Top 4 Theories of Capital Structure (With Calculations)

The following points will highlight the top four theories of capital structure.

Capital Structure Theory # 1. Net Income (NI) Approach:

According to NI approach a firm may increase the total value of the firm by lowering its cost of capital.

When cost of capital is lowest and the value of the firm is greatest, we call it the optimum capital structure for the firm and, at this point, the market price per share is maximised.

The same is possible continuously by lowering its cost of capital by the use of debt capital. In other words, using more debt capital with a corresponding reduction in cost of capital, the value of the firm will increase.

The same is possible only when:

(i) Cost of Debt (Kd) is less than Cost of Equity (Ke);

(ii) There are no taxes; and

(iii) The use of debt does not change the risk perception of the investors since the degree of leverage is increased to that extent.

Since the amount of debt in the capital structure increases, weighted average cost of capital decreases which leads to increase the total value of the firm. So, the increased amount of debt with constant amount of cost of equity and cost of debt will highlight the earnings of the shareholders.

Illustration 1:

X Ltd. presents the following particulars:

EBIT (i.e., Net Operating income) is Rs. 30,000;

The equity capitalisation ratio (i.e., cost of equity) is 15% (Ke);

Cost of debt is 10% (Kd);

Total Capital amounted to Rs. 2,00,000.

Calculate the cost of capital and the value of the firm for each of the following alternative leverage after applying the NI approach.

Leverage (Debt to total Capital) 0%, 20%, 50%, 70% and 100%.

From the above table it is quite clear that the value of the firm (V) will be increased if there is a proportionate increase in debt capital but there will be a reduction in overall cost of capital. So, Cost of Capital is increased and the value of the firm is maximum if a firm uses 100% debt capital.

It is interesting to note the NI approach can also be graphically presented as under (with the help of the above illustration):

The degree of leverage is plotted along the X-axis whereas Ke, Kw and Kd are on the Y-axis. It reveals that when the cheaper debt capital in the capital structure is proportionately increased, the weighted average cost of capital, Kw, decreases and consequently the cost of debt is Kd.

Thus, it is needless to say that the optimal capital structure is the minimum cost of capital if financial leverage is one; in other words, the maximum application of debt capital.

The value of the firm (V) will also be the maximum at this point.

Capital Structure Theory # 2. Net Operating Income (NOI) Approach:

Now we want to highlight the Net Operating Income (NOI) Approach which was advocated by David Durand based on certain assumptions.

They are:

(i) The overall capitalisation rate of the firm Kw is constant for all degree of leverages;

(ii) Net operating income is capitalised at an overall capitalisation rate in order to have the total market value of the firm.

Thus, the value of the firm, V, is ascertained at overall cost of capital (Kw):

V = EBIT/Kw (since both are constant and independent of leverage)

(iii) The market value of the debt is then subtracted from the total market value in order to get the market value of equity.

S – V – T 

(iv) As the Cost of Debt is constant, the cost of equity will be

Ke = EBIT – I/S

The NOI Approach can be illustrated with the help of the following diagram:

Under this approach, the most significant assumption is that the Kw is constant irrespective of the degree of leverage. The segregation of debt and equity is not important here and the market capitalises the value of the firm as a whole.

Thus, an increase in the use of apparently cheaper debt funds is offset exactly by the corresponding increase in the equity- capitalisation rate. So, the weighted average Cost of Capital Kwand Kd remain unchanged for all degrees of leverage. Needless to mention here that, as the firm increases its degree of leverage, it becomes more risky proposition and investors are to make some sacrifice by having a low P/E ratio.

Illustration 2:

Assume:

Net Operating Income or EBIT Rs. 30,000

Total Value of Capital Structure Rs. 2,00,000.

Cost of Debt Capital Kd 10%

Average Cost of Capital Kw 12%

Calculate Cost of Equity, Ke: value of the firm V applying NOI approach under each of the following alternative leverages:

Leverage (debt to total capital) 0%, 20%, 50%, 70%, and 100%

Although the value of the firm, Rs. 2,50,000 is constant at all levels, the cost of equity is increased with the corresponding increase in leverage. Thus, if the cheaper debt capital is used, that will be offset by the increase in the total cost of equity Ke, and, as such, both Ke and Kd remain unchanged for all degrees of leverage, i.e. if cheaper debt capital is propor­tionately increased and used, the same will offset the increase of cost of equity.

