11, 12, BBA, BCom, MBA, CA, UGC and UPSC- Notes, Project Report, Case Study and Assignment solution: MM hypothesis

Links to Financial Management notes: -
Time Value of Money
https://gyanvikalpa.blogspot.com/2021/06/time-value-of-money-solved-problems-pdf.html
Leverage Analysis
https://gyanvikalpa.blogspot.com/2021/08/financial-management-notes-leverage.html
Cost of Capital
https://gyanvikalpa.blogspot.com/2021/08/cost-of-capital-solved-problems.html
EBIT – EPS Analysis
https://gyanvikalpa.blogspot.com/2021/08/ebit-eps-analysis-financial-break-even.html
Capital Structure Analysis
https://gyanvikalpa.blogspot.com/2022/02/capital-structure-theories-and-solved.html
Estimation of Cash Flow in Capital Budgeting
https://gyanvikalpa.blogspot.com/2021/06/cash-flow-estimation-in-capital.html
Techniques of Capital Budgeting

https://gyanvikalpa.blogspot.com/2021/06/techniques-of-capital-budgeting-solved.html

Capital Structure Theories and Solved Problems

Leverage, Cost of Capital and Firm Value

Value of Firm

The value of a firm depends on the earnings of the firm and the earnings of the firm depend upon the investment decisions of the firm. The earnings of the firm are capitalized at a rate equal to the cost of capital in order to find out the value of the firm. Thus, the value of the firm depends on two basic factor ie, the earnings of the firm and the cost of capital.

Value of Firm = Value of Equity + Value of Debt

NI Approach

There is a relationship between capital structure and the value of the firm. The firm can affect its value by increasing or decreasing the debt proportion in overall financing mix.

Assumptions of NI Approach

· Cost of Debt (K_d) is less than Cost of Equity (K_e).

· Value of Firm remains constant.

· K_dand K_eremains constant. Increase in financial leverage (increase in debt in financing mix) does not impact risk perception of investors and K_eremains constant in case of increase in debt.

· Increase in debt will lead to decrease in overall cost of capital and increase in value of the firm.

· Higher the degree of leverage, better it is, as the value of the firm would be higher. In other words, a firm can increase its value just by increasing the debt proportion in the capital structure.

· Value of firm = Value of Debt + Value of Equity

· K_d = Interest / Value of Debt

· K_e= EBT or EAT / Value of equity

· K₀= EBIT / Value of Firm

· K₀ = (D/V) × K_d + (E/V) × K_e

The NI approach, though easy to understand is too simple to be realistic. It ignores, perhaps the important aspects of leverage that the market price depends upon the risk which varies in direct relation to the change in proportion of debt in the capital structure.

NOI Approach

The Net Operating Income (NOI) approach is opposite to NI approach. This is also known as Independence Hypothesis. According to the NOI approach, the market value of the firm depends upon the net operating profit or EBIT and the over cost of capital, WACC. The financing mix or the capital structure is irrelevant and does not affect the value of the firm.

Assumptions of NOI Approach

· Overall cost of capital (K₀) remains constant.

· Cost of Debt (K_d) is constant.

· Increase in debt increases risk perception of shareholders resulting into increase in cost of equity (K_e) and offsetting the benefits of low cost debt into capital structure thus keeping overall cost of capital and value of firm (V) constant at any level of Debt – equity mix in its financing structure.

· There is no tax.

· The NOI approach is based on the argument that the market values the firm as a whole for a given risk complexion. Thus, for a given value of EBIT, the value of the firm remains same irrespective of the capital composition and instead depends on the overall cost of capital.

The value of the Equity may be found by deducting the value of debt from the total value of the firm i.e.

V = EBIT ÷ K₀

E = V – D

K_e= (EBIT – I) ÷ (V - D)

The NOI approach considers overall cost of capital (K₀), to be constant and therefore, there is no optimal capital structure; rather every capital Structure is as good as any other one and every capital structure is optimal one.

Traditional Approach

The Traditional view states that value of firm increases with increase in financial leverage but up to a certain limit only. Beyond this limit, the increase in financial leverage will increase its WACC and value of firm will decline.

Cost of debt (K_d) is assumed to be less than the cost of equity (K_e). In case of 100% equity firm, overall cost of capital (K₀) is equal to the Cost of Equity (K_e), but when cheaper debt is introduced in the capital structure and financial leverage increases, K_e remains same as the shareholders expect a minimum leverage in every firm. K_e does not increase even with increase in leverage. The argument for K_e remaining unchanged may be that up to a particular degree of leverage, the interest charge may not be large enough to pose a real threat to the dividend payable to the shareholders. This constant K_e and K_d makes K₀ to fall initially reflecting benefits of cheaper debts available to the firm.

The increase in leverage beyond a limit increases risk of equity investors also resulting into increase in K_e. However, the benefits of use of debt may be so large that even after offsetting the effects of increase in K_e, K₀ may still go down or may become constant for some degree of leverages.

If firm increases the leverage further, then the risk of debt investor may also increase and consequently K_dalso starts increasing. The already increasing K_e and now increasing K_e, makes K₀ to increase. Therefore, the useof leverage beyond a point will have the effect of increasein overall cost of capital of the firm and decrease in value of firm.

MODIGLIANI-MILLER MODEL: BEHAVIOURAL JUSTIFICATION OF NOI APPROACH

MM Model shows that the financial leverage does not matter and the cost of capital and value of firm are independent of capital structure. There is nothing which may be called the optimal capital structure, they have, in fact, restated the NOl approach and have added to it the behavioural justification for this model.

Assumptions of MM Model

· The capital markets are perfect and complete.

· information is available to all the investors free of cost. The implication of this assumption is that investors can borrow and lend funds at the same rate and can move quickly from one security to another without incurring any transaction cost.

· The securities are infinitely divisible.

· Investors are rational and well informed about the risk return of all the securities.

· All investors have same probability distribution about expected future earnings.

· There is no corporate income-tax. (However, this assumption was relaxed later).

· The personal leverage and the corporate leverage are perfect substitute.

On the basis of these assumptions, the MM Model derived that -

(a) The total value of the firm is equal to the capitalized value of the operating earnings of the firm. The capitalization is to be made at a rate appropriate to the risk class of the firm.

(b) The total value of the firm is independent of the financing mix i.e. the financial leverage.

(c)The cut-off rate for the investment decision of the firm depends upon the risk class to which the firm belongs and thus is not affected by the financing pattern of this investment.

MM Model can be discussed in terms of two propositions I and II.

MM Proposition I:

Proposition I states that it is completely irrelevant how a firm arranges its capital funds.

MM model argues that if two firms are alike in all respect except that they differ in respect of their financing pattern and their market value, then the investors will develop a tendency to sell the shares of the overvalued firm (creating selling pressure) and to buy the shares of the undervalued firm (creating a demand pressure). This, buying and selling pressures will continue till the two firms have same market values.

The Arbitrage Process

The arbitrage process refers to undertaking by a person of two related actions or steps simultaneously in order to derive some risk- less benefit e.g, buying by a speculator in one market and selling the same at the same time in some other market; or selling one type of investment and investing the proceed in some other investment. The profit or benefit from the arbitrage process may be in any form: increased income from the same level of investment or same income from lesser investment. This arbitrage process has been used by MM to testify their hypothesis of financial leverage, cost of capital and value of the firm.

MM Proposition II

Proposition II states that the cost of equity depends upon three factors i.e. overall cost of capital of the firm, cost of debt and the firm's debt equity ratio. In MM model, there is a linear relationship between the cost of equity and the leverage (as measured by the Debt-equity ratio D/E). When the leverage is increased, the earnings available for the equity shareholder will increase, but the cost of equity will also increase as a result of increase in financial risk. The benefits of increasing leverage are completely offset by the increase in cost of equity capital and consequently the market value of the firm remains same.

As per MM model:

K_e = K₀ + (K₀ - K_d) × D/E

As per MM model, the overall cost of capital (K₀) will not rise even if the degree of financial leverage is increased.

Under MM Model, the value of levered firm is found out as follows:

V_u = EBIT (1- t )/ K₀ or K_e

V_L = V_u + Debt × tax rate

V_L = V_u + PV of Interest Tax shield

MM Model without Taxes

· Firm's capital structure is irrelevant.

· WACC is same no matter what mixture of debt and equity is used to finance the firm.

· Total value of the firm is independent of level of debt in the capital structure, and the value can be calculated by capitalizing the operating profit at appropriate rate. The value of the levered firm is equal to the value of the unlevered firm, and

K_e = K₀ + (K₀ - K_d) × D/E

MM Model with Taxes

· The value of the levered firm is equal to the value of unlevered firm + the present value of the interest tax shield, i.e.

V_L = V_u + Debt × tax rate

· The WACC of the firm decreases, as the firm relies more and more on debt financing.

K_e = K₀ + (K₀ - K_d) × D/E

Or K_e = K₀ + (K₀ - K_d) × D (1 – t )/E

K₀ is the WACC of the unlevered firm.

1. The expected EBIT of a firm is Rs. 5,00,000. It has issued Equity Share capital with K_e @ 20% and 10% Debt of Rs. 10,00,000. Find out the value of the firm and the overall cost of capital, WACC using NOI Approach.

