Finance task due Monday 10pm PST - I need the calculations clearly shown in excel and report in word
Arun1990
j.1745-6622.1997.tb00132.x.pdf
Journal of Applied Corporate Finance S P R I N G 1 9 9 7 V O L U M E 1 0 . 1
Two DCF Approaches for Valuing Companies Under Alternative Financing Strategies (And How to Choose Between Them)
by Isik Inselbag and Howard Kaufold, University of Pennsylvania
114 JOURNAL OF APPLIED CORPORATE FINANCE
TWO DCF APPROACHES FOR VALUING COMPANIES UNDER ALTERNATIVE FINANCING STRATEGIES (AND HOW TO CHOOSE BETWEEN THEM)
by Isik Inselbag and Howard Kaufold, University of Pennsylvania*
114 BANK OF AMERICA JOURNAL OF APPLIED CORPORATE FINANCE
or decades now, finance theorists and practitioners have been debating the validity of various approaches to valuing a levered corporation. The weighted
shown that, if the firm maintains a constant ratio of debt to equity in market value terms, the weighted average cost of capital method is an appropriate valuation technique regardless of the pattern or duration of the firm’s cash flows. In this paper, we take this finding a step further to show that the two valuation methods give the same answer—again, regardless of the pattern and duration of the cash flows—for a much more general set of financing strategies in which the debt/ equity ratio is changing over time. As one example, we show the equivalence of the techniques for the case in which a company commits to a schedule in which the absolute dollar value of debt principal outstanding is paid down over time.
We argue further that past confusion can prob- ably be traced to assumptions the separate camps have implicitly made about the corporation’s finan- cial policy. While we will show the methods are equivalent under different financing strategies, our analysis suggests that it is more practical to apply the APV technique when the firm targets the dollar level of debt outstanding in the future, and the WACC approach when the firm instead intends to hold the debt/value ratio fixed in the future.
average cost of capital (WACC) method, in which a firm’s value is determined by its unlevered cash flows discounted by WACC, appears to be the reigning favorite among practitioners. The main challenger is the Adjusted Present Value (APV) technique, which values the firm as an all-equity entity plus any incremental worth created by leverage.1
Authors of corporate finance papers and text- books seem to feel obligated to choose sides in this debate. Proponents of WACC argue that, although there are problems with this approach when the firm’s capital structure is changing over time, it is easier to use because the expected equity returns in this approach can be directly observed. Those who favor APV counter that the WACC method is correct only under restrictive assumptions about the firm’s cash flows and financing mix.
To our knowledge, there are only two studies— one by one of the present writers—that have attempted to reconcile the two views.2 Both of these studies have
*We wish to thank Jeffrey Jaffe and Saman Majd. 1. The Adjusted Present Value method was originally presented by Stewart
Myers in “Interactions of Corporate Financing and Investment Decisions— Implications for Capital Budgeting,” Journal of Finance, March 1974, pp. 1-25. While we cast our argument in terms of valuing an entire firm, our findings are equally relevant in a capital budgeting context. The reader need only substitute the marginal required return on assets and debt capacity appropriate to the project in question.
2. See I. Inselbag, “Project Evaluation and Weighted Average Cost of Capital,” in Cees van Dam, editor, Trends in Financial Decision-Making, Martinus Nijhoff,
Boston, 1978, pp. 153-160; and J. Miles and R. Ezzell, “The Weighted Average Cost of Capital, Perfect Capital Markets and Project Life: A Clarification,” Journal of Financial and Quantitative Analysis, September 1980, pp. 719-730. For a compari- son of alternative approaches to valuing levered cash flows, see D. Chambers, R. Harris, and J. Pringle, “Treatment of Financing Mix in Analyzing Investment Opportunities,” Financial Management, Summer 1982, pp. 24-41. In contrast to the findings presented below, they conclude that the various methods yield different values. See footnote 7 for our explanation of their findings.
F
115 VOLUME 10 NUMBER 1 SPRING 1997
We illustrate these points by using the separate valuation methods to appraise a hypothetical corpo- ration under each of these financial policies. This process shows how the required return on equity and the weighted average cost of capital evolve under the separate policies. The result is a clearer understanding of the appropriate application of each of the valuation techniques.
To make these points, we invoke three as- sumptions that are standard in the related literature. The required return on the firm’s assets is taken as given and fixed over time. We also ignore costs of financial distress, since our objective is to clarify the effect of the corporate tax subsidy of debt financing per se in several popular valuation ap- proaches. Finally, we finesse issues arising from the differential personal taxation of debt and equity returns to investors.