Capital Structure Theory # 3. Traditional Theory Approach:

It is accepted by all that the judicious use of debt will increase the value of the firm and reduce the cost of capital. So, the optimum capital structure is the point at which the value of the firm is highest and the cost of capital is at its lowest point. Practically, this approach encompasses all the ground between the Net Income Approach and the Net Operating Income Approach, i.e., it may be called Intermediate Approach.

The traditional approach explains that up to a certain point, debt-equity mix will cause the market value of the firm to rise and the cost of capital to decline. But after attaining the optimum level, any additional debt will cause to decrease the market value and to increase the cost of capital.

In other words, after attaining the optimum level, any additional debt taken will offset the use of cheaper debt capital since the average cost of capital will increase along with a corresponding increase in the average cost of debt capital.

Thus, the basic proposition of this approach are:

(a) The cost of debt capital, Kd, remains constant more or less up to a certain level and thereafter rises.

(b) The cost of equity capital Ke, remains constant more or less or rises gradually up to a certain level and thereafter increases rapidly.

(c) The average cost of capital, Kw, decreases up to a certain level remains unchanged more or less and thereafter rises after attaining a certain level.

The traditional approach can graphically be represented under taking the data from the previous illustration:

It is found from the above that the average cost curve is U-shaped. That is, at this stage the cost of capital would be minimum which is expressed by the letter ‘A’ in the graph. If we draw a perpendicular to the X-axis, the same will indicate the optimum capital structure for the firm.

Thus, the traditional position implies that the cost of capital is not independent of the capital structure of the firm and that there is an optimal capital structure. At that optimal structure, the marginal real cost of debt (explicit and implicit) is the same as the marginal real cost of equity in equilibrium.

For degree of leverage before that point, the marginal real cost of debt is less than that of equity beyond that point the marginal real cost of debt exceeds that of equity.

Illustration 3:

Calculate the cost of capital and the value of the firm under each of the following alternative degrees of leverage and comment on them:

Thus, from the above table, it becomes quite clear the cost of capital is lowest (at 25%) and the value of the firm is the highest (at Rs. 2,33,333) when debt-equity mix is (1,00,000 : 1,00,000 or 1: 1). Hence, optimum capital structure in this case is considered as Equity Capital (Rs. 1,00,000) and Debt Capital (Rs. 1,00,000) which bring the lowest overall cost of capital followed by the highest value of the firm.

Variations on the Traditional Theory:

This theory underlines between the Net Income Approach and the Net Operating Income Approach. Thus, there are some distinct variations in this theory. Some followers of the traditional school of thought suggest that Ke does not practically rise till some critical conditions arise. Only after attaining that level the investors apprehend the increasing financial risk and penalise the market price of the shares. This variation expresses that a firm can have lower cost of capital with the initial use of leverage significantly.

This variation in Traditional Approach is depicted as:

Other followers e.g., Solomon, are of opinion the Ke is being saucer-shaped along with a horizontal middle range. It explains that optimum capital structure has a range where the cost of capital is rather minimised and where the total value of the firm is maximised. Under the circumstances a change in leverage has, practically, no effect on the total firm’s value. So, this approach grants some sort of variation in the optimal capital structure for various firms under debt-equity mix.

Such variation can be depicted in the form of graphical representation:

Capital Structure Theory # 4. Modigliani-Miller (M-M) Approach:

Modigliani-Miller’ (MM) advocated that the relationship between the cost of capital, capital structure and the valuation of the firm should be explained by NOI (Net Operating Income Approach) by making an attack on the Traditional Approach.

The Net Operating Income Approach, supplies proper justification for the irrelevance of the capital structure. In Income Approach, supplies proper justification for the irrelevance of the capital structure.

In this context, MM support the NOI approach on the principle that the cost of capital is not dependent on the degree of leverage irrespective of the debt-equity mix. In the words, according to their thesis, the total market value of the firm and the cost of capital are independent of the capital structure.

They advocated that the weighted average cost of capital does not make any change with a proportionate change in debt-equity mix in the total capital structure of the firm.

The same can be shown with the help of the following diagram:

Proposition:

The following propositions outline the MM argument about the relationship between cost of capital, capital structure and the total value of the firm:

(i) The cost of capital and the total market value of the firm are independent of its capital structure. The cost of capital is equal to the capitalisation rate of equity stream of operating earnings for its class, and the market is determined by capitalising its expected return at an appropriate rate of discount for its risk class.

