In this essay we will discuss about the alternative capital structure theory regarding financial leverage of a company.

Modigliani and Miller offered an alternative theory of capital structure. They published theoretical papers that changed the way people thought about financial leverage. They won Nobel prizes in economics because of their work. MM’s papers were published in 1958 and 1963. Miller had a separate paper in 1977. This paper differed in assumption about taxes.

MM proposition:

1. Firms can be grouped into homogeneous classes based on business risk.


2. Investors have identical expectations about firms’ future earnings.

3. There are no transactions costs.

4. All debt is riskless, and both individuals and corporations can borrow unlimited amounts of money at the risk-free rate.

5. All cash flows are perpetuities. This implies perpetual debt is issued, firms have zero growth, and expected PBIT is constant over time.


6. There is no tax.

Proposition I:

VL = VU. VL = Value of levered firm, VU = Value of unlevered firm

To prove this proposition Modigliani and Miller provided arbitrage support theorem.


Arbitrage Support for Proposition I:

Consider two companies identical in all respects except that Company U is not levered but Company L is levered. Shareholders of the levered company will demand higher return as compensation of higher financial risk undertaken by the company.

KeL > KeU

In a no tax regime, Profit Before Tax (PBT) becomes the Profit Available to Equity Shareholders. In an unlevered firm PBIT = PBT as there is no interest.

PBTL< PBTU as PBTL = PBIT – Interest whereas PBIT-Interest whereas PBTU = PBIT-0.

this situation may arise if KeL is not appropriate. See Illustration 1 wherein it has been assumed that KeU = 12% and KeL = 13.5%. By this VL = Rs.170.37 million but Vu = Rs.166.27 million.


Illustration 1:

Total capital employed in both the companies is Rs.100 million. Company L has 6% Debt of Rs.40 million in its capital structure. Assume that cost of unleverd equity is KeU = 12% and KeL = 13.5%.

MM contended that this position cannot continue; arbitrage will drive the total values of the two firms together:


1. B cannot command a higher value simple because of financing mix.

2. By investing in A, investors of B are able to obtain the same dollar with no increase in financial risk.

Let us take an example.

Suppose a rational investor holds 10% equity of L market value of which is Rs.13.037 million. He may sell such equity holding. He can borrow Rs.4 million @ 6% which is equal to 10% of the debt of Company L. The assumption is that there is no difference in the borrowing rates for an individual and a company. So the investor replicated leverage of Com­pany L in his personal finance. Now he has Rs.17.037 million with him. But to buy 10% of equity he needs only Rs.16.667 million!


Prior to these transactions, return on investment in Company L was Rs.1.76 million.

His return on investment after levered investment will be:

a) An investor will prefer to invest in A because of lower investment coupled with personal leverage.

b) The action of a number of investors undertaking similar arbitrage transaction will tend drive up the price of A, lowers its Ke and drive down the price of B, increases its Ke.

c) This will continue until there is no further opportunity for reducing investment outlay. At this equilibrium total value of two firms must be the same.


Therefore, VU should be equal to VL. What will make this possible? This will be possible only if the KeL is set at a reasonable level. The equity shareholders of levered company cannot demand any higher return whatever they like.

Proposition II:

KeL = KeU + (KeU – kd)(D/E).

KeL = Cost of levered equity

KeU = Cost of unlevered equity

D/E = Debt – equity ratio

Let us another illustration.

Illustration 2:

Continue with the data given in Illustration 1.

Since Vu = VL therefore, VL as per Illustration 1 = Rs.166.27 million VL= Value of Equity (S) + Value of Debt (D) E = VL – D = Rs.166.27 Million – Rs.40 Million = Rs.126.67 Million.

If you now compute WACC for levered firm, you will get 12%

WACC = Cost of Debt × D/VL + Cost of Equity × E/VL 

= 6% × (40/126.67) + 13.89% × (60/126.67) = 12%

Therefore, WACC of levered and unlevered firms remains the same. It is not affected by leverage. In other words, choice of debt – equity ratio (financing mix) does not have any impact on WACC and on the value of the firm. Thus there is no relevance of capital structure planning. Now check the valuation Table given in Illustration 1 as modified below by cost of equity at 13.89% which makes the value of the companies equal:

See Figure below which depicts the MM theory of capital structure in no tax regime.

Conclusions of Modigliani and Miller theory:

a) The more debt the firm adds to its capital structure, the riskier the equity becomes and thus the higher its cost.

b) Although kd remains constant, ke increases with leverage. The increase in ks is exactly sufficient to keep the WACC constant.

However, this theory has limited applicability because of its restrictive assumptions. In particular assumption of no tax regime makes the MM theory impractical. Therefore, Miller in a subsequent paper re-explained the theorem assuming a tax regime.

Miller Proposition with Tax – With corporate taxes added, the MM propositions become:

Proposition I:

VL= Vu + TD, T = Tax rate, D = Debt

Proposition II:

ksL = ksU + (ksU – kd)(1 – T)(D/S).

1. When corporate taxes are added,

VL ≠ VU. VL increases as debt is added to the capital structure, and the greater the debt usage, the higher the value of the firm.

2. ksL increases with leverage at a slower rate when corporate taxes are considered.

Let us take an illustration.

Illustration 3:

Total capital employed in both the companies is Rs.100 million. Company L has 6% Debt of Rs.40 million in its capital structure. Assume that cost of unlevered equity is KeU =12% and KeL =13.89%. These are in fact data given in Illustration 1 and cost of equity decided in Illustration 2. Tax rate is 30%.

Given corporate tax, Value of equity = PAT/Ke

Now you may observe that equilibrium value of the unlevered and levered companies achieved in Illustration 2 is lost. Again, value of levered company becomes greater than the value of unlevered com­pany. Tax advantage has created this value. Check that levered company has lesser tax obligation than the unlevered company.

Vu + TD = Rs.116.67 Million + 40 Million × 30% = Rs.116.67 Million + 12 Million = Rs.128.67 Million.

Thus VL > V U and VL – Vu= TD = Value of tax advantage.

With tax advantage, WACCu > WACCL

ksL = ksU + (ksU – kd)(1 – T)(D/S)

= 12% + (12% – 6%) × (1 – .3) × (40/88.67)

= 13.89%, i.e. cost of equity remain unchanged which is expected because book value of debt and equity remains at the same level.

Now let us Calculate WACC:


12% > 11.44%

See the figure given below which illustrates graphically Miller’s revision to Modigliani and Miller theory.

Thus with the availability of tax advantage, WACC reduces continuously as debt equity ratio increases.

In fact, the fallacy of the Miller’s revision is that he computed cost of equity ignoring the market risk factor. Hamada has given the best solution for computing cost of levered and unlevered equity. In case cost of levered equity is computed properly taking into account market risk factor and cost debt is not kept constant across the debt equity ratio, WACC will not fall continuously as has been proposed by Miller. Logically, higher borrowing will increase interest rate.

Therefore, it is advisable to moderate Modigliani and Miller theory with practical data input.