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Home , Adjusted present value, Net present value

FINDING VALUE WHERE by Laurence Booth, NONE EXISTS: PITFALLS University of Toronto IN USING ADJUSTED

here are many different conceptually model could be used to examine interactions be- “correct” methods for valuing firms and tween the investment decision and the financing T projects. Perhaps the best known is the decision.1 This use of the M&M framework weighted average (WACC) has come to be called (APV) approach, which involves unlevered or the valuation-by-components method. The cen- (ie., pre-interest, but after-tax) cash flows at a rate tral idea is simply that the overall value of the firm that reflects a blend of the costs of the different can be “unbundled” into two separate components:its sources of . For example, the overall enter- debt-free or unlevered value and the value of its debt prise value can be calculated by discounting the . operating or unlevered cash flows to the firm as a Under normal simplifying assumptions, the whole at the firm’s weighted average cost of capital. WACC, FTE, and APV frameworks should all If desired, the firm’s equity value can then be the same answers if correctly implemented.2 But calculated by subtracting the value of the debt to the problem has always been interpreting what “back out” the equity value. Alternatively, the value “correctly implemented” means. The key issue is of the equity can be calculated directly by discount- in the assumption about the firm’s debt policy— ing the cash flows to the equity holders at the equity that is, whether that policy is framed in terms of holders’ required . This latter approach maintaining a fixed debt ratio or a fixed dollar is commonly referred to as the flows to equity (FTE) amount of debt.3 This distinction has been picked method. Both the WACC and FTE frameworks have up by a number of researchers, who have demon- been in use for many years. strated the advantages of APV by focusing on In 1963, Franco Modigliani and Merton Miller highly-leveraged transactions (HLTs) like LBOs (M&M) first analyzed how corporate income taxes and leveraged .4 Some have even interact with a firm’s financing choices to create gone so far as to assert that “using the weighted value. They showed that, under certain assumptions, average cost of capital (WACC) is obsolete...One the value of a firm with debt was equal to the value alternative, called adjusted present value, is espe- of the firm without debt plus the value of the tax cially versatile and reliable, and will replace shields from using tax-deductible debt financing. WACC as the DCF [] method- Stewart Myers subsequently showed how the M&M ology of choice among generalists.”5

1. S. Myers, “Interactions of Corporate Financing and Investment Decisions - 4. I. Inselbag and H. Kaufold, “How to Value Recapitalizations and Leveraged Implications for ,” Journal of Finance (March 1974), pp. 1-25. ,” Journal of Applied , Vol. 2 (Summer 1989), pp. 87-93; 2. R. Taggart, “Capital Budgeting and the Financing Decision: An Exposition,” idem, “Two DCF Approaches for Valuing Companies under Alternative Financing Financial Management (Summer 1977), pp. 59-64. Strategies (and How to Choose Between Them),” Journal of Applied Corporate 3. J. Miles and J. Ezzell, “The Weighted Average Cost of Capital, Perfect Capital Finance, Vol. 10 (Spring 1997), pp. 114-122; E. Arzac, “Valuation of Highly Markets and Project Life: A Clarification,” Journal of Financial and Quantitative Leveraged Firms,” Financial Analysts Journal (July/August 1996); and T. Luehrman, Analysis, Vol. 15 (September 1980), pp. 719-730; L. Booth, “Capital Budgeting “Using APV: A Better Tool for Valuing Operations,” Harvard Business Review (May- Frameworks for the Multinational Corporation,” Journal of International Business June 1997), pp. 2-10, (Fall 1982), pp. 113-123. 5. Luehrman (1997), cited above.

8 JOURNAL OF APPLIED CORPORATE FINANCE The goal of this paper is to examine the relative project or acquisition is similar to the firm’s existing advantages of these frameworks and offer guidance projects, so that the firm can use its current cost of as to when each is likely to be most useful. In this capital. In other words, business risk is held constant. respect this paper is similar to the recent paper by Isik In the WACC framework, the cost of capital captures Inselbag and Howard Kaufold that appeared in this the financing of the firm in the discount rate: journal.6 Unlike previous work, however, my focus is on how to implement the three valuation frame- E D K = K + K (1 − T ) works and on theproblems that are likely to arise in a e V d V actual applications. The key recommendation of this paper is to where K is the weighted average of the equity cost a caution against the use of APV: it is frequently K and the after-tax debt cost K (1 – T), with the e d unreliable and should only be used in conjunction weights determined by the debt (D/V) and equity (E/ with more conventional valuation frameworks. In V) ratios based on market values. The critical as- particular, it only has general applicability in trans- sumption is that the firm estimates the debt and actions that involve a structured financing, like equity costs from current capital market data and leveraged buyouts (LBOs), project financing, and uses its optimal or target to deter- real estate financing. Even in these cases, however, mine the financing mix. its use depends on theoretical concepts that in Using the perpetuity formula, the overall enter- practical applications have a wide margin of error. prise (or project) value is simply

THE CLASSIC VALUATION FRAMEWORK: EBIT(1 − T ) V = WACC K a There are several layers of difficulty in using We will illustrate how the methods differ in applica- valuation techniques, and sometimes hidden as- tions, so let’s start with a firm (or project) with sumptions creep in. For this reason, we will start with expected EBIT of $20 million. If the firm’s tax rate is the simplest possible case, which is the standard 50%, the perpetuity free cash flows are $10 million. M&M perpetuity framework. The main assumptions With a target capital structure of 50% debt, and debt of this model will then be relaxed. But, as will and equity costs of 10% and 15%, respectively, then become clear, most of the insights of the M&M model K = 10%. In this case, the total is a continue to hold in the more complicated frame- $100 million ($20mm × 50%/10%). works. At this point it is important to note the implicit To start out, the firm has a series of expected free assumption of the WACC approach. The perpetuity cash flows. These are estimated in the normal way formula uses the sum of an infinite series, with both as after-tax operating earnings, calculated as earn- the expected free cash flows and the discount rate ings before interest and taxes multiplied by one assumed to be constant (in addition to the normal minus the tax rate [EBIT × (1 – T)], plus non-cash assumptions of constant tax rates, interest rates, and charges, minus changes in net working capital and business risk premiums). For the WACC to be capital expenditures. Since we are dealing with a constant, one of two assumptions must be made: perpetuity, the depreciation cash flows fund capital either debt financing has no impact on the WACC, expenditures and there are no net changes in which is the original M&M irrelevance argument;7 or working capital. As a result, the free cash flows are the debt ratio, and thus the financial risk, is constant simply the expected after-tax operating cash flows. through time. If debt financing affects the WACC and The next step is to determine a discount rate and the future debt ratio is expected to change, then the a valuation framework, which is where differences WACC will no longer be constant and thus techni- in extant approaches arise. Let’s assume that the cally we cannot use the perpetuity formula.8 Of

6. Inselbag and Kaufold (1997), cited earlier. 8. There will still be a number that discounts the expected free cash flows and 7. See F. Modigliani and M. Miller, “The Cost of Capital, Corporate Finance and gives the correct market value, but it will not be the current WACC. the Investment Decision,” American Economic Review (June 1958), pp. 261-297; M. Miller, “Debt and Taxes,” Journal of Finance (May 1977), pp. 261-275.

9 VOLUME 15 NUMBER 1 SPRING 2002 course, temporary deviations from the optimal capi- of the acquisition itself, which belongs to the equity tal structure will occur over time. These deviations holders who own the project. In a fundamental do not invalidate the WACC approach, as long as sense, the financing follows from the valuation of the they are not expected at the time of the analysis. project or acquisition—after it is accepted—and not Now let’s consider how we implement the from its direct cost.10 In this way the frameworks for WACC approach. Suppose, for example, the free valuing a standard project or an acquisition are both cash flows in the example are from a project conceptually identical. requiring an initial investment of $60 million. In this Understanding how the debt decision is treated case, the project’s is $40 million in the WACC approach is critical for understanding ($100mm – $60mm). For a standard project, this is all the differences between standard project valuation the operating manager needs to know: that the NPV and the valuation of stand-alone investments. For is $40 million and the project should therefore be standard project valuation, the financing is ignored undertaken. In most capital budgeting decisions, since it is “in” the WACC. What this means is that the there is a separation of responsibility between the operating manager is concerned only about the operating and financing functions. The cost of project’s NPV—a value that implicitly “spills over” to capital of 10% is centrally determined by the the firm as a whole. The actual financing costs of Treasurer’s office, and the operating manager is then even large projects are thus not allocated to a simply told to discount the operating cash flows of particular project, since every project’s value spills potential investment projects at a 10% rate and over to the overall enterprise value. In this sense, the recommend acceptance of all positive-NPV projects. $100 million project value will increase the enter- This separation of financing from investment deci- prise value by the same amount. Consequently, the sions is typical for most corporations since the firm’s use of debt is not the actual project debt, but operating manager is usually unaware of the firm’s the firm’s optimal debt ratio times its market value. financing policies or, for that matter, its tax status. In This spillover assumption in WACC is critical. other words, most operating decisions are decentral- Consider, for example, a multinational’s foreign ized and most financing decisions are centralized. investment decision, where the local government The WACC approach is quite consistent with this limits the amount of debt financing to, say, 50% of functional separation. This is probably why surveys the project cost. Such restrictions are common in have found the WACC approach to be so popular, both developed and emerging markets, and are even in the valuation of acquisitions, where there is often referred to as “thin capitalization” rules. They generally some interaction between the financing are designed to limit the allowable interest tax and investment decisions.9 deductions and prevent tax arbitrage across coun- It is clear in the case of a project that the tries. If our project has this restriction, then the local functional separation embodied in the WACC frame- debt financing is limited to $30 million, or half the work normally makes sense. However, much the project cost. However, the spillover assumption in same analysis follows for an acquisition. In this case, the WACC approach assumes that a further $20 the value of the target would be $100 million and the million in debt will be raised at the parent level. As cost $60 million, again leaving a $40 million NPV. the profits from the subsidiary are consolidated and However, the firm in all probability would now show up in the parent’s income stream, the parent’s directly consider the acquisition financing. The market value will increase, allowing it to raise assumed debt ratio is 50%. But the critical question additional debt to maintain its optimal debt ratio. If, is 50% of what? The right answer, at least in theory, on the other hand, local debt is subsidized, so that is that it is 50% of the target’s total market value. In the firm is able to raise $70 million in local debt, the this case the firm would raise $50 million in debt and firm will reduce its borrowing elsewhere to maintain $10 million in equity. The extra $40 million in equity its 50% debt ratio. In both cases, the spillover necessary to maintain the 50% equity ratio is the NPV assumption in WACC assumes that the debt financ-

