(178)---THE COST OF CAPITAL FOR PROJECTS

The Cost of Capital for Projects

The procedure described for calculating the cost of capital for divisions can be followed in the case of large projects. Many times it may be quite difficult to identify comparable firms. You can estimate a project’s beta based on its operating leverage. You may also consider the variability of the project’s earnings to estimate the beta.

A simple practical approach to incorporate risk differences in projects is to adjust the firm’s or division’s WACC to evaluate the investment project:

Adjusted WACC = WACC +/- R

That is, a project’s cost of capital is equal to the firm’s or division’s weighted average cost of capital (WACC) plus or minus a risk adjustment factor, R. The risk adjustment factor would be determined on the basis of the decision maker’s past experience and judgment regarding the project’s risk. It should be noted that adjusting or division’s WACC for risk differences is not theoretically a very sound method; however, this approach is better than simply using the firm’s or division’s WACC for all projects without regard for their risk.

Companies in practice may develop policy guidelines for incorporating the project risk differences. One approach is to divide projects into broad risk classes, and use different discount rates based on the decision maker’s experience.

For example projects may be classified as:

• Low risk projects
• Medium risk projects
• High risk projects

(177)---THE PURE PLAY TECHNIQUE

The Pure Play Technique

Calculate the division’s equity cost of capital

The asset or unlevered beta for the division is 0.67. We need to convert the asset or unlevered beta into the equity or levered beta for calculating the cost of equity for the division. To obtain the equity beta, the asset beta should be levered to reflect the target capital structure of the division. What is the target capital structure of the division? The company may use the firm’s target capital structure for the division as well. Alternatively, it may decide the division’s target capital structure based on the average debt ratio of the pure play firms.

Calculate the division’s cost of capital

The cost of capital for the division is the weighted average cost of equity and the cost of debt. It should be clear from the approach discussed here that each division has its own operating risk and debt capacity. Therefore, for calculating the cost of capital for each division, you should determine its operating risk and debt capacity. Assets of the firm are the aggregate of assets of the divisions. Therefore, the beta of assets for the firm should be the weighted average of betas for the divisions:

Firms asset beta = beta of division1 X weight of division1 + beta of division2 X weight of division2 +……………. + beta of division n X weight of division n

It seems plausible that weights may be expressed in terms of market value of assets. In practice, the market value of assets of divisions are not available, therefore, weights may be expressed in terms of book value assets or sales.

(176)---THE PURE PLAY TECHNIQUE

The Pure Play Technique

Calculate the division’s beta

We can use the average asset beta of the pure play firms as a proxy for the asset beta. We can use either simple or the weighted average. We can use either sales or assets or the value of the firms as weights. The theory does not tell us whether we should use simple or weighted average and what should be the weights. In practice, financial analysts will have to use their judgment. We think that since there is no theory and since we do not know the nature of measurement error, a simple average will do a good job.

Calculate the division’s all equity cost of capital

Suppose that the risk free rate is 6% and the market premium is 9%.

Ka = rf + risk + Premium X Ba

Ka = 0.06 + 0.09 X 0.67 = 0.12 or 12%

The all equity cost of capital is without financial risk. As it reflects only the business risk, it is also referred to as the asset or unlevered cost of capital.

(175)---THE PURE PLAY TECHNIQUE

The Pure Play Technique

Estimate asset beta for comparable firms

The comparable firms also employ debt to finance their assets. The equity betas of these firms are affected by their debt ratios. The firm may have a different target capital structure that the debt ratio of the proxy firms. Therefore, the pure play technique requires that the leverage equity betas of the proxy firms should be changed to unlevered or all-equity beta. Unlevered or all-equity betas are also called asset betas.

If we consider that debt is risk free, then Bd is zero, and we can find unlevered beta as follows:

Bu = B1 (E/V) = B1 (1- D/V)

Where Bu is the beta of the pure play firm after removing the effect or leverage: B1 is its equity beta with leverage: and E/V is the ratio of the pure play firm’s equity to its total market value. Note above equation is based on two important assumptions.

1. That debt is risk free and hence the beta foe debt is zero
2. All pure play firms maintain target capital structure and therefore, the amounts of debt change with the change in the values of firms.

The unlevered or all-equity beta is also called the asset beta as it incorporates only the firm’s operating risk and is not influenced by the financial risk arising from the use of debt.

(174)---THE PURE PLAY TECHNIQUE

The Pure Play Technique

Identify Comparable Firms

The critical step is the identification of comparable or pure play firms. These firms should have business identical to the division or the project. It is rate to find perfectly comparable or pure play firms in practice, as any two firms in the same line of business cannot have exactly similar features; they would have some differences. However, it is not impossible to identify approximately equivalent matches in terms of product line and product mixes. One or two good matches would suffice as proxy for the division or the project. If good matches cannot be found, the average data of a broader sample of firms should be used to even out the differences.

