benefits valuation methods, often called discounted cash flow methods, are at once, theoretically sound, fairly straightforward in terms of concept, widely used, and widely misunderstood.
[**Reader Clue Number 1. I’ve tried to minimize the technical elements in this discussion to focus on a few key areas of judgment that are important for users of valuation reports and for appraisers. And I’ve tried to keep the length to a minimum. Nevertheless, the subject is an important one. If, as you begin to read this issue, you find that your tolerance for "the technical" is running low or your patience with length has reached its limits, print this newsletter and file it or bookmark our website so you can easily retrieve it. This issue of the E-Law newsletter will be important for you the next time you or one of your associates needs to understand a discounted cash flow valuation method.**]
DISCOUNTED FUTURE BENEFITS DEFINED
Discounted future benefits is a method used to determine the net present value of future income flows. The most frequently used variation of the discounted future benefits family is called discounted cash flow (DCF). Discounted future benefits is the flip side of the concept of compound interest. We learn in school that a dollar invested "at interest" will grow over time, and that a dollar regularly (or periodically) invested at interest will grow even faster. Normally, then, we begin with the investment and determine or estimate what it will be worth at some point in the future.
With discounted future benefits, we begin with the future stream of benefits and ask what is the PRESENT VALUE of that stream of benefits. In order to answer the question, we must discount the expected future benefits to the present at an appropriate discount rate.
OVERVIEW OF DISCOUNTED FUTURE BENEFITS
In essence, the discounted future benefits methodology requires just three basic elements.
(1) Forecast of Expected Future Benefits. Generally, analysts develop forecasts of earnings and/or cash flows for periods ranging from 3 to 5 or 10 years. The most popular forecast period is 5 years, probably because that is the model found in most finance texts. Conceptually, one would forecast discrete earnings for as many periods as necessary until a stabilized earnings stream could be anticipated.After reading this newsletter, readers may never have the same confidence in a single DFB method that they have had in the past absent a testing of the model’s sensitivity to changes in key assumptions and/or a corroboration from other valuation methods.
(2) Determination of Terminal Value. The terminal value is the value of all income flows beyond the immediate, discrete forecast period. The terminal value is generally determined based on capitalizing earnings at the end of the forecast period. Earnings capitalization methods vary from a single-period earnings capitalization at that point using a variation of the Gordon model, to the application of current market multiples to forecasted income statement items.
(3) Selection of Appropriate Discount Rate. The discount rate is used to "discount" the forecasted benefits to the present. The sum of the present values of all the forecasted income flows (both the discretely forecasted years and the terminal value) is the net present value, or the present value of the expected flows, and is the value indication for a specific set of forecast assumptions.
TYPES OF DISCOUNTED FUTURE BENEFITS METHODS
Appraisers use two different sub-methods of the DFB method, equity methods (DCF or DNI, which project measures of earnings available to the equity holders of a business) and total capital measures (DFNCF or DFNI, which project earnings available to the equity and debt holders, i.e., to the total capital of the enterprise).
EQUITY METHODS
DISCOUNTED (NET) CASH FLOW (DCF). This is the basic DCF method. Net cash flow is forecasted into the future and is generally defined as:
Net Income
+ Depreciation and Amortization
- Capital Expenditures
+/- Net Changes in Working Capital
Some appraisers attribute great weight and importance to the DCF method, suggesting that the method is theoretically more rigorous than, for example, a direct capitalization of earnings method. But the DCF method is not inherently better or worse than other valuation methods. As you will see below, appraisers must use common sense, informed judgment and reasonableness in the utilization of the DCF method as with any other valuation method.
DISCOUNTED NET INCOME (DNI). The net income of a business is projected into the future.
With either the DCF or DNI methods, which measure cash flows available to equity owners of a business, an appropriate equity discount rate should be used. There is a debate among appraisers regarding whether a discount rate developed using the Capital Asset Pricing Model is applicable to net income or net cash flow. I have generally taken the position that the Adjusted Capital Asset Pricing Model, which is the basic build-up method used by most appraisers, yields discount rates applicable to the net income of a business, although other writers have disagreed with me. [See Mercer, "The Adjusted Capital Asset Pricing Model for Developing Capitalization Rates ...", BUSINESS VALUATION REVIEW, Vol. 8, No. 4, December, 1989, pp. 147-156. See also "Exhibit 8-2, The Adjusted Capital Asset Pricing Model," found in Mercer, QUANTIFYING MARKETABILITY DISCOUNTS (Memphis's Peabody Publishing, LP: 1997), pp. 260-267. This book is available from the publisher by calling 1-800-769-0967.]
I tend to use the basic build-up equity discount rate to discount net income, although I have, in some circumstances, used it to capitalize net cash flow. As a result of wrestling with this issue, I wrote what has become a widely cited article that develops a method for estimating any differences between net income and net cash flow discount rates. The article indicated that the difference between a net income and a net cash flow discount rate may not be, for many closely held business situations, as great as many appraisers think. [Mercer, "Adjusting Capitalization Rates for the Difference Between Net Income and Net Free Cash Flow," BUSINESS VALUATION REVIEW, Vol. 11, No. 4, December, 1992, pp. 201-207.]
