Session 3: Value of the Firm and Cost of Capital

Learning Outcomes
The students should be able to find the combined cost of capital by the use of the Weighted Average Cost of Capital and MM models

A. Weighted Average Cost of Capital

The appropriate weights assigned to each capital component are derived from the firm's optimal capital structure

The optimal capital weights minimize the firm's WACC for a given structure of component capital costs

Example: Assume the firm has $10 million in total assets. Debt, preferred stock, and equity are used in the proportions of 50%, 20%, and 30%, respectively, to pay for the assets. The dollar amount from each capital component is:

Debt $5,000,000/$10,000,000 = 50%

Pref. Stock $2,000,000/$10,000,000 = 20%

Equity $3,000,000/$10,000,000 = 30%

Computing the WACC -- An Example:
Simu Tel Ltd after-tax cost of debt = 10%; the cost of preferred stock = 11%; the cost of retained earnings equity = 15%. The optimal weights are 50% for debt, 20% for preferred stock, and 30% for equity.

The traditional view of WACC assumes that:
a) As the level of debt financing increases the cost of debt remains unchanged up to a certain level of gearing. Beyond this level, the cost of debt will increase
b) The cost of equity rises as the level of gearing increases
c) The weighted average of cost doesnot remain constant, but rather falls initially as of the proportional of debt capital increases, and then begins to increase as the rising cost of equity (and possibly of debt0 becomes more significant.
d) The optimal level of gearing is where the company’s WACC is minimized.

The net operating Income View of WACC
The net operating income approached takes a different view of the effect of gearing on WACC. It assumes that the WACC is unchanged, regardless of the level of gering, because of the following factors:

1. The cost of debt remains constant as the level of gearing increases.
2. The cost of equity raises in such a way as to keep the WACC constant.

The net operating income approach is that the level of gearing is a matter of indifference to an investor because it does not affect the market value of the company nor an individual share. This is because the level of gearing rises, so as the cost of equity in such a way to keep both the WACC and the market value of the shares constant.

B: The Modigliani-Miller (MM) Theory
MM theory developed a defense of the net operating income approach to WACC to the effect of gearing on the cost of capital. Their view was that investors would use arbitrage to keep the WACC constant when changes in the company gearing occurs.

Modigliani and Miller’s argument in a world with no taxes
The capital structure decision was first tackled in a rigorous theoretical analysis by the financial economists Franco Modigliani and Merton Miller (M and M or MM) in 1958. MM created a simplified model of the world by making some assumptions. Given the assumptions they concluded that the value of a firm remains constant regardless of the debt level. As the proportion of debt is increased, the cost of equity will rise just enough to leave the WACC constant. If the WACC is constant then the only factor which can influence the value of the firm is its cash flow generated from operations. Capital structure is irrelevant. Thus, according to MM, firms can only increase the wealth of shareholders by making good investment decisions. This brings us to MM’s first proposition.

The total market value of any company is independent of its capital structure

The assumptions
Some of the assumptions upon which this conclusion is reached need to be mentioned.
a) There is no taxation
b) There are perfect capital markets, with perfect information available to all economic agents and no transaction costs.
c) There are no costs of financial distress and liquidation (if a firm is liquidated, shareholders will receive the same as the market value of their share prior to liquidation).
d) Firms can be classified into distinct risk classes.
e) Individuals can borrow as cheaply as corporations.

Clearly, there are problems relating some of these assumptions to the world in which we live. For now, it is necessary to suspend disbelief so that the consequences of the MM model can be demonstrated. Many of the assumptions will be modified later in the session.

The MM no-tax capital structure argument can best be illustrated with the help of an example. In the following example it is assumed that the WACC remains constant at 15% regardless of the debt-equity ratio.

Example:
CelNet Communication Ltd is about to be established. It needs US$ 100 million capital to buy equipments and buildings. The business generated by the investment has a given systematic risk and the required return on that level of systematic risk for an all-equity firm is 15%.

The expected annual cash flow is a constant $15 million in perpetuity. This cash flow will be paid out each year to the suppliers of capital. The prospective directors are considering three different finance structures

Structure 1: All equity (1,000,000 shares selling at $100 each).

Structure 2: $ 50 million of debt capital giving a return of 10% per annum. Plus $ 50 million of equity capital (500,000 shares at $100 each).

Structure 3: $70 million of debt capital giving a return of 10% per annum. Plus $ 30 million of equity capital (300,000 shares at $100 each).

