capital structure and valuation

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CAPITAL STRUCTURE, COST OF CAPITAL AND VALUATION

Capital Structure Theories

Net Income Approach

Net Operating Income (NOI) Approach

Traditional Approach

Moodiglani- Miller Approach

Solved Problems

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Capital StructureCapital Structure

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.

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Assumptions

1) There are only two sources of funds used by a firm: perpetual riskless debt and ordinary shares.

2) There are no corporate taxes. This assumption is removed later.

3) 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.

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

5) 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.

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

7) All investors are assumed to have the same subjective probability distribution of the future expected EBIT for a given firm.

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

9) Perpetual life of the firm.

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Definitions and Symbols

In addition to the above assumptions, we shall make use of some symbols in our analysis of capital structure theories:

S = total market value of equity

B = total market value of debt

I = total interest payments

V = total market value of the firm (V = S + B)

NI = net income available to equity-holders.

where D1 = net dividend; P0 = current market price of shares and g is the expected growth rate. According to assumption (3), the percentage of retained earnings is zero. Since g = br, where r is the rate of return on equity shares and b is the retention rate, g = 0, the growth rate is zero. This is consistent with assumption (6). In operational terms D1 = E1, g = 0. Therefore,

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where E1 = earnings per share. Equation 4 is on a per share basis. Multiplying both the numerator and the denominator by the number of shares outstanding (N) and assuming there are no income taxes, we have

Thus, ke may be defined on either per share or total basis. From Eqs. 4 and 5 follow the equations of determining the value of equity shares on per share basis and total basis.

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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 and

4) Traditional approach.

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Net Income ApproachNet Income Approach

According to the NI approach, capital structure is

relevant as it affects the k0 and V of the firm. The core

of this approach is that as the ratio of less expensive source of funds (i.e., debt) increases in the capital

structure, the k0 decreases and V of the firm increases.

With a judicious mixture of debt and equity, a firm can

evolve an optimum capital structure at which the k0

would be the lowest, the V of the firm the highest and the market price per share the maximum.

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Example 1

A company’s expected annual net operating income (EBIT) is Rs 50,000. The company has Rs 2,00,000, 10% debentures. The equity capitalisation rate (ke) of the company is 12.5 per cent.

Solution: With no taxes, the value of the firm, according to the Net Income Approach is depicted in Table 1.

TABLE 1 Value of the Firm (Net Income Approach)

Net operating income (EBIT) Rs 50,000

Less: Interest on debentures (I) 20,000

Earnings available to equity holders (NI) 30,000

Equity capitalisation rate (ke) 0.125

Market value of equity (S) = NI/ke 2,40,000

Market value of debt (B) 2,00,000

Total value of the firm (S + B) = V 4,40,000

Overall cost of capital = k0 = EBIT/V (%) 11.36

Alternatively: k0 = ki (B/V) + ke(S/V) where ki and ke are cost of debt and cost of equity respectively, = 0.10 [(Rs 2,00,000/Rs 4,40,000) + 0.125 (Rs 2,40,000 / Rs 4,40,000)] % 11.36

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Increase in Value

In order to examine the effect of a change in financing-mix on the firm’s overall (weighted average) cost of capital and its total value, let us suppose that the firm has decided to raise the amount of debenture by Rs 1,00,000 and use the proceeds to retire the equity shares. The ki and ke would remain unaffected as per the assumptions of the NI Approach. In the new situation, the value of the firm is shown in Table 2.









K0 = (Rs 50,000 / Rs 4,60,000) or 0.10 (Rs 3,00,000 / Rs 4,60,000) +

0.125 (Rs 160,000 / Rs 4,60,000)

10.9 %

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Decrease in Value

If we decrease the amount of debentures in Example 1, the total value of the firm, according to the NI Approach, will decrease and the overall cost of capital will increase. Let us suppose that the amount of debt has been reduced by Rs 1,00,000 to Rs 1,00,000 and a fresh issue of equity shares is made to retire the debentures. Assuming other facts as given in Example 1, the value of the firm and the weighted average cost of capital are shown in Table 3.









k0 = (Rs 50,000 / Rs 4,20,000) or 0.10 (Rs 1,00,000 / Rs 4,20,000) + 0.125 (Rs 3,20,000 / Rs 4,20,000)(%)

11.9

Thus, we find that the decrease in leverage has increased the overall cost of capital and has reduced the value of firm.

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Market Price

Thus, according to the NI Approach, the firm can increase/decrease its total value (V) and lower/increase its overall cost of capital (k0) as it increases/decreases the degree of leverage. As a result, the market price per share is affected.

To illustrate, assume in Example 1 that the firm with Rs 2,00,000 debt has 2,400 equity shares outstanding. The market price per share works out to Rs 100 (Rs 2,40,000 ÷ 2,400). The firm issues Rs 1,00,000 additional debt and uses the proceeds of the debt to repurchase/retire Rs 1,00,000 worth of equity shares or 1,000 shares. It, then, has 1,400 shares outstanding. We have observed in Example 1 that the total market value of the equity after the change in the capital structure is Rs 1,60,000 (Table 2). Therefore, the market price per share is Rs 114.28 (Rs 1,60,000 ÷ 1,400), as compared to the original price of Rs 100 per share.

Likewise, when the firm employs less amount of debt, the market value per share declines. To continue with Example 1, the firm raises Rs 1,00,000 additional equity capital by issuing 1,000 equity shares of Rs 100 each and uses the proceeds to retire the debenture amounting to Rs 1,00,000. It would then have 3,400 shares (2,400 old + 1,000 new) outstanding. With this capital structure, we have seen in Example 1 that the total market value of equity shares is Rs 3,20,000 (Table 3). Therefore, the market price per share has declined to Rs 94.12 (Rs 3,20,000 ÷ 3,400) from Rs 100 before a change in the leverage.

We can graph the relationship between the various factors (ke, ki, k0) with the degree of leverage (Fig. 1).

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The degree of leverage (B/V) is plotted along the X-axis, while the percentage rates of ki, ke and k0 are on the Y-axis. This graph is based on Example 1. Due to the assumptions that ke and ki remain unchanged as the degree of leverage changes, we find that both the curves are parallel to the X-axis. But as the degree of leverage increases, k0 decreases and approaches the cost of debt when leverage is 1.0, that is, (k0 = ki). It will obviously be so owing to the fact that there is no equity capital in the capital structure. At this point, the firm’s overall cost of capital would be minimum. The significant conclusion, therefore, of the NI Approach is that the firm can employ almost 100 per cent debt to maximise its value.

5.0

10.0

15.0

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Degree of Leverage (B/V)

Figure 1: Leverage and Cost of Capital (NI Approach)

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ki

ke

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Net Operating Income (NOI) Net Operating Income (NOI) ApproachApproach

The NOI approach is diametrically opposite to the NI approach. 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.

The NOI Approach is based on the following propositions.Overall Cost of Capital/Capitalisation Rate (k0) is Constant

The NOI Approach to valuation argues that the overall capitalisation rate of the firm remains constant, for all degrees of leverage. The value of the firm, given the level of EBIT, is determined by Eq. 13.

V = (EBIT/ko) (13)

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Changes in Cost of Equity Capital

The equity-capitalisation rate/cost of equity capital (ke) increases with the degree of leverage. The increase in the proportion of debt in the capital structure relative to equity shares would lead to an increase in the financial risk to the ordinary shareholders. To compensate for the increased risk, the shareholders would expect a higher rate of return on their investments. The increase in the equity-capitalisation rate (or the lowering of the price-earnings ratio, that is, P/E ratio) would match the increase in the debt-equity ratio. The ke would be

K0 + (k0 – ki) [B/S]

Residual Value of Equity

The value of equity is a residual value which is determined by deducting the total value of debt (B) from the total value of the firm (V). Symbolcially, Total market value of equity capital (S) =V – B.

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Cost of Debt

The main argument of NOI is that an increase in the proportion of debt in the capital structure would lead to an increase in the financial risk of the equityholders. To compensate for the increased risk, they would require a higher rate of return (ke) on their investment. As a result, the advantage of the lower cost of debt would exactly be neturalised by the increase in the cost of equity.

