Interactions of Corporate Financing and Investment DecisionsImplications for Capital Budgeting Stewart C. Myers The Journal of Finance, Vol. 29, No. 1. (Mar., 1974), pp. 125. Stable URL: http://links.jstor.org/sici?sici=00221082%28197403%2929%3A1%3C1%3AIOCFAI%3E2.0.CO%3B24 The Journal of Finance is currently published by American Finance Association.
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The Journal of FINANCE
VOL. XXIX
MARCH1974
No. 1
INTERACTIONS O F CORPORATE FINANCING AND INVESTMENT
DECISIONSIMPLICATIONS FOR CAPITAL BUDGETING
EVERYONE seems to agree that there are significant interactions between corporate financing and investment decisions. The most important argument to the contraryembodied in Modigliani and Miller's (MM's) famous Proposition Ispecifically assumes the absence of corporate income taxes; but their argument implies an interaction when such taxes are recognized. Interactions may also stem from transaction costs or other market imperfections. The purpose of this paper is to present a general approach for analysis of the interactions of corporate financing and investment decisions, and to derive the approach's implications for capital investment decisions. Perhaps the most int~restingimplication is that capital budgeting rules based on the weighted average cost of capital formulas proposed by M M and other authors are not generally correct. Although the rules are reasonably robust, a more general "Adjusted Present Value" rule should, in principle, be used to evaluate investment opportunities. The paper is organized as follows. Section I1 presents the framework for my analysis, which is a mathematical programming formulation of the problem of financial management. The conditions for the optimum and the implications for corporate investment decisions are derived. In Section 111, the usual weighted average cost of capital rules are derived as special cases of the more general analysis. Section IV examines the errors that can occur if weighted average cost of capital rules are used in practice, and evaluates the rules' robustness. Finally, I discuss the Adjusted Present Value rule as an alternative for practical applications. I t must be emphasized that this paper is not intended to catalogue or deal with all possible interactions of financing and investment decisions; in other words, there is no attempt to specify the problem of financial management in
*
Associate Professor of Finance, Sloan School of Management, Massachusetts Institute of Technology. This paper was greatly improved by comments of G . A. Pogue. I also thank Mr. Swaminathan Iyer for programming assistance. Any deficiencies in the paper are my own.
2
The Journal of Finance
full detail. I present an approach to analyzing interactions and a specific analysis of the most important ones. Another limitation is that the model developed in the paper is staticthat is, it does not consider how future financial decisions might respond to information which will become available in future periods. Instead the model specifies a financial plan which is optimal given that current expectations are realized. Since there is no assurance that sequential application of a static model constitutes optimal strategy under uncertainty, this paper is only of intermediate generality. In this respect it is no better or worse than the existing theory of financial management, which is likewise static. The analysis is nevertheless of immediate interest. As far as I know the literature of finance contains no full analysis of the use of the weighted average cost of capital as a standard for capital budgeting. Most authors present sufficient conditioqs for its use, and are careful to warn the reader against assuming it to be generally va1id.l They clearly regard it as a special caie of some more general standard. But they do not specify the general standard in operational form, and therefore cannot offer much perspective on how special the special case really is, or on how dangerous it is to use the special rule generally. This paper, on the other hand, formulates a general model, states its implications in reasonably operational form (as the Adjusted Present Value rule), and then goes on to evaluate traditional procedures as special cases. I do not mean this to minimize previous work on capital budgeting and the weighted average cost of capital, but simply to designate this paper's contrib ~ t i o n My . ~ debt to the literatureparticularly the ModiglianiMiller papers" will be evident throughout.
We will consider the firm's problem in the following terms. I t begins with a certain initial package of assets and liabilities. For a brandnew firm, this will be simply money in the bank and stock outstanding. For a going concern, the package will be much more complicated. Any firm, however, has the opportunity to change the characteristics of its initial package by transactions in real or financial assetsi.e., by investment or financing decisions. The problem is to determine which set of current and planned future transactions will maximize the current market value of the firm. Market value is taken to be 1. See, for example, Miller and Modigliani 1141, esp. pp. 346343; Fama and Miller [71, pp. 170175; Haley and Schall [9], ch. 13; Vickers 1281 and Beranek [21. Other authors who have expressed concern about the general applicability of the weighted average cost of capital include Robichek and McDonald [Zll, Arditti [ l l , and Tuttle and Litzenberger 1261. 2. The paper most similar to this one is Beranek's 121. He analyzes the necessary conditions for use of the weighted average cost of capital, and obtains a list of conditions essentially equivalent to the one presented below. However, his method of analysis is difierent, he is concerned only with the "textbook" formula (defined below), and he does not go on to evaluate robustness or propose general procedures. His paper does cover certain other issues not addressed here, for example the proper definition of "cash flow" for an investment project. 3. Miller and Modigliani [I41 contains the most precise and compact exposition of their theory. See also their other papers, [I51 and 1161.
Interactions of Corporate Financing and Investment Decisions
3
an adequate proxy for the firm's more basic objective, maximization of current shareholders' wealth. This type of problem can be approached by (1) specifying the firm's objective as a function of investment and financing decisions and ( 2 ) capturing interactions of the financing and investment opportunities by a series of constraints.
General F o ~ m u l a t i o n Consider a firm which has identified a series of investment opportunities. I t must decide which of these "projects" to ~ n d e r t a k e .At ~ the same time it wishes to arrive at a financing plan for the period t = 0, 1, . . ., T. The financing plan is to specify for each period the planned stock of debt outstanding, cash dividends paid, and the net proceeds from issue of new shares. Let: xj = proportion of project j accepted. yt = stock of debt outstanding in t. D t = total cash dividends paid in t. E, = net proceeds from equity issued in t. Ct = expected net aftertax cash inflow to the firm in t, with net outflow (i.e. investment) represented by Ct < 0. Zt = debt capacity in t, defined as the limit on y,. Zt depends on firm's investment decisionj5i.e., 6Zt/6xj will normally be positive.
Also, let Q equal AV, the change in the current market value of the firm, evaluated cum dividend at the start of period t = 0. In general, Q is a function of the x's, y's, D's and E's. The problem is to maximize Q, subject to: + j = ~ j 1<0,
j=1,2
4:=
Ct  [yt  y t  ~ ( l t = O , l , . . . , T. Xj,
,... ,J.
+ ( 1  t ) r ) ] + D,
yt, Dt, Et
2 0.
(la)
Et= 0
(1~) (Id)
The borrowing rate, r, is assumed constant for simplicity, as is the corporate tax rate t. In general, r will be a function of the other variables. This formulation of the firm's financial planning problem is perfectly general in the sense of not imposing restrictions (e.g., linearity) on the functions determining 9 or Z,. I t is by no means a detailed formulation. The maturity structure of the planned stock of debt is not treated, for example. Stock repurchases are not allowed. These "details," while important to the firm's overall financial planJ6 are not critical to this paper. 4. Some projects may be future investment opportunities anticipated for t = 1, 2, . . . . Accepting such a project does not imply immediate investment, but simply that the project is included in the firm's financial plan. 5. The limit may be imposed by capital markets or it may simply reflect management's judgment as to the best level of debt. 6. These "details" are considered in Myers and Pogue [201, who develop mathematical programming models for overall financial planning.
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4
Conditions for the Optimum Eqs. (1) define the nature of the interactions between the firm's financing and investment decisions. The effects of the interactions can be better understood by examining the necessary conditions for the optimal solution. In order to simplify notation define Aj = 6W/6xi, F, = 6$/6yt, Zjt 6Zt/6xj, and Cj, = 6Ct/6x,. Also, note that each of the following equals 1 : 64,/Sxj, 64y/6yt and 64:/6yt. Finally, note that 64:/6xj = Cjt. The shadow prices for 4:. are h, for +j, h: for 4; and With these simplifications, the necessary conditions for the optimum can be written as follows. For each project:
For debt in each period,
For dividends in each period,
For equity issued in each period,
In each of these equations a strict equality holds if the corresponding decision variable is positive in the optimal solution. Eq. (2a) is particularly interesting because it states the condition for evaluating a marginal investment in a project. Marginal investment is justified if project j's "Adjusted Present Value" (APV,) be positive, i.e., Expand Investment if:
APV,
+
T
[h:Zj,
+ h:Cj+] > 0.