(ii) The second proposition includes that the expected yield on a share is equal to the appropriate capitalisation rate of a pure equity stream for that class, together with a premium for financial risk equal to the difference between the pure-equity capitalisation rate (Ke) and yield on debt (Kd). In short, increased Ke is offset exactly by the use of cheaper debt.

(iii) The cut-off point for investment is always the capitalisation rate which is completely independent and unaffected by the securities that are invested.

Assumptions:

The MM proposition is based on the following assumptions:

(a) Existence of Perfect Capital Market It includes:

(i) There is no transaction cost;

(ii) Flotation costs are neglected;

(iii) No investor can affect the market price of shares;

(iv) Information is available to all without cost;

(v) Investors are free to purchase and sale securities.

(b) Homogeneous Risk Class/Equivalent Risk Class:

It means that the expected yield/return have the identical risk factor i.e., business risk is equal among all firms having equivalent operational condition.

(c) Homogeneous Expectation:

All the investors should have identical estimate about the future rate of earnings of each firm.

(d) The Dividend pay-out Ratio is 100%:

It means that the firm must distribute all its earnings in the form of dividend among the shareholders/investors, and

(e) Taxes do not exist:

That is, there will be no corporate tax effect (although this was removed at a subsequent date).

Interpretation of MM Hypothesis:

The MM Hypothesis reveals that if more debt is included in the capital structure of a firm, the same will not increase its value as the benefits of cheaper debt capital are exactly set-off by the corresponding increase in the cost of equity, although debt capital is less expensive than the equity capital. So, according to MM, the total value of a firm is absolutely unaffected by the capital structure (debt-equity mix) when corporate tax is ignored.

Proof of MM Hypothesis—The Arbitrage Mechanism:

MM have suggested an arbitrage mechanism in order to prove their argument. They argued that if two firms differ only in two points viz. (i) the process of financing, and (ii) their total market value, the shareholders/investors will dispose-off share of the over-valued firm and will purchase the share of under-valued firms.

Naturally, this process will be going on till both attain the same market value. As such, as soon as the firms will reach the identical position, the average cost of capital and the value of the firm will be equal. So, total value of the firm (V) and Average Cost of Capital, (Kw) are independent.

It can be explained with the help of the following illustration:

Let there be two firms, Firm ‘A’ and Firm ‘B’. They are similar in all respects except in the composition of capital structure. Assume that Firm ‘A’ is financed only by equity whereas Firm ‘B’ is financed by a debt-equity mix.

The following particulars are presented:

From the table presented above, it is learnt that value of the levered firm ‘B’ is higher than the unlevered firm ‘A’. According to MM, such situation cannot persist long as the investors will dispose-off their holding of firm ‘B’ and purchase the equity from the firm ‘A’ with personal leverage. This process will be continued till both the firms have same market value.

Suppose Ram, an equity shareholder, has 1% equity of firm ‘B’. He will do the following:

(i) At first, he will dispose-off his equity of firm ‘B’ for Rs. 3,333.

(ii) He will take a loan of Rs. 2,000 at 5% interest from personal account.

(iii) He will purchase by having Rs. 5,333 (i.e. Rs. 3,333 + Rs. 2,000) 1.007% of equity from the firm ‘A’.

By this, his net income will be increased as:

Obviously, this net income of Rs. 433 is higher than that of the firm ‘B’ by disposing-off 1% holding.

It is needless to say that when the investors will sell the shares of the firm ‘B’ and will purchase the shares from the firm ‘A’ with personal leverage, this market value of the share of firm ‘A’ will decline and, consequently, the market value of the share of firm ‘B’ will rise and this will be continued till both of them attain the same market value.

We know that the value of the levered firm cannot be higher than that of the unlevered firm (other things being equal) due to that arbitrage process. We will now highlight the reverse direction of the arbitrage process.

Consider the following illustration:

In the above circumstances, equity shareholder of the firm ‘A’ will sell his holdings and by the proceeds he will purchase some equity from the firm ‘B’ and invest a part of the proceeds in debt of the firm ‘B’.

For instance, an equity shareholder holding 1% equity in the firm ‘A’ will do the following:

(i) He will dispose-off his 1% equity of firm ‘A’ for Rs. 6,250.

(ii) He will buy 1% of equity and debt of the firm ‘B’ for the like amount.

(iii) As a result, he will have an additional income of Rs. 86.

Thus, if the investors prefer such a change, the market value of the equity of the firm ‘A’ will decline and, consequently, the market value of the shares of the firm ‘B’ will tend to rise and this process will be continued till both the firms attain the same market value, i.e., the arbitrage process can be said to operate in the opposite direction.

