Modigliani and Miller (MM) Approach | Proposition I | Proposition II | Arbitrage Theory (Criticism of Net Income and Traditional Approach) | MM approach With Tax | Capital Structure Theories
Modigliani and Miller Theory
Table of Contents
Modigliani and Miller commonly known as MM theory is most acceptable and widely used capital structure theory which support NOI approach and criticize the Net Income theory and Traditional theory of capital structure. Franco Modigliani and Merton Miller jointly worked on this theory originally published in 1958 entitled “The cost of capital, Corporation finance and the theory of Investment”, received Noble Prize for their contribution. They argue cost of capital and value form remains constant irrespective of change in capital structure.
MM approach theory of capital structure is categorized as proposition I and proposition II.
Proposition I
The market value of any firm is independent of its capital structure and is given by capitalizing its expected return at the overall capitalization rate appropriate to its risk class.
This theory also based on assumptions, and those assumptions are as follows;
- Similar nature firms have similar operating risk
- All earnings are distributed as dividend.
- No existence of tax.
- Rational Investors.
- Perfect capital market where no transaction cost exists and investors freely can sell and buy the securities.
On the basis of above mentioned assumptions, it can be concluded that in perfect capital market, without tax and bankruptcy cost value of firm is invariant with the capital structure. The value of firm is the function of earning power and risk involved in investment rather than the capital structure. Based on above mentioned assumptions, it can be concluded as;
Value of levered firm (V_{L} ) = Value of Unlevered firm ( V_{U}) = NOI /Ks(U)
Where,
- NOI= Net Operating Income
- Ks(U) = Cost of equity of Unlevered firm
Value of Unlevered firm and levered firm should be equal because there is no existence of tax and no tax saving. The value of firm depends on underlying profitability and risk rather than structure. If value of unlevered firm and levered firm is not equal arbitrage will occur and again reach to balanced state.
Proposition II
The expected yield of a share is equal to the appropriate capitalization rate for a pure equity stream in the class plus a premium related to financial risk equal to the debt to equity ratio times the spread between pure equity capitalization rate and debt capitalization rate.
According to this theory cost of equity linearly increase as debt ratio increase. So, Cost of equity of levered firm is greater than the cost of equity of unlevered firm. Levered equity has greater risk; it should have a greater expected return as compensation. It can be presented as;
Ke(L) + Ke(U) + [Ke(U) – Kd](B/S)
Where,
- Ke(L) = Cost of Levered equity
- Ke(U) = Cost of unlevered equity
- Kd = cost of debt
- B/S = the debt equity ratio
Numerical Illustration
Two companies Apple and Samsung are Identical in every respect that Apple is unlevered and Samsung has 5 lakha of 6 percent bonds outstanding. Assume (1) that all of MM assumptions are met, (2) that there are no corporate and personal taxes, (3) EBIT is Rs 2 lakh and, (4) that the Cost of equity of Apple is 10 percent.
- What would MM estimate for each firm?
- What is the value of Ks for Apple and Samsung Company?
- What is the WACC for Apple and Samsung Company?
Solution:
Unlevered firm (Apple) | Levered firm (Samsung) | |
Debt | Rs.5,00,000 | |
Cost of debt | 6% | |
Cost of equity | 10% | |
EBIT | Rs.2,00,000 | Rs. 2,00,000 |
a. Calculation of value of each firm
Value of unlevered and levered firm = EBIT / Ks(U) = 200000/0.10 = Rs. 20,00,000
b. Calculation of cost of equity(Ks) for each firm
- Cost of equity for Apple Ks (U) = 10%
- Cost of equity for Samsung Ks(L) = Ks(U) + [Ks(U) –Kd] *Debt equity ratio
= 10% + [10%-6%] * (500000 /1500000) = 11.33%
c. Calculation of overall cost of capital or WACC
- Overall cost of capital (K_{o}) = EBIT / V = 200000 / 2000000 = 10%
Arbitrage Theory (Criticism of Net Income and Traditional Approach)
MM approach suggest that if the value of firm differs due to capital structure only there exists arbitrage opportunity. It means that in this situation Investors can get opportunity to earn same level of return at remaining same level of financing risk and control position but with low investment from overvalued firm to undervalued firm. It can be illustrated by following example.