The table above shows that the returns to equity holders, in this MM world with no tax, rises as gearing increases so as to leave the WACC and total value of the company constant. Investors purchasing a share receive higher returns per share for a more highly geared firm but the discount rate also rises because of the greater risk to leave the value of each share at $100.
Note that the relationship given in the tabulation in table above can be plotted as graphs as shown in the figure below. Under the MM model the cost of debt remains constant at 10%, and the cost of equity rises just enough to leave the overall cost of capital constant.

The Capital Structure Decision in a World with tax
The real world is somewhat different from that created for the purposes of MM's original 1958 model. One of the most significant differences is that individuals and companies do have to pay taxes. MM corrected for this assumption in their 1963 version of the model – this changes the analysis dramatically. Most tax regimes permit companies to offset the interest paid on debt against taxable profit. The effect of this is a tax saving which reduces the cost of debt capital.

In the previous no-tax analysis the advantage of gearing-up (a lower cost of debt capital) therefore an increased kE). The introduction of taxation brings an additional advantage to using debt capital: it reduces the tax bill. Now value rises as debt is added to the capital structure because of the tax benefits (or tax shield). The WACC declines for each unit increase in debt so long as the firm has taxable profits. This argument can be taken to its logical extreme, such that WACC is at its lowest and corporate value at its highest when the capital of the company is almost entirely made up of debt.

Example:
Example: A profitable firm's cost of debt falls from a pre-tax 10% to only 6.9% after the tax benefits:
10% (1 - T) = 10% (1 – 0.31) = 6.9%

For a perpetual income firm, the value is V = Cl/WACC. As WACC falls, the value of the company rises, benefiting ordinary shareholders.

The conclusion from this stage of the analysis, after adjusting for one real-world factor, is that companies should be as highly geared as possible.

C: Determining the Firm's Average Cost of Capital (ACC), Marginal Cost of Capital (MCC) and MCC Breakpoints

• The Firms ACC is the average cost of the funds normally represented by the WACC.
• The firm's MCC is the additional cost the firm will pay to raise an additional dollar of capital, assuming the capital is raised using the optimal capital proportions.
• An MCC breakpoint is identified by the dollar amount of total capital spending where the MCC function shifts upward

The average basis cost of capital is calculated using the company’s balance sheet data. In this case, the computed WACC represents the cost of the capital currently employed. This represents financial decisions taken in previous periods. Alternatively, the cost of raising the next increment of capital can be determined – this is what is termed the marginal cost of capital. The relationship between marginal (MC) and average (AC) cost of capital can be represented graphically, as indicated by figure 1.

Note: Any factor which increases the cost of a capital component will cause the MCC to shift upward and produce a breakpoint. There can be many breakpoints in the WACC function.

Factors which cause the MCC to shift are:

1) Increases in the cost of debt, kd
2) Increases in the cost of preferred stock, kp
3) Increases in the cost of internal equity capital, ks
4) Increases in flotations costs, F
5) Increase in tax rates, T

The MCC Breakpoint (BP) Formula

QUESTIONS FOR DISCUSSION

1. The cost of equity of Jambo CelCom Ltd, an all equity company is 15%. What is the WACC of the company?

2. CelNetworks Ltd has return to equity of 15%. The debt:equity ratio is 1:4. The cost of debt capital is 5% and his is a risk free cost of debt. What is the company’s WACC?

3. NOW Telecoms is all equity company and its cost of equity is 12%. Telecom (T) Ltd is similar to Now Telecoms except that it is a gearing company, financed by $100,000 of 3% debentures (current market price $5) and 100,000 ordinary shares (Current market price is $1.5 Ex dividend).
What is Telecom (T) Ltd cost of equity and WACC?

4. State Mobile Company has a WACC of 16%. It is financed partly by equity (cost 18%) and partly by debt capital (cost 10%). The company is considering a new project which would cost $50,000 and would yield annual profit of $8,500 before interest charges. It would be financed by loan at 10%. As a consequence of the higher gearing, the cost of equity would rise to 20%. The company pays out all profits as dividends, which are currently $22,500 a year.

a) What would be the effect on the value of equity undertaking of the project?
b) To what extent an you analyze the increase or decrease in equity value into two causes, the NPV of the project at the current EACC and the effect of the method of financing?
Ignore taxation and assume that traditional view of WACC and gearing.

5. You as a regulator in telecommunication you will treat all equity firm differently form debt financed telephone company. Explain your answer.