(3)
t=o
In the optimal solution APV, = hj if the project is accepted (xj = 1). If it is rejected (x, = OJ then APV, is negative and h, = 0. If it is partially accepted, then APV, = hj = 0. The term adjusted present value is used because in the optimal solution Aj, the project's direct contribution to the objective, is "adjusted for" the project's side effects on other investment and financing options. The side effects occur because of the project's effects on the debt capacity and sources/uses constraints. Eflects of financial leverage when' dividend policy is irrelevant.Suppose that dividend policy is irrelevant, in the sense that 6W/6Et = 6q/6Dt = 0 for all T.7Then h:, = 0, from Eqs. ( l c ) and ( I d ) . 7. +his defines irrelevance of dividend policy in the same way as Miller and Modigliani 1141. That is, given values for the xj's and y;s, a marginal change in Dt and an offsetting change in Et will not affect shareholder's wealth.
Interactions of Corporate Financing and Tnzestment Decisions
5
Also, assume that 6$/6y, is positivewhich is realistic, given the tax deductibility of debt, regardless of whether one agrees with MM. Then the constraints 4; will always be binding, Eqs. (2b) will be strict equalities, and A: for all t. Substituting in Eq. ( 3 ) )
Eq. (4) implies that APVj, the contribution of a marginal investment in j to the firm's value, is measured by A,, plus the present value of the additional debt the project supports. Eflects of dividend policy.In practice, however, dividend policy may not be completely irrelevant. At very least, 69/6Et will be negative because of transaction costs associated with stock issues. I t is not clear whether 69/6Dt is positive, negative or zero in real life.' Suppose that the optimal solution calls for an equity issue in a period t. Then A: =  6 ~ / 6 E , and A: > 0. Examination of Eq. (2a) shows that this is reflected in the optimal solution in two ways. First, project j is penalized if Cjt < 0. On the other hand, the project is relatively more attractive if Cjt > 0: in this case the project generates funds and this reduces the need for a stock issue. Second, if the project contributes to debt capacity in t, this in turn reduces the need for the stock issue. This is evident in Eq. (2b), which shows that A:, the marginal value of debt capacity in t, depends on A: as well as on 6$/6yt. The same type of interactions exists if dividends are paid in t and 6$/6Dt # 0. Conditions for independence of financing and investment decisions.In a world with no taxes and perfect capital markets, both debt policy and dividend policy are irrelevant, i.e., F, = 69/6Dt = 64)/6Et = 0. In this case the investment and financing decisions are independent, and APV, equals simply Aj. The independence of financing and investment decisions in a "pure MM world" is well known, but worth mentioning here because it reveals the economic interpretation of A,. Aj is the contribution to firm value of marginal investment in project j, assuming allequity financing and irrelevance of dividend policy. In a pure MM world that is all the financial manager needs to know. In effect, the APV concept first evaluates the project in this base case and then makes appropriate adjustments (via the shadow prices A: and A ): when debt and/or dividend policy is relevant and influenced by adoption of the project. 8. I t can be argued that dividends decrease shareholder wealth because dividends are taxed more heavily than capital gains. On the other hand, it is possible that some investors positively prefer dividends because of the convenience of having a regular, "automatic" cash income, or for other reasons. Although the matter of dividend policy is still controversial, recent evidence does not indicate that it is a11 that important, apart from the "informational content" of dividends which is not germane here. (See [ l j l , pp. 36770, [31 and [81 for empirical evidence consistent with the irrelevance of dividend policy.) Thus most of the analysis later in the paper assumes 6v/6Dt = 0.
The Journal of Finance
6
Decentralized capital budgeting systems.The shadow prices A: and 1: can, in principle, be used as a basis for a decentralized capital budgeting system. Consider the acceptreject decision on an individual project j. The first step is to estimate the project's contribution to firm value in the base case just described; call this AVO.Then, given estimates of the project's yearbyyear contribution to debt capacity (AZ,) and aftertax cash flow (Act), the decision is: T
A 9 = AV., +
+
(AZth: AC,h;) > 0. t=O
This may be written in the same form as Eq. ( 3 ) ) i.e.,
Accept if:
T
Accept if:
APVj = Aj
+ C (Zjth: + Cjth;)
> 0,
t=O
with the understanding that APV,, Aj, Zjt and C,, are interpreted as discrete amounts rather than partial derivatives. The distinction between Eqs. (3) and (3a) is important. The discrete form (3a) is relevant for the simple acceptreject choice, given the project's scale. The continuous version (3) is relevant to the choice of optimal scale. The APV's computed according to the two formulas will not be the same unless the various partial derivatives in (3) are constants. The remainder of the paper is concerned with the discrete acceptreject decision. This was done solely to simplify exposition. The reader can verify that the formal argument could just as well have been based on Eq. (3) as (3a); and that the major results also apply to the problem of determining optimal project scale. I t is, of course, necessary to take I: and h: as given regardless of the interpretation. This may be justified in two ways. One assumption is that project j is "small." Another is that the project, regardless of size, does not affect F,, 69/6Dt or 6q/6Et. The second assumption requires further explanation. Inspection of Eqs. (2c) and (2d) shows that A: will equal either 69/6D, or 6~/6E, a t the optimum, depending on whether the optimal plan calls for issuing stock or paying dividends. Thus, so long as 6$/6D, or 6$/6Et is constant, is independent of the decision to accept or reject j. This could be entirely realistic: 6q/6Et might reflect a constant transaction cost per dollar of equity issued, for example. If the debt constraint ( l b ) is binding, then Eq. (2b) will be an equality, and I: will be a constant if I?,, A: and I:,, are constants. Again, this seems plausible: for example, in an MM world with corporate taxes, Ft is simply present value of the tax shield generated per dollar of debt outstanding at t. The practical implications of APV for project by project capital budgeting decisions are discussed in more detail later in the paper. Before that I will use the APV concept to analyze capital budgeting rules based on the weighted average cost of capital.
At
Interactions of Corporate Financing and Investment Decisions
7
111. A REEXAMINATION OF THE WEIGHTED AVERAGE COSTOF CAPITALCONCEPT lntroduction and Definitions I t is widely accepted that the accept/reject decision for investment projects ought to be evaluated on a "DCF," or discounted cash flow, basis. This i s done by one of two decentralized rules. The first is to compute project j's internal rate of return, Rj, from the formula
t=O
and to accept the project if R j exceeds p?, the "cost of capital'' for j. The second rule is to compute the net present value of j's cash flows, discounted at py, and accept j if this figure is positive. Thus, j is accepted if
In either rule, py is the "hurdle rate" or minimum acceptable expected rate of return. Comparing Eq. (3a) to ( 5 ) and ( 6 ) ) it is evident that NPVj and APV, are intended to measure the same thing: the net contribution of j to market value, taking account of the interactions of j with other investment and financing opportunities. There is always some value of py which will insure that NPV, = APV,, or that
Eq. (7) may be regarded as an implicit definition of p*. An analogous, but narrower definition is Cjt t=o
>O
if and only if
APVj > 0.
This interprets pT simply as a hurdle rate, or minimum acceptable expected rate of return. A p r derived from Eq. (7a) does not necessarily give a correct valuation (i.e., NPVj = APV,) for projects of more than minimum profitability. The conditions under which Eqs. ( 7 ) and (7a) are consistent are given later in this paper. For the moment we will work with Eq. (7a). The problem is, how should pT be computed, if not directly from Eq. (7a)? Of the many procedures for calculating p?, two are of particular interest. The first is MM's. They proposeQ
9. [IS], p. 342. I n MM's notation p* is C ( L ) and P , , ~is simply p j
The Journal of Finance
8
where: p,j = The appropriate discount rate assuming allequity financing; t
= The corporate tax rate;
L = The firm's "longrun" or "target" debt ratio: and
9:
= A proposed value for py.
M M interpret pOjas the rate at which investors would capitalize the firm's expected average aftertax income from currentlyheld assets, if the firm were allequity financed." This would restrict application of the formula to projects whose acceptance will not change the firm's risk characteristics. (However, we will see that this is an unnecessarily narrow interpretation of the M M formula.) T h e second proposed formula is:
where: r = the firm's borrowing rate at t = 0; k = "the cost of equity capital"that is, the expected rate of return required by investors who purchase the firm's stock; B = market value of currently outstanding debt;
S = market value of currently outstanding stock, and
V =B
+ S, the total current market value of the firm.
