Question

You are currently an investor in ABC Company that earns an EBIT of $ 10,000 each year. The firm’s total assets are currently worth $ 80,000. 30% of the firm’s assets are currently funded by debt at a cost of 8%. There are totally 1000 shares outstanding of which you own 10 shares. In the recent board meeting, the executives have come up with the decision to push the firm’s leverage to 45% by replacing suitable amount of equity with debt. Suppose there are no taxes, the firm’s WACC is 10%, and you can lend/borrow at 8%, prove that increasing leverage is a value neutral proposition for you.

Answer 1

The proof is a direct result of Modigliani Miller theorem without taxes.

Modigliani Miller theorem states that in the absence of taxes, bankruptcy costs, agency costs and asymmetric information and in an efficient market, the value of the firm is unaffected by how the firm is financed.

It is commonly referred to as the capital structure irrelevance principle.The value of the firm remains the same regardless of the capital structure.

Proof:-

Using Modigliani Miller proposition 2 without taxes,

The old WACC eith a capital structure of 30% debt ,70% equity would be

0.3*r-d +0.7*r-e------------------------(1)

And from MM proposition 2

R-e = R-o+0.3/0.7(R-o - R-d)------(2)

Where R-e is the levered cost of equity

R-o is the unlevered cost of equity

R-d is the cost of debt

Substituting (2) in (1)

WACC = 0.3*r-d + 0.7*(R-o+0.3/0.7(R-o - R-d))

=0.3*r-d+0.7*r-0+0.3*r-0-0.3*r-d = r-o

When the capital structure changes to debt of 45% qnd equity of 55%

WACC = 0.45*r-d +0.55*r-e---------------(3)

Also by MM proposition 2

r-e = r-o+0.45/0.55(r-o - r-d)---------------------(4)

substtutng (4) in (3)

WACC = 0.45*r-d +0.55*(r-o+0.45/0.55(r-o - r-d)) = 0.45*r-d + 0.55*r-o+0.45*r-o-0.45*r-d = 0.55r-o + 0.45r-o = r-o

In both the cases WACC is the same as r-o

So, when we do the valuation and find the market price of the share

The simplest way would be to find the discounted valuation, which would need EBIT and WACC as the major inputs in the simplest case, and as shown before WACC remains unchanged as well as the EBIT is assumed to be $1000 every year.

This means that the valuation would yield the same value regardless of the capital structure. Also, given that there have been no stock splits or rights issue, the number of shares owned remain the same.

The same number of shares and the same market price would yield no change in value and thus increasing leverage becomes a value neutral proposition.