9. See the survey by John Graham and Campbell Harvey in this issue. Another M. Fall, D. Kaufman, and B. Winger, “Acquisition/Divestiture Valuation Practices survey found that on a 1-7 scale, DCF was rated the highest at 6.1 for large firms, in Major U.S Firms,” Financial Practice and Education (Spring 1981), pp. 73-81. whereas various valuation multiples such as earnings were generally rated at the 10. Note that if the firm borrowed 50% of the acquisition cost, it would end 4.0 level, and firms generally used the acquiring firm’s cost of capital; see N. Mohan, up with a 30% debt ratio: $30 million in debt and a $70 million equity market value. In this case there are internal inconsistencies in the debt ratio.

10 JOURNAL OF APPLIED CORPORATE FINANCE ing is 50% of the market value of the project, even With the cash flows extended into infinity by rolling if the firm actually raises a different amount specifi- over any term debt (at comparable interest rates), the cally for the project! expected cash flows to the equity holders are $7.5 The same logic for valuing a project also applies million per year discounted at 15%, or $50 million. to an acquisition. Suppose that the financing for the Since $50 million of the $60 million acquisition cost is acquisition is actually 50% of the $60 million cost, or financed by debt, the NPV from the equity holders’ $30 million. Once the acquisition is accepted, the perspective is $40 million ($50mm – $10mm). value of the firm will still increase by $100 million and This example shows the consistency of the the firm will still increase its debt financing by a total WACC and FTE models: they both give an NPV of $40 of $50 million. Otherwise, its debt ratio will gradually million. However, a closer reading will indicate trend down with every profitable acquisition that it problems with the logic of the FTE method. To get makes, contradicting the assumption embedded in the $5 million interest expense requires knowing the WACC. As long as the firm maintains an optimal that the debt financing is $50 million at a 10% interest debt ratio, the WACC assumption is that any unused cost. Yet how do we know that $50 million in debt debt capacity will spill over to the firm as a whole and will be raised? All we know at the outset is that debt the firm will raise debt according to the WACC is to be 50% of the market value of the project; but weights applied to the project’s or acquisition’s that value is unknown until it is calculated. market value. Suppose instead that the FTE value is estimated by using the optimal debt ratio times the $60 million THE CONTENDER: THE FLOWS TO EQUITY acquisition cost. In this case, interest costs would be METHOD $3 million rather than $5 million and the equity value would be after-tax net income of $8.5 million Now consider the traditional challenger to the [($20mm – $3mm)(1 – 0.5)] discounted at 15%, or WACC, which is the flows to equity or FTE method. $56.6 million. Although the equity value is $56.6 The cash flows to the equity holder are discounted million rather than our previous $50 million, there at the cost of equity capital to determine equity value are two problems. First, the estimated NPV to the directly, rather than backing it out by subtracting the equity holder is smaller, at $26.6 million, since the debt value from the overall enterprise value: equity holder is now assumed to put up 50% of the cost of the project or $30 million. Second, the 15% ( EBIT − K D)(1 − T ) equity discount rate may be an overestimate since E = d (1) K there is now less financial risk to the equity holder e if debt is only $30 million rather than the $50 million The FTE framework is not normally used for indi- as assumed in the WACC. vidual projects, since the analyst needs to know the One possibility is that we could “iterate” to- debt costs, and most decentralized operating man- wards the optimal debt level.11 For example, starting agers do not have the necessary financing expertise at $30 million in debt, the NPV is $26.6 million, so the to estimate this. More to the point, it is difficult to debt ratio is 35% ($30mm/$86.6mm); therefore man- imagine setting up an efficient capital budgeting agement should increase the debt level to say $35 framework, in which on top of all the operating cash million and keep increasing it until the target debt flow data, the operating manager also has to deter- ratio is the optimal 50%. But rather than clumsily mine the financing and tax status for each individual moving to the optimal debt ratio, we can substitute project! it directly into the FTE equation, that is, q = D/V, The FTE method is most relevant for acquisitions where q is the optimal debt ratio. However, as soon and very large projects. Consider our acquisition target. as we do this, and solve for the unknown enterprise With expected EBIT of $20 million, the manager could value, the FTE method collapses to the standard project interest costs of $5 million, so that earnings WACC equation—in which case, we may as well use before tax are $15 million and $7.5 million after tax. the WACC approach from the start.12