I will refer to Eq. (9) as the "textbook formula," for lack of a better name. (The formula, or some variation on the same theme, appears in nearly all finance texts.)" I t is not necessarily inconsistent with the M M formula, but it is recommended by many who explicitly disagree with MM's view of the world. The task now is to determine what assumptions are necessary to derive Eqs. (8) and/or (9) from Eq. (3a), the general condition for the optimal investment decision. I will present a set of sufficient conditions, and then argue that, in most cases, the conditions are necessary as well. Derivation of the M M Cost of Capital Rule If MM's view of the world is correct, then the value of the firm will be V,, the value of the firm assuming allequity financing, plus PVTS, the present value of tax savings due to debt financing actually employed. Dividend policy is irrelevant. Assuming this view is correct, the objective function in the mathematical programming formulation is :
10. Ibid., pp. 337, 340. 11. See Johnson 1111, Ch. 11; Weston and Brigham 1291, Ch. 11; Van Horne 1271, Ch. 4.
Interactions of Corporate Financing and Investment Decisions
9
That is, F, is rt, the tax saving per dollar of debt outstanding in t, discounted to the present. ( I t is assumed that the interest is paid at t 1.) Second, assume that
+
A.1 C./ JP03.  I 3..
(lob)
That is, project j is expected to generate a constant, perpetual stream of cash returns.12 The third assumption is that undertaking project f does not change the risk characteristics of the firm's assets. That is, where p, is the firm's cost of capital given allequity financing. Fourth, assume that project j is expected to make a permanent and constant contribution to the firm's debt capacity: Finally assume
z, = LI,, where L is the longrun "target" debt ratio which applies to the firm overall. Eq. (10e) implies that adoption of project j will not change this target. Rewriting Eq. (3a) using Eqs. (10a) through (lOe), we have:
From Eq. (7a), the cost of capital is the project's internal rate of return (Cj/Ij) when APV, = 0. Eq. (11) implies that this is given by MXl's formula:
Extension of MM's Result to Projects of Varying Risk Let us make one further assumption, that AV, is a linear function of the present values of accepted projects:
Eq. (10f) assumes that projects are riskindependent, in the sense that there are no statistical relationships among projects' returns such that some , co, then Eq. (lob) simply states the project's 12. If C.~t = C., J a constant for t = 1, 2, . . net present value when discounted at pOj, the "appropriate rate" for j given allzquity fi~ancing. C However, MM interpret Cj as the expectation of the mean of the series Cjl, Cjz,. . . , CjE. See [14],p. 337. This does not require that Cjt is constant, but there must be conditions to insure that this mean is finite. The reader may choose the interpretation he likes best. The form of the argument to follow is not affected.
10
T h e Journal of Finance
combinations of projects affect stock price by an amount different than the sum of their present values considered separately. In particular, riskindependence implies that there is no advantage to be gained by corporate diversification. Riskindependence is a necessary condition for equilibrium in perfect security markets.13 Eq. (10f) also assumes that projects are "physically independent" in the sense that there are no causal links between adoption of project j and the probability distributio; of cash returns to other projectsthat is, it rules out "competitive" or "complementary" projects. Such interactions make it impossible to specify an unique hurdle rate for project j, since the minimum acceptable rate of return on j may depend on whether or not other projects are accepted. However, I am not concerned with this problem in this paper. Let us adopt Eq. (10f) and drop Eqs. (10c) and (10e). We can recalculate the minimum acceptable rate of return on the project. This has the same form as Eq. (8) but is not restricted to projects within a single risk class. However, it is not plausible to identify Zj/Ij, project j's marginal contribution to debt capacity, with L, the firm's overall target capitalization ratio. Presumably Zj/Ij will be more or less than L, depending on the risk or on other characteristics of the project in question. In short, MM's formula can be extended to independent projects which differ in risk and in their impact on the firm's target debt ratio.
What If Investment Projects Are Not Perpetuities? So far we have established that Eqs. (lOa, b, d and f) are sufficient for the generalized M M formula, Eq. (12). Eqs. (10a) and (10f) are clearly necessary as well. But what about ( l o b ) and (lOd), which require all projects to be perpetuities? In general, they are necessary: Eq. (13) does not give the correct "hurdle rate" for projects of limited life.14 (The question of whether the resulting errors are serious is taken up in the next section.) This can be shown by a simple example. Consider a pointinput, pointoutput project requiring an investment of Ij and offering an expected cash flow of Cjl in t = 1, and Cjt = 0 for t > 1. Assume p,, = p, and Zj, = LI, (and, of course, Zjt = 0 for t > 1). Then
The internal rate of return on the project is given by R, = Cij/Ij  1, and the cost of capital is given by R j when APVj = 0. Thus 13. Myers [I91 and Schall [241. See Merton and Subramanyam [I31 for a recent review of work relating to this aspect of capital market equilibrium. 14. Of course, the importance of project life has been recognized by M M (in [171, for example) and others (e.g., [ I ] , [ 2 1 , and [71, esp. p. 173n). But the implications for the cost of capital p*i have not'been developed in the literature.
Interactions of Corporate Financing and Investment Decisions
11
Eqs. (12) and (13) are equivalent only in the uninteresting case of p, = r.
The Text book Formula Let us reconsider Eq. (9),
p:
= r (1  t )B/V
+ k(S/V) .
>:
Probably it is intuitively clear from the foregoing that = p; only under very restrictive assumptions. First, let us assume that Eqs. (10a) through (10e) hold.15 (Remember that (10a) implies that dividend policy is irrelevant.) Also, assume that
That is V,, the current market value of the firm if it were all equity financed, is found by capitalizing the firm's aftertax operating income a t p,. C is, of course, calculated assuming allequity financing. Also Eq. (14a) presumes C t = C, t = 1, 2 , . . . , m.16 Finally, assume that the firm is already at its target debt ratio. Lj = B/V.
(14b)
Note that Eqs. (14a) and (14b) constrain the initial characteristics of the firm's assets and financing mix, whereas the assumptions underlying MM's cost of capital formula relate only to the marginal effects of adopting the project in question. Now the task is to show that $f = pf under assumptions (1Oae) and (14ab). Note first that the sum of payments to bondholders and earnings after interest and taxes is rB kS = C trB, so that C = r ( l  t ) B kS and
+
+
+
,.
I n an M M world, V is also given by
which is equivalent to Eq. (1 1). We now combine Eqs. (15) and (16) and solve for :
;:
15. Eq. (101) is not relevant, since Eq. (10c) implies that project j will not change the risk characteristics of the firm's assets. ,., 16. Altezatively, we could regard C as the expected value of the mean of the stream C1, w C2, . . . , C ., See fn. 12 above.
The Journal of Finance
But &/C = 1/V, and B/V = Lj, so
which was previously demonstrated to be the correct value. Thus we have shown that the textbook formula gives the correct cutoff rate for projects under a long list of assumptions, one of which is that M M are correct. However, it can be readily shown that the formula is correct even if M M are wrong, providing the other assumptions hold.17 T o summarize, the textbook formula gives the correct hurdle rate i f : 1. The project under consideration offers a constant, perpetual stream of cash flows, and is expected to make a permanent contribution to debt capacity. 2. The project does not change the risk characteristics of the firm's assets. 3. T he firm is already at its target debt ratio, and adoption of the project will not lead the firm to change the ratio. 4. The firm's currentlyheld assets are expected to generate a constant aftertax cash flow C per annum. This stream is expected to continue indefinitely. The last of these assumptions may be surprising. We know from Eq. ( 7 ) or (7a) that the cost of capital p5 does not depend on the pattern of expected cash flows offered by the firm's existing assets. But it can be readily shown that the pattern does affect the observed value 3;. Let us assume that the life of the firm's existing assets will end at the close of t = 1. Retain all the other assumptions for the textbook formula, and assume M M are right. We must thus replace Eq. (14a) with 17. If MM are wrong, then w
where Ft reflects not only the present value of tax savings but also the impact of any relevant market imperfections. Then it is readily shown that the true cost of capital is
Proceeding as before, we observe
C
V=+B t=O
Solving for $*j we find it t o be the value given by Eq. (N2). Incidentally, Eq. (N2) is an attractive alternative for those who disagree with MM but are also uncomfortable with the textbook formula.
Interactions of Corporate Financing and Investment Decisions
13
Also, V = Vo
+ PVTS
+
c1 1
+
Po
trLV + . l+r
Observe that rB kS, the total return received by stock and bondholders is equal to C, trB  V. This implies
+
r(l t)B
+ kS =C1V=ij?V.
