COST OF CAPITAL
Buckle and Thompson (1992) suggest that the current price of a share can be determined:
E 1 tD
P t t
Et is expectation at time t
Pt + 1 is price of the share at time t+1
Dt is dividend paid during the period t to t+1
R is the required rate of discount
g is annual rate of growth of dividends (assumed constant).
Equity capital: New Issues
In evaluating any new issue of shares a company must consider the yield on existing
shares, the expenses associated with the new issue and the discount it must offer on the
new issue to make it sufficiently attractive for takeup. The company must also ensure
that the existing shareholders are not disadvantaged due to the new issue. Some existing
shareholders will purchase new issue shares and the remainder of the new issue will ,
therefore, be purchased by new shareholders.
Thus,the cost of capital = y1c+ y2k + e
where y1 = existing yield on the company's shares
y2 = projected yield after new issue
c = proportion of new issue taken up by existing shareholders
k = proportion of new issue taken up by new shareholders and
e = issue expenses
(derived from Merrett and Sykes 1973).
The firm must pay dividends sufficient to provide the shareholders with their required
yield on the investment, so from the firm's viewpoint the yield is the ratio of the dividend
to the capital provided by the shares.
Equity capital: rights issues
2 1 e
where e, y1 and y2 are as previous example
kn = capital from new shareholders
k0 = capital from existing shareholders
s = proceeds from sale of rights and
K = total new capital
(derived from Merrett and Sykes 1973).
On the face of things, retained earnings have no cost to the firm. However, they do
constitute an increased stake in the firm by the shareholders as they represent profits
which have not been distributed as dividends. Thus, retained earnings have an
opportunity cost. Merrett and Sykes (1973) argue that a firm employing retained
earnings to finance its activities is able to accept a return on its investments which is
lower than the return on shareholders' alternative investments by the difference between
the tax deducted at source on distribution (Advance Corporation Tax – ACT- from 6
April 1999, the UK government abolished the ACT requirement so, dividends are paid
gross) and the rate of personal taxation of the shareholders. (This presumes that the
shareholders are taxed on their income at an average rate in excess of standard
rate. This analysis also ignores any capital gains tax payable on the increased market
value of shares arising from the retained earnings.)
Depreciation provisions may be considered in a similar manner to retained earnings -
they have an opportunity cost and represent an increased stake in the firm by its
shareholders. However, a distribution of depreciation provisions would produce a capital
reduction, probably requiring outstanding debts to be repaid due to the depletion of the
capital base, the security against which the debt was obtained. This indicates a
proportional combination between the cost of debt repaid and the cost of retained
earnings to calculate the cost of capital in the form of depreciation provisions.
Usually, debentures are issued at a discount. They are subject to a prescribed rate of
interest per year until they reach maturity, at which time, the loan is repaid by the
Hay and Morris (1991) consider the cost of debenture finance to the company to be i in
B t N
Where B0 = issue price
BN = terminal value
b = nominal interest rate on the debenture
n = life of the debenture.
t = time elapsed from issue.
It must be noted that interest paid on debentures is allowed as a cost of the firm's
operations prior to the computation of any corporation tax liability. This effectively
reduces the cost of this source of capital.
Merrett and Sykes (1973) argue that only discounts allowed or foregone should be used
to compute the cost of capital from trade creditors. They consider it preferable to treat
payment delays, the true credit element, as adjustments to cash flow and their reasoning
has been followed in this analysis.
Discounts for prompt payment are very common in construction in respect of almost all
types of subcontractors' and suppliers' accounts. However, due to the ravages of
inflation there has been a marked tendency for domestic suppliers particularly to tighten
their credit control, thus domestic suppliers and subcontractors should each be
considered on an individual basis (possibly leading to a weighted average calculation for
practical uses). It is usual for only the discount to be forfeited by late payment and not
for interest to be charged on the outstanding account. The cost of foregoing discount is
100 R p.a.
where d = per cent discount offered
n = period for payment in weeks
R = rate of interest per annum as cost of foregoing the discount.
The annual equivalent rate of interest obtained must be reduced by a factor of (1 - T),
where T is the rate of tax which the firm pays as loss of discount adds to the firm's costs
which are, of course, tax deductable.
Marginal cost of capital
The marginal cost of capital is of use to a firm in deciding whether or not to undertake a
project or to expand. It considers the cost of the requisite capital from the possible
sources and is, obviously, likely to produce a cost in excess of the firm’s average cost of
capital due, inter alia, to the additional risks likely to be involved.
Weighted average cost of capital
The weighted average cost of capital for a firm is of use in two major areas: in
consideration of the firm's position and in evaluation of proposed changes necessitating a
change in the firm's capital. Thus, a weighted average technique may be used in a quasi-
marginal way to evaluate a proposed investment project, such as the construction of a
The weighted average cost of capital is obtained by multiplying the net of tax cost of
capital (usually expressed as a percentage per annum) for each source of capital by the
proportion of total capital (for the firm or project) from that source and summing these
products to obtain a single percentage.
Optimum capital structure
The optimum capital structure is that which provides the greatest benefit to the firm.
This may be considered to be providing the greatest possible return to the owner's
investments in the firm. Naturally, this is a somewhat complex goal; the requirements
and views of the owners will vary (especially for a public company), short-term and
long-term objectives and possibilities may conflict and so, given these and other
problems of optimizing, it is likely, in fact, that, satisficing, will be employed to
determine the capital structure of a firm. (A 'satisficing' situation is one of compromise;
it is acceptable in respect of each individual criterion, but is suboptimal.)
The optimum capital structure would be such that, within the physical parameters, the
marginal cost of capital employed by the firm will be equal from all available sources.
This minimzes the cost of capital to the firm and so, in consequence, should maximize
the owners' returns.
Satisficing, in the context of the long-period minimum return which must be earned on
the owners' investment (normal profit), should permit greater flexibility in the selection
of the capital structure. In practice, the selection of a firm’s capital structure will be
subject to the objectives of the firm, notably the main objective which managers are
believed to pursue – growth – as well as the return on investment considerations; further,
the availability of capital in the market, given restrictions of time etc. in searching for
capital, are important. Thus, it is useful to reconsider the primary objectives of firms in
the modern market economies in which management has become divorced from
ownership such that Baumol (1959) concluded that firms operate to maximise growth of
turnover subject to a minimum profit constraint. Hutton (1996) argues that, due to
pressures form investors, mostly institutions, expressed via stock exchange activities,
firms are forced to behave in ways to provide short term returns, especially growth in
dividends. Further, despite advances in information technology, search patterns for
capital remain subject to bounded rationality. Hence, within limits, the capital structures
of firms are becoming increasingly oriented to facilitation of expansion and provision of
short term returns.