11. Arzac (1996, cited earlier) tries this in a slightly different context. 12. Let E = (EBIT – Kd qV)(1 – T))/Ke where E and V are unknown. Multiplying by Ke, rearranging, factoring for V, and dividing while noting that E/V is just (1– q) allows us to solve for V as EBIT(1 – T)/Ka, which is just the WACC value.

11 VOLUME 15 NUMBER 1 SPRING 2002 The conflict over financing assumptions is the change over time. Again let’s consider the simplest central difference between the two valuation meth- perpetuity case, in which the tax advantage to debt ods. The use of WACC assumes that the optimal or is the corporate tax rate multiplied by each period’s target debt ratio is given, so that value and the interest payment. This assumption is the one made amount of debt financing spills over to the firm as by M&M and used in most APV examples. The M&M whole. A project is thus implicitly credited with the model is target debt capacity, even if it is not immediately used. In contrast, the FTE framework requires the EBIT(1 − T ) optimal amount of debt both for the projected V = + DT (2) K 0 interest cost as well as the net equity investment. The FTE approach can thus be useful when dealing with In the first term, the after-tax EBIT is discounted at absolute amounts of debt, although once a target the equity cost for an all-equity firm, K . This term is 0 debt ratio is substituted into the FTE it becomes then simply the value of an unlevered firm. The indistinguishable from the WACC method. This in second term is the value of the tax shield from debt turn means that either there is a complete absence financing, with the debt, like EBIT, assumed to be a of any spillover from the project to the firm as a perpetuity (or, equivalently, term debt that will be whole, or that prior to using FTE we already know rolled over at the same interest rate). the project value—that is, we already know the value In our example, the firm has $50 million in debt. before we calculate it! So with a 50% corporate tax rate the value of the tax To be sure, FTE will consistently give the same shield is $25 million. If the unlevered equity cost is answer as WACC when the NPV is zero.13 In this case, 13.33%, then the unlevered equity value is $10 the optimal amount of financing is the same whether million discounted in perpetuity at 13.33%, or $75 we multiply by the cost or the value of the project, million. The total APV of $100 million is then and by definition there can be no spillover of the consistent with both the WACC and FTE estimates. NPV to the firm as a whole. Otherwise, as the NPV However, APV has a further advantage in that this changes so will the optimal amount of debt. Another $100 million is allocated into its separate compo- way of stating this is to recognize that FTE gives the nents—the $75 million value of the operating cash correct NPV only if the NPV has no impact on the flows and the $25 million debt tax shield value. This subsequent financing decision. In this case, the in turn allows a sensitivity analysis with respect to the financing isfixed regardless of whether the project’s different components of value, namely the firm’s NPV is $5 million, $50 million, or $500 million.14 For operating cash flows and its capital structure. most valuations, however, this assumption is not The APV framework is clearly attractive in that likely to be appropriate in either the short or long it allows a deeper understanding of what creates run. value. However, a closer reading of the above example again reveals logical problems (in this case THE GREAT HOPE: ADJUSTED PRESENT not one as with FTE, but two!) First, similar to FTE, VALUE? we need to know the optimal amount of debt to determine the value of the debt tax shield. However, Once the constant debt ratio assumption is before knowing the NPV (APV), how can we know violated, the cost of equity has to be changed to how much debt is optimal? If there is any spillover reflect changing financial risk. This requires adjust- from the NPV, APV will give an incorrect answer. ments in both the WACC and FTE methods, making Second, and even more problematic, where did the them both more difficult to implement. It is the great unlevered equity cost of 13.33% come from? In fact, hope of proponents of Adjusted Present Value that it has to be 13.33% to give the right answer. But APV solves this problem, which is why most ex- without knowing that, how do we calculate it? amples advocating APV involve valuing highly le- In the APV framework, the absolute amount of vered transactionsin which the debt ratio tends to debt must be known before we can calculate the tax