In the next section, we present the unlevered free cash flows for a hypothetical company used throughout the paper to illustrate the financing strategies and resulting valuations. Then we com- pare the APV and WACC methods under the assump- tion that the firm targets the absolute dollar value of debt outstanding. Next we present the same com- parison for the case in which the firm maintains a constant debt/value blend. Finally, we discuss the implications of our analysis for a third popular valuation approach that involves capitalizing the firm’s flows to equity.
AN EXAMPLE
A newspaper chain is planning to set up a new division, Media, Inc., with projected cash flows as presented in Table 1. The new operation would require an initial investment in plant and equip- ment of $100 million, plus an infusion of $7.5 million of working capital (equal to 10% of ex- pected first-year sales). Media’s sales are projected to be $75 million during the first year of operation. Sales are expected to rise 12% per year over the next two years, with growth stabilizing at a 4% rate indefinitely thereafter. Management estimates that cash costs (cost of goods sold, general and admin- istrative expenses, etc.) will constitute 60% of rev- enue. New investments in plant and equipment will match depreciation each year, starting at 10% of the initial $100 million asset cost and growing in tandem with sales thereafter. The firm plans to maintain working capital levels at 10% of the fol- lowing year’s projected sales. With Media in the 35% tax bracket, unlevered free cash flow (asset cash flow) would approach $16 million in three years, and grow 4% per year thereafter.
The all-equity value of a firm at any point in time should equal the discounted value of future unlevered free cash flows, which we will denote as Ci:
(1)
TABLE 1 PROJECTED CASH FLOW STATEMENT OF MEDIA, INC. ($000’s)
Year 0 Year 1 Year 2 Year 3 Year 4
Sales 75,000 84,000 94,080 97,843 Cash Costs 45,000 50,400 56,448 58,706 Depreciation 10,000 11,200 12,544 13,046
Earnings before interest and taxes 20,000 22,400 25,088 26,092 Corporate tax 7,000 7,840 8,781 9,132
Earnings before interest after taxes 13,000 14,560 16,307 16,959 +Depreciation 10,000 11,200 12,544 13,046
Gross cash flow 23,000 25,760 28,851 30,005
Investments into: Fixed Assets 100,000 10,000 11,200 12,544 13,046 Net Working Capital 7,500 900 1,008 376 391
Unlevered free cash flow (107,500) 12,100 13,552 15,931 16,568
V C
(1 r ) U,t
i
A i t
i t 1
= + −= +
∞ ∑
116 JOURNAL OF APPLIED CORPORATE FINANCE
where rA is the required return on the firm’s assets. In the example, with growth constant after year 3, the current all-equity value of Media takes the form:
VU,0 = C1/(1 + rA) + C2/(1 + rA) 2 + C3/(1 + rA)
2(rA – g).
We will take the asset return as given in our analysis, and assume it is fixed at 18%. Applying this discount rate to the free cash flows given in Table 1 implies that Media is worth approximately $102 million in unlevered form:
VU,0 = 12.1/(1.18) + 13.6/(1.18) 2 + 15.9/(1.18)2(.18 – .04).
≅ $101.7 million.
One can use equation (1) to trace the evolution of Media’s all-equity value through time. The result- ing estimates are shown in Table 2.
Media’s value as a levered company depends on the financing policy the firm pursues. We now outline two plausible financing strategies, indicating how the APV and WACC methods can be applied in either context. In the first case, Media chooses a target for the absolute dollar value of its outstanding debt. In the second, the company instead chooses to fix its market debt/value ratio over time.
TARGETING THE DOLLAR VALUES OF DEBT OUTSTANDING
Many firms agree to financing contracts that specify debt service payments and outstanding fu- ture debt levels over the life of the contract, as opposed to adhering to a target capital structure by fixing the firm’s debt as a constant proportion of firm
value. In leveraged buyouts, for example, owners typically finance the newly acquired company with unusually high debt amounts, and then gradually pay down debt principal over the life of the transac- tion.3 At some point, the firm again achieves its desired long-run debt/value ratio.
Suppose, for example, that Media, Inc. arranges to borrow $77.5 million initially. The firm agrees to repay $8.5 million of principal at the end of each of the first three years of the contract, bringing debt outstanding at the end of the third year to $52 million (see Table 3). From that point on, Media will increase debt outstanding by 4% per year, in line with the expected growth of operating cash flows. Because of the firm’s highly levered position in the early years, we assume the borrowing rate is 11% initially, falling to 9% once it re-achieves a stable capital structure (after year 3).