The cost of debt has two components: (i) explicit, represented by rate of interest, and (ii) implicit, represented by the increase in the cost of equity capital. Therefore, the real cost of debt and equity would be the same and there is nothing like an optimum capital structure.

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Example 2

Assume the figures given in Example 1: operating income Rs 50,000; cost of debt, 10 per cent; and outstanding debt, Rs 2,00,000. If the overall capitalisation rate (overall cost of capital) is 12.5 per cent, what would be the total value of the firm and the equity-capitalisation rate?

Solution: The computation is depicted in Table 4.

TABLE 4 Total Value of the Firm (Net Operating Income Approach)

Net operating income (EBIT)Overall capitalisation rate (k0)

Total market value of the firm (V) = EBIT/k0

Total value of debt (B)Total market value of equity (S) = (V – B)Equity-capitalisation rate, ke = [(EBIT – I) / (V – B)] = (Earnings available

to equityholders / Total market value of equity shares) = [(Rs 50,000 – Rs 20,000) / Rs 2,00,000]Alternatively, ke = k0 + (k0 – ki)B/S: 0.125 + (0.125 – 0.10) (Rs 2,00,000 /

Rs 2,00,000)

Rs 50,0000.125

4,00,0002,00,0002,00,000

0.15

0.15

The weighted average cost of capital to verify the validity of the NOI Approach:

k0 = ki(B/V) + ke(S/V) = 0.10 (Rs 2,00,000 / Rs 4,00,000) + 0.15 (Rs

2,00,000 / Rs 4,00,000)

0.125

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Thus, we find that the overall cost of capital is 12.5 per cent as per the requirement of the NOI Approach.

In order to examine the effect of leverage, let us assume that the firm increases the amount of debt from Rs 2,00,000 to Rs 3,00,000 and uses the proceeds of the debt to repurchase equity shares. The value of the firm would remain unchanged at Rs 4,00,000, but the equity-capitalisation rate would go up to 20 per cent as shown in Table 5.

TABLE 5 Value of the Firm (NOI Approach)


Overall capitalisation rate (k0) 0.125

Total market value of the firm (V) = EBIT/k0 4,00,000

Total value of debt (B) 3,00,000

Total market value of equity (S) = (V – B) 1,00,000

ke = [(Rs 50,000 – Rs 30,000) / Rs 1,00,000] 0.20

Alternatively: ke = 0.125 + (0.125 – 0.10) (Rs 3,00,000 / Rs 1,00,000) 0.20

k0 = 0.10 (Rs 3,00,000 / Rs 4,00,000) + 0.20 (Rs 1,00,000 / Rs 4,00,000)

0.125

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Let us further suppose that the firm retires debt by Rs 1,00,000 by issuing fresh equity shares of the same amount. The value of the firm would remain unchanged at Rs 4,00,000 and the equity-capitalisation rate would come down to 13.33 per cent as manifested in the calculations in Table 6.

TABLE 6 Total Value of the Firm (NOI Approach)


Overall capitalisation rate (k0) 0.125

Total market value of the firm (V) = EBIT/k0 4,00,000

Total value of debt (B) 1,00,000

Total market value of equity (S) = (V – B) 3,00,000

ke =[(Rs 50,000 - Rs 10,000) / Rs 3,00,000] 0.133

Alternatively: ke = 0.125 + (0.125 – 0.10) (Rs 1,00,000 / Rs 3,00,000) 0.133

K0 = 0.10 (Rs 1,00,000 / Rs 4,00,000) + 0.133 (Rs 3,00,000 / Rs

4,00,000)

0.125

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Market Price of Shares

In example 2, let us suppose the firm with Rs 2 lakh debt has 2,000 equity shares (of Rs 100 each) outstanding. The firm has issued additional debt of Rs 1,00,000 to repurchase its shares amounting to Rs 1,00,000; it has to repurchase 1,000 shares of Rs 100 each from the market. It, then, has 1,000 equity shares outstanding, having total market value of Rs 1,00,000. The market price per share, therefore, is Rs 100 (Rs 1,00,000 ÷ 1,000) as before.