13. Booth (1982), cited earlier. difficult to believe that there is a complete disconnect between the actual NPV and 14. This explains why most applications of FTE, like APV, involve high-debt future financing. transactions like leveraged buyouts or project financing. However, even here it is

12 JOURNAL OF APPLIED CORPORATE FINANCE shield value, in the same way that we needed the of debt. The WACC NPV estimate of $40 million absolute amount of debt to calculate the interest implicitly assumes that another $20 million in debt is payments and equity investment with FTE. We might raised based on the estimated NPV: the calculation then ask what happens when we incorporate an is automatic. As with FTE, for APV to give the same optimal debt ratio assumption, that is, q = D/V, into value as WACC requires that an additional tax shield the APV equation? We start with value of $10 million be included. Only if there is no debt spillover or, equivalently, no impact of the NPV EBIT(1 − T ) on the debt financing will APV give the right answer. V = + TθV Yet it is difficult to conceive of a situation where K 0 knowing the NPV does not affect the financing However, solving for V gives: decision.16,17

q V = EBIT (1 – T)/ K0(1 – T ) (3) GROWTH OPPORTUNITIES This may look different from the standard WACC The previous results are based on a perpetuity equation, but the denominator is just the M&M framework, but very few investments are perpetu- expression for the WACC (as I will show formally ities. What happens, for example, if there is growth later). With our numbers, K is 13.33%, T = 50%, and in the expected EBIT? For WACC, if EBIT is expected 0 q = 50%. And so K (1 – Tq) is 13.33% × 0.75, or 10%. to grow at an average long-run growth rate g, we get 0 This 10% is just the WACC we calculated initially. the standard constant growth formula:18 Consequently, iterating the amount of debt or incor- porating the optimal debt ratio into the APV equation EBIT(1 − T ) V = causes it to collapse to the standard WACC. − K a g As with FTE, the APV framework will give the same answer as WACC as long as the optimal amount If the firm starts at its optimal debt ratio, the of debt is used. Again, however, it is a question of equivalent APV formula is how APV is used in practice. Suppose APV is implemented by estimating the amount of debt EBIT(1 − T ) K TD V = + 0 based on the debt ratio multiplied by the project’s − − (4) K 0 g K0 g cost.15 If the unlevered equity cost is correctly estimated at 13.33%, the unlevered project value is This is the same as the perpetuity model. APV gives $75 million. The value of the tax shield then depends the value of the operating cash flows and the value on whether the firm is using the optimal amount of of the tax shield. In both cases they are expected to debt. With the project cost of $60 million and debt grow at the long-run growth rate. However, the tax of $30 million, the tax shield value will be $15 million advantage to debt needs some explanation. The for a total project value of $90 million. This under- perpetuity tax shield from existing debt, TD, has estimates the WACC value by $10 million, or the been converted to a flow by multiplying by the value of the tax shield from the additional $20 million unlevered equity cost, K . Since the firm is expected 0 in debt that results from knowing that the total to grow at the long-run average growth rate, we can project value is $100 million and the NPV is $40 find the current value of this growing flow of tax million. This is the spillover of the NPV to the firm’s benefits by discounting at K . We use the unlevered 0 financing decisions. equity cost (K ) to discount the future flow of debt 0 As in the case of FTE, The critical question with tax shields because they stem from the expected APV is whether knowing the NPV affects the amount growth in EBIT. Consequently, and unlike the exist-

15. I have yet to come across an analysis that has based the debt financing on will differ across all three methods since the discount rate is either the WACC, the the ultimate project value. In almost all cases the estimated financing comes from unlevered equity cost (APV), or the levered equity cost (FTE). What is then critical the target debt ratio times the project cost. is the objecive of the sensitivity analysis: Is it to consider the effect of an EBIT change 16. Of course the optimal amount of debt may not be $20 million, but say $10 in isolation (APV), or the cumulative effect of the EBIT change with the associated million. As a result, the WACC estimate is incorrect, but this just means that the optimal financing change, or neither (FTE)? optimal debt ratio has not been used in the WACC estimate. 18. This is from the Gordon constant growth model; see M. Gordon, The 17. The same valuation problems exist if the analyst performs a sensitivity Investment, Financing and Valuation of the Corporation (Homewood, Illinois: analysis, for example with respect to forecase EBIT. In this case the change in NPV Richard D. Irwin, 1961).