One can use either the APV or WACC method to value a company choosing this type of financial policy. But, under these circumstances, we will show that the APV method is more direct.
The APV Method
The APV method treats the value of a levered firm at any point in time (VL,t) as its value as an all- equity entity (VU,t), plus the discounted value of the interest tax shields from the debt its assets will support (DVTSt):
4
VL,t = VU,t + DVTSt. (2)
The principle is straightforward. The firm’s unlevered value is determined by the operating
TABLE 2 ALL-EQUITY VALUE OF MEDIA, INC. ($000’s)
Value as of time: Year 0 Year 1 Year 2 Year 3
Unlevered Value 101,711 107,919 113,792 118,344
TABLE 3 DEBT REPAYMENT SCHEDULE OF TARGETED DEBT POLICY OF MEDIA, INC. ($000’s)
As of time: Year 0 Year 1 Year 2 Year 3 Year 4
Debt Level 77,500 69,000 60,500 52,000 54,080
3. For a discussion of such an example, see I. Inselbag and H. Kaufold, “How to Value Recapitalizations and Leveraged Buyouts,” Journal of Applied Corporate Finance, Volume 2, Number 2, Summer 1989, pp. 87-96.
4. To be entirely true to Myers’ concept, we should also deduct from this value any costs of having the debt outstanding, such as the costs of liquidating the firm’s
assets if it is unable to service the debt (costs of financial distress). We ignore these costs to focus on the tax effects of leverage.
117 VOLUME 10 NUMBER 1 SPRING 1997
income generated by its assets (as illustrated in the projections presented above). The debt supported by these operating cash flows increases levered value because interest (unlike dividends) is deduct- ible from the firm’s income for corporate tax pur- poses. As a result, for given operating income, the after-tax amount available for payment to both bondholders and stockholders taken together in- creases as more of the payout is in the form of interest rather than dividends.
Under this financial policy, projected debt lev- els are “exogenous”—that is to say, they do not depend on future firm performance, but are pre- determined by the schedule of debt service. As a result, the borrowing rate, rD, is the appropriate discount rate for current and future interest tax shields:
= T[ + + + ...] (3)
where T is the corporate tax rate, and Di is the outstanding debt balance at the end of year i.
In the Media example, the value of interest tax shields as of the beginning of the first year is:
DVTS0 = T[ + + +
≅ $30.5 million.
The value of the company is easily calculated as $132.2 million, the sum of these tax shields and the value of the all-equity company (see Table 2). Using the fact that the levered value of the company is equal to the sum of its debt and equity, VL,t = Dt + Et, the evolution of corporate value, debt and equity is given in Table 4.
The Weighted Average Cost of Capital (WACC) Method
Under the WACC method, a widely used ap- proach to corporate valuation, the firm’s value in a
given period is calculated as the discounted value of its projected unlevered free cash flows, discounted by the weighted average cost of capital:
(4)
The weighted average cost of capital for each period is the weighted average of the after-tax debt and equity required returns, weighted by the relative size of each source of financing in the market value capital structure of the firm:
(5)
If the firm targets dollar future debt levels in absolute terms, the debt/value ratio changes over time, thus causing changes in both the required equity return and the weighted average cost of capital. To see how a company’s required equity return is affected by changes in its debt/value ratio, consider equation (6a), which shows how the firm’s after-tax income stream (represented by its asset returns plus its annual tax savings) is divided among the bondholders and stockholders:
(6a)
On the left-hand side of the equation, the unlevered value of the asset cash flows is VU, the all- equity value of the company. These assets generate an annual expected return of rA, which is determined by the riskiness of the operating cash flows. As we have seen, this all-equity value is supplemented by the value of interest tax shields, DVTS. Given the “exogenous,” or pre-determined, character of future debt levels and interest tax shields, this asset gener- ates the return of rD, which is compatible with the lower risk of these cash flows.
As shown on the right-hand side of the equa- tion, these two sources of after-tax income are shared
TABLE 4 DEBT, EQUITY AND TOTAL VALUE OF MEDIA, INC.: DOLLAR VALUE OF DEBT TARGETED ($000’s)
DVTSt r D
(1 + r ) D t
D
r D
(1+ r ) D t+1
D 2
r D
(1+ r ) D t+2
D 3
.11(77,500)
(1.11)
.11(69,000)
(1.11)
2
.11(60,500)
(1.11)3
.09(52,000)
(1.11) (.09-.04)3
V C
r
C
r r L,t
t
WACC t
t
WACC t WACC t =
+ +
+ + + +
+
1 2
11 1 1( ) ( )( ), , ,
+ + + +
++ + +
C
r r r t
WACC t WACC t WACC t
3
1 21 1 1( )( )( ) ....