Solution

Particulars	Amount (Rs.)
EBIT	5,00,000
Less: Interest	(1,00,000)
EBT / PAT	4,00,000
K_e	0.2
Value of Equity = PAT / K_e	4,00,000/.2 = 20,00,000
Value of Debt	10,00,000
Value of Firm (V)= Value of Debt + Value of Equity	30,00,000
WACC (K₀) = EBIT / V	5,00,000 / 30,00,000 = .1667or 16.67%
WACC = (D/V × K_d) + (E/V × K_e)	(10,00,000 / 30 × .1) + (20,00,000/30,00,000 ×.2) = .1667 = 16.67%

2. A firm has an EBIT of Rs. 4,00,000 and belongs to a risk class of 10 %. What is the value of cost of equity capital if it employs 8% debt to the extent of 30%, 40% or 50% of the total capital fund of Rs. 15,00,000.

Solution

	30% Debt	40% Debt	50% Debt
Value of Debt (D)	4,50,000	6,00,000	7,50,000
K₀(WACC)	0.1	0.1	0.1
EBIT	4,00,000	4,00,000	4,00,000
Value of Firm	40,00,000	40,00,000	40,00,000
Value of Equity (E)	35,50,000	34,00,000	32,50,000
Int.	(36,000)	(48,000)	(60,000)
PAT = EBIT – Int.	3,64,000	3,52,000	3,40,000
K_e = PAT / E	.1025	.1035	.1046

3. RBL Ltd. having an EBIT of Rs.2,00,000 is contemplating to redeem a part of the capital by introducing debt financing. Presently, it is a 100% equity firm with equity capitalization rate, K_e of 20%. The firm is to redeem the capital by introducing debt financing up to Rs.4,00,000 i.e., 40% of total funds or up to Rs. 5,00,000 i.e., 50% of total funds. It is expected that for debt financing up to 30%, the rate of interest will be 10% and K_e will increase to 21%. However, if the firm opts for 50 % debt financing, then interest will be payable at the rate of 12% and the K_e will be 24%. Find out the value of the firm and its WACC under different levels of debt financing.

Solution

On the basis of the information given, the total funds of the firm seems to be of Rs.10,00,000 (whole of which is provided by the equity capital) out of which 40% or 50% i.e. 4,00,000 or 5,00,000 may be replaced by the issue of debt bearing interest at 10% or 12% respectively, value of firm and WACC is calculated as follows:

	0 % Debt	40% Debt	50% Debt
Value of Debt (D)	-----	4,00,000	5,00,000
Interest rate	-----	10%	12%
EBIT	2,00,000	2,00,000	2,00,000
Less: Int.	-----	(40,000)	(60,000)
EBT or NP	2,00,000	1,60,000	1,40,000
K_e	.2	.21	.24
Value of Equity (E) = NP ÷ K_e	10,00,000	7,61,905	5,83,333
Value of Firm (V) = E + D	10,00,000	11,61,905	10,83,333
WACC (K₀) = EBIT ÷ V	0.2	0.1721	0.1846

4. A Ltd. and B Ltd. are in the same risk class and are identical in all respects except that company A uses debt while company B does not use debt. The levered firm has Rs. 10,00,000 debentures carrying 10% rate of interest. Both the firms earn 20% operating profit on their total assets of Rs. 20,00,000. The company is in the tax bracket of 50% and capitalization rate of 15% on all equity shares.

Solution

Particulars	A Ltd	B Ltd
Total Assets	20,00,000	20,00,000
Operating Profit	20 %	20 %
EBIT	4,00,000	4,00,000
Less: Interest	(1,00,000)
EBT	3,00,000	4,00,000
Less: Tax @ 50%	(1,50,000)	(2,00,000)
PAT	1,50,000	2,00,000
K_e	.15	.15
Value of Equity (K_e) = PAT ÷ K_e	10,00,000	13,33,333
Value of Debt (D)	10,00,000	-------
Total Value of Firm (V) = D + E	20,00,000	13,33,333

5. RBL Steel Ltd. has employed 15% debt of Rs. 15,00,000 in its capital structure. The net operating income of the firm is Rs. 6,00,000 and has an equity capitalization rate of 20%. Assuming that there is no tax, find out the value of the firm under the NI Approach.

Solution

Net operating income (EBIT)	6,00,000
Less: Interest on Debt (15 % of 15,00,000)	(2,25,000)
EBT or Net Profit (NP)	3,75,000
Equity Capitalization rate (K_e)	20%
Value of Equity = NP ÷ K_e(3,75,000 ÷ .2)	18,75,000
Value of Debt	15,00,000
Total value of the firm	33,75,000

6. RBL Ltd. belongs to a risk class of 12 % and expects EBIT of Rs. 5,00,000. It employs 10 % debt in the capital structure. Find out the value of the firm and cost of equity capital K_e. If it employs debt to the extent of 30%, 40% or 50% of the total financial requirement of Rs.20,00,000.