13 VOLUME 15 NUMBER 1 SPRING 2002 ing tax benefits, they are as risky as the future − − = ( EBIT K d D)(1 T ) unlevered cash flows and should be discounted at K e E the same rate.19 Similar to the perpetuity case, with an optimal This is just M&M’s equity cost equation rearranged. debt ratio we can set q = D/V to find the conditions However, we can solve for EBIT(1 – T) from the for consistent valuation between APV and WACC. M&M valuation equation and substitute to get Subtracting the tax shield advantages from the project value in equation (4), multiplying by the − − − = K 0(V DT ) K d D(1 T ) adjusted discount rate (K – g), and setting EBIT(1 – K e 0 E T) equal in both equations, we can solve for the WACC as Since the enterprise value is the market value of the debt and equity (V = D + E) we can rearrange to get = − θ K a K 0 (1 T ) M&M’s equity cost equation: which is the same as previously: the traditional cost D K = K + [K − K (1 − T )] (5) of capital (WACC) is equal to the M&M expression e 0 0 d E for WACC. Adding future growth in EBIT does not affect the prior results, as long as the tax shields from This simply states that the equity cost is equal to K , 0 the growth in EBIT are recognized to be as risky as the cost for an all-equity firm, plus a financial EBIT itself. leverage risk premium. As the use of debt financing By assuming an optimal or target capital struc- increases, common equity becomes riskier and ture, WACC automatically adjusts financing for fu- attracts a financial leverage risk premium in addition ture growth opportunities. To be consistent with this to the business risk premium. The “pure” financial approach, the future tax shields in the growth- leverage effect is the unlevered equity cost multi- extended APV equation need to be discounted at the plied by (1 + D/E). However, with the M&M assump- unlevered equity cost. If the future tax shield ben- tion of a tax shield value of TD, the negative effect efits, as well as the current tax benefits, are dis- of increased financial risk on firm value is partially counted at the cost of debt, or a rate close to it, the offset by the positive effect of the tax shield. Conse- tax shield value is vastly overstated and the results quently, the increase in the equity cost is moderated are inconsistent with the WACC estimates.20 The by (1 – T). With a constant debt cost,21 the equity cost critical assumption in comparing APV, WACC, and increases by [1 + (1 – T)D/E]. Many readers will notice FTE is not the time pattern of the expected cash a similarity to the familiar beta adjustment formula flows, but the financing assumption. developed by Robert Hamada.22 In that formula, the beta of an unlevered firm (derived from the Capital CHANGING DEBT RATIOS Asset Pricing Model) also increases by (1 + (1 – T)D/ E) with the addition of debt to the capital structure, As long as there is a constant optimal debt ratio, so that b = b (1 + (1 – T)D/E). L 0 APV and FTE valuations turn into WACC valuations. The M&M equity cost equation indicates how But what happens when the debt ratio is changed? the equity risk premium changes with the firm’s use Since the existence of growth does not change the of debt. As a result, we can reverse the process and results in a material way, we can revert to the standard calculate the unlevered equity cost from either M&M perpetuity model. In this case, the levered equity equation. In our example, the levered equity cost at cost is the earnings yield, or simplythe expected net a 50% debt ratio and a 50% tax rate was 15%. Inserting income divided by the market value of equity: these values into equation (5), we estimate the

19. The financing of existing assets generates an interest tax shield whose value unlevered equity value is $157 million and the value of the interest tax shields $102 is derived by discounting at the cost of debt. It is the tax shields from the growth million—we could all wish that the government were this generous! in EBIT that are as risky as the EBIT growth. If the growth rate is zero, the tax shield 21. M&M assumed zero bankruptcy costs, so the debt is risk-free debt; see F. is the standard perpetuity formula for the tax shields from existing debt. Modigliani and M. Miller, “Corporate Income Taxes and the Cost of Capital,” 20. See Luehrman (1997, cited earlier) for an inappropriate application of APV, American Economic Review (June 1963), pp. 433-443. where future tax shields are valued at a rate “a bit higher than the average cost of 22. R. Hamada, “The Effect of the Firm’s Capital Structure on the Systematic debt” to vastly overstate the value of interest tax shields. In his example, the Risk of Common ,” Journal of Finance (May 1972), pp. 435-452.