, , ,
r r T D
V r
E
V WACC t D t
t
L,t E t
t
L,t , , ,( )= − +1
V r DVTS r D r E rU t A t D t D t E t, ,( ) ( ) ( ) ( )+ = +
Value as of time: Year 0 Year 1 Year 2 Year 3
Unlevered value 101,711 107,919 113,792 118,344 Discounted value of tax shields 30,501 30,872 31,612 32,760 Levered value 132,212 138,791 145,404 151,104 Value of debt 77,500 69,000 60,500 52,000 Value of equity 54,712 69,791 84,904 99,104
Our analysis suggests that it is more practical to apply the APV technique when the firm targets the dollar level of debt outstanding in the future, and the WACC approach when the firm instead intends to hold the debt/value ratio fixed in
the future.
118 JOURNAL OF APPLIED CORPORATE FINANCE
between the bondholders and the equityholders according to their proportional representation in the capital structure and the returns required by these two investor groups (rD and rE, respectively).
Then, by manipulating the basic balance sheet identity, VL,t = VU,t + DVTSt = Et + Dt, we can solve for (rE) as follows:
(7)
As Table 4 indicates, the debt/equity ratio, and (Dt - DVTSt)/Et, change over the early years of the transaction. The return the shareholders require therefore fluctuates, and can be computed by direct substitution from Table 4 into equation (7). These returns are given in the first row of Table 5.
To calculate the weighted average cost of capital, we substitute the required equity return (equation (7)) into equation (5) to get:
(8)
In this targeted debt case, WACC also changes if the debt/value ratio is not constant. Specifically, a decline in the debt/value ratio implies an increase in the cost of capital, since the reduction in leverage means a loss of interest tax shields.5,6
The cost of capital for Media is given in the second row of Table 5. After year 3, the value of the firm (levered and unlevered), and the debt and
equity, grow at the steady-state rate of 4%. Therefore, the required return on levered equity as well as the weighted average cost of capital remain stable at the level reached by the end of year 3.7
Using the WACC method to value Media, the firm’s unlevered free cash flows are discounted by the rates given in the second row of Table 5. The value of the firm at time 0 is therefore:
VL,0 = + + +
= $132.2 million.
This solution is identical to that derived using the APV method. Under this financial policy, though, the APV approach is clearly preferred. In fact, as equation (7) shows, one must know the value of the firm’s tax shields to calculate the correct equity return and weighted average cost of capital. That is, one must already have calculated the firm’s value (using APV or some other means) to be able to derive the discount rates necessary to value the firm using the WACC method.8 In addi- tion, the variation in the WACC shown in Table 5 illustrates the well-known problem with using a constant cost of capital, or “hurdle rate,” for capital budgeting when capital structure is chang- ing over time.
TABLE 5 REQUIRED RETURN TO EQUITY AND WEIGHTED AVERAGE COST OF CAPITAL MEDIA, INC.: TARGETED DEBT POLICY
For the Year: Year 0 Year 1 Year 2 Year 3 Year 4 ...
Required equity return 24.0% 21.8% 20.4% 19.7% 19.7% Weighted average cost of capital 14.1% 14.5% 14.9% 15.0% 15.0%
5. This result may be altered in the presence of costs of financial distress. 6. There is a related special case in which the equity return is fixed, even
though the firm is targeting the dollar level of debt outstanding. In the standard textbook example, the firm’s expected unlevered cash flows are assumed to be constant and perpetual, and the firm sets borrowings at the same dollar level, D, in perpetuity. In this case, the present value of the tax shields is simply TD, so that the required equity return of equation (7) reduces to:
rE,t = rA + ((Dt – TDt)/Et)(rA – rD). = rA + (Dt/Et)(1 – T)(rA – rD).
Since the expected future asset cash flows are constant, both the debt and equity values are stable as long as the firm makes a commitment to maintaining the same dollar debt level. The equity return is therefore independent of time in this case. Substituting the equity return into equation (5) implies a weighted average cost of capital of:
rWACC,t = rA(1 – T(D/VL)),
which, of course, is also constant over time. The reader will recognize these findings as the well-known Modigliani-Miller (1963) results. (See F. Modigliani and M. Miller, “Corporate Income Taxes and the Cost of Capital: A Correction,” American Economic Review, June 1963, pp. 433-443.) While the weighted average cost of capital is independent of the absolute cost of borrowing under these conditions, this will not generally be true as shown by equation (8).