Thus :
Now we can solve for
fly:
This establishes that the pattern of expected cash flows offered by the firm's existing assets does affect the observed value F:, which in this case is simply the hurdle rate for a oneperiod project. (See Eq. (13).)18 Summary
Table 1 summarizes the necessary and sufficient conditions for the derivation of MM7s cost of capital formula, the generalized MM formula, and the textbook formula. Obviously, these conditions are quite stringent, particularly in the case of the textbook formula. The next section considers whether serious errors result when the conditions do not hold.
IV. How ROBUSTARE
THE WEIGHTED AVERAGE COSTOF
CAPITALFORMULAS ?
Introduction The derivation of a cost of capital py for practical use involves two steps. The first is to measure the ~ , , ~ the ' s , market opportunity costs of investing in assets of different levels of risk. The second is to adjust these opportunity costs to reflect the tax effects of debt financing, transaction costs of external financing, etc. These two steps are explicit in the MM cost of capital formulas and implicit in the textbook formula. The difficulties in step (1) are notorious. My experience suggests that the confidence limit on empirical and/or subjective estimates of pOj is at least a 18. This leads to the conjecture that the textbook rule is valid if, instead of Eqs. (14a) and (14b), i t can be assumed that the stream of expected cash flows is strictly proportional over time t o the cash pows of the firm's existing assets. However, I have not proved this generally. In any case, if Cjt = hjCt, where h j is a constant, then we hardly need worry about the cost of capital. I t suffices to determine whether Ij hjV, where Ij is the initial investment required for the project.
<
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14
TABLE 1
NECESSARY AND SUFFICIENT CONDIT~IONS FOR COSTOF CAPITALFORMULAS Formula 
Condition
MM
Dividend policy irrelevant Leverage irrelevant except for corporate income taxes Investment projects are perpetuities Project does not change firm's risk characteristics Project makes a permanent contribution to debt capacity Acceptance of project does not lead to shift of target debt ratio Riskindependence
x
x
x
x x
x x
x
(Equation)

(lla)
(lib) (11~) (114
(lie) (llf) (1 s a )
(1 s b )
* n.a. = not
Generalized MM Textbook
Firm's assets expected t o generate a constant a n d perpetual earnings stream Firm is already a t target debt ratio
x
x
x
x
x
x
n.a.*
x
x
n.a.*

x x
applicable.
percentage point under the most favorable conditions. This implies a certain tolerance for minor errors in step ( 2 ) . How serious can these errors be, considered relative to the possible errors in step ( I ) ? The purpose of this section is to begin exploring this question. There are eight distinct assumptions listed in Table 1. Any one or any combination of them could be violated in practice. I t is not feasible to compute the error for all possible cases. Instead, I will focus on assumptions (lob) and (lOd), which require that the project being considered is expected to make a permanent contribution to the firm's earnings and debt capacity. These are the only assumptions necessary for all three cost of capital rules. The decision to concentrate on ( l o b ) and (lOd) was based on several points concerning the other assumptions. 1. Assumptions (10a) and (10f) were not considered because they may well hold in fact. The empirical evidence to date does not lead to rejection of the MM and riskindependence hypotheses, and a strong theoretical case can be made for them.1° 19. Probably the most extensive and sophisticated test or the M M propositions is MM's own study of the electric industry [IS]. This study supports their theory. There is controversy about MM's tests: see, for example, Robichek, McDonald and Higgins [ 2 2 ] , Crockett and Friend [SI, Brigham and Gordon [4] and Elton and Gruber [ 6 ] . There clearly is room for a good deal more work, but despite the problems, we can at least say that recent work is not inconsistent with the MM hypotheses. The proposition of risk independence is even harder to test directly. There is circumstantial evidence indicating that diversification is not an appropriate goal for the firmfor example, if investors were willing to pay for diversification would not closedend mutual funds sell at a premium over asset value? And there is certainly no lack of diversification opportunitieseven the small investor can buy mutual funds.
Interactions of Corporate Financing and Investment Decisions
15
2. Assumptions ( 10c) and ( 10e) are not necessary for the generalized MM
formula. I t is clear, of course, that substantial errors can result if either assumption is violated and either the original M M or textbook formula is used. But the extent of the error can be readily estimated by comparing the rate obtained from the original M M formula or textbook formula with the rate obtained from the MM formula. Note that if (10c) does not hold, (10e) is not likely to hold either. A lowrisk project will probably also make a large contribution to the firm's debt capacity. 3. Assumptions (14a) and (14b) were not analyzed explicitly because the results of violating them will be similar in magnitude to the results of violating (lob) and (10d) respectively.
Efects of Expected Project Life I will start with an extreme case, by comparing the cost of capital obtained via the M M rule with the true cost of capital for a oneperiod project. Remember that the MM formula generates a proposed value fi?, given by The correct value is h
py = poj Lrz (I;). For simplicity, we will omit the j's henceforth. Comparing Eqs. (9) and (14), it is clear that p* of L and p,. The error, E, is
> p*
for reasonable values
> 0 and that 6~/8p, = Lz(1 ) From this we see that ? J E / ~ L
> 0.
l+r is highest for highrisk projects that can be heavily debt 
;
The error in fi* financed. Table 2 consists of values of E computed for values of p, from 8 per cent to 25 per cent and for debt to value ratios of 10 to 60 per cent. E ranges from .1 per cent to about 5 per cent. The errors shown in the bottom right of the table are dramatic, but the figures in the center, top right and bottom left of the table reflect the most reasonable combinations of capitalization rates and debt ratios. These errors are on the order of one percentage point, which is not serious. (Note that a one percentage point error in p* for a one period project implies an error in NPV of only about one per cent of project investment.) Tests of the "capital asset pricing model" of Sharpe [251, Lintner [I21 and Mossin [IS] may shed light on the riskindependence hypothesis. (The capital asset pricing model is sufficient but not necessary for riskindependence.) The empirical work t o date indicates that the capital asset pricing model is probably an oversimplification, but it is too early t o say for sure. Jensen [ l o ] reviews the theory and evidence.
The Journal of Finance
16 ERROR^
IN
TABLE 2 MM COSTOF CAPITALFORMULA FOR ONEPERIOD PROJECT
p,, Cost of
Capital for allequity financing
L, Target Debt Ratio .2
.1
a Rounded to third decimal place. The riskfree rate is assumed to be r
.5
.4
.3
.6
= .07 and the tax rate is assumed to be z = .5.
Evidently the error in p* will be smaller, the longer the life of the project under consideration. However, a more important statistic is the error in NPV caused by use of an incorrect discount rate. This error at first increases as a percentage of project investment as project life is lengthened but finally decreases to zero for projects of infinite life. Take, for example, a tenyear, opportunity requiring investment of $1000 a t t = 0 and offering a constant expected cash return for t = 1, 2, . . . , 10. Table 3 shows the difference between (1) NPV computed using p* from the MM or textbook formulas and (2) the projects' true APV.20 The errors in this case are more serious than for a oneperiod project, but still on the order of two to four per cent of project investment. These mental experiments indicate that the MM or textbook rules are reasonably robust with respect to variations in project life. An unqualified endorsement is not in order, however. First, use of these rules makes investERROR^ p,, Cost of capital for allequity financing
IN
TABLE 3
INDICATED NPV FROM USINGMM COSTOF CAPITALFORMULA
TO EVALUATE TENPERIOD PROJECTREQUIRING$1000 INVESTMENT^,^ L, Target Debt Ratio .1
.2
.3
.5
.4
.6
a Project investment and cash flows were taken a s givensee note b below. Figures shown are NPV computed at 8" = p , ( l  T,L), minus .4PV. Figures rounded to nearest dollar. b The riskfree rate is assumed as r = .07 and the tax rate is assumed to be 2 = .5. The project's expected cash flows are $150.00 per period from t = 1 lo t = 10, and zero for t 10. e APV calculated by procedure described at pp. 2728 below.
>
20. APV was computed by the procedure described a t pp. 2728 below.
Interactions of Corporate Financing and Investment Decisions
17
ment projects look more valuable than they actually are. Second, the seriousness of the error depends on the specific pattern of project cash flows; the fact that the error was minor for the cases investigated does not prove the financial manager is safe in using the rules for projects with unusual patterns of cash flow over time.
Weak and Strong Definitions of the Cost of Capital Let us suppose we have used Eq. (7a) to calculate the correct value of p* for project j using the weak definition of the cost of capital. Then we can be assured that the project is a good one if NPV computed a t p* is positive. However, if projects j and k are mutually exclusive, and both have positive NPV's computed a t correct hurdle rates, it is not generally correct to accept j over k if NPVj > NPV,. The general rule is to compare APV, and APV,, but Eq. (7a) insures that NPVj = APV, only when APVj = 0. Under what conditions will discounting at the correct hurdle rate give correct value for NPV, when project j is more than minimally profitable? To put it another way, under what conditions is p*, calculated according to the strong definition of Eq. (7)) independent of project profitability? Assume the pattern of project cash flows over time is fixed. That is, Ct = ytC, for t 2 1, where the yt's are constants, and C is varied to reflect changes in project profitability. C,, project investment, is a fixed number, and the project's "risk class" is taken as given. Now consider Eq. (7) :
Now divide through by C, after representing Aj by the usual present value formula and subtracting C, from both sides
+LC
(g)
'I'
+&?t t=l
(23)
Eq. (23) is an alternative definition of p*. C can be eliminated if the following conditions hold. 1. The project's expected periodbyperiod contributions to debt capacity are proportional to C. 2. = 0. That is, the dividend reduction (or stock issue) required to supply equity financing for the project must not affect shareholders' wealth;
[email protected]/6D, (or 6+/6E,) must equal zero. 3. The shadow prices A: and A: must be independent of C. In any case, a violation of it will underThe third condition is not impla~sible.~' 21. See p. 6 above.
T h e Journal of Finance
18
mine any decentralized capital budgeting rule. The second condition could be handled by redefining the project's required investment as C,(1 A:), in which case the term A('(C,/C) would not appear in Eq. (23). The first condition is more interesting. I t will clearly not be satisfied if the firm's target debt ratio is specified in book terms, since in that case Zjt is independent of C. I t will be satisfied if planned debt is related to the project's market value. Specifically, suppose
+
that is, the firm's planned borrowing in t is a given proportion Lt of APV,, the project's contribution to firm value in t, after receipt of project cash flow in t.= I n this case p* is independent of C, as is shown in the Appendix. Thus, we can add one more condition to the list of assumptions in Table 1: weighted average cost of capital formulas give correct project valuation (i.e., NPV @ p* = APV) only if the firm's target debt levels are specified in market value terms, or if the project has APV = 0. If the firm specifies target debt levels in book terms, then discounting at the P*'s will, other things equal, overstate project APV if APV > 0, and understate APV if APV < 0."' The magnitude of possible error may be illustrated by the following numerical example. A project requires investment of C, = 1000, but offers a constant expected stream of cash returns, C. The target debt ratio is L = .4, p, = .12 and t = .5. Dividend policy is irrelevant as is financial leverage except for corporate taxes. In this case the correct p* is given by Eq. (8)) the MM formula. I t is
+
C/.096. The project's APV is 1000 Another alternative would be to compute APV directly, as the sum of the project's value assuming all equity financing and the present value of tax savings generated due to the project's contribution to debt capacity. APV =
(G+ + Co)
C
APV = (TiZ 
rL(APV  C.)
+ .5(.4) (APV + 1000).
22. An alternative rule,
would also allow p* to be calculated independent of project profitability. At is defined by
23. This, of course, assumes debt capacity is valuable. I t should also be noted that the level of profitability consistent with APV = 0 will depend on whether debt targets are in book or market terms, since book and economic depreciation are not generally equivalent.
Interactions of Corporate Financing and Investment Decisions
19
Now compare this result to APV if the target debt ratio is set in book terms: APVz (book debt target)
(z
1000 +..5(.1)(1000).
.I2
The difference is .5 (.4) (APV), that is 20 per cent of APV. This seems to me a serious erroralthough the error would be less for shorterlived projects or for lower debt ratios. Summary
Whether capital budgeting rules based on the weighted average cost of capital deserve the label "robust7' depends entirely on one's tolerance for error. I would consider the generalized M M formula acceptably accurate for acceptreject decisions on runofthemill projects. The original M M formula is acceptably accurate if attention is restricted to projects which do not shift the firm's risk class or target debt ratio. The textbook rule is inferior on all countsz4 if used directly" as a standard for investment decisionmaking. Of course, it is always possible to find the correct value of p* from Eqs. (7) or (7a). The procedure is relatively simple: first, calculate APV, and then find the discount rate which gives the correct NPV, i.e., NPV = APV. But once a project's APV is known, there is no need to calculate its p * ; it is sufficient to know whether APV > 0. Why not forget about p* and use APV as the capital budgeting standard? The next section considers whether this is a practical alternative.
An alternative procedure is clearly needed for cases in which one or more of the assumptions underlying the weighted average cost of capital formulas are seriously violated. The natural choice is to accept project j if its adjusted present value is positive, i.e., if: 24. I t might be argued that the textbook formula should be used by those who disagree with MM. But it is entirely feasible to develop a formula exactly like the M M formulas except for the assumed benefit of debt financing. See Eq. (NZ),fn. 17 above. 25. The textbook formula may be helpful in measuring p,. Suppose a firm can estimate k, the expected rate of return investors in the firm's stock. Then p* can be directly calculated.
This value is not an appropriate standard for capital budgeting unless a variety of conditions hold, among them the equality of target and actual debt ratios (L = B/V). However, if the target were B/V, then, assuming M M are correct,
So an estimate of $* can be translated into an estimate of p,
The Journal of Finance
I n the event that dividend policy is relevant and/or there are significant transaction costs in new external financing, the criterion should be expanded to :
Calculating APV The general procedure for calculating APV is obvious from the definition of the concept. First, A,, the project's base case value, has to be calculated. This can be done by the usual NPV formula, except that the discount rate is p,,. However, if the discounting procedure is i n a p p r ~ p r i a t e ,then ~ ~ any other procedure for estimating value may be followed. (This is a further advantage of the APV rule.) The next step is to estimate the project's contribution to firm debt capacity, assign a value to this contribution and add it to Aj. (In an MM world, this amounts to adding the present value of tax shields generated by debt supported by the project. However, the APV rule does not assume MM are right.) The third step is to determine whether the marginal source of equity financing is additional retained earnings, additional stock issue or a reduction in share repurchases. If there are special costs or benefits associated with the source (vs. the base case of irrelevance of dividend policy) then these can be incorporated in the h:s' and the project value adjusted by adding ZC,,. Perhaps the most difficult step in this process is to determine the Z,,'s. This is simple if the firm's debt limits are determined by book debt ratios, since the Zj,'s are then fixed ex ante and independent of project profitability or value (given book depreciation policy). Calculating a project's adjusted present value turns out to be a moderately complex task when Z,, is related to market value. The problem is that APV,,, adjusted present value of project j as of t = 0, depends on estimated values of APV,, for later periods. If the horizon is t = T , we have to calculate APVj,Tl, APVj,T2,etc., and then finally APV,,. For present purposes we will drop the j's and assume that Zt is a constant proportion L of APV,  C,, except that ZT = 0. We also assume that AC's are zero. That is, it is assumed that the firm plans to readjust its debt level at the end of every period in terms of its value at that time, and that this level is maintained during the next tr period. Also we assume that MM are right, i.e., that F, = . Thus ( 1 r)t+l
+
26. Due to the problems cited by Robichek and Myers [231, for example.
Interactions of Corporate Financing and Investment Decisions
Let f = rrL . Then 1tr APVTP1 = AT1
+ ~(APVTI

21
CT1)
Having calculated APVT_, we can determine APVT, from:
The general formula for any interim period t = T

S is
Of course Eq. (26) reduces to (24) when S = T. This backwardsiteration procedure is tedious to work through manually, but I did not find it difficult to construct a computer program to do the calculations. Also, note that the calculations are done as a byproduct of the linear programming models of Myers and P ~ g u e . ' ~ Comments
This calculation procedure leads to two interesting theoretical observations. First, we might question the rationality of planning to keep L constant over time. Consider an equity investor in a single project firm with bonds B outstanding and equity worth S. Note V = B S = APV = A PVTS, where PVTS is the present value of the tax shield due to debt financing. The equity may be thought of as a portfolio long in assets A, long in the tax shield PVTS and short in debt B. If PVTS and B are equivalentrisk assets, then the portfolio weights are as follows. Long position in firm's assets:
+
A APV Short position in B, net of PVTS:  APVA S APV 27. See L201.