For the reasons cited in the 1989 and 1992 articles, I believe that the ACAPM discount rate is generally applicable to the net income of a business. While appraisers may differ in opinions, there are two practical considerations that can mitigate differences in DFB valuations relative to this issue.
(1) After discounting net cash flow for a three-to-five-year (or longer) discrete period, many appraisers then capitalize net income (using, e.g., current market multiples) to determine the terminal value. As we will see in a moment, the terminal value normally comprises the great majority of the value of a DCF or DNI method. If 60% or more of a forecast is dependent on the capitalization of net income, any inherent differences between net income or net cash flow discount rates would be mitigated.TOTAL CAPITAL MEASURES
(2) Further, if the judgmental criteria used by appraisers are applied consistently, differences between appraisers on this issue can be rendered moot.
DEBT FREE NET CASH FLOW (DFNCF). This method is analogous to the DCF method, except that Earnings Before Interest and Taxes (EBIT) is generally fully taxed (to put the subject enterprise on a "debt-free" basis). Debt free net cash flow is then projected for the finite forecast period.
DEBT FREE NET INCOME (DFNI). Again, the analyst goes to the EBIT line on the income statement (before debt service) and taxes operating earnings to place the income statement on a debt-free basis.
With either of the total capital (debt-free) methods, the appropriate discount rate is the Weighted Average Cost of Capital (WACC). Appraisers make an assumption about the portion of equity and debt in the capital structure of a business and then weight the costs of equity (the equity discount rate) and of debt (the after-tax cost of borrowings) to develop a WACC. One common mistake is to weight debt and equity on a book value basis, when WACC should be determined based on market value weightings.
We have already identified four versions of the basic discounted future benefits methodology. An appraiser must decide which variation of DFB will be used and make decisions regarding the appropriate discount rate. So the conceptually simple discounted future benefits method is a bit more complex than it might at first seem.
THE PRACTICAL IMPACT OF DFB ASSUMPTIONS
To illustrate the importance of the assumptions in any discounted future benefits valuation, consider the following situation. Assume that we have found eight appraisers who agree on several assumptions with regard to a Discounted Net Income (DNI) valuation method:
- Net income in the base period is $1.0 million
- There is a discrete forecast period of five years, during which net income is expected to grow at 10% per year.
- After the fifth year, net income growth is expected to slow to 6% (into perpetuity).
- The net income discount rate is 15%
- With such substantial agreement, one might think that all eight appraisers would develop quite similar value indications from their DNI methods. But the subtleties of discounted future benefits valuation methods can cause surprising variation. The seemingly minor assumptions that can make a significant difference include:
- The Compounding Assumption. Appraisers typically use one of two compounding assumptions in discounted future benefits methods, the mid-year convention or the end-of-year convention. Under the mid-year convention, earnings to be discounted are assumed to be received at the middle of each year of the forecast (to approximate an even receipt of earnings over the year). Under the end-of-year convention, earnings are assumed to be received at the end of each year of the discrete forecast period. The mid-year convention might be quite reasonable for a company with no seasonality to its earnings. The end-of-year convention might be more appropriate for a retailer, for example, that makes the majority of its earnings in the fourth calendar quarter of each year. [**Reader Clue Number 2: Other things being equal, the mid-year convention yields a higher result than the end-of-year convention (because the cash flows are received sooner).**]
- The Terminal Value Capitalization Assumption. Theoretically, one would capitalize the forecasted earnings for the next year after the end of the discrete forecast period. But some appraisers will capitalize the terminal year’s forecasted earnings to develop their terminal value indication. Appraisers who use current multiples from publicly traded guideline companies will tend to capitalize items from the last discrete forecast period. [**Reader Clue Number 3: Capitalizing the next year’s forecast will generally yield a higher result than capitalizing the last year of the finite forecast.**]
- The Terminal Value Compounding Assumption. Once the terminal value is developed, it must be discounted to the present. While it may seem intuitively obvious that a terminal value based on the fifth year or sixth year’s forecasted earnings would be discounted to the present from the end of the fifth year, some appraisers use an assumption of 4.5 years. [**Reader Clue Number 4: This is a subtle one. Compounding for 4.5 years rather than 5.0 years can have a surprisingly positive impact on conclusions. Appraisers who use this assumption often hide it, or rather, do not make it explicit.**]
The model assumptions noted above can generate eight possible combinations, and therefore, eight possible DNI values for the forecast upon which so much was apparently agreed upon by our eight appraisers. The remainder of this discussion will focus on the range of conclusions indicated by the low and high results under each assumption set.