7. In concluding that various methods imply different values for the same cash flows and financing policy, Chambers, Harris and Pringle (1982) assume time- independent discount rates for each of the valuation approaches. As equations (7) and (8) show, the costs of equity and the weighted average cost of capital will change over time as long as the capital structure is not constant (as occurs in their example). Applying equations (7) and (8) to their example implies identical values for their project, independent of the valuation method used.
8. We elaborate on this point in our discussion of the “flows to equity” approach later in the paper.
r r D DVTS
E r rE t A
t t
t A D,
( ) ( )= +
− −
r r DVTS
V r
DVTS TD
V WACC t A
t
L,t D
t t
L,t , ( )
( ) = − +
− 1
16.6
(1.141)(1.145)(1.149)(.15-.04)
12.1
(1.141)
13.6
(1.141)(1.145)
15.9
(1.141)(1.145)(1.149)
119 VOLUME 10 NUMBER 1 SPRING 1997
THE CONSTANT DEBT/VALUE RATIO CASE
In weighing the pros and cons of debt funding, many firms conclude that it is optimal to set and adhere to a targeted blend of debt and equity.9 In these circumstances, unless the company’s cash flows are constant over time, the firm will need to undertake regular debt-equity swaps to maintain this target capital structure. We now describe the proper application of the APV and WACC methods under this financing policy.
The APV Method
If the company maintains a fixed debt/value capital structure in market value terms, the present value of interest tax shields at time t will be:
(9)
Why this blending of rA and rD as discount rates in this expression?10 Consider the calculation of DVTS at time 0. At that time, the value of the levered firm, and the dollar level of debt financing for that year (equal to a fixed fraction of firm value), are known. This debt level and borrowing rate fix the interest the firm will pay at the end of the first year. The expected tax savings resulting from this single year’s interest tax shield is therefore pre-determined. As a result, this cash flow is as risky as the interest payment itself, so that rD is the appropriate discount rate.
But thereafter, because the firm expects to maintain debt as a fixed fraction of total value, the amount of debt and interest payments will vary with the actual (rather than the expected) future asset cash flow outcomes for the company. Since future interest payments and tax shields will therefore be as risky as the asset cash flows, one must use the higher rate rA to discount tax shields after the first year.
Suppose, for example, that Media fixes its debt/ value ratio at 40% (debt/equity at 66.7%), and that the firm can borrow at an interest rate of 9%. How much would the resulting tax shields add to the all-equity value? Since debt and levered firm value are simul- taneously determined under this policy, we must solve for the levered value of the firm using the “iterative” process illustrated below.
Beginning at the end of year 3 (the point at which growth stabilizes), we can use equations (2) and (9) to determine the value of Media as:
Since the expected debt level grows at a constant rate g after year 3, this relation can be simplified as:
Defining L to be the debt/value ratio, D/VL, Media in period three will be worth:
From Table 2, the all-equity value of Media at the end of year 3 is approximately $118 million. Substituting this value and the other parameters into the expres- sion for VL,3, the levered value of Media at the end of year 3 is expected to be $131 million. The debt level would be 40% of this amount, or $52 million. The difference between the levered and unlevered values of $13 ($131-$118) million is the value of all interest tax shields expected from year 4 on.
Solving recursively, we can describe the ex- pected evolution in the value, debt, and equity of Media under the fixed debt/value policy. The value of the firm at the end of year 2 is:
DVTS T
r D
r
r D
r r
r D
r r
t
D t
D
D t
D A
D t
D A
= +
+ + +
+
+ + +
+
+
( ) ( )( )
( )( ) ...
1 1 1
1 1
1
2 2
9. In this paper, we use a targeted blend of debt and equity expressed in terms of market values. Some companies, however, set capital structure targets in terms of book values. That characterization of debt capacity leads to a somewhat different financing strategy—one that requires a modification of the analysis presented below. Our focus on market values in this paper reflects the well-known principle that use of book values is likely to understate debt capacity because the book values of assets reflect “historical costs” rather than current values of assets based on their cash-flow-generating capacity. Nevertheless, for companies whose current value consists primarily of intangible future growth opportunities as opposed to tangible “assets in place,” targeting debt-equity ratios in terms of book values may still make
sense. For an excellent discussion of these issues, see Michael J. Barclay, Clifford W. Smith, Jr. and Ross L. Watts,”The Determinants of Corporate Leverage and Dividend Policies,” Journal of Applied Corporate Finance, Vol. 7 No. 4 (Winter, 1996), 4-19.
