Structure – basics

Finding factors that are immanently important is the key to a successful analysis of company’s value with respect to its capital structure. Cash that is generated by a company finds its way to one of three groups:

• shareholders

• debt holders

• government

The cash flows can be denoted as:

• dividends

• interest payments

• tax payments

The present value of the cash flows will be denoted as:

• E

• D

• G

The sum of the three gives an amount that is not affected by either the level of tax, or changing proportions between equity and debt. If the tax rates are altered (the government changes its fiscal policy), a different pro-portion of profits generated by a company goes to the government. If the tax rate is increased, the first two groups will receive less, but the total amount will not change. The change in capital structure will influence the amount of paid tax, because debt is closely related to the tax shield. Tax shield is a result of a law that enables companies to deduct interest before calculating the amount of tax owed. Thus, the higher the debt is, the lower the tax to be paid. The sum of the three streams of cash flows is constant, but the change in one component is likely to affect the other two. Let us denote the sum asV_T (total):

The value of equity is the present value of cash flow for shareholders (CF), and tax payments (TP) are (we temporarily ignore depreciation and assume that the level of debt does not change):

We already know that:

This implies:

The same is true as far as the present values of dividends, CF and tax pay-ments are concerned (assuming perpetuities). G in the formula below is the

The formula for the total value of a company can be rewritten as follows:

.

Let us suppose now that we are dealing with an unleveraged (hence sub-script u) company, devoid of the tax shield effect. The value of such a company can be shown as the sum of two components: the value of equity (no debt) and the value of tax payments (no tax shield):

The values are given by:

This implies:

The same is true with regard to the present values (assuming perpetuities):

The relationships yield the following:

Please note that a change in T does affect Vu, since it does not affect the to-tal value of a company. A comparison of the two formulae for the toto-tal value of a company generates the following:

Hence:

Let us denote the cost of capital of an unleveraged company (financed by debt only) by ku. From the portfolio theory we get the following important re-lationship:

The cost of capital does not depend (by definition) on the level of debt, so it is assumed that it is not related to any changes in the capital structure either.

Debt, cost of equity, and equity will change in a way that the right side of the formula is unaffected.

Whenever the capital structure changes, the cost of debt, equity, and obviously the value of equity and debt will change too. For simplicity, let us as-sume that the cost of debt remains the same. The formula may be now rewritten with respect to the cost of equity:

There is a slight problem with applying the formula to real life calculations.

It gives us some idea of how E affects the cost of equity, but on the other hand the very cost of capital is needed to determine the value of equity. However, we went through the chore of solving many such problems (logical loops) in the previous chapter.

It is worth emphasizing that in the case of a company that is partly financed by debt, the value of the company (D + E) is bigger than the value of the com-pany that is financed by equity only (V_u). The difference can be attributed to the tax shield effect. For a perpetuity, it is TD (a product of tax rate and the value of debt).

The formulae developed so far in this section were obtained for perpetui-ties. Still, they are precise enough for any other situations and are widely used in literature. Even more precise solutions can be found in M.Capinski, “A New Method of DCF Valuation”, Nowy Sacz Academic Review, 2005/2 – they are based on the same idea: cash flows that flow to the government, sharehold-ers and debt holdsharehold-ers. Using a spreadsheet and the “goal seek” tool makes it easy to find the final values, whereas an analytic formula, though possible to derive, would be very complicated. Here we only present the solution for a single- period case.

The crucial relationship is concerned with two ways of decomposing the to-tal value of the firm (which is the present value of the toto-tal generated cash). The company may contribute to debt holders, shareholders and the government and on the other hand to shareholders and the government in a hypothetical

situa-We then compute the value of all components at time t on the basis of known expected cash flows and the values at the end of year t +1. For notational sim-plicity we sett=0 and the general relationship is as before:

We assume that the cost of debt k_D(0) and the cost of an unleveraged com-pany k_u(0) are given. The formula for the cost of equity k_e(0) will be derived be-low. We assume that the values V_t(1), D(1), E(1), G (1), V_u(1), G_u (1)are known.

We identify some groups of cash flows at the end of year one, including:

1. C_t(1) – the total cash flow composed of the cash generated by the compa-ny together with the terminal value V_t(1), discounted by k_u(0) and giving V_t(0) ,

2. C_D – the cash for debt holders composed of the interest, change of debt, and the value of debt D(1), discounted atk_D(0),

3. C_e – the cash for the shareholders composed of the cash flow at the end of the year and the value E(1), discounted by k_E(0),

4. C_G – the cash for the government (taxes) including the value G(1) also discounted by k_E(0) (the taxes are proportional to the cash flow to the shareholders so the returns are the same and so is the risk).

The inclusion of the terminal value in the cash available is justified since, for instance, the shareholders can sell the shares and debt holders can sell the bonds, except for the government that is regarded as an investor in an abstract sense.

Application of the basic idea of portfolio theory, regarding the company as a portfolio of debt, equity and government, results in the following relationship:

In this formula the only unknown quantity is the cost of equity (k_E ), and so it can be calculated.

To complete the analysis, it is now sufficient to give the formulae for the nu-merators as:

In the example below, we limit ourselves to showing the perpetuity case.

Example 16.

A company expects EBIT of 60 every year. The company is financed by debt of 100, and the cost of debt is 6% (perpetuity too). The tax rate is 30%. We assume that the depreciation each year is at the same level as the capital investment. We inquire about the cost of equity and capital structure.

Calculating cash flows is quite straightforward:

Given equity

The value of equity may be estimated if the company is listed on a stock ex-change. Suppose the value of equity is:

E = 300.

Then, from Gordon’s model (E is equivalent to S (0), zero growth) we get:

We also receive the financial structure:

Both, the rate of return and the value of the unleveraged company can be

We can also compute WACC and then find independently the value of the company:

The difference (30) stems from the fact that the company uses financial lev-erage and hence it is the present value of the tax shield.

Given cost of equity

Let us suppose the cost of equity (12%) was found using CAPM. The value of equity (divide CF by k_E) and the financial structure can now be easily deter-mined:

Next, both the cost of capital and the value of an unleveraged company can be found:

Given the cost of capital of an unleveraged company

Let us supposeku can be estimated (11%) for example as a result of a com-parison with another company that is equity financed or historical data was used for that purpose. Then: