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Monday, January 28, 2013


Total Marks
Starting Date
Monday, January 28, 2013
Closing Date
Wednesday, January 30, 2013
Capital Structure

Learning objective
The purpose of this GDB is to learn the implications of capital restructuring under Modigliani & Miller (M&M) proposition.

Learning Outcomes
After attempting the GDB, students will be able to analyze the impact of restructuring on weighted average cost of capital under different circumstances.  

Suppose you are a financial analyst of ABC Company which was 100% equity financed with net worth of Rs. 10 million and Weighted Average Cost of Capital of 22%. 
Management of the company has decided to change its capital structure by adding Rs. 4 million in debt at 14% cost of debt. Net income and cost of equity were Rs. 2,040,000 and 16.4% respectively after this restructuring. Moreover, Tax rate is 30%.

A.       Keeping in view the Modigliani & Miller (M&M) theorem, you are required to calculate:
                             i.      WACC of levered firm by ignoring tax.
                              ii.      WACC of levered firm by considering tax.

B.       On the basis of above calculation you are required to prove that M&M proposition are applied or not. Justify your answer with logical reasoning.


Solution IDEA :

A calculation of a firm's cost of capital in which each category of capital is proportionately weighted. All capital sources - common stock, preferred stock, bonds and any other long-term debt - are included in a WACC calculation. All else equal, the WACC of a firm increases as the beta and rate of return on equity increases, as an increase in WACC notes a decrease in valuation and a higher risk.

The WACC equation is the cost of each capital component multiplied by its proportional weight and then summing:

WACC = (E/V)*Re + (D/V)*Rd * (1-Tc)

Re = cost of equity
Rd = cost of debt
E = market value of the firm's equity
D = market value of the firm's debt
V = E + D
E/V = percentage of financing that is equity
D/V = percentage of financing that is debt
Tc = corporate tax rate

Businesses often discount cash flows at WACC to determine the Net Present Value (NPV) of a project, using the formula:

NPV = Present Value (PV) of the Cash Flows discounted at WACC.


Broadly speaking, a company's assets are financed by either debt or equity. WACC is the average of the costs of these sources of financing, each of which is weighted by its respective use in the given situation. By taking a weighted average, we can see how much interest the company has to pay for every dollar it finances.

A firm's WACC is the overall required return on the firm as a whole and, as such, it is often used internally by company directors to determine the economic feasibility of expansionary opportunities and mergers. It is the appropriate discount rate to use for cash flows with risk that is similar to that of the overall firm.

WACC = RD (1- Tc )*( D / V )+ RE *( E / V )

rD = The required return of the firm's Debt financing
This should reflect the CURRENT MARKET rates the firm pays for debt. calculates the cost of debt as the firm's total interest payments diveded by the firm's average debt over the last year.

(1-Tc) = The Tax adjustment for interest expense
Interest paid on debt reduces Net Income, and therefore reduces tax payments for the firm. This value of this 'interest tax shield' depends on the firm's tax rate. We calculate the tax rate as the firm's total Taxes divided by pre-Tax income for the last 3 years.

(D/V) = (Debt/Total Value)

rE= the firm's cost of equity
The firm's cost of equity is best (or, at least, most easily) calculated using the CAPM (Capital Asset Pricing Model).
Cost of Equity rE = rf + β(rM - rf) where...
rf = the 'Risk Free' rate of return
β = the firm's 'Beta'; the correlation between the firm's returns and the market
rM = the historical "Market" return
(E/V) = (Equity/Total Value)

(E/V) = (Equity/Total Value)
The % of the firm's value that is comprised of Equity. This is based on the firm's intra-day market cap (stock price x shares outstanding).


If you read the chapter on Weighted Average Cost of Capital (WACC), you know that the best capital structure for a corporation is when the WACC is minimized. This is partly derived from two famous Nobel prize winners, Franco Modigliani and Merton Miller who developed the M&M Propositions I and II.

M&M Proposition I

M&M Proposition I states that the value of a firm does NOT depend on its capital structure. For example, think of 2 firms that have the same business operations, and same kind of assets. Thus, the left side of their Balance Sheets look exactly the same. The only thing different between the 2 firms is the right side of the balance sheet, i.e the liabilities and how they finance their business activities.