10. The argument in the text is a heuristic version of ideas presented in Miles and Ezzell (1980). In that paper, the authors show the equivalence of the APV and WACC approaches in a finite-lived capital budgeting context when the project is financed with a constant blend of debt and equity. As we show, their approach can be extended to the case in which the firm’s unlevered cash flows are expected to continue indefinitely.
V V T
r D
r
r D
r r
r D
r r
L, U
D
D
D
D A
D
D A
3 3
3 4
5 2
1 1 1
1 1
= + +
+ + +
+
+ + +
,
( ) ( )( )
( )( ) .......
The APV method treats the value of a levered firm at any point in time as its value as an all-equity entity plus the discounted value of the interest tax shields from the debt
its assets will support.
V V Tr D r
r r g L, U
D A
D A 3 3
3 1
1 = +
+ + −,
( )
( )( )
V V
Tr L r
r r g
L, U
D A
D A
3 3
1 1
1
= −
+ + −
,
( )
( )( )
120 JOURNAL OF APPLIED CORPORATE FINANCE
because of the dependence of the debt outstanding on the realizations of future cash flows. It is not surprising that the value of interest tax shields as of the end of year 3 is much lower in this case than under the targeted debt case ($12.8 million vs. $32.8 million; see Tables 6 and 4). Though the expected tax savings are approximately the same from that point on, the risk of these cash flows is significantly higher in the constant debt/value case because future debt levels depend on as yet unknown operating results for the firm.11,12
The example reveals the complexity of us- ing the APV technique to value a firm that fol- lows the constant debt/value policy. Since the amount of the firm’s outstanding debt depends on realizations of future cash flows, dollar debt levels are not pre-determined as in standard APV calculations. The simultaneous determination of debt and value requires an iterative solution. While this method is perfectly legitimate, the WACC method is simpler when the firm pursues this financial strategy.
The Weighted Average Cost of Capital (WACC) Method
Reconsider equation (5) describing the firm’s weighted average cost of capital. If the company follows a fixed debt/value policy, Dt/VLt and Et/VLt will, by definition, be constant over time. If we assume the borrowing rate is fixed, the weighted average cost of capital will be independent of time since the equity return will also be constant under these conditions.
To show that the equity return will be constant under this financial policy, let’s go back to the analysis of the distribution of the firm’s income
V V T
r D
r
r D
r r
r D
r r
L, U
D
D
D
D A
D
D A
2 2
2 3
4 2
1 1 1
1 1
= + +
+ + +
+
+ + +
, ( ) ( )( )
( )( ) .......
V V Tr D
r
DVTS
r L, U
D
D A 2 2
2 3
1 1 = +
+ +
+, ( ) ( )
V
V DVTS
r Tr L
r
L,
U A
D
D
2
2 3
1
1 1
= +
+
− +
, ( )
( )
TABLE 6 DEBT, EQUITY AND TOTAL VALUE OF MEDIA, INC.: 40% DEBT/VALUE MIX ($000’s))
Value as of time: Year 0 Year 1 Year 2 Year 3
Unlevered value 101,711 107,919 113,792 118,344 Levered value 113,012 119,712 126,076 131,110 Discounted value of tax shields 11,301 11,794 12,284 12,775 Value of Debt (40% of value) 45,205 47,885 50,430 52,447 Value of Equity (60% of value) 67,807 71,827 75,645 78,671
which can be rewritten as:
Since D2 = L VL,2, the value of the company at the end of year 2 is:
Using the all-equity value as of the end of year 2 of $114 million, the end-of-year 3 tax shields of $13 million, and the other parameters of the example, Media will be worth approximately $126 million at the end of year 2. Debt and equity will again be 40% and 60%, respectively, of the total value of the firm.
Continuing the solution process in this fashion, one can calculate the present value of the company and its debt and equity. Table 6 summarizes the results of the recursive solution process. Media is initially worth approximately $113 million: $45 mil- lion (40%) is debt, $68 million (60%) is equity. The present value of the interest tax shields on projected borrowings is:
≅ $11 Million
To repeat, the return on assets plays a promi- nent role in calculating the value of the tax shields
11. Even in the targeted debt example, one might argue that after year 3 the firm would vary its borrowings as future cash flow outcomes are realized. One would then value the tax shields from year 3 on using the method described in this section of the paper. We assume in the previous section that the firm commits to exogenous debt levels in order to show the two financing policies in their purest forms.