In the second situation the firm issues, 1,000 equity shares of Rs 100 each to retire debt aggregating Rs 1,00,000. It will have 3,000 equity shares outstanding, having total market value of Rs 3,00,000, thus, giving a market price of Rs 100 per share.

Thus, we note that there is no change in the market price per share due to change in leverage.

We have portrayed the relationship between the leverage and the various costs, viz. ki, ke and k0 in Fig. 2.

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The graph is based on Example 2. Due to the assumption that k0 and ki remain unchanged as the degree of leverage changes, we find that both the curves are parallel to the x-axis. But as the degree of leverage increases, the ke increases continuously.

5.0

10.0

15.0

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Degree of Leverage (B/V)

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Traditional ApproachTraditional ApproachThe traditional approach is mid-way between the two extreme (the NI and NOI) approaches. The crux of this approach is that through a judicious combination of debt and equity, a firm can increase its value (V) and reduce its cost of capital (k0) upto a point. However, beyond that point, the use of additional debt will increase the financial risk of the investors as well as of the lenders and as a result will cause a rise in the k0. At such a point, the capital structure is optimum. In other words, at the optimum capital structure the marginal real cost of debt (both implicit and explicit) will be equal to the real cost of equity.

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Example 6

Let us suppose that a firm has 20 per cent debt and 80 per cent equity in its capital structure. The cost of debt and the cost of equity are assumed to be 10 per cent and 15 per cent respectively. What is the overall cost of capital, according to the traditional Approach?

Solution

The overall cost of capital (k0) = ki i.e. 0.10 (20 / 100) + ke i.e. 0.15 (80 / 100) = 14%

Further, suppose, the firm wants to increase the percentage of debt to 50. Due to the increased financial risk, the ki and ke will presumably rise. Assuming, they are 11 per cent (ki) and 16 per cent (ke), the cost of capital (k0) would be: = 0.11 (50 / 100) + 0.16 (50 / 100) = 13.5%

It can, thus, be seen that with a rise in the debt-equity ratio, ke and ki increase, but, k0 has declined presumably because these increases have not fully offset the advantages of the cheapness of debt.

Assume further, the level of debt is raised to 70 per cent of the capital structure of the firm. There would consequently be a sharp rise in risk to the investors as well as creditors. The ke would be, say, 20 per cent and the ki 14 per cent. The k0 = 0.14 (70 / 100) + 0.20 (30 / 100) = 15.8%

The overall cost of capital has actually risen when the firm tries to employ more of what appeared, at the previous debt-equity ratio, to be the least costly source of funds, that is, debt. Therefore, the firm should take into account the consequences of raising the percentage of debt to 70 per cent on the cost of both equity and debt.

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Example 7

Assume a firm has EBIT of Rs 40,000. The firm has 10 per cent debentures of Rs 1,00,000 and its current equity capitalisation rate is 16 per cent. The current value of the firm (V) and its overall cost of capital would be, as shown in Table 12.

TABLE 12 Total Value and Cost of Capital (Traditional Approach)


Less: Interest (I) 10,000

Earnings available to equityholders (NI) 30,000


Total Market value of equity (S) = NI/ke 1,87,500

Total Market value of debt (B) 1,00,000

Total value of the firm (V) = S + B 2,87,500

Overall cost of capital, k0 = EBIT/V 0.139

Debt-equity ratio (B/S) = (Rs 1,00,000 ÷ Rs 1,87,500) 0.53

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The firm is considering increasing its leverage by issuing additional Rs 50,000 debentures and using the proceeds to retire that amount of equity. If, however, as the firm increases the proportion of debt, ki

would rise to 11 per cent and ke to 17 per cent, the total value of the

firm would increase and k0 would decline as shown in Table 13.






Total Market value of equity (S) = NI/ke 1,38,235

Total Market value of debt (B) 1,50,000



Debt-equity ratio (B/S) 1.08

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Let us further suppose that the firm issues additional Rs 1,00,000 debentures instead of Rs 50,000 (that is, having Rs 2,00,000 debentures) and uses the proceeds to retire that amount of equity. Due to increased financial risk, ki

would rise to 12.5 per cent and ke to 20 per cent, the total value of the firm

would decrease and k0 would rise as is clear from Table 14.