M&M Proposition II

M&M Proposition II states that the value of the firm depends on three things:

1) Required rate of return on the firm's assets (Ra)
2) Cost of debt of the firm (Rd)
3) Debt/Equity ratio of the firm (D/E)

If you recall the tutorial on Weighted Average Cost of Capital (WACC), the formula for WACC is: WACC = [Rd x D/V x (1-5)] + [Re x E/V]

The WACC formula can be manipulated and written in another form:Ra = (E/V) x Re + (D/V) x Rd

The above formula can also be rewritten as:Re = Ra + (Ra - Rd) x (D/E)

This formula #3 is what M&M Proposition II is all about.



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  2. 1)WACC of levered firm by ignoring tax.
    WACC=(E/V) * re + (D/V) * rd
    WACC=(10,000,000/14,000,000 )*16.4%+ (4,000,000 / 14,000,000 )* 14 %
    WACC = 15.6%
    2) WACC of levered firm by considering tax.
    WACC = (E/V) * re + (D/V) * rd * (1-Tc)
    WACC = (10,000,000 / 14,000,000 ) * 16.4% + (4,000,000 / 14,000,000 )* 14 % *(1-30%)
    WACC = 14.4%

  3. Net worth mean ka matlab hai total Asset hai 1000000 ok jin MAY 400000 KAY DEBT hai to equity hue simple 600000 ok ab clear hai
    E = 10,000,000
    D = 4,000,000
    V= 10,000,000 + 4,000,000
    V= 14,000,000
    Re= 16.4 %
    Rd= 14 %
    Tc= 30%
    Put these values in these formulas ok
    WACC of levered firm by ignoring tax:
    WACC = E / V * Re + D / V * Rd
    WACC of levered firm by considering tax:
    WACC = E / V * Re + D / V * Rd * (1 – Tc)

  4. 1st to solve ho gya...

    2nd ka koi logic bta do...

    book ma M&M proposition kon se page pr hai???

  5. 15.56 without tax
    14.39 with tax
    Now please anybody tell me
    M&M proposition are applied or not

  6. E = Rs.600000
    D = Rs.400000
    V= 600000+400000=Rs.1000000
    Re= 16.4 % and Rd= 14 % and Tc= 30%
    WACC of levered firm by ignoring tax:
    WACC = E / V * Re + D / V * Rd
    WACC = 0.154 => 15.4%
    WACC of levered firm by considering tax:
    WACC = E / V * Re + D / V * Rd * (1 – Tc)
    WACC = 13.7%

  7. GDB OF MGT201
    rd = 14%
    NI = 2040000
    re = 16.4%
    debt = D = 4000000

    Equity = NI/re
    =2040000/0.164 = 12439024
    VL = Equity + Debt
    =12439024 + 4000000

    WACCL = r DL (1 – Tc) Xd +...

  8. mgt201 gdb current solution 2013
    E = 10000000
    D = 4000000
    V= 10000000 + 4000000
    V= 14000000
    re= 16.4 %
    rd= 14 %
    Tc= 30%

    WACC of levered firm by ignoring tax:
    WACC = E / V * Re + D / V * Rd
    WACC = 2040000* 0.164 + 4000000 * 0.14
    WACC of levered firm by considering tax:
    WACC = E / V * Re + D / V * Rd * (1 – Tc)
    WACC = 2040000* 0.164 + 4000000 * 0.14*(1-0.30)

  9. Application of M&M Proposition:
    The M&M proposition is applicable as WACC is less when the company uses debt in its capital structure due to nonpayment of tax on interest payments. If only tax payments are kept in mind, the company should prefer to raise debt capital.

  10. E = 10000000
    D = 4000000
    V= 10000000 + 4000000
    V= 14000000
    Re= 16.4 %
    Rd= 14 %
    Tc= 30%
    Put the Values in Formula:

    WACC of levered firm by ignoring tax:
    WACC L = E / V * Re + D / V * Rd
    WACCL = 6000000/10000000* 16.4%+ 4000000/10000000 * 14%
    WACCL =15.44%

    WACC of levered firm by considering tax:
    WACCL = E / V * Re + D / V * Rd * (1 – Tc)
    WACC L= 6000000/10000000* 16.4% + 4000000/10000000 * 14 %*( 1-30%)
    =0.6*16.4%+0.4*14 %( 1-0.3)
    =0.6*16.4%+0.4*14 %( 0.7)
    = 9.84%+3.92%
    WACC L =13.76%

    In my point of view ABC Company should consider M&M proposition because they use capital 14% cost of debt. Also one of the reason tax payments

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