Solution

	30 % Debt	40% Debt	50% Debt
Debt (D)	6,00,000	8,00,000	10,00,000
Interest rate	.1	.1	.1
EBIT	5,00,000	5,00,000	5,00,000
Less: Int.	(60,000)	(80,000)	(1,00,000)
EBT or NP	4,40,000	4,20,000	4,00,000
K₀	.12	.12	.12
Value of Firm (V) = EBIT ÷ K₀	41,66,667	41,66,667	41,66,667
Value of Equity (E) = V – D	35,66,667	33,66,667	31,66,667
K_e = NP ÷ E	.1234	.1248	.1263

7. The net operating profit of a firm is Rs. 3,00,000 and the total market value of its 12% debt is Rs. 5,00,000. The equity capitalization rate of an unlevered firm of the same risk class is 20 %. Find out the value of the levered firm given that the tax rate is 50% for both the firms.

Solution

Value of Unlevered firm = [EBIT × (1- t )] ÷ K_e

= [3,00,000 × (1 – 0.5) ] ÷ .15

= 1,50,000 ÷ .2 = Rs. 7,50,000

Value of Levered Firm = Value of Unlevered firm + (D × t)

=> Rs. 7,50,000 + (Rs.5,00,000 × .5) = Rs.10,00,000

8. ABC Ltd. with EBIT of Rs. 5,00,000 is evaluating a number of possible capital structures, given below. Which of the capital structure will you recommend and why?

Capital Structure	Debt	K_d %	K_e %
I	3,00,000	11	12
II	4,00,000	11	15
III	5,00,000	12	16
IV	6,00,000	13	17

Solution

In this case, the K_d and K_e, of the firm are given and changing. The firm may adopt that capital structure which has the least overall cost of capital or the maximum value. The overall cost of capital, K₀ of the firm may be calculated by applying the traditional approach as follows:

K₀= EBIT ÷ Value of Firm

Value of Firm = V

Value of Equity (E) = Net Profit ÷ K_e

Value of Debt = D

Particulars	Plan I	Plan II	Plan III	Plan IV
EBIT	5,00,000	5,00,000	5,00,000	5,00,000
Less: Int.	(33,000)	(44,000)	(60,000)	(78,000)
Net Profit	4,67,000	4,56,000	4,40,000	4,22,000
K_e	.12	.15	.16	.17
E	38,91,667	30,40,000	27,50,000	24,82,355
D	3,00,000	4,00,000	5,00,000	6,00,000
V	41,91,667	34,40,000	32,50,000	30,82,355
K₀	.1193	.1453	.1538	.1622

The capital structure of Plan I is having Rs. 3,00,000 of debt and has the lowest overall cost of capital and consequently the highest market value. Hence Plan I should be accepted.

9. Two companies are identical except that A Ltd. has a debt of Rs. 15,00,000 at 10% whereas B Ltd. does not have debt in its capital structure. The total assets of both the companies A and B are same i.e. Rs. 30,00,000 on which each company earns 20 % return. Find the value of each company and overall cost of capital using net operating income (NOI) Approach. Equity capitalisation rate for B Ltd. is 15%. The tax rate is 50%.

Solution

NOI Approach with Taxes:

EBIT = 20 % of Rs. 30,00,000 = Rs. 6,00,000

Value of B Ltd (Unlevered) = [EBIT × (1- t)] ÷ K_e

=> [6,00,000 × (1 – 0.5 )] ÷ .15

=> 20,00,000

Value of A Ltd (Levered) = Value of Unlevered firm + (D × t)

=> Rs. 20,00,000 + (Rs.15,00,000 × .5) = Rs.27,50,000

10. RBL Ltd. has Earnings before Interest and Taxes (EBIT) of Rs. 6,00,000. The firm currently has outstanding debts of Rs. 15,00,000 at an average cost, K_d of 10%. Its cost of equity capital K_e is estimated to be 20 %.

i. Determine the current value of the firm using the Traditional valuation approach.

ii. Determine the firm's overall capitalization rate, K_0.

iii. The firm is considering to issue capital of Rs. 10,00,000 in order to redeem Rs. 10,00,000 debt. The cost of debt is expected to be unaffected. However, the firm's cost of equity capital is to be reduced to 16% as a result of decrease in leverage. Would you recommend the proposed action?

Solution

EBIT	6,00,000
Less: Int.	(1,50,000)
EBT or Net Income	4,50,000
K_e	0.2
Value of Equity (E)= Net Income ÷ K_e	22,50,000
Value of Debt (D)	15,00,000
i. Value of Firm (V) = D + E	37,50,000
ii. Overall Capitalization rate (K₀) = EBIT ÷ V	0.16

iii. Effect of Proposed redemption of debt:

EBIT	6,00,000
Less: Int.	(50,000)
EBT or Net Income	5,50,000
K_e	0.16
Value of Equity (E)= Net Income ÷ K_e	34,37,500
Value of Debt (D)	5,00,000
Value of Firm (V) = D + E	39,37,500
Overall Capitalization rate (K₀) = EBIT ÷ V	0.1524

The proposal should be accepted as it will increase value of firm from Rs. 37,50,000 to Rs. 39,37,500. The cost of capital will also reduce from 16 % to 15.24%.