The lowest value of the eight possibilities $13.3 million, is reached by the appraiser who selected the end of year convention, capitalized year five earnings for the terminal value, and discounted the terminal value to the present for a period of five years. The highest value, $15.2 million, is reached by the appraiser who selected the mid-year convention, capitalized year six earnings to develop the terminal value, and discounted the terminal value for a period of 4.5 years (the period of receipt of the last year’s earnings).
AFTER AGREEING ON SO MUCH, THE APPRAISERS HAVING THE LOWEST AND HIGHEST ANSWERS ARE $1.9 MILLION APART, OR 13%-14%, DEPENDING ON WHETHER THE DIFFERENCE IS MEASURED FROM THE HIGHER OR THE LOWER VALUE.
We commented on the terminal value assumption above. The present values of the eight terminal values calculated accounted for between 65% and 70% of the total discounted present value indications. So we see that the assumptions made regarding the terminal value are critical. This fact lends support to appraisers who sometimes eschew discounted future benefits methods in favor of single-period income capitalization methods.
We ran the model above with all assumptions remaining the same, except that the equity discount rate was raised to 20%. The low and high indications were reduced to $8.5 million and $9.8 million respectively by the use of the higher discount rate. However, the percentage differences rose to the range of 13% to nearly 16%. The present values of the terminal values accounted for between 52% and 59% of the total discounted present value indications.
Although we have used a discounted net income model above, the sensitivity of a discounted cash flow model to variations based on seemingly minor assumptions would be similar for similar levels of net cash flow.
DEBT-FREE METHODS INCREASE SENSITIVITY
We can use the same basic model to simulate the sensitivity of debt-free discounted future benefits methods. All the assumptions above remain the same, except that the WACC (Weighted Average Cost of Capital) is assumed to be 13.25%. This is consistent with a 15% equity discount rate, a pre-tax debt rate of 8% (after-tax cost of 4.8% assuming a 40% tax rate), and an 83%-17% weighting of equity and debt in the capital structure (in this case, based on an assumed agreed upon guideline company group on a market value basis).
We are assuming that we have a debt-free net income of $1.7 million. We further assume that the subject enterprise has $14.0 million of debt. These assumptions are made to assure that our debt-free model is reasonably comparable with the net income model above in terms of equity valuation.
The market values of total capital (debt and equity) under the eight sets of assumptions range from $27.6 million to $31.5 million, a dollar difference of $3.9 million, and a percentage difference between 12% and 14%, depending on whether the high or the low is used as the base. This seems consistent with the earlier modeling.
But we are attempting to value the equity of the enterprise. If we subtract the $14.0 million of debt from the indicated values of total capital, the range of equity values is between $13.6 million ($31.5 million - $14.0 million) and $17.5 million ($31.5 million - $14.0 million). The indicated dollar range of equity values for presumably the same company as discussed above is $3.9 million. But the percentage differences widen substantially, ranging from 22% to 29%, depending upon whether the higher or lower equity value is considered the base.
For another perspective on the importance of the terminal value assumption, consider that under our DFNI model, the present value of the terminal value accounts for between 83% and 85% of the total value indicated by the method ON A TOTAL CAPITAL BASIS. However, when the terminal value, which is based on total capital, is compared with the resulting value of EQUITY, the present value of the terminal value accounts for between 180% and 203% of the resulting equity indications. All I can say is, wow!
We haven’t discussed the issue capital structure. Had one of the appraisers used a 75%/25% equity/debt weighting, a seemingly small difference (which lowers the WACC to 12.45%), other assumptions being the same, her equity values would have been about 25% higher.
One writer concluded a chapter on WACC with the following sentence: "There is much controversy about the potential impact on the WACC as a result of altering the capital structure." [Pratt, Shannon P., COST OF CAPITAL: ESTIMATION AND APPLICATIONS, (New York: John Wiley & Sons, 1998), p. 53] What understatement! And the quoted writer did not discuss the impact of the other issues raised in this newsletter.
LESSONS TO BE LEARNED
(1) Discounted future benefits valuation methods are quite sensitive to assumptions that many appraisers, do not acknowledge in their appraisals. I have known about these sensitivities for many years, but was amazed at the cumulative significance of the seemingly minor assumptions on discounted future benefits valuations, and astounded at the sensitivity of debt-free methods to changes in these assumptions.A future issue of E-Law Business Valuation Perspective will contain a further discussion of the discounted future benefits method as well as a users’ checklist of questions to ask about DFB methods.
(2) Appraisers should make clear what assumptions are being used and why. My preference is that the discounting convention used and the discounting period for the terminal value be shown specifically, together with the calculated present value factors, and that the specific calculations imbedded in the development of the terminal value be shown explicitly.
(3) It should go without saying that appraisers should make their assumptions clear regarding their basic forecasts, and should be able to discuss the reasonableness of those assumptions in the context of a company’s recent historical performance, realistic outlook for the future, and general market constraints.
(Reprinted from Mercer Capital's E-Law Newsletter 99-01, January 8, 1999)