14 JOURNAL OF APPLIED CORPORATE FINANCE unlevered equity cost at 13.33%.23 This is how we the general equation if we know l, but we can not derived the baseline, unlevered equity cost and firm relever using l with different debt levels. This is value of $75 million. With $50 million in debt there because l varies with the debt ratio depending on, is an additional $25 million tax shield value to get the for example, the marginal agency or distress costs. overall enterprise value of $100 million. To relever we need to know the functional form of However, considering the effect of changes in both the advantages and disadvantages to debt. leverage immediately brings out the fundamental Suffice it to say that generally we don’t know these. weakness of M&M, which is that the value of the firm Further, these schedules differ from firm to firm, or constantly increases with the use of debt. 24 If that is at least industry to industry, which means that true, why stop with $50 million in debt—why not $70 adjustments differ across firms, just as optimal capital million or $80 million? After all, the M&M equation structures do. This destroys one of the key advan- has no offset to the huge tax advantage to debt tages of using a constant adjustment formula across financing. In practice, of course, firms cannot finance firms as well as across debt ratios. with 100% debt, since in there are obvious problems This same reasoning applies to the Hamada beta with a loss in financial flexibility and the increased adjustment. With an optimal capital structure, the chance of . beta of a levered firm is b = b (1 + (1 – l)D/E). But L 0 Suppose we consider all of these factors in what the change in terms from T to l is not trivial. The tax Stewart Myers has dubbed the static trade-off model, rate T can be looked up in the tax code, implying a discussed throughout this journal issue (and in every standard beta adjustment formula that can be ap- introductory finance textbook).25 In this case, the plied to any firm in a mechanical fashion. Yet corporate tax and agency advantages to debt are financial distress and other agency cost advantages offset by the personal tax, financial distress, and and disadvantages to debt depend on a variety of agency cost disadvantages. At the firm’s optimal firm-specific factors, all of which interact to create capital structure, the enterprise value can be ex- unique tax advantage and disadvantage schedules. pressed as Consequently, levered betas cannot be mechanically determined. Although the Hamada beta adjustment − is commonly used, it is inconsistent with the exist- = EBIT(1 T ) + λ V D ence of an optimal capital structure and a gross K 0 oversimplification of reality. In this case, the net overall average advantage to The second implication is that the APV formula using debt is l. Algebraically, this is identical with the allocates the overall enterprise value between the M&M results, so that the equivalent equity cost is just debt-free value of the firm plus the value of other effects, such as the net tax advantage and the agency/ D financial distress disadvantages of debt. Suppose, for K = K + ( K (1 − λ) − K (1 − T )) 28 e 0 0 d E example, that there are no advantages to debt. Then l = 0, the unlevered value of the firm is $100 However, although the equation looks similar to the million, and the unlevered equity cost is 10%. With standard M&M equations, there are important differ- M&M, the unlevered cash flow/debt value split is $75 ences with profound implications.26 million/$25 million and the unlevered equity cost is First, with M&M, the marginal and average 13.33%. With an optimal capital structure, the split in advantages to using debt both equal the corporate value and unlevered equity cost would be some- tax rate, T. Consequently, we can unlever and relever where in between. The state of financial knowledge using the same corporate tax rate.27 However, with is such that we really don’t know exactly where, an optimal capital structure, we can unlever using although APV assumes that we do!29

23. Insert into the M&M equity cost equation or use K0 = WACC/(1 – TD/V). 26. For simplicity, a couple of issues are glossed over: whether the debt has Since WACC is 10%, and T and D/V are both 50%, K0 is estimated as 13.33%. systematic risk and whether the promised yield or expected rate of return on debt 24. James Poterba points out that financial policy was much the same prior should be used in the WACC. These just compound the problems discussed below. to the introduction of the corporate income tax as after it! See J. Poterba, “Tax Policy 27. Just use the M&M equation K0 = WACC/(1- lD/V). The only thing that is and Corporate Savings,” Brookings Papers on Economic Activity, Vol. 18 (1987), pp. different is the average advantage to debt. 455-503. 28. Miller (1977), cited earlier. 25. Myers (1984), cited earlier. 29. We need a beta adjustment formula to unlever betas since most of the observed betas are levered.