Estimate equity betas for comparable firms

Once the comparable or the pure play firms have been identified, their betas should be calculated using CAPM framework and a market index such as senses. Alternatively, we can use betas computed by organizations like the stock exchange or any other agency. These betas are based on the share price and the market index data. Hence they are the equity betas for the pure play firms. An equity beta is also called leverage beta.

(173)---THE PURE PLAY TECHNIQUE

The Pure Play Technique

Suppose XYZ Company limited has three divisions: pharmaceutical division, financial services division and power generation division. The company’s cost of capital is 12%. Since the company has three diverse businesses with different operating characteristics, it cannot use its overall cost of capital as the required rate of return for its divisions. It should estimate the required rate of return for each division separately. Suppose XYZ Company limited is considering an investment in the pharmaceutical division, and therefore, it would like to estimate the required rate of return for each division. A most commonly suggested method for calculating the required rate of return for a division (or project) is the pure play technique. The basic idea is to use the beta of the comparable firms, called pure play firms, in the same industry or line of business as a proxy for the beta of the division or the project. The application of the pure play approach for calculating the pharmaceuticals division’s cost of capital will involve the following steps:

1. Identify comparable firms
2. Estimate equity betas for comparable firms
3. Estimate asset betas for comparable firms
4. Calculating the division’s beta
5. Calculating the division’s all equity cost of capital
6. Calculating the division’s equity cost of capital
7. Calculate the division’s cost of capital

(172)---DIVISIONAL AND PROJECT COST OF CAPITAL

Divisional and Project Cost of Capital

We emphasize that the required rate of return, or the cost of capital is a market determined rate and it reflects compensation to investors for the time value of money and risk of the investment project. It is, thus, composed of a risk free rate (compensation for time) plus a risk premium rate (compensation for risk). Investors are generally risk-adverse, and demand a premium for bearing risk. The grater the risk of an investment opportunity, the grater the risk premium required by investors therefore, the required rate of return of a division or a project depends on its risk. Since investors are risk adverse, divisions and projects with differing risks should be evaluated using their risk adjusted rates of return.

The firm’s risk is composed of its overall operating risk and financial risk. Operating risk arises due to the uncertainty of cash flows of the firm’s investments. Financial risk arises is also a composite risk of assets financed by the firm. Thus, the firm’s cost of capital reflects the rate of return required on its securities commensurate with the perceived average risk. The firm’s cost of capital therefore cannot be used for evaluating individual divisions or investment projects that have different degree of risk. The firm’s cost of capital as a required rate of return for all projects may work well in case of companies that have single line of business or where different businesses are highly correlated. In highly diversified, multiple business firms, all projects cannot have same risk. Even a business, which basically operates in fast moving consumer products markets, has distinct markets for its consumer products. In each, market segment, business is exposed to different degree of competition and other environmental forces, which results in different risks for all its market segments. Hence, it is essential to estimate the required rate of return for each market segment or division than using the firm’s cost of capital as a single, corporate-wide required rate of return for evaluating project of divisions rather, projects within a single division may differ in risk. For example, the risk of introducing a new, innovative project will be higher than the expansion of an existing project. Hence, there is need for calculating the required rate of return for projects within a division.

The capital asset pricing model (CAPM) is healthful in determining the required rate of return (or the cost of capital) for a division or a project. The risk free rate and the market premium for divisions or projects are same as for the firm. What we need the divisional or project betas. In practice, it is difficult to estimate divisional or project betas.

(171)---FLOTATION COSTS, COST OF CAPITAL AND INVESTMENT ANALYSIS

Flotation Costs, Cost of Capital and Investment Analysis

A new issue of debt or shares will invariable involves flotation costs in the form of legal fees, administration expenses, brokerage or underwriting commission. One approach is to adjust the flotation costs in the cancellation of the cost of capital.

(170)---BOOK VALUE VS MARKET VALUE WEIGHTS

Book Value VS Market value Weights

You should always use the market value weights to calculate WACC. In practice, firms do use the book value weights. Generally, there will be difference between the book value and market value weights, and therefore, WACC will be different. WACC, calculate using the book value weights, will be understand if the market value of the share is higher than the book value and vice versa.

Why do managers prefer the book value weights for calculating WACC?

Beside the simplicity of the use, managers claim following advantages for the book value weights:

• Firms in practice set their target capital structure in terms of book values.
• The book value information can be easily derived from the published sources.
• The book value debt equity ratios are analyzed by the investors to evaluate the risk of the firms practice.

The use of the book value weights can be seriously questioned on theoretical grounds.

1. The component costs are opportunity rates and are determined in the capital markets. Te weights should also be market determined.
2. The book value weights are based on arbitrary accounting policies that are used to calculate retained earnings and value of assets. Thus they are not reflecting economic values. It is very difficult to justify the use of the book value weights in theory.
   Market value weights are theoretically superior to book value weights. They reflect economic values and are not influenced by accounting policies. They are also consistent with the market determined component costs. The difficulty in using market value weights is that the market prices securities fluctuate widely and frequently. A market value based target capital structure means that the amounts of debt and equity are continuously adjusted as the value of the firm charges.

(169)---THE WEIGHTED AVARAGE COST OF CAPITAL

The Weighted Average Cost of Capital

Once the component costs have been calculated, they are multiplied by the proportions of the respective source of capital to obtain the weighted average cost of capital (WACC). The proportions of capital must be based on target capital structure. WACC is the composite or overall cost of capital. You may note that it is the weighted average concept, not the simple average, which is relevant in calculating the overall cost of capital. The simple average cost of capital is appropriate to use because firms hardly use various sources of funds equally in the cost of structure.

The following steps are involved for calculating the firm’s WACC:

• Calculate the cost of specific sources of funds
• Multiply the cost of each source by its proportion in the capital structure
• Add the weighted component costs to get the WACC

In financial decision making, the cost of capital should be calculated on tax after basis. Therefore, the component costs should be after tax costs. If we assume that a firm has only debt and equity in its capital structure, then the WACC (Ko) will be:

Ko = (Kd (1-T)wd) + (KeWe)

Ko =Kd (1- T)(D/D+E) + Ke (E/D+E)

Where Ko is the WACC, Kd(1+T) and Ke are, respectively, the after tax cost of debt and equity, D is the amount of debt and E is the amount of equity. In a general form, the formula for calculating WACC can be written as follows:

Ko = K1w1+K2w2+-----------------

Where K1, K2 ----------are component costs and w1, w2------------weights of various types of capital employed by the company

Weighted marginal cost of capital (WMCC)

Marginal cost is the new or incremental cost of new capital (equity and debt) issued by the firm. We assume that new funds are raised at new costs according to the firm’s target capital structure. Hence, what is commonly known as the WACC is in fact the weighted marginal cost of capital (WMCC); that is, the weighted average cost of new capital given the firm’s target capital structure.

(168)---CAPM VS DIVIDEND GROWTH MODEL

Capital Asset Pricing Model VS Dividend Growth Model

The dividend growth model approach limited application in practice because of its two assumptions.

1. It assumes that the dividend per share will grow at a constant rate, g, forever
2. The expected dividend growth rate, g, should be less than the cost of equity, Ke, to arrive at the simple growth formula.

The growth formula is,

Ke = (DIV1 / Po) + g

These assumptions imply that the dividend growth approach cannot be applied to those companies, which are not paying any dividends, or whose dividend per share is growing at a rate higher than Ke, or whose dividend policies are highly volatile. The dividend growth model approach also fails to deal with risk directly. In contrast, the CAPM has a wider application although it is based on restrictive assumptions. The only condition for its use is that the company’s share is quoted on the stock exchange. Also, all variables in the CAPM are market determined and expect the company specific share price data; they are common to all companies. The value of beta is determined in an objective manner by using sound statistical method. One practical problem with the use of beta, however, is that it does not probably remain stable over time.

(167)---COST OF EQUITY AND CAPITAL ASSET PRICING MODEL

Cost of Equity and Capital Asset Pricing Model

The Capital asset pricing model (CAPM) provides an alternative approach for the calculation of the cost of equity. As per the CAPM, the required rate of return on equity is given is given by the following relationship:

Ke = Rf + (Rm – Rf) Bi

Above equation requires the following three parameters to estimate a firm’s cost of equity:

1. The risk free rate (Rf).
2. The market risk premium (Rm – Rf).
3. The beta of the firm’s share.

(1). the risk free rate

The yields on the government treasury securities are used as the risk-free rate. You can use returns either on the short term or the long term treasury securities. It is a common practice to use the return on the short term treasury bills as the risk free rate. Since investments are long term decisions, many analysts prefer to use yields on long term government bonds as the risk free rate. You should always use the current risk free rate rather than the historical average.

(2). the market risk premium

The market risk premium is measured as the difference between the long term, historical arithmetic average of market return and the risk free rate. Some people use a market risk premium based on returns of the most recent years. This is not a correct procedure since the possibility of measurement errors and variability in the short term, recent data is higher. As we explained in our previous posts the variability (standard deviation) of the estimate of the market risk premium will reduce when you use long serious of market returns and risk free rates.

(3). the beta of the firm’s share

Beta is the systematic risk of an ordinary share in relation to the market. In our previous posts, we have explained the regression methodology for calculating beta for an ordinary share. The share returns are regressed to the market returns to estimate beta. A broad based index like the BSE, sensitivity (senses) index is used as a proxy for the market.