Criticisms of the MM Hypothesis:

We have seen (while discussing MM Hypothesis) that MM Hypothesis is based on some assumptions. There are some authorities who do not recognise such assumptions as they are quite unrealistic, viz. the assumption of perfect capital market.

We also know that most significant element in this approach is the arbitrage process forming the behavioural foundation of the MM Hypothesis. As the imperfect market exists, the arbitrage process will be of no use and as such, the discrepancy will arise between the market value of the unlevered and levered firms.

The shortcomings for which arbitrage process fails to bring the equilibrium condition are:

(i) Existence of Transaction Cost:

The arbitrage process is affected by the transaction cost. While buying securities, this cost is involved in the form of brokerage or commission etc. for which extra amount is to be paid which increases the cost price of the shares and requires a greater amount although the return is same. As such, the levered firm will enjoy a higher market value than the unlevered firm.

(ii) Assumption of borrowing and lending by the firms and the individual at the same rate of interest:

The above proposition that the firms and the individuals can borrow or lend at the same rate of interest, does not hold good in reality. Since a firm holds more assets and credit reputation in the open market in comparison with an individual, the former will always enjoy a better position than the latter.

As such, cost of borrowing will be higher in case of an individual than a firm. As a result, the market value of both the firms will not be equal.

(iii) Institutional Restriction:

The arbitrage process is retarded by the institutional investors e.g., Life Insurance Corporation of India, Commercial Banks; Unit Trust of India etc., i.e., they do not encourage personal leverage. At present these institutional investors dominate the capital market.

(iv) “Personal or home-made leverage” is not the prefect substitute for “corporate leverage.”:

MM hypothesis assumes that “personal leverage” is a perfect substitute for “corporate leverage” which is not true as we know that a firm may have a limited liability whereas there is unlimited liability in case of individuals. For this purpose, both of them have different footing in the capital market.

(v) Incorporation of Corporate Taxes:

If corporate taxes are considered (which should be taken into consideration) the MM approach will be unable to discuss the relationship between the value of the firm and the financing decision. For example, we know that interest charges are deducted from profit available for dividend, i.e., it is tax deductible.

In other words, the cost of borrowing funds is comparatively less than the contractual rate of interest which allows the firm regarding tax advantage. Ultimately, the benefit is being enjoyed by the equity-holders and debt-holders.

According to some critics the arguments which were advocated by MM, are not valued in the practical world. We know that cost of capital and the value of the firm are practically the product of financial leverage.

MM Hypothesis with Corporate Taxes and Capital Structure:

The MM Hypothesis is valid if there is perfect market condition. But, in the real world capital market, imperfection arises in the capital structure of a firm which affects the valuation. Because, presence of taxes invites imperfection.

We are, now, going to examine the effect of corporate taxes in the capital structure of a firm along with the MM Hypothesis. We also know that when taxes are levied on income, debt financing is more advantageous as interest paid on debt is a tax-deductible item whereas retained earning or dividend so paid in equity shares are not tax-deductible.

Thus, if debt capital is used in the total capital structure, the total income available for equity shareholders and/or debt holders will be more. In other words, the levered firm will have a higher value than the unlevered firm for this purpose, or, it can alternatively be stated that the value of the levered firm will exceed the unlevered firm by an amount equal to debt multiplied by the rate of tax.

The same can be explained in the form of the following equation:

Illustration 4:

Assume:

Two firms—Firm ‘A’ and Firm ‘B’ (identical in all respects except capital structure)

Firm ‘A’ has financed a 6% debt of Rs. 1,50,000

Firm ‘B’ Levered

EBIT (for both the firm) Rs. 60,000

Cost of Capital is @ 10%

Corporate rate of tax is @ 60%

Compute market value of the two firms.

Thus, a firm can lower its cost of capital continuously due to the tax deductibility of interest charges. So, a firm must use the maximum amount of leverage in order to attain the optimum capital structure although the experience that we realise is contrary to the opinion.

In real-world situation, however, firms do not take a larger amount of debt and creditors/lenders also are not interested to supply loan to highly levered firms due to the risk involved in it.

Thus, due to the market imperfection, after tax cost of capital function will be U-shaped. In answer to this criticism, MM suggested that the firm would adopt a target debt ratio so as not to violate the limits of level of debt imposed by creditors. This is an indirect way of stating that the cost of capital will increase sharply with leverage beyond some safe limit of debt.

MM Hypothesis with corporate taxes can better be presented with the help of the following diagram:

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