12. One should not conclude, however, that the targeted debt policy is superior to the constant debt/value strategy based on the levered values as calculated in the two examples. The former may involve higher costs of financial distress which are ignored in this analysis.
DVTS Tr
r D
D
r
D D
r g
r D
D A
A
A 0 0
1 2
3
21 1 1 =
+ +
+ +
+ −
+
( ) ( )
( )
( )
121 VOLUME 10 NUMBER 1 SPRING 1997
between bondholders and stockholders we pre- sented earlier. Once again, the value of the company is the sum of its all-equity value and the expected present value of interest tax shields. As we argued in the APV section above, the value of the interest tax shield for the first year (TrDD/(1+rD)) is pre- determined, and therefore earns a return of rD. But since subsequent tax shields (DVTS-TrDD/(1+rD)) vary with future free cash flow outcomes for the firm, the appropriate return for these tax shields is the higher asset rate, rA.
Revising equation (6a) to take account of the greater risk of future tax shields under this financial policy,
(6b)
One can again use the balance-sheet equalities, VL,t = VU,t + DVTSt = Et + Dt, to solve equation (6b) for the equity return:13
(10)
It follows that the equity return is constant if the firm fixes its debt/value (debt/equity) ratio. Using the parameters of the example, the required equity return is:
≅ $23.8%
Substituting this equity return (equation (10)) into the weighted average cost of capital (equa- tion (5)), we obtain the following expression for WACC:
(11)14
This constant weighted average cost of capital properly accounts for the higher discount rate ap- propriate given the greater riskiness of future interest tax shields.
Using the parameters of our example in equa- tion (11), the weighted average cost of capital for Media, Inc. is found as:
rWACC,t = .18 - (.35)(.09)(.40)((1.18)/(1.09)) = 16.6%.
To value Media, we discount the unlevered cash flows (given in Table 1) by this constant weighted average cost of capital:
+ +
≅ $113.0 million.
This answer is identical to that derived using the more complicated APV method (see Table 6). While the APV and WACC methods yield the same results, the simplicity of the WACC approach in this case indicates that it is far more practical than APV if the firm being valued follows a constant debt/value policy.15,16
When a company’s debt ratio is changing over time, one must already have calculated the firm’s value (using APV or some other means) to be able to derive the
discount rates necessary to value the firm using the WACC method.
V r Tr D
r r
DVTS Tr D
r r D r E r
U t A D t
D D
t D t
D A t D t E t
,
,
( ) ( )
( )
( ( )
)( ) ( ) ( )
+ +
+
− +
= +
1
1
r r D
E
Tr
r r rE t A
t
t
D
D A D, (
( ) )( )= + −
+ −1
1
rE = + − + −. (
. (. )
. )(. . )18
2
3 1
35 09
1 09 18 09
r r Tr L r
r WACC t A D
A
D ,
( )
( ) = −
+ +
1
1
13. For the reader who is uncomfortable with the informality of this derivation, one can calculate the return shareholders earn in the following way. Note that the cash flow to stockholders, CEt, is the unlevered free cash flow net of debt service and taxes:
CEt = Ct – rDDt–1(1 – T) + Dt – Dt–1 (F-1)
At any point in time, the required return on equity, rE,t, must satisfy the equality:
Et = (CEt+1 + Et+1)/(1 + rE,t) (F-2)
where Et and Et+1 are the values of equity at time t and t+1, respectively. Since VL,t+1 = Dt+1 + Et+1, equation (F-2) can be inverted and rewritten using
equation (F-1) as:
(1 + rE,t) = (Ct+1 + VL,t+1 - Dt[1 + rD(1 – T)])/Et. (F-3)
From our prior observation that future interest tax shields are as risky as corresponding unlevered cash flows under this financial policy, we know that the firm’s value evolves intertemporally according to:
VL,t = (Ct+1)/(1 + rA) + (TrDDt)/(1 + rD) + (VL,t+1)/(1+rA).
Solving this relation for Ct+1 and substituting into equation (F-3),
1 + rE,t = ((1 +rA)VL,t – Dt[1 + rD(1 – T) + TrD(1 + rA)/(1 + rD)])/Et.
Finally, dividing the numerator and denominator of the right hand side of this expression by VLt, we can simplify to get:
rE,t = rA + (Dt/Et)(1 – [TrD/(1 + rD)])(rA – rD). (10)
14. This formula is derived in Miles and Ezzell (1980), equation (20). 15. The relative simplicity of the WACC method for a firm using a constant debt-
equity blend is recognized by R. Brealey and S. Myers, Principles of Corporate Finance, 5th Edition, McGraw-Hill, New York, 1996. See Chapter 19.
