Capital Structure and the Cost of Capital: TheoryChapter 13 :Financial Theory and Corporate Policy (Copeland and Weston) INTRODUCTION
In the summary of the following chapter is shown the mixture of the financial source of a company. There are the sources of debt and equity but also the financing affects of the cost of capital. Furthermore, it shows its connections to the shareholder's wealth and how to calculate the cost of capital in a specific situation where the risk is depending from the case.
THE VALUE OF THE FIRM GIVEN CORPORATE TAXES ONLY
THE VALUE OF THE LEVERED FIRM
According to the theory of cost od capital, corporate valuation and capital structure of Modgliani and Miller there is either implicity or explicity assumed for the folowing expressions: Capital markets are frictionless.
Individuals can borrow and lend at the risk-free rate.
There are no costs to bankruptcy.
Firms issue only two types of claims: risk-free debt and (risky) equity. All firms are assumed to be in the same risk class.
Corporate taxes are the only form of government levy (i.e., there are no wealth taxes on corporations and no personal taxes). All cash flow streams are perpetuities (i.e., no growth). Corporate insiders and outsiders have the same information (i.e., no signaling opportunities). Managers always maximize the shareholder's wealth (i.e., no agency costs) The theory is not realistic but later we will se that the discrepancy is not very high and does not really effect the values of the model. Let us be more specific with the point “All firms are assumed to be in the same risk class.” The return I is the same return J when we assume that the cash flow just differ by an factor and is given by:
because the the return is given by
and with the assumption
The value of an unlevered firm is
This represents the value for an unlevered firm because it contains the discounted value of a perpetual. To distinguish between net operating income after taxes and free cash flow there are the following equations:
For these equations we get that the free cash flow and the net operating income is the same if we assume that all cash flows are perpetuities. Later we can write the value of an unlevered firm in two different ways
but now we must distinguish between dept holders and shareholders, because debt is assumed. Shareholders gain net cash flow after interest, taxes and replacement investment Formel and bondholders receive interest on debt (kdD). For an nongrowing firm dep=I is assumed and
Formelis given with Formel
because Formelthe cash flow is for the unlevered firm with the same risk at all. We can discount the equation per ρ, because we have a perpetual stream. The other part of the sum is assumed to be risk free. Therefore we discount it per kb. for the levered firm there is
In the end, we have the value for the levered firm in relation of the unlevered firm with :
The difference between the values is just the value of the tay shield in case of debt. The Value of the market is independent of the capital structure and depends on the rate ρ depending on the risk class.
THE WEIGHTED AVERAGE COST OF CAPITAL
if we want to determine the cost of capital we can use the fact that shareholders want that new investments are profitable, which means that the return of the new projets is higher than the opportunity cost of the funds offered by shareholders and bondholders. The change of the value of an levered firm is defined by: or with respect to new investment
with S standing for Shareholder, B for Bondholder, O or old and N for new. But we know that the new investment is the sum of supply by new shareholders and new bondholders so we can assume that:
and with that assumption we have:
so we have to make the profit of at least one unit to increase their wealth.
If corporate tax is 0 the cost of new capital is independent of the capital structure. The...
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