11. The following estimates of the cost of debt and cost of equity capital have been made at various level of the debt-equity mix for ABC Ltd.

% of Debt	Cost of Debt K_d (%)	Cost of Equity K_e (%)
0	6	12
10	6	12
20	6	13
30	7	14
40	8	15
50	9	16
60	10	20

Assuming no tax, determine the optimal debt equity ratio for the company on the basis of the overall cost of capital, WACC.

Solution

Overall Cost of Capital = (D/V) × K_d + (E/V) × K_e

V = Value of Firm or Total Capital = 100%

E = Percentage of Debt in total capital = 100% – Debt Percentage

D = Percentage of Debt in total capital

D (%)	E (%)	K_d	K_e	D/V	E/V	K₀
0%	100%	.06	.12	0	1	.12
10%	90%	.06	.12	.1	.9	.114
20%	80%	.06	.13	.2	.8	.116
30%	70%	.07	.14	.3	.7	.119
40%	60%	.08	.15	.4	.6	.122
50%	50%	.09	.16	.5	.5	.125
60%	40%	.10	.20	.6	.4	0.14

The optimal debt equity mix for the company occurs at a point when the overall cost of capital (K₀) is minimum. K₀ is minimum at a point when the debt is 10 % of the total capital employed and equity is 90 %. Therefore, the firm should use 10% debt and 90% equity in its capital structure.

12. The following information is available for RBL Ltd. and Gyan Ltd in respect of their present position. Compute the equilibrium values (V) and equity capitalization rate of the two companies, assuming (i) there is no income tax, and (ii) the overall rate of capitalization (K₀) for such companies in the market is 16%.

	RBL Ltd	Gyan Ltd
EBIT	2,00,000	2,00,000
Less: Int. @10%	(50,000)	------
Net Income for Equity Shareholders	1,50,000	2,00,000
Equity Capitalization rate (K_e)	.15	.13
Market Value of Equity (E)	15,00,000	16,00,000
Market Value of Debt (D)	5,00,000	------
Total Value of Firm	20,00,000	16,00,000
Overall Cost of Capital (K₀) = EBIT ÷ Total Value of Firm	.1	.125

Solution:

In order to find out the equilibrium value of the firm, the EBIT of both the firm should be capitalised at K₀ and then it will be bifurcated into value of debt and value of equity as follows:

	RBL Ltd	Gyan Ltd
EBIT	2,00,000	2,00,000
Overall capitalization K₀	.16	.16
Total value of the firm (equilibrium values)	12,50,000	12,50,000
Less: Market value of the Debt	(5,00,000)	-----
Market value of Equity, E	6,50,000	12,50,000
Earnings for Equity holders (NP)	1,50,000	2,00,000
K_e (Equity Capitalization Rate) = NP ÷ E	.2308	.16

13. Following is the data regarding two companies X and Y belonging to the same risk class:


No. of Equity Shares	1,00,000	1,50,000
Market Price per Share	15	10.5
10 % Debentures	1,00,000	-----
Profit before Interest	2,50,000	2,50,000

All profits after debenture interest are distributed as dividends. Explain how under Modigliani & Miller approach, an investor holding 10% of shares in Company X will be better off in switching his holding to Company Y.

Solution

Both the firms have EBIT of Rs. 25,000. Company X has to pay interest of Rs. 10,000 (i.e. 10% on Rs.1,00,000) and the remaining Profit of 15,000 is being distributed among the shareholders. Company Y, on the other hand, has no interest liability and therefore, is distributing Rs. 25,000 among the shareholders. The investor will be well off under MM model, by selling shares of X and shifting to shares of Y Company through the arbitrage process as follows:

If he sells shares of company X, he gets Rs. 1,50,000, (10,000 shares @ Rs. 15 per share). He now takes a 10% loan of Rs. 10,000 (i.e. 10 % of Rs. 1,00,000) and out of the total cash of Rs.1,60,000, he purchase 10 % of shares of Company Y for Rs. 1,57,500. His position with regard to income from Company X and Company Y would be as follows:

	Company X	Company Y
Dividend (10% of Profit)	24,000	25,000
Less: Interest (10 % on Rs. 10,000)	---	(1,000)
Net Income	24,000	24,000

Thus, by shifting from Company X to Company Y, the investor is able to get same income of Rs. 24,000 and still having funds of Rs. 10,000 (i.e., Rs. 1,60,000 – Rs. 1,57,500) at his disposal. He is better off, not in terms of income, but in terms of having capital funds of Rs. 2,500 with him, which he can invest elsewhere.