(I+:)
+
22
The Journal of Finance
where APV  A 3 PVTS. If the investor wants to maintain a constant degree A B of financial risk, he will set (1 ) = Q, a constant. This implies APV S
+
z,
1
L, =  1 APVt Q
(A). APV
A Thus we would expect L, to decline as the project ages and  approaches APV 1. The empirical prediction is that firms with longlived assets would have higher debt ratios. The second observation concerns the discount rate used in computing PVTS. I have followed M M who argue that it should be the riskfree rate r. This is clearly appropriate if the debt levels Zjt are fixed at t = 0 and not changed thereafter. If Z,, is determined by book debt ratios, for example, then there is no uncertainty about future tax shields, since there is no uncertainty about future profitability. On the other hand, suppose management wishes to main"
Ljt
tain a constant ratio Lj =  over time. This means that Zjt is a random APV,, variable that is perfectly correlated with APV,, and thus has the same risk characteristics. The implication is that PVTS should be computed at p,, not r. The intuitive meaning of this is that, although the tax shield associated with any debt instrument is safe, the aggregate value of instruments obtainable is uncertain. We have in effect a compound lottery; the fact that the second stage is riskfree does not mean that the lottery itself is safe. There are a number of reasons why firms do not immediately adjust the value of bonds outstanding to every change in project or firm value. But to the extent that future debt capacity is contingent on future value of the firm's assets, the debt tax shield takes on the assets' risk characteristics. This is another reason why use of, say, the generalized M M formula for p* would tend to overestimate APV. (So would use of Eq. (3a) or ( 4 ) unless the F,'s were computed using a discount rate greater than r.)
Using APV Objections to the practical use of APV might be made on the basis of lack of realism, increased complication, the unfamiliarity of managers with the concept and the deficiencies of a static model. Realism is not a valid objection relative to traditional rules. As was shown above, APV is a more general concept and therefore is more adaptable to whatever assumptions are considered "realistic." The extra complication of the APV rule is a valid point for decisionmakers concerned with runofthemill projects. However, for large and/or unusual projects the extra effort involved in using APV does not seem large relative to the'magnitude of errors that might be avoided.
Interactions of Corporate Financing and Investment Decisions
23
Lack of familiarity is a valid temporary objection. Understanding and interpreting the concept does require financial sophisticationalthough I have found it easier to explain to beginning finance students than to sophisticated financial managers who have "learned" the concept of discounting at "the" cost of capital. The static assumptions underlying APV are a real liability, although it is no worse than traditional approaches on this dimension. Whether to advise use of APV in spite of its static assumptions is a question that requires balancing possible errors due to the deficiencies of APV against the improved decisions stemming from its use. But it would seem that anyone who now advises use of traditional capital budgeting rules should be willing to advise a definite improvement. Perhaps the greatest advantage of the APV concept is that it guides the corporate financial manager through various problems that turn into a can of worms when analyzed by any approach relying on the cost of capital. Here are some examples. 1. APV provides a natural basis for analysis of the lease vs. buy or lease vs. borrow decision. 2 . APV can readily incorporate the impact of dividend policy, if relevant, without making awkward distinctions between the cost of retained earnings vs. the cost of stock issue. Transaction costs in financing can also be accommodated. (The effect of transaction costs on the cost of capital is a relatively complicated function of project life. Under the APV rule, dollar transaction costs are simply subtracted.) 3. Suppose subsidized borrowing is available for certain investments (e.g., for pollution control facilities). How does this affect the investments7 value? The impact is clear in the APV framework.
I suggest the reader analyze these cases with and without APV and make his or her own judgment about the concept's usefulness.
In principle corporate investment and financing decisions should be made simultaneously, since the decisions interact in important ways. This paper presents a framework in which the interactions can be analyzed. Further, the framework has been used to evaluate the most widely accepted weighted average cost of capital formulas, and to derive a more general and flexible capital budgeting rule. There are other uses for the framework. Specifically, it is possiblegiven some additional assumptionsto develop a linear programming model that can be of direct assistance to management responsible for overall financial planning. This model is described in another paper written jointly with Professor G. A. Pogue [ 2 0 ] .
24
The Journal of Finance
APPENDIX
OF PROJECT PROFITABILITY WHEN DEBTTARGETS ARE
PROOFTHATp* ISINDEPENDENT SPECIFIEDIN TERMSOF MARKETVALUES Once APV, is calculated for a project, then the true cost of capital p* can be calculated via Eq. (7). But there is nothing evident in Eq. (7) that rules out the possibility of p* being a function of the C,'s. I t turns out that p* is independent of project profitability only under certain special conditions. We can restate the cash flows in terms of a scale factor and a pattern over time. That is, Ct = Y,C where y l , y2, . . . , yT are weight summing to 1. Also, let pf be the true cost of capital, under the strong definition of Eq. (7), for the project at some intermediate point O
Note that this assumes dividend policy is irrelevant (hy's = 0) and that MM are correctsee Eq. (24). The first assumption is necessary to the fillowing proof, but the second is not. is indepenDividing both sides of Eq. (A.1) by C, we have an expression for dent of C. Now consider , which is defined by
that
PZ~
But fro'm Eq. (26),
However, all terms within the brackets in Eq. (A.3) are proportional to C. (This is obviously true for A,,, CT, and C T p l ; we have just shown it to be true for APVTI). Thus, we can equate Eqs. (A.2) and (A.3), divide through by C, and obtain a definition of p*T2 that is independent of C. Similarly, p*TW3 can be defined in terms of P ; , ~ ~p,Z P l and the Y'S. By working backwards we eventually find that p* evaluated at t = 0 is independent of C. I t is also independent of C,, the initial investment, since C, is not discounted. The same result follows if L, is variable and defined by Eq. (28). REFERENCES 1. F. D. Arditti. "The Weighted Average Cost of Capital: Some Questions on its Definition, Interpretation and Use." Journal of Finance, Vol. XXVIII (September 1973), 100108. 2. W. Beranek. "The Cost of Capital, Capital Budgeting and the Maximization of Shareholder Wealth." Unpublished manuscript, University of Pittsburgh, 1973. 3. F. Black and M. Scholes. "Dividend Yields and Common Stock Returns: A New Methodology." Working paper, Sloan School of Management, M.I.T. (1971). 4. E. Brigham and M. J. Gordon. "Leverage, Dividend Policy and the Cost of Capital," Journal o f Finance, Vol. X X I I I (March 1968), pp. 85104. 5. J. Crockett and I. Friend. 'LSome Estimates of the Cost of Capital to the Electric Utility Industry 195457: Comment," American Economic Review, Vol. 57 (December 1957), pp. 125967. 6. E. J . Elton and M. J . Gruber. "Valuation and the Cost of Capital in Regulated Industries," Journal o f Finance, Vol. XXVI (June 1971), pp. 66170. 7. E. F. Fama and M. H. Miller. The Theory of Finatzce (New York: Holt, Rinehart and Mrinston, 1972).
Interactions of Corporate Financing and Investment Decisions
25
8. I. Friend and M. Puckett. "Dividends and Stock Prices," American Economic Review, Vol. 54 (September 1964), pp. 65682. 9. C. W. Haley and L. D . Schall. T h e Theory of Financial Decisions (New York: McGrawHill, 1973). 10. M. E. Jensen. "The Foundations and Current State of Capital Market Theory," in M. C. Jensen, Ed., Studies in the Theory o f Capital Markets (New York: Praeger, 1972). 11. R. W. Johnson. Financial Management, Fourth Edition (Boston: Allyn and Bacon, 1971). 12. J. Lintner. "The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets," Reviezv of Economics and Statistics, Vol. 47 (February 1965), pp. 1317. 13. R. Merton and M. Subramanyam. "The Optimality of a Competitive Stock Market." Forth
coming in the Bell Journal of Economics and Management Science. 14. M. H. Miller and F. Modigliani. "Dividend Policy, Growth and the Valuation of Shares," Journal o f Business, Vol. XXXIV (October 1961), pp. 41133. 15. . "Some Estimates of the Cost of Capital to the Electric Utility Industry: 195457," American Economic Review, Vol. LVI (June 1966), pp. 33391. 16. F. Modigliani and M. H. Miller. "Corporate Income Taxes and the Cost of Capital: a Correction," American Economic Review, Vol. 53 (June 1963), pp. 33391. . "The Cost of Capital, Corporation Finance and the Theory of Investment," 17. American Economic Review, Vol. 48 (June 1958), pp. 26197. 18. J. Mossin. "Equilibrium in a Capital Asset Market," Econometrica, Vol. 34 (October 1966), pp. 76883. 19. S. C. Myers. "Procedures for Capital Budgeting under Uncertainty," Industrial Management Review, Vol. 9 (Spring 1968), pp. 120. and G. A. Pogue. "A Programming Model for Corporate Financial Manage20. ment." Working Paper, Sloan School of Management, M.I.T., November 1972. Revised version forthcoming in Journal o f Finance (May 1974). 21. A. A. Robichek and J. G. McDonald. "The Cost of Capital Concept: Potential Use and Misuse." Financial Executive, Vol. 33 (June 1965), pp. 28. and R. C. Higgins. "Some Estimates of the Cost of Capital to the Electric 22. Utility Industry 195457: Comment," American Economic Review, Vol. 57 (December 1957), pp. 127888. 23. A. A. Robichek and S. C. Myers. "Conceptual Problems in the Use of RiskAdjusted Discount Rates." Jozmzal o f Finance, Vol. XXI (December 1966), pp. 72730. 24. L. D. Schall. "Asset Valuation, Firm Investment and Firm Diversification," Journal of Business, Vol. 45 (January 1972), pp. 1128. 25. W. F. Sharpe. "Capital Asset Prices: A Theory of Market Equilibrium Under Conditions of Risk," Journal o f Finance, Vol. 19 (September 1964), pp. 42542. 26. D. L. Tuttle and R. H. Litzenberger. "Leverage, Diversification and Capital Market Effects in a RiskAdjusted Capital Budgeting Framework," Journal o f Finance, Vol. X X I I I (June 1968), Pp. 42943. 27. J. C. Van Horne. Financial Management and Policy, Second Edition (Englewood Cliffs, New Jersey: PrenticeHall, Inc. 1971). 28. D. Vickers. "The Cost of Capital and the Structure of the Firm," Journal o f Finance, Vol. XXV (March 1970), 3546. 29. J. F. Weston and E. F. Brigham. Managerial Finance (New York: Holt, Rinehart and Winston, 1971).