Total Market value of equity (S) = NI/ke 75,000

Total Market value of debt 2,00,000



Debt-equity ratio (B/S) (Rs 2,00,000 ÷ Rs 75,000) 2.67

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Increased Valuation and Decreased Overall Cost of Capital

During the first phase, increasing leverage increases the total valuation of the firm and lowers the overall cost of capital. As the proportion of debt in the capital structure increases, the cost of equity (ke) begins to rise as a reflection of the increased financial risk. But it does not rise fast enough to off set the advantage of using the cheaper source of debt capital. Likewise, for most of the range of this phase, the cost of debt (ki) either remains constant or rises to a very small extent because the proportion of debt by the lender is considered to be within safe limits. Therefore, they are prepared to lend to the firm at almost the same rate of interest. Since debt is typically a cheaper source of capital than equity, the combined effect is that the overall cost of capital begins to fall with the increasing use of debt. Example 7 has shown that an increase in leverage (B/S) from 0.53 to 1.08 has had the effect of increasing the total market value from Rs 2,87,500 toRs 2,88,235 and decreasing the overall capitalisation rate from 13.9 to 13.8 per cent.

Constant Valuation and Constant Overall Cost of Capital

After a certain degree of leverage is reached, further moderate increases in leverage have little or no effect on total market value. During the middle range,the changes brought in equity-capitalisation rate and debt-capitalisation rate balance each other. As a result, the values of (V) and (k0) remain almost constant.

The effect of increase in leverage from zero, on cost of capital and valuation of the firm, can be thought to involve three distinct phase.

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Decreased Valuation and Increased Overall Cost of Capital

Beyond a certain critical point, further increases in debt proportions are not considered desirable. They increase financial risks so much that both ke and ki start rising rapidly causing (k0) to rise and (V) to fall. In example 7, the effect of an increase in B/S ratio from 1.08 to 2.67 is to increase (k0) from 13.8 to 14.5 per cent and to decrease (V) from Rs 2,88,235 to Rs 2,75,000.

A numerical illustration, given in Table 15 and its graphic presentation in Fig. 4 further help to clarify the relationship between leverage and cost of capital. They present hypothetical changes similar to those envisaged by the traditional approach and examine the effect of leverage on the individual variables. We have assumed, in addition to other assumptions already stated at the beginning of the chapter, that given capital market conditions, the company can repurchase its own shares. The face value of a share is Rs 10 and that of debentures Rs 100 each. The symbols used in Table 15 have the same meaning as explained at the beginning of the chapter.

Table 15 as well as Fig. 4 reveal that with an increase in leverage (B/V) from zero to 0.27, the market value of the firm increases (from Rs 1,000 to Rs 1,111) and the overall cost of capital declines from 10 to 9 per cent (Phase I). With further increases in leverage from 0.27 up to 0.54, there is no change either in (V) or in (k0); both the values remain constant, that is, Rs 1,111 and 9 per cent respectively (Phase 2). During Phase 3, with an increase in the ratio beyond 0.54 up to 0.79, there is a decrease in market value of the firm (from Rs 1,111 to Rs 1,013) and an increase in (k0) (from 9 to 9.4 per cent), suggesting that the optimal leverage lies within the range of 0.27 to 0.54 debt-equity ratio.

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x

Y

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ki a

nd

k0 (%

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Figure 5: Leverage and Cost of Capital (Traditional Approach)

ke

k0

ki

The traditional view on leverage is commonly referred to as one of ‘U’ shaped cost of capital curve (as shown in Fig. 5). In such a situation, the degree of leverage is optimum at a point at which the rising marginal cost of borrowing is equal to the average overall cost of capital. For this purpose, marginal cost of a unit of debt capital consists of two parts: (i) the increase in total interest payable on debt; (ii) the amount of extra net earnings required to restore the value of equity component to what it would have been under the pre-existing capitalisation rate before the debt is increased.

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Modigliani-Miller (MM) Approach

Modigliani and Miller (MM) concur with NOI and

provide a behavioural 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.