14. From the following selected data, determine the value of the firms, P and Q belonging to the homogeneous risk class.

	Firm A	Firm B
EBIT	3,00,000	3,00,000
Interest @ 15%	75,000
Equity capitalization rate, K_e or K₀		20%
Corporate Tax	50%

Which of the two firms has an optimal capital structure under NOI approach?

Solution:

Valuation of the firm (Net Operating Income approach with Tax):

The NOI approach is based on the assumptions that there is no tax. However, in the present case, both the firms have tax liability @ 50%. So, their valuation may be found by applying MM model (with taxes) which is an extension of NOI approach. Under the MM Model, the value of levered firm is taken as equal to the value of unlevered firm plus the premium for interest tax shield on debt financing.

V_L= V_U + (Debt × tax rate)

V_L= Value of Levered Firm = Firm A

V_U = Value of Unlevered Firm = Firm B

In case of Unlevered firm, K_e = K₀

V_U (Firm B) = [EBIT × (1 – t)] ÷ K₀

=> [3,00,000 × (1 – .5)] ÷ .2 = Rs. 7,50,000

V_L(Firm A) = V_U + (Debt × tax rate)

=> 7,50,000 + (5,00,000 × .5) = Rs.10,00,000

Value of Debt of Firm A = Interest amount ÷ Pre Tax Cost of debt => 75,000 ÷ .15= Rs. 5,00,000

Post Tax Cost of Debt = Pre Tax Cost of debt × (1 – tax rate) => .15 × .5 = .075

Value of Equity of Firm A = Value of Firm A – Value of Debt = Rs. 10,00,000 – Rs.5,00,000 = Rs. 5,00,000

Cost of Equity (K_e) = PAT ÷ Value of Equity

=> [(3,00,000 – 75,000)× (1- 0.5)] ÷ 5,00,000

=> 1,12,500 ÷ 5,00,000 = .225

WACC (K₀) = D/V × Post tax K_d + E/V × K_e

=> (5,00,000 / 10,00,000) × .075 + (5,00,000 / 10,00,000) × .225 = .15 = 15 %

Second Method:

WACC = [EBIT (1 – t)] ÷ Value of Firm A

=> 1,50,000 ÷ 10,00,000 = 0.15 or 15 %

WACC of firm A is 15 %. Firm A has optimal Capital structure as it is having higher total Firm value than value of Firm B and lower overall cost of capital than Firm B.

15. Companies U and L are identical in every respect except that the former does not use debt in its capital structure, while the latter employs Rs. 6,00,000 of 10% debt. Assuming that all MM assumptions are met, corporate tax rate is 50%, EBIT being Rs. 4,00,000, and equity capitalization of the unlevered company is 20%, what will be the value of the firms, U and L ? Also determine the weighted average cost of capital for both the firms.

Solution

V_L= V_U + (Debt × tax rate)

V_L= Value of Levered Firm = Firm L

V_U = Value of Unlevered Firm = Firm U

In case of Unlevered firm, K_e = K₀

V_U (Firm B) = [EBIT × (1 – t)] ÷ K₀

=> [4,00,000 × (1 – .5)] ÷ .2 = Rs. 10,00,000

V_L(Firm A) = V_U + (Debt × tax rate)

=> 10,00,000 + (6,00,000 × .5) = Rs.13,00,000

Overall cost of Capital (K₀)of Unlevered firm = 20% = 0.2

Calculation of overall Cost of Capital (K₀) of Levered Firm:

EBIT	4,00,000
Less: Interest	(60,000)
EBT	3,40,000
Less: Tax @ 50%	(1,70,000)
PAT	1,70,000
Total Value of Levered Firm	13,00,000
Less: Value of Debt (D)	(6,00,000)
Value of Equity (E)	7,00,000
Cost Of Equity (K_e) = PAT ÷ E	1,70,000 ÷ 7,00,000 = .2429
K₀ = EBIT (1 – t ) ÷ Value of Firm	2,00,000 ÷ 13,00,000 = .1538
Or K₀= (D/V × Post Tax K_d) + (E/V × K_e) = (6L / 13 L × 0.05) + (7L / 13 L × .2429)	.1538

16. The expected annual net operating income of a company is Rs. 15,00,000. The company has Rs. 60,00,000, 10% debentures. The overall cost of capital is 12.5%. Calculate the value of the firm and cost of equity according to NOI Approach. If the company increases the debt from Rs. 560,00,000 to Rs. 70,00,000, what would be the value of the firm?