16. We have outlined two plausible financial policies. A third case, observed in many highly levered transactions, occurs when a firm is required (by debt covenants) to dedicate its entire free cash flow to interest and principal payments. Under these conditions, the amount of debt outstanding and, therefore, the interest tax shields at any point in time are a direct function of the unlevered free cash flows of the firm. Since the debt balance then becomes as risky as the operating cash flows, the required return on assets, rA, is the appropriate discount rate to be used in calculating the present value of interest tax shields. This is yet another case in which the APV and WACC methods yield identical values. One can demonstrate this equivalence using the procedures given in the previous section with proper adjustment of the discounting of the tax shields. This case corresponds to the “Compressed Adjusted Present Value” technique referred to in S. Kaplan and R. Ruback, “The Market Pricing of Cash Flow Forecasts: Discounted Cash Flow vs. The Method of ‘Comparables’,” Journal of Applied Corporate Finance, Volume 8, Number 4, Winter 1996, pp. 45-60.
VL,0 = 12.1
(1.166)
13.6
(1.166)
2
15.9
(1.166) (.166-.04)2
(11)14
122 JOURNAL OF APPLIED CORPORATE FINANCE
SOME COMMENTS ON THE “FLOWS TO EQUITY” APPROACH
A third approach to valuation, popular among certain practitioners,17 is the “flows to equity” method. To use this method to calculate the value of a company, one first values the outstanding equity, and then adds the market value of debt. To estimate the value of the levered equity, one must first project the cash flows the stockholders expect to receive net of debt service (as described in equation (F-1) in footnote 13). One must then discount these flows by the required equity return as given by equation (7) or (10), depending on the financial policy of the firm.
It is useful to recognize that, whether the firm pursues the targeted debt strategy or the constant debt/value policy, the flows to equity approach is not an independent valuation technique. Suppose, for example, that the firm targets an absolute dollar debt level. Under these conditions, the cash flows to the shareholders are exogenous, given the unlevered cash flows and pre-determined debt repayment schedule. However, as equation (7) shows, the required return to equity (the discount rate to be used in this approach) depends on the present value of interest tax shields. If the value of these tax shields is known, the value of the company can also be calculated directly as the sum of the tax shields and the firm’s unlevered value.
Suppose, instead, the firm pursues the constant capital structure policy. It is then impossible to estimate the equity cash flows without first having used one of the two methods described above to value the firm as a whole. While the projected unlevered cash flow is assumed known, and the debt level as of the beginning of the year is pre-deter- mined, the debt outstanding at year end will depend on the value of the company at that time. This value
fluctuates based on unlevered cash flows yet to be realized. Thus, the change in outstanding debt principal, and the equity cash flow, depend on the value of the firm. It follows that, under the constant capital structure financial policy, the estimation of the flows to equity requires prior knowledge of total firm value.
In sum, application of the “flows to equity” approach to valuation in each financing case re- quires prior knowledge of what the company is worth. It still may be of interest, for purposes other than valuation, to calculate the cash flow to share- holders and the required equity return. But one will already be in a position to use the APV or WACC methods to value the company directly.
CONCLUSION
In this paper, we have compared two popular approaches to valuing a company, the Adjusted Present Value (APV) and the Weighted Average Cost of Capital (WACC) methods. To illustrate the ap- proaches, we have assumed that the company being valued follows one of two plausible financing strat- egies: In the first, the company commits to a pre- determined schedule for the absolute amount of debt to be used. Under a second scenario, the firm is financed with a constant blend of debt and equity.
We have shown that both valuation methods, when properly formulated to take into account the evolution of the firm’s cash flows and capital struc- ture, give identical results under each of these financing alternatives. But, although the approaches are equivalent, our analysis also reveals that it is more practical to apply the APV technique when the firm targets the dollar level of debt outstanding over time, and the WACC approach when the firm instead intends to maintain a fixed debt/value ratio.
17. Particularly those involved in real estate investments, leveraged buyout, leveraged leasing and project finance transactions.
ISIK INSELBAG
is Adjunct Professor of Finance, as well as the former Vice Dean and Director of the Graduate Division, at the University of Pennsylvania’s Wharton School of Business.
HOWARD KAUFOLD
is Adjunct Professor of Finance and the Director of the Executive MBA Program at the Wharton School.
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