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Basic Propositions

1) The overall cost of capital (k0) and the value of the firm (V) are independent of its capital structure. The k0 and V are constant for all degrees of leverage. The total value is given by capitalising the expected stream of operating earnings at a discount rate appropriate for its risk class.

2) The second proposition of the MM Approach is that the ke is equal to the capitalisation rate of a pure equity stream plus a premium for financial risk equal to the difference between the pure equity-capitalisation rate (ke) and ki times the ratio of debt to equity. In other words, ke increases in a manner to offset exactly the use of a less expensive source of funds represented by debt.

3) The cut-off rate for investment purposes is completely independent of the way in which an investment is financed.

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Assumptions

a) Perfect capital markets: The implication of a perfect capital market is that (i) securities are infinitely divisible; (ii) investors are free to buy/sell securities; (iii) investors can borrow without restrictions on the same terms and conditions as firms can; (iv) there are no transaction costs; (v) information is perfect, that is, each investor has the same information which is readily available to him without cost; and (vi) investors are rational and behave accordingly.

b) 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.

c) Business risk is equal among all firms within similar operating environment. That means, all firms can be divided into ‘equivalent risk class’ or ‘homogeneous risk class’. The term equivalent/homogeneous risk class means that the expected earnings have identical risk characteristics. The dividend payout ratio is 100 per cent.

d) There are no taxes.

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Example 3

Assume there are two firms, L and U, which are identical in all

respects except that firm L has 10 per cent, Rs 5,00,000

debentures. The earnings before interest and taxes (EBIT) of both

the firms are equal, that is, Rs 1,00,000. The equity-capitalisation

rate (ke) of firm L is higher (16 per cent) than that of firm U (12.5 per

cent).

Solution:

The total market values of firms L and U are computed in Table 7.

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TABLE 7 Total Value of Firms L and U

Particulars Firms

L U

EBIT Rs 1,00,000 Rs 1,00,000

Less: Interest 50,000 —

Earnings available to equity-holders 50,000 1,00,000

Equity-capitalisation rate (ke) 0.16 0.125

Total market value of equity (S) 3,12,500 8,00,000

Total market value of debt (B) 5,00,000 —

Total market value (V) 8,12,500 8,00,000

Implied overall capitalisation rate/cost of capital (k0)

= EBIT/V

0.123 0.125

Debt-equity ratio = B/S 1.6 —

Thus, the total market value of the firm which employs debt in the capital structure (L) is more than that of the unlevered firm (U). According to the MM hypothesis, this situation cannot continue 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.

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Arbitrage Process The modus operandi of the arbitrage process is as follows:

Suppose an investor, Mr X, holds 10 per cent of the outstanding shares of the levered firm (L). His holdings amount to Rs 31,250 (i.e. 0.10 × Rs 3,12,500) and his share in the earnings that belong to the equity shareholders would be Rs 5,000 (0.10 × Rs 50,000).

He will sell his holdings in firm L and invest in the unlevered firm (U). Since firm U has no debt in its capital structure, the financial risk to Mr X would be less than in firm L. To reach the level of financial risk of firm L, he will borrow additional funds equal to his proportionate share in the levered firm’s debt on his personal account. That is, he will substitute personal leverage (or home-made leverage) for corporate leverage.

In other words, instead of the firm using debt, Mr X will borrow money. The effect, in essence, of this is that he is able to introduce leverage in the capital structure of the the unlevered firm by borrowing on his personal account. Mr X in our example will borrow Rs 50,000 at 10 per cent rate of interest. His proportionate holding (10 per cent) in the unlevered firm will amount to Rs 80,000 on which he will receive a dividend income of Rs 10,000. Out of the income of Rs 10,000 from the unlevered firm (U), Mr X will pay Rs 5,000 as interest on his personal borrowings. He will be left with Rs 5,000 that is, the same amount as he was getting from the levered firm (L). But his investment outlay in firm U is less (Rs 30,000) as compared with that in firm L (Rs 31,250). At the same time, his risk is identical in both the situations. The effect of the arbitrage process is summarised in Table 8.

