Capital structure

Irrelevance theory

By:Hassan Jan Habib

Capital structure is the proportion of debt and

preference and equity shares on a firm’s balance sheet.

Optimum capital structure is the capital structure at which the weighted average cost of capital is minimum and thereby maximum value of the firm.

Capital Structure

Capital structure theories explain the

theoretical relationship between capital structure, overall cost of capital (k0) and valuation (V ). The four important theories are:

1. Net income (NI) approach, 2. Net operating income (NOI) approach,3. Modigliani and Miller (MM) approach and4. Traditional Approach

Capital structure theories

There are only two sources of funds used by a

firm: perpetual riskless debt and ordinary shares. There are no corporate taxes. This assumption is

removed later. The dividend-payout ratio is 100. That is, the

total earnings are paid out as dividend to the shareholders and there are no retained earnings.

The total assets are given and do not change. The investment decisions are, in other words, assumed to be constant.

Assumptions

The total financing remains constant. The firm can

change its degree of leverage (capital structure) either by selling shares and use the proceeds to retire debentures or by raising more debt and reduce the equity capital.

The operating profits (EBIT) are not expected to grow.

Business risk is constant over time and is assumed to be independent of its capital structure and financial risk.

Perpetual life of the firm.

Cont’d

The essence of this approach is that capital

structure decision of a corporate does not affect its cost of capital and valuation, and, hence, irrelevant.

Net Operating Income (NOI) Approach

The NOI Approach is based on the

following propositions. Overall cost of capital/ capitalization Ratio(K◦)

is constant Residual Value of Equity Changes in cost of equity capital Optimum Capital Structure

Propositions

Market Price of Share Cost of Debt

Explicit Cost Implicit Cost

Cont’d

5

10

15

0 0.5 1.0

Degree of Leverage (B/V)Leverage and Cost of Capital (NOI Approach)

X

Y

Ke,

ki a

nd

k0 (%

)k0

ki

ke2025

k0 and ki remain unchanged as the degree of leverage changes, but as the degree of leverage increases, the ke increases continuously.

Modigliani-Miller (MM) Approach

P resented by Modigliani and Miller in 1958 Modigliani and Miller (MM) concur with NOI

and provide a operational justification for the irrelevance of capital structure.

They maintain that the cost of capital and the

value of the firm do not change with a change in leverage.

x

(in Rs)v

k 0 (

%)

Degree of Leverage (B/V)

Leverage and Cost of Capital (MM Approach)

V0

k0

The overall cost of capital (k0) and the value

of the firm (V) are independent of its capital structure

The cost of equity of a levered firm is equal to the cost of equity of an unlevered firm plus a financial risk premium, which depends on the degree of financial leverage

The discount rate for investment purposes is completely independent of the way in which an investment is financed.

Propositions

Perfect capital markets: The implication of a

perfect capital market is that investors are free to buy/sell securities investors can borrow without restrictions on the

same terms and conditions as firms can there are no transaction costs information is perfect, that is, each investor has

the same information which is readily available to him without cost and

investors are rational and behave accordingly.

Assumptions

Given the assumption of perfect information

and rationality, all investors have the same expectation of firm’s net operating income (EBIT) with which to evaluate the value of a firm.

Business risk is equal among all firms within similar operating environment.

The dividend payout ratio is 100 per cent. There are no taxes. (This assumption is removed later)

Assumptions

MM’s Proposition 1 The market value of any firm is independent

of its capital structure.

If a company has a given set of assets, changing debt to equity will change the way net operating income is divided between lenders and shareholders but will not change the value of the company.

Value of a company is given by:

0

annual net operating incomeV

k

According to the MM hypothesis, this situation cannot continue for long time, as the arbitrage

process, based on the substitutability of personal leverage for corporate leverage, will operate and the values of the two firms will be brought to an

identical level.

Proof of Proposition 1

But What if 2 identical firms except having different capital structure

and market value?

Arbitrage ProcessBuying a security in a market where price is low and selling

where it is high.

As a result, equilibrium is restored in the market price of

securities.

Example:

Suppose two firms one Levered “L” and the other unlevered “U” identical by nature i.e. capital, and profits falling in the same risk class but having different capital structure and Market value.

L U

Equity 100,000 150,000

8% Debentures 50,000 -

Market price per share

Rs. 13 Rs. 10

EBIT Rs. 20,000 Rs. 20,000

Same amount

Of capital

Same Profit

Suppose there is an investor “Mr. X”, holding 10% shares of Levered firm “L”

Since the market value of L is greater than U, where as profit is the same

So, Mr. X will sell his 10% shares in firm L=Rs. 13,000

And will raise a personal loan in the same proportion i.e. 10%

=Rs. 50,000×10%=Rs. 5000

Total cash in hand is: Rs. 13,000+5000= Rs.18,000

He will invest that amount in shares of firm U. which amounts to 12% of total shares in firm U

L U

EBIT Rs. 20,000 Rs. 20,000

Less: Interest (4000) -

EBT/NI 16,000 20,000

Dividend 10% i.e. 1600 12% i.e. 2400

Profit earned by Mr. X from Unlevered firm = Rs. 2400Less: Interest to be paid on loan(50,000×8%) = (400)

Total profit earned = Rs. 2000

By getting involved in Arbitrage process, income of Mr. X has increased from Rs. 1600 to Rs. 2000

Arbitrage process will continue till the share prices of Firm L fall and Firm U’s rises. So as to make the market prices of both firms

identical