Solution

EBIT	15,00,000
WACC (K0)	.125
Value of Firm(V)= EBIT ÷ K0	1,20,00,000
Value of Debt (D)	60,00,000
Value of Equity (E) = V – D	60,00,000
Ke = (EBIT – Int.) ÷ E	9,00,000 ÷ 60,00,000 = 0.15
If Debt increases to Rs. 70,00,000
Value of Firm(V)= EBIT ÷ K0	1,20,00,000
Value of Debt (D)	70,00,000
Value of Equity (E) = V – D	50,00,000
Ke = (EBIT – Int.) ÷ E	8,00,000 ÷ 50,00,000 = 0.16

So, as per NOI, the value of the firm remains at Rs. 1,20,00,000 but the value of equity decreases to Rs. 50,00,000. Consequently, K_e also increases from 15 % to 16 %.

17. Two companies V and L, belong to same risk class. These two firms are identical in all respect except that V company is unlevered while Co. L has 10% debentures of Rs. 5,00,000. The other relevant data regarding their valuation and capitalisation rates are as follows:


EBIT	1,00,000	1,00,000
Less: Interest	50,000
Earnings available to Equity-holders	50,000	1,00,000
Equity capitalisation rate	0.16	0.125
Market value of Equity	3,12,500	8,00,000
Market value of Debt	5,00,000
Total Market value	8,12,500	8,00,000
Overall Cost of Capital (K₀)	0.123	0.125
Debt-Equity Ratio	1.6	----

i. An investor owns 10% equity shares of company L. Show the arbitrage process and amount by which he could reduce his outlay through the use of leverage.

ii. According to Modigliani and Miller, when will this arbitrage process come to an end?

Solution

Arbitrage Process by Investor:
Sale of 10% Equity Shares in L Ltd.		31,250
Add: 10% Loan (equal to 10% of Rs. 5,00,000)		50,000
Total Funds		81,250
Less: Purchase of 10% Equity of V Ltd.		(80,000)
Capital funds saved		1,250
Analysis of Income Position
	L Ltd		V Ltd
Dividend	5,000		10,000
Less: Interest Payable			(5,000)
Net Income	5,000		5,000

So, through arbitrage (sale of equity shares of L and buying Equity Shares of V), the investor can reduce his outlay by Rs. 1,250 and still getting same income of Rs. 5,000. The arbitrage process will come to an end when the difference in value of L and V comes to zero.

18. Two companies, X and Y belong to equivalent risk group. The two companies are identical in every respect except that company Y is levered, while X is unlevered. The outstanding amount of debt of the levered company is Rs. 5,00,000 in 10% debenture. The other information for the two companies is as follows:

	X	Y
EBIT	1,70,000	1,70,000
Less: Interest	______	(50,000)
Earnings to Equity Holders	1,70,000	1,20,000
Equity Capitalization Rate (K_e)	.17	.20
Market Value of Equity (E)	10,00,000	6,00,000
Market Value of Debt (D)	______	5,00,000
Total Value of Firm (V)	10,00,000	11,00,000
Overall capitalization rate K₀ = EBIT / V	.17	.1545
Debt Equity Ratio	0	1

An investor owns 5% equity shares of company Y. Show the process and the amount by which he could reduce his outlay through use of arbitrage process? Is there any limit to the process?

Solution

Current position of investor in Firm Y:

Dividend Income = 5 % of 1,20,000 = Rs. 6,000

Market Value of Investment = 5 % of 6,00,000 = Rs. 30,000.

He sells his holdings in Firm Y and creates a personal leverage by borrowing Rs. 25,000 (5 % of Rs.5,00,000).

Total amount with him now = Rs. 25,000 + Rs.30,000 = Rs.55,000.

Now, he purchase 5 % equity in Firm X by investing Rs.50,000 (5 % of Rs.10,0000).

Now his position with respect to income in both companies:

	X	Y
Dividend (5% of Profit)	8,500	6,000
Less: Interest 10% of 25,000	(2,500)	_________
Net Income	6,000	6,000

Investor has saved Rs. 5,000 (55,000 – 50,000) using leverage and continues to earn same earnings as before. Remaining Rs.5,000 can be invested somewhere to increase earnings.

Yes, there is limit to arbitrage process. It comes to an end when market value of both firms remain same

19. Firms A and B are similar except that A is unlevered while B has Rs.2,00,000 of 5% debentures outstanding. Assume that the tax rate is 50 %, NOI is Rs. 50,000 and cost of equity is 10 %.

i. Calculate the value of the firm, if the MM assumptions are met.

(ii) If the value of the firm B is Rs. 3,60,000 then do these values represent equilibrium values. If not, how will equilibrium be set? Explain.

Solution

I. Value of Unlevered Firm A (V_A) = EBIT (1 – t ) / K_e or K₀

= 50,000 (1 – 0.5 ) / 0.1 = 2,50,000

Value of Levered Firm B = V_A + Debt × tax rate

=2,50,000 + 2,00,000 × .5 = Rs. 3,50,000

II. Value of Firm B is given Rs. 3,60,000 however it came Rs. 3,50,000 as calculated above which indicates that it does not represent equilibrium value and Firm B is overvalued by Rs. 10,000.

Arbitrage process to restore equilibrium:

	Firm B
Value of Firm as given (V)	3,60,000
Value of Debt D	2,00,000
Value of Equity E = V - D	1,60,000
EBIT	50,000
Less: Interest (5% of 2,00,000)	(10,000)
EBT	40,000
Less Tax @ 50%	(20,000)
PAT	20,000

Assuming an investor owns 10 % of firm B shares. His investment is-

10 % of 1,60,000 = Rs.16,000

And Return on investment is 10 % of 20,000 = Rs.2,000.

The investor can get same income by shifting his investment to Firm A.

He sells his holdings in Firm B and creates a personal leverage by borrowing Rs. 10,000 (10% of Rs.2,00,000 × (1 – tax rate)).

Total amount with him now = Rs. 16,000 + Rs.10,000 = Rs.26,000.

Now, he purchase 10 % equity in Firm A by investing Rs.25,000 (10 % of Rs.2,50,000).

Now his position with respect to income in both companies:

Net profit of Firm A = EBIT (1 – t ) = 50,000 × .5 = 25,000

	A	B
Dividend (10% of Profit)	2,500	2,000
Less: Interest 5% of 10,000	(500)	_________
Net Income	2,000	2,000

Investor has saved Rs. 1,000 (26,000 – 25,000) using leverage and continues to earn same earnings as before. Remaining Rs.1,000 can be invested somewhere to increase earnings. This process will continue till equilibrium is restored.

20. Two companies, L and U belong to the same risk class. The two firms are identical in every respect except that company L has 10% debentures. The valuation of the two firms as per the Traditional theory is as follows:

	L	U
Net Operating Income (EBIT)	22,50,000	22,50,0000
Less: Interest	(1,50,000)	------
Earnings to Equity holders	21,00,000	22,50,000
Equity capitalization rate (K_e)	.15	.12
Market value of Equity	1,40,00,000	1,87,50,000
Market value of Debt	15,00,000	________
Total Value of Firm (V)	1,55,00,000	1,87,50,000
Overall Capitalization Rate K₀ = EBIT ÷ V	14.52%	12%
Debt Equity Ratio	.1071	----------

Show the arbitrage process by which an investor having shares worth Rs.18,75,000 in company U will be benefited by switching over to company L.

Solution

Investors total worth of Equity share in Company U = 18,75,000 / 1,87,50,000 = 0.1 = 10 %

Dividend Income = 10 % of Rs. 22,50,000 = Rs. 2,25,000

Now in arbitrage process, he sells his investment from U Ltd of Rs. 18,75,000 and makes investment in 10 % equity of L Ltd of Rs. 14,00,000. He also invests Rs.1,50,000 i.e. 10% of Rs. 15,00,000 in 10 % interest bearing Debt of L Ltd.

As a result of this investment, his income would be as follows:

=>Dividend income + Interest income = Rs.2,25,000

Dividend income = 10 % of Rs.21,00,000 = Rs.2,10,000

Interest income = 10 % of Rs. 1,50,000 = Rs.15,000

Thus, investor is able to maintain same level of earning with a saving of fund of Rs. 3,25,000 (18,75,000 – 14,00,000 – 1,50,000) through arbitrage process.

21. ABC Ltd. has the required rate of return of 15% on its assets. It can borrow in the market @ 10%. Assuming MM model (without taxes), what would be the cost of equity of the firm, if it has target capital structure of 80% equity or 50% equity?

Solution

As per MM proposition II, cost of equity (K_e) is –

K_e = K₀ + (K₀ - K_d) × D/E

If equity is 80 %

= .15 + (.15 - .1) × (.2/.8) = .1625

If equity is 50 %

= = .15 + (.15 - .1) × (.5/.5) = .2

22. Following information is available in respect of L Ltd. and U Ltd.

	L Ltd	U Ltd
EBIT	15,00,000	15,00,000
Less: Interest @ 10 %	(2,50,000)	_______
EBT	12,50,000	15,00,000
Less: Tax @ 50 %	(6,25,000)	(7,50,000)
PAT	6,25,000	7,50,000

Show and verify that value of levered firm is equal to value of unlevered firm plus PV of tax shield on interests. Use MM Model (with taxes), given the k. for U Ltd. is 20%.

Solution

In case of U Ltd, K_e or K₀ is 20% and EBIT is 15,00,000. So, value of Equity or value of firm is-

V_u = EBIT (1- t )/ K_e

= 15,00,000 × (1 - .5 ) / .2 = 37,50,000

As per question:

V_L = V_u + PV of Interest Tax shield

= 37,50,000 + (2,50,000 × .5) / .1

= 50,00,000

As per MM model

V_L = V_u + Debt × tax rate

= 37,50,000 + (2,50,000/.1) × .5

= 50,00,000