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TABLE 8 Effect of Arbitrage

(A) Mr X’s position in firm L (levered) with 10 per cent equity-holding

(i) Investment outlay Rs 31,250

(ii) Dividend Income 5,000

(B) Mr X’s position in firm U (unlevered) with 10 per cent equity holding

(i) Total funds available (own funds, Rs 31,250 + borrowed funds, Rs 50,000)

81,250

(ii) Investment outlay (own funds, Rs 30,000 + borrowed funds, Rs 50,000) 80,000

(iii) Dividend Income:

Total Income (0.10 × Rs 1,00,000) Rs 10,000

Less: Interest payable on borrowed funds 5,000 5,000

(C) Mr X’s position in firm U if he invests the total funds available

(i) Investment costs 81,250.00

(ii) Total income 10,156.25

(iii) Dividend income (net) (Rs 10,156.25 – Rs 5,000) 5,156.25

It is, thus, clear that Mr X will be better off by selling his securities in the levered firm and buying the shares of the unlevered firm.

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Arbitrage Process:

Reverse Direction According to the MM hypothesis, since debt

financing has no advantage, it has no disadvantage either. In other

words, just as the total value of a levered firm cannot be more than

that of an unlevered firm, the value of an unlevered firm cannot be

greater than the value of a levered firm. This is because the arbitrage

process will set in and depress the value of the unlevered firm and

increase the market price and, thereby, the total value of the levered

firm. The arbitrage would, thus, operate in the opposite direction.

Example 4

Assume that in Example 3, the equity-capitalisation rate (ke) is 20 per

cent in the case of the levered firm (L), instead of the assumed 16

per cent. The total values of the two firms are given in Table 9.

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TABLE 9 Total Value of Firms L and U

Particulars L U

EBITLess: InterestIncome to equity holdersEquity-capitalisation rate (ke)Market value of equityMarket value of debtTotal value (V)(k0)B/S

Rs 1,00,00050,00050,000

0.202,50,0005,00,0007,50,000

0.1332

Rs 1,00,000 —

1,00,0000.125

8,00,000 —

8,00,0000.125

0

Since both firms are similar, except for financing-mix, a situation in which their total values are different, cannot continue, as arbitrage will drive the two values together.

Suppose, Mr Y has 10 per cent shareholdings of firm U. He earns Rs 10,000 (0.10 × Rs 1,00,000). He will sell his securities in firm U and invest in the undervalued levered firm, L. He can purchase 10 per cent of firm L’s debt at a cost of Rs 50,000 which will provide Rs 5,000 interest and 10 per cent of L’s equity at a cost of Rs 25,000 with an expected dividend of Rs 5,000 (0.10 × Rs 50,000). The purchase of a 10 per cent claim against the levered firm’s income costs Mr Y only Rs 75,000, yielding the same expected income of Rs 10,000 from the equity shares of the unlevered firm. He would prefer the levered firm’s securities as the outlay is lower. Table 10 portrays the reverse arbitrage process.

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TABLE 10 Effect of Reverse Arbitrage Process

(A) Mr Y’s current position in firm U

Investment outlay Rs 80,000

Dividend income 10,000

(B) Mr Y sells his holdings in firm U and purchases 10 per cent of the levered firm’s equity and debentures

Investment Income

Debt Rs 50,000 Rs 5,000

Equity 25,000 5,000

Total 75,000 10,000

Y would prefer alternative B to A, as he is able to earn the same income with a smaller outlay.

(C) He invests the entire sum of Rs 80,000 in firm L

Investment Income

Debt Rs 53,333.00 Rs 5,333.30

Equity 26,667.00 5,333.40

Total 80,000,00 10,666.70

He augments his income by Rs 666.70.

The above illustrations establish that the arbitrage process will make the values of both the firms identical. Thus, Modigliani and Miller show that the value of a levered firm can neither be greater nor smaller than that of an unlevered firm; the two must be equal

© Tata McGraw-Hill Publishing Company Limited, Financial Management © Tata McGraw-Hill Publishing Company Limited, Financial Management © Tata McGraw-Hill Publishing Company Limited, Financial Management © Tata McGraw-Hill Publishing Company Limited, Financial Management 19-19-4040

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SOLVED PROBLEMSSOLVED PROBLEMS

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SOLVED PROBLEM 1

Company X and Company Y are in the same risk class, and are identical in every respect except that company X uses debt, while company Y does not. The levered firm has Rs 9,00,000 debentures, carrying 10 per cent rate of interest. Both the firms earn 20 per cent operating profit on their total assets of Rs 15 lakhs. Assume perfect capital markets, rational investors and so on; a tax rate of 35 per cent and capitalisation rate of 15 per cent for an all-equity company.

