Question

The Star Company has a WACC of 20%. The cost of debt is 12%, which is equal to the risk-free rate of interest. If Star’s debt to equity ratio is 2, Star’s equity beta is 1.5.

1. What are the M&M propositions I, II and III, please use graphs/charts and words to explain. (7marks)
2. Based on the M&M proposition II, what is the beta of the entire firm? What is the cost of equity capital?

Answer 1

Modigilani prepositions

1) value of a firm is not affected by its level of leverage i.e. value of levered firm V(L) is equal to the value of unlevered firm V(U)

V(L)=V(U)

2) overall cost i.e. WACC or( Ko )of a firm remains unchanged irrespective of the level of debt. why? Because if the level of debt rises ,equity shareholders would feel insecured to Address this they would have to be offered a higher cost of equity (Ke) and since debt's rate is lower but weight is higher but equity's rate is higher and weight is lower so overall cost of capital Ko will remain same.

Ke = Ko + (Ko-Kd)D/E

Where

Ke =cost of equity

Ko= cost of overall capital = intercept of line = constant

Kd= cost of debt

D/E= debt equity ratio

These two prepositions are based on the following assumptions:( some are realistic some are not)

1) there are no taxes(unrealistic)

2) there are no transaction cost and bankruptcy cost (unrealistic)

3)symmetry of information i.e. every one has the access of same information ( may be realistic in today's digital world)

4)there is no floatation cost like underwriting commission ,merchant banker fees etc.( unrealistic)

5) cost of borrowing is same for all investors ( unrealistic)

6)No corporate dividend tax( may be possible in same countries)

because most if these assumptions were unrealistic MM developed a new preposition which violated one of his assumptions of no taxes .let us see what is that.

Preposition 3

In case there are taxes ,then value of a levered firm will be higher than the value of an unlevered firm and the difference between these two would be the interest tax shield which the levered firm will enjoy.

V(L)>V(U)

V(L)= V(U)+Pv of ITS

Where Pv of ITS = Debt ×tax rate

The graphs are shown below

in the graph of preposition 3 we can see after the optimal debt level value of firm is declining this is because bankruptcy cost is getting higher than tax shield benifits which cause danger to the solvency of the firm.

Part b

New cost of equity for the levered firm as per preposition 2

Ke = Ko +(Ko-Kd)D/E

Where Ko = 20% overall cost of an unlevered firm which aslo the old Ke since an unlevered firm's capital is all equity i.e. debt equity ratio D/E= 0

Kd = cost of debt=12% which is also the risk free rate rf

D/E= 2

Equity beta (Be)= 1.5

New cost of equity Ke = 20+(20-12)×2= 36%

As per CAPM

Ke= rf + MRP×Be

rf =12%

MRP= market risk premium =???

Be = 1.5

Old Ke =20%

20= 12 +MRP×1.5

MRP= 5.333%

new beta

36= 12 +MRP× new beta

SINEC MRP= 5.333%

24= 5.333×new beta

New beta= 4.5

It can also be calculated by using

Beta(L) = beta(U)×(1+D/E)

= 1.5×(1+2)=4.5