© 2000 John Petroff

1)- Minimum average cost of capital

The starting point of this approach is that funds are received by a firm for the purpose of undertaking projects (as they have been analyzed in capital budgeting in the previous chapter). What limits the number of projects that can be undertaken is the cost of funds. Thus, the optimal capital structure is the one which gives the minimum cost of funds because that is the one that permits the largest number of projects to be started and guarantees maximum growth of the firm.

The various types of funds (i.e. credit, long term debt, preferred stock, common stock and retained earnings) used by a firm have each different costs (as has been established in the first section of this chapter). It is necessary to study how the combination of different proportions can lower the overall cost of capital. To do that, the weights are the proportions of each type of fund in the balance sheet. (In pure theory, the weights should not be the proportion of each type of fund used but the proportion of each type of fund available in the market. But, historical and company specific circumstances which justify assets and funds composition, and which are discussed later, do not justify inclusion of the entire spectrum of financial sources.)

To make the analysis workable the assortment of funds is reduced to two: long term debt and common stock. The weighted average cost of capital WACC is given by

WACC = d * kd (1-T) + e * ke

where d = proportion of debt in total assets
e = proportion of equity in total assets (note that d + e = 1)
kd = long term bond yield
ke = rate of return on common stock
T = average corporate income tax rate

To illustrate the calculation of weighted average cost of capital we take data from Lucent Technologies 1999 Annual Report. Table T-11.19 shows the yields on equity and different bond issues. The amounts and yields of bonds are taken from Note #9 to financial statements. Since the actual amounts are known, they are used as weights rather than the proportion of debt in total funding. Table T-11.19 shows that Lucent's correct cost of capital is neither a straight average of 9.35% nor an average of after tax cost equivalent of 7.21%, but weighted average cost of capital of 19.86% or rounded at 20%. Table T-11.19 Lucent Technologies weighted average cost of capital . return % after tax return % amounts weights wacc % Equity 24.45 24.45 13584 0.77 18.83 LTD 6.90 4.38 750 0.04 0.18 LTD 7.25 4.60 750 0.04 0.18 LTD 5.50 3.49 500 0.03 0.10 LTD 6.50 4.13 300 0.02 0.08 LTD 6.45 4.10 1360 0.08 0.33 LTD 8.40 5.33 502 0.03 0.16 Total . . 17746 1 19.86 Average 9.35 7.21 . . 19.86

a)- Effect of financial leverage on rate of return on common stock

The rate of return required by investors increases as financial leverage is increased. Initially, the reason for a moderate rise in risk premium has been established earlier as the increased volatility observed in Table T-11.8. As soon as the level of financial leverage used becomes substantial, a bankruptcy cost adds to the volatility. One will recall that increased potential for default on additional debt will prompt lenders to impose restrictions on company activity and raise interest charges. Bankruptcy costs are not born by lenders alone. Whereas lenders may be protected by pledged collateral and other clauses, shareholders assume the brunt of corporate risk, and their risk premium for bankruptcy cost will rise much higher. Finally, to the extent that debt is used to finance automation and sales expansion, the previous section showed that an additional risk to shareholders comes from the increased commercial risk. These explanations justify the rising curve shown in Graph G-11.6 for the rate of return to common stock ke .

b)- Effect of financial leverage on long term bond yield

Yields on long term bonds do not suffer from the effect of volatility initially. But the bankruptcy cost starts to kick in earlier than for stocks, and at high level of debt, the bond yield line rises very fast as can be observed in Table T-11.8. The long term bond yield kd must be restated net of tax. Thus, in Graph G-11.2, the after tax bond yield kd (1-T).

c)- Pattern of average cost of capital

The weighted average cost of capital is calculated in Table T-11.14 below and was shown graphically in Graph G-11.6 above.

The table and the graph reveal that the pattern is initially downsloping because an ever greater proportion of low cost tax shielded bond interest expense is mixed with more expensive equity. After passing through a minimum which appears to be around 30% of debt, the average cost of capital starts to rise moderately at first, then asymptotically to the steep portion of the after tax bond yield as the proportion of equity vanishes.

d)- Significance of the minimum cost of capital

The presence of a minimum of the weighted average cost of capital establishes that, after taking into account all the harmful effects of financial leverage (in the form of profit variability, stock volatility, bankruptcy cost and aggravated commercial risk), an optimum financial leverage strategy exists that indicates that the proportion of debt in the funding of a firm ought to be larger than zero. In the numbers of our example used in Table T-11.14, it is important to note that the weighted average cost of capital is lower than even the lowest cost of capital. This verifies that a firm that would only use equity financing would have a suboptimal value. The reason for that is that capital budgeting projects would be accepted if the weighted cost of capital is the cut-off rate, but would be rejected if the cost of equity is the cut-off rate instead.

This minimum is, therefore, more significant than just being the lowest number: it tells that more projects will be chosen and more value will be added to the firm if the firm strives to have a capital structure corresponding to it. This also implies that the value of the entire firm is maximum where the average cost of capital is minimum, which is also the optimum debt to equity proportion. This is shown in Graph G-11.7 below using numbers generated in Table T-11.14 below.

In Graph G-11.7, earnings per share reach a maximum at a level of debt somewhere between 40% and 50%, corresponding to the minimum weighted average cost of capital shown in Graph G-11.6

e)- Applying the theory in practice

A first difficulty with the theory is that it is formulated in a static context. Because a firm must continuously seek to grow, an optimum capital structure at one point in time may not be optimal when new funds have to be obtained. These additional funds will cost more than the average cost of capital: the marginal cost of capital will always be higher than the average cost of capital. And the marginal cost will be the new cut-off rate for new projects. The basis for optimizing firm's value is marginal cost and no longer average cost. But funds cannot usually be obtained form equity and debt in the same proportions as the existing funds: this implies that the new mix of debt and equity will not be optimal (i.e. new funds come in lumps).

A second difficulty is that the assumption that a firm is only financed by two types of funds must be relaxed, and when it is, the number of different funds used not only adds some minor complexity to the calculation of weighted cost of capital, but offers new choices between different alternatives (e.g. should more trade credit be used or more bank revolving line of credit). More importantly, the cost of each alternative changes over time: this suggests that there isn't one optimum: it changes all the time. Change does not come from outside economic conditions only, but from project opportunities and strategies as well. In other words, the theoretical model needs to be made dynamic.

While theoretically, including a large number of types of funds, outside conditions and internal change is a challenge difficult to handle, a practical application is far more straight forward. Such application is usually conducted by entering financial data in a spreadsheet where simulations allow modifications ad infinitum. The starting point is not any hypothetical value, but it is the actual recent data of the company under study, and the variations in yields are those that are foreseen in the near future. Thus, changes in all reasonable financing combinations can be put to the test of sales instability and changing corporate strategy. As mentioned earlier, a Monte Carlo simulation can generate a probability distribution needed to evaluate an expected value.

A more direct approach is to study the actual cost of the different financing sources to gather information that may suggest whether or not the harmful effects of variability of bankruptcy cost start to influence the funds the company uses. Studying the cost of borrowing of a firm is a useful way of determining what lenders, who are most diligent financial analysts, think of the firm. It is useful to know what terms were offered in each individual borrowing (bank credit, short term loans, installment loans and long term bonds). These numbers must appear in notes to the financial statements. There, the face value, maturity and coupon rate must be stated, as well as any premium or discount given when a bond was floated and other important terms such as
- whether the bond is secured or unsecured ,
- method of redemption,
- right to conversion.

An indirect, but quicker method of arriving at an average cost of borrowing than weighted cost of capital, is by dividing the interest expense by the outstanding debt. In the debt amount, one must be aware that all non-interest earning liabilities, such as accrued expenses, advances, deferred income tax and provisions should be excluded.

The analyst can tell from the interest that had to be offered and the additional incentives present in the bond covenants, whether the firm had to pay more than it should have. For this, it is usually necessary to read prior years annual reports and the annual reports of other firms in the industry. Only for some 2,000 major American firms, ratings by rating services (such as Standard & Poor or Moody's) are indicative benchmarks, but these may not be applicable to given companies or industries.

One method is to look at the yields on a company's bonds which were issued over the past few years in comparison to the industry. This can be done by calculating the risk premium on each issue: each company bond yield in excess of an industry average (or alternatively over a risk free rate such as a treasury bills rate). If the risk premium has been decreasing or remained steady, it is an indication that the firm has not reached the optimum lowest cost of capital. On the contrary, if the risk premium has increased substantially recently, it shows that the company may be exceeding its optimum cost of capital. Naturally, the interest paid is not the only factor to consider. The more incentives a company has to offer, the more it shows that lenders consider the newer issues riskier. The incentives can also tie the hands of the company and prevent it from the needed freedom for bold investments and innovations. For instance, restrictions on acquisition or disposal of assets that can be part of a mortgage clause that would clearly interfere with corporate strategic planning.

The yields on a company's bonds and the additional incentives offered to lenders must also be studied by the analyst in order to determined if the firm is capable of borrowing in the future. If a firm has already offered lenient conversion privileges, beneficial call or put provisions, and mortgaged all its assets, it has little to offer in new bond issues. If it has exhausted all its borrowing capability, it means that either future planned expansion is unlikely or that it would have to be financed either internally or by issuing new shares; these subjects are discussed in the following sections. Thus the analysis of the cost of capital and bond covenants is important knowledge for the determination of current strategic flexibility and future growth potential.

In Russia, in 1995, companies have virtually no access to domestic long term borrowing discussed in this section. The interest they pay on credit obtained from banks is not disclosed in their annual reports. Thus, it will be a while before the Russian analyst will be able to glean fruitful information from this approach.

See review questions Q-11E1.1 through Q-11E1.11.

See research assignment R-11E1.1.

Previous: Optimal debt level

Last modified: Jun/01/01

Next: 2-Corporate life cycle