(a)Compute the value of firms X and Y using the Net Income (NI) Approach.

(b)Compute the value of each firm using the Net Operating Income (NOI) Approach.

(c)Using the NOI Approach, calculate the overall cost of capital (k0) for firms

X and Y.

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Solution

(a) Valuation under NI approach

Particulars Firm X Firm Y

EBITLess: InterestTaxable incomeLess: TaxesEarnings for equity holdersEquity capitalisation rate (ke)Market value of equity (S)Market value of debt (B)Total value of firm (V)

Rs 3,00,00090,000

2,10,00073,500

1,36,5000.15

9,10,0009,00,000

18,10,000

Rs 3,00,000 —3,00,0001,05,0001,95,000 0.15

13,00,000 —

13,00,000

cent per 15 yoK Similarly,

cent per 12.1 16,15,000Rs

7,15,000Rs0.191ek

16,15,000 Rs

9,00,000 Rs.065dkoxK (c)

16,15,000 Rs (0.35) 9,00,000 Rs 13,00,000 Rs XV

13,00,000 Rs0.150.35-13,00,000 Rs

YV

ApproachNOI under Valuation(b)

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Working Notes

EBIT Rs 3,00,000

Less: Interest 90,000

Taxable income 2,10,000

Less: Taxes 73,500

NI 1,36,500

V as determined in (ii) 16,15,000

B 9,00,000

S (V – B) 7,15,000

Ke = (Rs 1,36,500/Rs 7,150,000) = 19.1 per cent or ke = k0 + (k0 – kd) B/S

= 12.1% + (12.1% - 6.5%) 9,00,000 / 7,15,000 = 19.1%

kd = 0.10 (1–0.35) = 6.5 per cent

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SOLVED PROBLEM 2

The two companies, U and L, belong to an equivalent risk class. These two firms are identical in every respect except that U company is unlevered while Company L has 10 per cent debentures of Rs 30 lakh. The other relevant information regarding their valuation and capitalisation rates are as follows:

Particulars Firm U Firm L

Net operating income (EBIT) Rs 7,50,000 Rs 7,50,000

Interest on debt (I) — 3,00,000

Earnings to equityholders (NI) 7,50,000 4,50,000

Equity-capitalisation rate (ke) 0.15 0.20

Market value of equity (S) 50,00,000 22,50,000

Market value of debt (B) — 30,00,000

Total value of firm (S + B) = V 50,00,000 52,50,000

Implied overall capitalisation rate (k0) 0.15 0.143

Debt-equity ratio (B/S) 0 1.33

(a) An investor owns 10 per cent equity shares of company L. Show the arbitrage process and the amount by which he could reduce his outlay through the use of leverage.

(b) According to Modigliani and Miller, when will this arbitrage process come to an end?

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Solution

(a) Arbitrage process

(i) Investor’s current position (in firm L)

Dividend income Rs 45,000

Investment cost 2,25,000

(ii) He sells his holdings of firm L for Rs 2,25,000 and creates a personal leverage by borrowing Rs 3,00,000 (0.10 × Rs 30,00,000 debt of firm L).

The total amount with him is Rs 5,25,000. Income required to break even would be:

Dividend income (L firm) 45,000

Interest on personal borrowing (0.10 × Rs 3,00,000) 30,000

75,000

(iii) He purchases 10 per cent equity holdings of the firm U for Rs 5,00,000.

Dividend income (U firm) (0.10 × Rs 7,50,000) 75,000

Amount of investment 5,00,000

He will reduce his outlay by Rs 25,000 through the use of leverage.

(b) According to Modigliani and Miller, this arbitrage process will come to an end when the values of both the firms are identical.

capital structure and valuation

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