Net Income and Traditional approach assume that value of levered firm (Over Valued) is greater than value of unlevered firm (Under Valued)
Unlevered firm XYZ | Levered firm ABC | |
Operating Income (EBIT) | Rs 2,00,000 | Rs 2,00,000 |
Debt | Rs 5,00,000 | |
Cost of Equity( Ke) | 10% | 10% |
Cost of debt (Kd) | 6% | 6% |
Market Value of Equity (S) | Rs. 20,00,000 | Rs. 17,00,000 |
Value Of firm (V) | Rs 20,00,000 | Rs 22,00,000 |
WACC (Ko) | 10% | 9.09% |
Debt equity ratio | 0 | 0.2941 |
undervalued | Overvalued |
Suppose Shyam has Rs. 17,000 worth investment in overvalued firm ABC. Show how Shyam could earn arbitrage benefit from shifting his investible fund from overvalued firm to undervalued firm.
Solution
Arbitrage Process
Step 1: Shyam sells the shares of overvalued firm ABC worth Rs 17,000 (i.e. 17000/1700000= 1% of holding)
Step 2: To maintain same level of financial risk Shyam creates home leverage and borrow worth Rs. 5,000. (i.e. 1% of Rs 5, 00,000)
Working Note: debt equity ratio = debt / equity
0.2941 = Debt /17000
Debt = Rs. 5000
Step 3: Shyam purchase the stock of undervalued firm XYZ maintaining the same control position as it was overvalued firm ABC.
1% of Rs. 20, 00,000 = Rs. 20,000 (debt = Rs 5,000 and equity = Rs15,000)
Note; Shyam has still additional equity fund remaining worth Rs. 2000. Arbitrage profit = Incremental profit without risk.
Step 4: Profitability position (personal)
Firm ABC | Firm XYZ | ||
Net income ( 17000 x 0.10) | Rs 1700 | EBIT (20000*0.10) | Rs2000 |
Less: Interest (5000*0.06) | Rs.300 | ||
Net Income | Rs.1700 | Net Income | Rs.1700 |
Equity Investment | Rs.17000 | Equity Investment | Rs.15000 |
Due to arbitrage opportunity the value of overvalued firm gradually decrease and value of undervalued firm gradually increases.
M & M Tax
MM approach suggest that if there is tax the firm using leverage can get tax advantage because interest in tax deductible expenses that save tax for corporation. Due to this tax saving, the value of levered firm is greater than of unlevered firm. When tax is exists value of levered firm is equal to value of unlevered firm plus tax advantage. There are different types taxes so, equilibrium position are also different according to tax nature of tax like corporate tax, personal tax.
Equilibrium Position; Value of levered firm = Value of unlevered firm +Tax saving (D*Tc) |
When there is only corporate tax
If there is only corporate tax value of levered firm increases linearly with the leverage ratio as tax saving increase. It suggests that if there is corporate tax maximum debt should be used so that value of firm is maximum.
Value of unlevered firm (Vu) = EBIT(1-T) /Ks(U)
Value of levered firm (VL) = Vu + PV of Tax saving (D*t)
Cost of levered equity (Ks(L)) = Ks(u) – [Ks(u) –Kd](1-T) debt equity ratio
If there is both personal and corporate tax
Value of unlevered firm (Vu) = EBIT(1-T) / Ks(U)
Value of levered firm (VL) = Vu + PV of Tax saving
Where, PV of Tax saving = D[ {(1-T_{c})(1-T_{ps})}/(1-T_{pd}]
MM Approach with tax and bankruptcy cost
Uses of debt save tax and increase the value of firm but excessively use of debt creates financial burden. Interest should be paid according to pre-specified terms and conditions in timely manner. If firm is not able to satisfy its bonds and debenture holders than firm may suffer from financial distress and that financial distress may leads to bankruptcy. Bankruptcy cost is indirect and direct administrative cost that may be opportunity cost and cost of reorganization incurred during bankruptcy auction caused by excess use of debt. Bankruptcy cost offsets the benefit of tax saving. When we consider the bankruptcy cost value of levered firm can be calculated as ;
V(L) = V(U) + BTc –PV of bankruptcy cost.
Where,
- V(L) = Value of levered firm
- V(U) = Value of unlevered firm
- Btc = Present value of tax saving