# METHODS/MODELS OF COMPUTING COST OF CAPITAL

The following models are used to establish the various costs of capital or required rate of return by the investors:

• Market model/investors expected yield
• Capital asset pricing model (CAPM)
• Dividend yield/Gordon’s model.

i) Risk adjusted discounting rate – This technique is used to establish the discounting rate to be used for a given project. The cost of capital of the firm will be used as the discounting rate for a given project if project risk is equal to business risk of the firm. If a project has a higher risk than the business risk of the firm, then a percentage risk premium is added to the cost of capital to determine the discounting rate i.e. discounting rate for a high risk project = cost of capital + percentage risk premium. Therefore a high risk project will be evaluated at a higher discounting rate.
ii) Market Model – This model is used to establish the percentage cost of ordinary share capital cost of equity (Ke). If an investor is holding ordinary shares, he can receive returns in 2 forms:

• Dividends
• Capital gains

Capital gain is assumed to constitute the difference between the buying price of a share at the beginning of the (P0), the selling price of the same share at the end of the period (P1). Therefore total returns = DPS +
Capital gains = DPS + P1 – P0.
The amount invested to derive the returns is equal to the buying price at the beginning of the period (P0) therefore percentage return/yield

Capital asset pricing model (CAPM) – CAPM is a technique that is used to establish the required rate of return of an investment given a particular level of risk. According to CAPM, the total business risk of the firm can be divided into 2:
Systematic Risk – This is the risk that affects all the firms in the market. This risk cannot be eliminated/diversified. It is thus called undiversifiable risk. Since it affects all the firms in the market, the share price and profitability of the firms will be moving in the same direction i.e. systematically. Examples of systematic risk are political instability, inflation, power crisis in the economy, power rationing, natural calamities – floods and earthquakes, increase in corporate tax rates and personal tax rates, etc. Systematic risk is measured by a Beta factor.
Unsystematic risk – This risk affects only one firm in the market but not other firms. It is therefore unique to the firm thus unsystematic trend in profitability of the firm relative to the profitability trend of other firms in the market. The risk is caused by factors unique to the firm such as:

• Labour strikes by employees of the firm;
• Exit of a prominent corporate personality;
• Collapse of marketing and advertising programs of the firm on launching of a new product;
• Failure to make a research and development breakthrough by the firm, etc

CAPM is only concerned with systematic risk. According to the model, the required rate of return will be highly influenced by the Beta factor of each investment. This is in addition to the excess returns an investor derives by undertaking additional risk

Dividend yield/Gordon’s Model – This model is used to determine the cost of various capital components in particular

Cost of Redeemable Debentures and Preference Shares
Redeemable fixed return securities have a definite maturity period. The cost of such securities is called yield to maturity (YTM) or redemption yield (RY). For a redeemable debenture Kd (cost of debt) = YTM = RY, can be determined using approximation method

WEIGHTED AVERAGE COST OF CAPITAL (W.A.C.C.)
This is also called the overall or composite cost of capital. Since various capital components have different percentage cost, it is important to determine a single average cost of capital attributable to various costs of capital. This is determined on the basis of percentage cost of each capital component.
Market value weight or proportion of each capital component.

In computation of the weights or proportions of various capital components, the following values may be used:

• Market values
• Book values
• Replacement values
• Intrinsic values

Market Value – This involves determining the weights or proportions using the current market values of the various capital components. The problems with the use of market values are:
The market value of each security keep on changing on daily basis thus market values can be computed only at one point in time.
The market value of each security may be incorrect due to cases of over or under valuation in the market.
Book values – This involves the use of the par value of capital as shown in the balance sheet. The main problem with book values is that they are historical/past values indicating the value of a security when it was originally sold in the market for the first time.
Replacement values – This involves determining the weights or proportions on the basis of amount that can be paid to replace the existing assets. The problem with replacement values is that assets can never be replaced at ago and replacement values may not be objectively determined.
Intrinsic values – In this case the weights are determine on the basis of the real/intrinsic value of a given security. Intrinsic values may not be accurate since they are computed using historical/past information and are usually estimates.

### Weaknesses of WACC as a discounting rate

WACC/Overall cost of capital has the following problems as a discounting rate:

• It can only be used as a discounting rate assuming that the risk of the project is equal to the business risk of the firm. If the project has higher risk then a percentage premium will be added to WACC to determine the appropriate discounting rate.
• It assumes that capital structure is optimal which is not achievable in real world.
• It is based on market values of capital which keep on changing thus WACC will change over time but is assumed to remain constant throughout the economic life of the project.
• It is based on past information especially when determining the cost of each component e.g in determining the cost of equity (Ke) the past year’s DPS is used while the growth rate is estimated from the past stream of dividends.

Note
When using market values to determine the weight/proportion in WACC, the cost of retained earnings is left out since it is already included or reflected in the MPS and thus the market value of equity. Retained earnings are an internal source of finance thus, when they are high there is low gearing, lower financial risk and thus
highest MPS.

Marginal cost of finance
This is cost of new finances or additional cost a company has to pay to raise and use additional finance

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