15 VOLUME 15 NUMBER 1 SPRING 2002 Finally, it is important to recognize that APV Further, it is inconceivable that a valuation simply allocates the enterprise value based on the be conducted without some form of sensitivity estimate of the unlevered equity cost. As long as analysis. If the expected operating cash flows we are consistent in using the same capital struc- are varied, the three valuation methods will ture model to unlever betas as well as to add up give different results. The reason again is sim- the components in APV, the only change is the ply the different financing assumptions. Both allocation of value. If we estimate the WACC APV and FTE assume that the financing is correctly at 10%, regardless of how we adjust for always constant, whereas WACC automatically leverage/unlever the equity cost, we will always assumes a financing adjustment. FTE further get back an APV value of $100 million. However, assumes that the cost of equity is independent our components of value are radically different! of financial risk. It is possible to fix the problems with APV and CONCLUSIONS FTE by incorporating the interaction between operating and financing decisions, but at a signifi- This paper has a number of important conclu- cant cost to their simplicity. However, the most sions, some of which have already appeared in the serious problem with APV is its misleading signals literature but are worth revisiting. In general, the about the value of debt financing. Normal appli- WACC is an appropriate valuation framework as cation of APV relies on the M&M tax model, which long as the debt ratio is expected to be constant. implies that the firm should optimally use 100% Further, APV and FTE can be formulated to be debt financing to take maximum advantage of the consistent with the WACC valuation. The issue, debt tax shield. And yet such a model is inconsis- however, is not whether the techniques can be tent with the reality of corporate practice or the rendered consistent through relatively complex ad- intent of most tax authorities. Moreover, it is also justments by sophisticated users, but rather what troubling that people can simultaneously recom- happens when they are used in everyday practice by mend the use of APV, an equity cost (or beta) practitioners unfamiliar with the somewhat arcane adjustment model, and the existence of an optimal valuation issues involved. capital structure (implicitly acknowledging that The critical question in choosing among the there are disadvantages to debt). It is important to three frameworks was first raised in a paper I recognize that the latter two models are mutually wrote 20 years ago, in which I said, “For APV and inconsistent. FTE to provide consistent results the amount of If disadvantages to debt are acknowledged, debt financing must equal the optimal debt ratio the APV equation needs significant modification times the value of the project and not the cost of to lower the tax shield value. The reality, of the project [emphasis added].” In other words, if course, is that the tax advantage to debt is not the firm has an optimal debt ratio, FTE and APV simply the corporate tax rate, and that financial require the project value as an input in order to distress and other agency cost factors all affect the perform the valuation! In contrast, APV and FTE optimal capital structure and with it the cost of are useful when knowing the NPV has no impact capital and the value of the firm. on the financing of the project. If the project is to It is clear that traditional valuation methods be financed with $10 million in debt, and its NPV based on WACC are more robust than either APV is subsequently estimated at $100 million, then or FTE. If the firm or project has an optimal debt this knowledge cannot feed back into the analysis ratio, use WACC. If the firm hasn’t got an optimal and prompt the company to take on more debt. debt ratio, perhaps this means that the cost of Obviously, complete independence between the capital is constant—in which case companies valuation and the financing is a very restrictive should still use WACC! If a firm knows how its cost assumption and some iteration is inevitable. How- of capital varies with its debt financing and can ever, this paper shows that if the iteration is accurately estimate this, please let people know, towards an optimal debt ratio, then both the APV since it is not obvious how to do it. Quite simply, and FTE techniques end up turning into the capital structure problems are too complex to standard WACC analysis, which renders the value allow us to use mechanical formulas to separate of the exercise moot. firm value into its unlevered and debt value

16 JOURNAL OF APPLIED CORPORATE FINANCE components (or to accurately unlever and relever as separate components of value. Similarly, if there betas).30 is a low-interest loan, it is straightforward to include Finally, APV is not necessarily the same as the true interest cost in the WACC and then add the valuation by components. In a corporate valuation, value of the interest subsidy as a separate component there are always extra pieces of value not captured of value. This use of valuation by components is in the discounted cash flow itself and it is important appropriate. What this paper takes issue with is the to remember that the DCF valuation only values the much more contentious APV approach of unbun- assets needed to generate the expected stream of dling the core WACC valuation into that of the cash flows. As a result, we always add in the value unlevered free cash flows and the tax and other of redundant assets or subtract contingent liabilities advantages and disadvantages to using debt.

30. A final caution is that many “solutions” to minimize WACC and determine implied by ratings. However, the yield on corporate debt is a promised yield, the optimal capital structure rely on an increasing yield to maturity schedule, as not an expected rate of return.

LAURENCE BOOTH holds the CIT Chair in Structured Finance at the University of Toronto’s Rotman School of Management.

17 VOLUME 15 NUMBER 1 SPRING 2002