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You have printed the following article: Interactions of Corporate Financing and Investment DecisionsImplications for Capital Budgeting Stewart C. Myers The Journal of Finance, Vol. 29, No. 1. (Mar., 1974), pp. 125. Stable URL: http://links.jstor.org/sici?sici=00221082%28197403%2929%3A1%3C1%3AIOCFAI%3E2.0.CO%3B24
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Dividend Policy, Growth, and the Valuation of Shares Merton H. Miller; Franco Modigliani The Journal of Business, Vol. 34, No. 4. (Oct., 1961), pp. 411433. Stable URL: http://links.jstor.org/sici?sici=00219398%28196110%2934%3A4%3C411%3ADPGATV%3E2.0.CO%3B2A 1
The Cost of Capital and the Structure of the Firm Douglas Vickers The Journal of Finance, Vol. 25, No. 1. (Mar., 1970), pp. 3546. Stable URL: http://links.jstor.org/sici?sici=00221082%28197003%2925%3A1%3C35%3ATCOCAT%3E2.0.CO%3B28 1
The Weighted Average Cost of Capital: Some Questions on its Definition, Interpretation, and Use Fred D. Arditti The Journal of Finance, Vol. 28, No. 4. (Sep., 1973), pp. 10011007. Stable URL: http://links.jstor.org/sici?sici=00221082%28197309%2928%3A4%3C1001%3ATWACOC%3E2.0.CO%3B2J
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Conceptual Problems in the Use of RiskAdjusted Discount Rates Alexander A. Robichek; Stewart C. Myers The Journal of Finance, Vol. 21, No. 4. (Dec., 1966), pp. 727730. Stable URL: http://links.jstor.org/sici?sici=00221082%28196612%2921%3A4%3C727%3ACPITUO%3E2.0.CO%3B2F 3
Dividend Policy, Growth, and the Valuation of Shares Merton H. Miller; Franco Modigliani The Journal of Business, Vol. 34, No. 4. (Oct., 1961), pp. 411433. Stable URL: http://links.jstor.org/sici?sici=00219398%28196110%2934%3A4%3C411%3ADPGATV%3E2.0.CO%3B2A 3
Some Estimates of the Cost of Capital to the Electric Utility Industry, 195457 Merton H. Miller; Franco Modigliani The American Economic Review, Vol. 56, No. 3. (Jun., 1966), pp. 333391. Stable URL: http://links.jstor.org/sici?sici=00028282%28196606%2956%3A3%3C333%3ASEOTCO%3E2.0.CO%3B24 3
Corporate Income Taxes and the Cost of Capital: A Correction Franco Modigliani; Merton H. Miller The American Economic Review, Vol. 53, No. 3. (Jun., 1963), pp. 433443. Stable URL: http://links.jstor.org/sici?sici=00028282%28196306%2953%3A3%3C433%3ACITATC%3E2.0.CO%3B2G 7
Dividend Policy, Growth, and the Valuation of Shares Merton H. Miller; Franco Modigliani The Journal of Business, Vol. 34, No. 4. (Oct., 1961), pp. 411433. Stable URL: http://links.jstor.org/sici?sici=00219398%28196110%2934%3A4%3C411%3ADPGATV%3E2.0.CO%3B2A 8
Some Estimates of the Cost of Capital to the Electric Utility Industry, 195457 Merton H. Miller; Franco Modigliani The American Economic Review, Vol. 56, No. 3. (Jun., 1966), pp. 333391. Stable URL: http://links.jstor.org/sici?sici=00028282%28196606%2956%3A3%3C333%3ASEOTCO%3E2.0.CO%3B24
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Dividends and Stock Prices Irwin Friend; Marshall Puckett The American Economic Review, Vol. 54, No. 5. (Sep., 1964), pp. 656682. Stable URL: http://links.jstor.org/sici?sici=00028282%28196409%2954%3A5%3C656%3ADASP%3E2.0.CO%3B2Y 9
Some Estimates of the Cost of Capital to the Electric Utility Industry, 195457 Merton H. Miller; Franco Modigliani The American Economic Review, Vol. 56, No. 3. (Jun., 1966), pp. 333391. Stable URL: http://links.jstor.org/sici?sici=00028282%28196606%2956%3A3%3C333%3ASEOTCO%3E2.0.CO%3B24 10
Some Estimates of the Cost of Capital to the Electric Utility Industry, 195457 Merton H. Miller; Franco Modigliani The American Economic Review, Vol. 56, No. 3. (Jun., 1966), pp. 333391. Stable URL: http://links.jstor.org/sici?sici=00028282%28196606%2956%3A3%3C333%3ASEOTCO%3E2.0.CO%3B24 12
Dividend Policy, Growth, and the Valuation of Shares Merton H. Miller; Franco Modigliani The Journal of Business, Vol. 34, No. 4. (Oct., 1961), pp. 411433. Stable URL: http://links.jstor.org/sici?sici=00219398%28196110%2934%3A4%3C411%3ADPGATV%3E2.0.CO%3B2A 13
Asset Valuation, Firm Investment, and Firm Diversification Lawrence D. Schall The Journal of Business, Vol. 45, No. 1. (Jan., 1972), pp. 1128. Stable URL: http://links.jstor.org/sici?sici=00219398%28197201%2945%3A1%3C11%3AAVFIAF%3E2.0.CO%3B2D 14
The Cost of Capital, Corporation Finance and the Theory of Investment Franco Modigliani; Merton H. Miller The American Economic Review, Vol. 48, No. 3. (Jun., 1958), pp. 261297. Stable URL: http://links.jstor.org/sici?sici=00028282%28195806%2948%3A3%3C261%3ATCOCCF%3E2.0.CO%3B23
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The Weighted Average Cost of Capital: Some Questions on its Definition, Interpretation, and Use Fred D. Arditti The Journal of Finance, Vol. 28, No. 4. (Sep., 1973), pp. 10011007. Stable URL: http://links.jstor.org/sici?sici=00221082%28197309%2928%3A4%3C1001%3ATWACOC%3E2.0.CO%3B2J 19
Some Estimates of the Cost of Capital to the Electric Utility Industry, 195457 Merton H. Miller; Franco Modigliani The American Economic Review, Vol. 56, No. 3. (Jun., 1966), pp. 333391. Stable URL: http://links.jstor.org/sici?sici=00028282%28196606%2956%3A3%3C333%3ASEOTCO%3E2.0.CO%3B24 19
Some Estimates of the Cost of Capital to Electric Utility Industry, 195457: Comment Alexander A. Robichek; John G. McDonald; Robert C. Higgins The American Economic Review, Vol. 57, No. 5. (Dec., 1967), pp. 12781288. Stable URL: http://links.jstor.org/sici?sici=00028282%28196712%2957%3A5%3C1278%3ASEOTCO%3E2.0.CO%3B2M 19
Some Estimates of the Cost of Capital to the Electric Utility Industry, 195457: Comment Jean Crockett; Irwin Friend The American Economic Review, Vol. 57, No. 5. (Dec., 1967), pp. 12581267. Stable URL: http://links.jstor.org/sici?sici=00028282%28196712%2957%3A5%3C1258%3ASEOTCO%3E2.0.CO%3B2S 19
Leverage, Dividend Policy, and The Cost of Capital Eugene F. Brigham; Myron J. Gordon The Journal of Finance, Vol. 23, No. 1. (Mar., 1968), pp. 85103. Stable URL: http://links.jstor.org/sici?sici=00221082%28196803%2923%3A1%3C85%3ALDPATC%3E2.0.CO%3B2%23 19
Valuation and the Cost of Capital for Regulated Industries Edwin J. Elton; Martin J. Gruber The Journal of Finance, Vol. 26, No. 3. (Jun., 1971), pp. 661670. Stable URL: http://links.jstor.org/sici?sici=00221082%28197106%2926%3A3%3C661%3AVATCOC%3E2.0.CO%3B26
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Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk William F. Sharpe The Journal of Finance, Vol. 19, No. 3. (Sep., 1964), pp. 425442. Stable URL: http://links.jstor.org/sici?sici=00221082%28196409%2919%3A3%3C425%3ACAPATO%3E2.0.CO%3B2O 19
The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets John Lintner The Review of Economics and Statistics, Vol. 47, No. 1. (Feb., 1965), pp. 1337. Stable URL: http://links.jstor.org/sici?sici=00346535%28196502%2947%3A1%3C13%3ATVORAA%3E2.0.CO%3B27 19
Equilibrium in a Capital Asset Market Jan Mossin Econometrica, Vol. 34, No. 4. (Oct., 1966), pp. 768783. Stable URL: http://links.jstor.org/sici?sici=00129682%28196610%2934%3A4%3C768%3AEIACAM%3E2.0.CO%3B23 26
Conceptual Problems in the Use of RiskAdjusted Discount Rates Alexander A. Robichek; Stewart C. Myers The Journal of Finance, Vol. 21, No. 4. (Dec., 1966), pp. 727730. Stable URL: http://links.jstor.org/sici?sici=00221082%28196612%2921%3A4%3C727%3ACPITUO%3E2.0.CO%3B2F
References 1
The Weighted Average Cost of Capital: Some Questions on its Definition, Interpretation, and Use Fred D. Arditti The Journal of Finance, Vol. 28, No. 4. (Sep., 1973), pp. 10011007. Stable URL: http://links.jstor.org/sici?sici=00221082%28197309%2928%3A4%3C1001%3ATWACOC%3E2.0.CO%3B2J
NOTE: The reference numbering from the original has been maintained in this citation list.
http://www.jstor.org
LINKED CITATIONS  Page 6 of 8 
4
Leverage, Dividend Policy, and The Cost of Capital Eugene F. Brigham; Myron J. Gordon The Journal of Finance, Vol. 23, No. 1. (Mar., 1968), pp. 85103. Stable URL: http://links.jstor.org/sici?sici=00221082%28196803%2923%3A1%3C85%3ALDPATC%3E2.0.CO%3B2%23 5
Some Estimates of the Cost of Capital to the Electric Utility Industry, 195457: Comment Jean Crockett; Irwin Friend The American Economic Review, Vol. 57, No. 5. (Dec., 1967), pp. 12581267. Stable URL: http://links.jstor.org/sici?sici=00028282%28196712%2957%3A5%3C1258%3ASEOTCO%3E2.0.CO%3B2S 6
Valuation and the Cost of Capital for Regulated Industries Edwin J. Elton; Martin J. Gruber The Journal of Finance, Vol. 26, No. 3. (Jun., 1971), pp. 661670. Stable URL: http://links.jstor.org/sici?sici=00221082%28197106%2926%3A3%3C661%3AVATCOC%3E2.0.CO%3B26 8
Dividends and Stock Prices Irwin Friend; Marshall Puckett The American Economic Review, Vol. 54, No. 5. (Sep., 1964), pp. 656682. Stable URL: http://links.jstor.org/sici?sici=00028282%28196409%2954%3A5%3C656%3ADASP%3E2.0.CO%3B2Y 12
The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets John Lintner The Review of Economics and Statistics, Vol. 47, No. 1. (Feb., 1965), pp. 1337. Stable URL: http://links.jstor.org/sici?sici=00346535%28196502%2947%3A1%3C13%3ATVORAA%3E2.0.CO%3B27 14
Dividend Policy, Growth, and the Valuation of Shares Merton H. Miller; Franco Modigliani The Journal of Business, Vol. 34, No. 4. (Oct., 1961), pp. 411433. Stable URL: http://links.jstor.org/sici?sici=00219398%28196110%2934%3A4%3C411%3ADPGATV%3E2.0.CO%3B2A
NOTE: The reference numbering from the original has been maintained in this citation list.
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LINKED CITATIONS  Page 7 of 8 
15
Some Estimates of the Cost of Capital to the Electric Utility Industry, 195457 Merton H. Miller; Franco Modigliani The American Economic Review, Vol. 56, No. 3. (Jun., 1966), pp. 333391. Stable URL: http://links.jstor.org/sici?sici=00028282%28196606%2956%3A3%3C333%3ASEOTCO%3E2.0.CO%3B24 16
Corporate Income Taxes and the Cost of Capital: A Correction Franco Modigliani; Merton H. Miller The American Economic Review, Vol. 53, No. 3. (Jun., 1963), pp. 433443. Stable URL: http://links.jstor.org/sici?sici=00028282%28196306%2953%3A3%3C433%3ACITATC%3E2.0.CO%3B2G 17
The Cost of Capital, Corporation Finance and the Theory of Investment Franco Modigliani; Merton H. Miller The American Economic Review, Vol. 48, No. 3. (Jun., 1958), pp. 261297. Stable URL: http://links.jstor.org/sici?sici=00028282%28195806%2948%3A3%3C261%3ATCOCCF%3E2.0.CO%3B23 18
Equilibrium in a Capital Asset Market Jan Mossin Econometrica, Vol. 34, No. 4. (Oct., 1966), pp. 768783. Stable URL: http://links.jstor.org/sici?sici=00129682%28196610%2934%3A4%3C768%3AEIACAM%3E2.0.CO%3B23 22
Some Estimates of the Cost of Capital to Electric Utility Industry, 195457: Comment Alexander A. Robichek; John G. McDonald; Robert C. Higgins The American Economic Review, Vol. 57, No. 5. (Dec., 1967), pp. 12781288. Stable URL: http://links.jstor.org/sici?sici=00028282%28196712%2957%3A5%3C1278%3ASEOTCO%3E2.0.CO%3B2M 23
Conceptual Problems in the Use of RiskAdjusted Discount Rates Alexander A. Robichek; Stewart C. Myers The Journal of Finance, Vol. 21, No. 4. (Dec., 1966), pp. 727730. Stable URL: http://links.jstor.org/sici?sici=00221082%28196612%2921%3A4%3C727%3ACPITUO%3E2.0.CO%3B2F
NOTE: The reference numbering from the original has been maintained in this citation list.
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Asset Valuation, Firm Investment, and Firm Diversification Lawrence D. Schall The Journal of Business, Vol. 45, No. 1. (Jan., 1972), pp. 1128. Stable URL: http://links.jstor.org/sici?sici=00219398%28197201%2945%3A1%3C11%3AAVFIAF%3E2.0.CO%3B2D 25
Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk William F. Sharpe The Journal of Finance, Vol. 19, No. 3. (Sep., 1964), pp. 425442. Stable URL: http://links.jstor.org/sici?sici=00221082%28196409%2919%3A3%3C425%3ACAPATO%3E2.0.CO%3B2O 26
Leverage, Diversification and Capital Market Effects on a RiskAdjusted Capital Budgeting Framework Donald L. Tuttle; Robert H. Litzenberger The Journal of Finance, Vol. 23, No. 3. (Jun., 1968), pp. 427443. Stable URL: http://links.jstor.org/sici?sici=00221082%28196806%2923%3A3%3C427%3ALDACME%3E2.0.CO%3B2D 28
The Cost of Capital and the Structure of the Firm Douglas Vickers The Journal of Finance, Vol. 25, No. 1. (Mar., 1970), pp. 3546. Stable URL: http://links.jstor.org/sici?sici=00221082%28197003%2925%3A1%3C35%3ATCOCAT%3E2.0.CO%3B28
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