    # Algebraic Approach - Indifference Point In order to understand the Indifference Point, a small recap of the terms Capital Structure, Financial Leverage.

Capital Structure:

Capital Structure represents the way in which a firm finances its assets. Capital structure is often the source of a firm's financial growth, the source of financing for its operations, etc. A firm's capital structure can be a mixture of debt and equity.

Debt:

Here, debt consists of long term debt, and particular shot term debt. Long term debt is any debt from external sources of finance that need not be paid in the current financial year of 12 months. Short term debt consists of obligations in the form of 1-year bonds, etc.

Equity:

Equity capital consists of common shareholders' equity and preferred stock. The common shareholders' equity actually represents the underlying ownership of the firm. When investors buy shares of the company in the capital market in which the firm is listed, they become part owners of the firm, depending on the number of shares they own (purchase). This is called owners equity or equity capital itself, sometimes. Preferred stock, on the other hand, is when specific investors, like some owners of the company, institutions, and others buy the shares of the firm. The preferred stock owners must be paid dividends before the common stock owners. The other rules for preferred equity are different in different firms.

Financial Leverage:

Financial leverage is the amount of debt in the capital structure of a firm. A highly leveraged firm runs a greater risk of making a default in its payments, since it has to pay larger amounts of interests from its earnings. From this emerges another term, Degree of Financial Leverage (DFL). The DFL captures the effect the financial leverage will have on the firm's earnings. This is in turn reflected in EPS.

Indifference Point:

The indifference point is used to determine a firm's optimal capital structure. As seen earlier, firms opt for two kinds of financing in terms of long term financing - Debt and Equity. When the firm has equal earnings per share from both the financing options, it is called an indifference point.

So, the algebraic expression for the same will be

EPS (With Debt) = EPS (Without Debt)

Or

EBIT

This can be explained with a numerical example:

• Emerson Co. Ltd wants to take up a new project that requires a capital of \$ 15, 00, 000. Interest on Debt is 12 % and the Tax rate is 30 %. The debt equity ratio must be 2:1, according to industry standards. The equity shares are going to be issued at \$ 50 (par value).

Solution:

First, we calculate the Debt and Equity, since the ratio is given:

15, 00,000 divided in the ratio 2:1 would be Debt = \$ 10, 00,000, Equity = \$ 5, 00,000

Next, we calculate interest on debt, 12 % = 10,00,000 *12/100 = 1, 20, 000

No. of shares (with equity of \$ 5, 00, 000) = 5, 00, 000/50 = 10, 000

No. of shares (with equity of \$ 15, 00, 000) = 15, 00, 000/50 = 30, 000

So, there are 2 alternatives to the capital investment:" Debt and Equity " or just " Equity "

Next, we proceed to calculating the indifference point:

The formula for EPS is:

EBIT/No. of Equity Shares (Here EBIT is what we have to find out or solve for)

With Debt, the EPS would be:

(EBIT - 1,20,000)/10, 000

Without Debt, the EPS would be:

(EBIT - 0)/30000

The indifference EBIT is obtained when the alternatives are equated:

(EBIT - 120000)/10000 = (EBIT - 0)/30000

Solving it, we get:

EBIT = \$ 3, 60, 000

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