where
Ko = weighted average cost of capital
Kd = cost of debt capital
Ke = cost of equity capital and
— = debt-asset ratio in the firm’s capital struc-
ture.
The cost of debt, Kd , is the after-tax effective
interest rate on debt and is calculated as follows:
Kd = Ed(I-T) (2)
where
Ed = current effective interest rate on debt and
T = marginal income tax rate.
Ke is the historical rate of return the owner has been
receiving on his equity capital with his particular
production and financial organization and is cal-
culated as follows:
NP - OL + LV (I-Tr)
Ke =----------(3)
where
NP = net farm profits after taxes
OL = value of unpaid family labor
LV = amount of increase in land value
Tc = capital gains tax rate and
E = owner equity.
The behavioral assumption of the theory of
optimal capital structure is that the firm operates at
that level of financial leverage, measured by D∕A,
which minimizes the weighted average cost of capital
in equation (1). To explore the implications of this
behavioral assumption, an understanding of likely
magnitudes of Ke and Kd and their responses to
increases in D/А is necessary. Ke and Kd in
equations (2) and (3) measure the rate of return that
owners and lenders, respectively, demand to supply
funds to a given firm. Like any rate of return, Ke and
Kd include the risk-free interest rate and a risk
premium. This risk premium varies directly with risks
associated with production and financial organization
of the firm. Furthermore, the risk premium asso-
ciated with equity capital is generally higher than that
for debt because of the greater risks associated with
ownership. This latter point results in Ke generally
being greater than Kd for any given production and
financial organization. Despite this generalization,
firms typically cannot minimize Ko by using all debt.
Increasing financial leverage increases risk for both
owners and lenders so that both Kp and Kτ-. are
increasing functions of financial leverage. The
standard formulation is that some level of debt, such
as O < D/А < 1, minimizes the cost of capital.
Derivation of hypotheses for empirical analysis in
this paper requires consideration of situations when
zero financial leverage results in the minimum
weighted average cost of capital. In equation (1), zero
financial leverage is reflected in D/А = O and
Ko = Kf . One obvious situation when zero D∕A
would be optimal is when Ke is less than Kd at all
levels of leverage. While this possibility is inconsistent
with general corporate finance theory, Brigham and
Smith argue that small business proprietors will
accept lower than competitive returns on their equity
capital because of the pecuniary and, more impor-
tant, nonpecuniary advantages of self-employment
and business ownership [2]. This finance proposition
is familiar to agricultural economists; in fact, Hopkin,
Barry and Baker hypothesized that farmers in the
past have judged equity capital as costing less than
debt capital [5, pp. 254-255].
The small firm situation of Ke < Kd is not
necessary for zero debt to minimize Ko. Situations
can exist when Ke > Kd, and zero D/А is also
optimal. Figure 1 illustrates these two possibilities.2
The curves Ke , Kd and Ko, which are linear for
graphic convenience, illustrate a case in which
Ke < Kd for all levels of leverage and the minimum
Ko occurs when D/А = 0. However, the curves Ke ,
Kd and Ko illustrate a case for which the minimum
Ko occurs at D/А = 0 even though Ke > Kd for all
levels of D/А. Salient features of this second case are:
(1) absolute difference between Ke and Kd is small
and (2) rate of increase in Kd with respect to changes
in leverage is equal to that for Ke . If the difference
between Ke and Kd was larger and/or if the increase
in Ke in response to increases in leverage was larger
relative to that for Kd , D/А = 0 would no longer be
optimal. The responsiveness of Ke and Kd to
leverage depends on risk preferences and impact of
leverage on riskiness of the owner’s equity and the
lender’s debt. For any given attitude of lenders
2Figure 1 is an abstraction from general theory and the institutional environment in agricultural finance. In the general
theory, the Kg, Kq and Kq curves are not linear. Kq for farmers would also not be continuous since lenders do not ration credit
with interest rates but with amounts of loans. However, representing these points in Figure 1 would not alter the basic
propositions and would complicate the graphic analysis. Weston and Brigham use similar theoretical abstractions in discussing the
theory of the cost of capital [11, pp. 636-657].
164