(166)---EARNING-PRICE RATIO AND THE COST OF EQUITY

Earning-Price Ration and the Cost of Equity

As a general rule, it is not theoretically correct to use the ration of earnings to price as a measure of the cost of equity. The earnings-price ratio (E/P ratio) does not reflect the true expectations of the ordinary shareholders.

For example, if the current market price of a share is 500$ (face value being 100$) and the earning per share is 10$, the E/P ratio will be, 10/500=0.02. Does this mean that the expectation of shareholders is 2%? They would, in fact, expected to receive a stream of dividends and a final price of the share that would result in a return significantly greater than the E/P ratio. Thus, the dividend valuation model gives the most of valid measure of the cost of equity.

There are expectations, however. One expectation that we have already pointed out is the no-growth firms. The cost of equity in the case of no-growth firms is equal to the expected E/P ratio:

Ke = (DIV1 / Po) + g

Ke = (EPS1 (1-b) / Po) + br

Ke = EPS1 / Po

Where b is the earnings retention rate, EPS1 is the expected earnings per share and r is the return investment (equity).

Another situation where the expected earnings-price ration may be used as a measure of the cost of equity is expansion, rather than growth faced by the firm. A firm is said to be expanding, not growing, if the investment opportunities available to it are expected to earn a rate of return equal to the cost of equity.

For example, above equation may be written as follows:

Po = (EPS1 (1-b))/ (Ke –rb)

If r = Ke, then

Po = (EPS1 (1-b))/ (Ke –rb) = (EPS1 (1-b) / Ke(1-b)) = EPS1 / Ke

And solving for Ke, w get

Ke = EPS1 / Po

(165)---COST OF EXTERNAL EQUITY: DIVIDEND GROWTH MODEL

Cost of External Equity: Dividend Growth Model

The firm’s external equity consists of funds raised externally through public or rights issues. The minimum rate of return, which the equity shareholders require on funds supplied by them by purchasing new shares to prevent a decline in the existing market price of the equity share, is the cost of external equity. The firm can induce the existing or potential shareholders to purchase new shares when it promises to earn a rate or return equal to:

Ke = (DIV 1 / Po) + g

Thus, the shareholders’ require rate of return from retained earnings and external equity is the same. The cost of external equity is, however, greater than the cost of internal equity for one reason. The selling price of the new shares may be less than the market price. The new issues of ordinary shares are generally sold at a price less than the market price prevailing at the time of announcement of the share issue. Thus, the formula for the cost of new issue of equity capital may be written as follows:

Ke = (DIV 1 / P 1) + g

Where P 1 is the issue price of new equity. The cost of retained earnings will be less than the cost of new issue of equity if P0 > P1.

(164)---THE DIVIDEND GROWTH MODEL: ZERO GROWTH

The Dividend Growth Model: Zero Growth

In addition to its use in constant and variable growth situations, the dividend valuation model can also be used to estimate the cost of equity of no growth companies. The cost of equity of a share on which a constant amount of dividend is expected perpetually is given as follows:

Ke = DIV1 / Po

The growth rate will be zero if the firm does not return any of its earnings; that is, the firm follows a policy of 100% payout. Under such case, dividends will be equal to earnings, and therefore above equation can also write as:

Ke = DIV 1 / Po = EPS1 / Po

Which implies that in a no-growth situation, the expected earnings price (E/P) ratio may be used as the measure of the firm’s cost of equity.

(163)---THE DIVIDEND GROWTH MODEL: SUPERNORMAL GROWTH

The Dividend Growth Model: Supernormal Growth

A firm may pass through different phases of growth. Hence, dividend may growth at different rates in the future. The growth rate may be very high for a few years, and afterwards, it may become normal indefinitely in the future. The dividend valuation model can also be used to calculate the cost of equity under different growth assumptions.

For example, if the dividends are expected to grow at a super normal growth rate gs, for n years and thereafter, at a normal, perpetual growth rate of, gn, beginning in year n+1, then the cost of equity can be determined by the following formula:

Po = ((1+gs)1/(1+Ke)1) + ((1+gs)1/(1+Ke)1) +-------------+((1+gs)t/(1+Ke)t) + (Pn/ (1+Ke)n)

Pn is the discounted value of the dividend stream, beginning in year n+1 and growing at a constant, perpetual rate gn at the end of year n, and therefore it is equal to:

Pn = DIV n+1 / Ke – gn

When we multiply Pn by 1(1+Ke) n we obtain the present value of Pn in year 0.

Po = (DIVo (1+gs)1)/ (1+Ke)1 + (DIV1 (1+gs)1)/ (1+Ke)1 +-----------+(DIVn (1+gs)t)/ (1+Ke)t + ((DIV n+1/(Ke – gn) X (1/ (1+Ke)n

The cost of equity, Ke, can be computed by solving above equation by trial and error.