Capital structure theories

The proportion of debt, preference and equity shares on a firm’s balance sheet.

Assumptions and Definitions

To understand relationship between financial leverage n cost of capital:

Only two source of financing: Debt and Equity The total assets are given and do not change. The net operating income is not expected to change overtime. There is no corporate tax (removed later). The firm has a policy of paying its total earnings as dividend. Investors have identical subjective probability distributions of net

operating income for each company. Without incurring transaction costs, a firm can change its capital

structure. Business risk is constant over time and independent of its capital

structure and financial risk.

Definitions

S = Market value of equity, B = Market value of debtV = Total market value of the firm (V=S+B)NI = Net income available to the shareholdersI = Interest payments, P0 = Current market price of sharesD1 = Net dividend, E1 = Earnings per share

Cost of Debt (ki) = I/B, => B = I/ki

Cost of Equity (ke) = g+ (D1/P0), g = expected growth rate

G=br, where r is rate of return on equity and b is the retention rate. Since b=0, therefore, g= br= 0

Formula:

P0 = E1/Ke (per share basis)

S = (EBIT-I)/Ke (Total basis)

Cost of capital Ko = (B/V)Ki + (S/V)Ke

Ko = EBIT/V or V = EBIT/Ko

V = B+S = I/Ki + (EBIT-I)/Ke

Ke = Ko + (Ko – Ki)B/S

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Theories

Net income (NI) approach. Net operating income (NOI) approach.

Traditional approach MM hypothesis with and without corporate tax.

Miller’s hypothesis with corporate and personal taxes. Trade-off theory: costs and benefits of leverage.

Net Income approach by “David Durand”

Capital structure is RELEVANT in determining the value of the firm.

Assumptions: The ‘Ki’ is cheaper than the ‘Ke’. Income tax has been ignored. The ‘Ki’ and ‘Ke’ remain constant. Use of debt does not change the risk perception of the

investors.

With a judicious mixture of debt and equity, a firm can evolve an optimal capital structure at which the value of the firm is highest and the overall cost of capital is lowest.

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Net Income (NI) Approach

Cost of debt (ki) & cost of equity (ke) = constant.

As a result, the overall cost of capital declines and the firm value increases with more debt.

This approach has no basis in reality; the optimum capital structure would be 100 per cent debt financing under NI approach.

ke

koki

Debt

Cost

ki

ke, ko

Degree of leverage

Computation of the Total Value of the Firm

Total Value of the Firm (V) = S + BWhere, S = Market value of Shares = EBIT-I = E = NI Ke Ke KeB = Market value of Debt = Face Value E = Earnings available for equity shareholdersKe = Cost of Equity capital or Equity capitalization

rate.K0 = EBIT/V = Ki (B/V) + Ke (S/V)

Ke = K0 + (K0 – Ki).B/S

Net Operating Income approach by Durand

Capital structure is IRRELEVANT in determining the value of the firm.

Any change in the leverage will not lead to any change in the value of the firm. The market value of shares as well as overall cost of capital is independent of the degree of leverage.

The advantage associated with the use of cheaper source of financing i.e., debt is exactly neutralized by the increase in cost of equity.

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Net Operating Income (NOI) Approach

The value of the firm and the weighted average cost of capital are independent of the firm’s capital structure.

In the absence of taxes, an individual holding all the debt and equity securities will receive the same cash flows regardless of the capital structure.

The value of the company is the same.

ke

ko

ki

Debt

Cost

Traditional Theory by Ezra Solomon:

• According to this theory, a firm can reduce the overall cost of capital or increase the total value of the firm by increasing the debt proportion in its capital structure to a certain limit.

• Because debt is a cheap source of raising funds as compared to equity capital, it would be beneficial at first but after a certain point increasing leverage would result in increase in cost of capital.

Effects of Changes in Capital Structure on ‘Ko’ & ‘V’

First Stage: The use of debt in capital structure increases the ‘V’ and decreases the ‘Ko’.

Second Stage: During this Stage, there is a range in which the ‘V’ will be maximum and the ‘Ko’ will be minimum.

Third Stage: The ‘V’ will decrease and the ‘Ko’ will increase.

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Traditional Approach

The traditional approach argues that moderate degree of debt can lower the firm’s overall cost of capital and thereby, increase the firm value.

The initial increase in the cost of equity is more than offset by the lower cost of debt.

But as debt increases, shareholders

perceive higher risk and the cost of equity rises until a point is reached at which the advantage of lower cost of debt is more than offset by more expensive equity.

ke

ko

ki

Debt

Cost

Modigliani Miller (MM) Approach

Capital structure is IRRELEVANT in determining the value of the firm.

The K0 and V are independent of its capital structure and are constant for all degrees of leverage.

The total value is given by capitalizing the expected stream of operating earnings at a discount rate appropriate for its risk class

Ke = K0 + (K0 – Ki) B/S

Assumptions:

Dividend pay out ratio is 100% There are no taxes

Perfect capital market All investors have the same expectations of

EBIT

Business risk is equal among all firms within similar operating environment

Limitations:

Risk perception Convenience

Cost Institutional restrictions

Double leverage Transaction cost

MM Approach with taxes

MM agree that the value of the firm will increase and cost of capital will decline with leverage, if corporate taxes are introduced.

The value of levered firm would exceed that of unlevered firm by an amount equal to the levered firm’s debt multiplied by the tax rate.

Vl = Vu + Bt, where, Vl & Vu are value of levered n unlevered firm, B is the total borrowings of the levered firm and t is the tax rate.