Question One

Beta is a measure of the sensitivity of an asset’s return in a portfolio (Cohn 2012). It determines the liquidity and volatility of an asset in the marketplace. It is a linear regression analysis where returns of a portfolio are linked to other returns of individual assets in a certain period. Beta is found through an analysis of regular share price returns over a period of time in relation to market’s daily returns (Cohn 2012).

The beta determines the level over which the price of a particular stock goes up or down when the stock market changes either upward or downwards (Nicholas 2011). When the share price of the stock is exactly in line with the market, the stock beta is 1; however, there are other times in which the share price and stock beta do not relate directly. In this case, they are not one on one with the market changes.

Beta of the portfolio assets of a firm equals a weighted average of the betas of the constituent assets. When average summations of individual betas of assets are added they equal to the total beta of the portfolio assets of the company. This condition is also true to the beta of the assets of the firm which equals to the weighted average betas for the debt, preferred equity and common equity of a firm.

Βn assets portfolio= ∑ xiβi = xd βd + xpsβps + xβcs

Where β is the beta of the portfolio asset

d - The debt

ps - The preferred stock

cs - Is the common stock

The risks that are involved with individual sources of finance for example preferred stock, affects the portfolio of assets both directly or indirectly. When the portfolio of an asset is affected directly, the proportionate changes in the beta of the individual finance source cause the beta in assets to change at the same rate. The risk is transferred to the portfolio assets at the same proportionate change (Cohn 2012).

The weighted average of the sources of finance is an overall representative of the company cost of Capital. It follows therefore the weighted average of the betas of constituents sources of finance will be equal to the beta of the assets in a company (Nicholas 2011). The weighted average of individual assets equals the beta of the portfolio assets. The sources of funds available to the company finance the assets that are there. When the sources of finance are available and free of risk, the portfolio assets will be least affected, however when there is conflict of interest amongst the sources of finance of finance, the assets will too be affected.

The beta measures the level of risk in which the assets in a company are exposed to.  The sources of funds which include the debt, preferred equity and common stock finance are also exposed to risk. The level of the risk in each of the source of finance is factored with the beta as it takes account of the risk. The risk also affects the sources of finance that are available. This risk is factored in through the beta that is in the formulae. When the betas in the sources of finance are weighted they are equal to the beta in the portfolio assets.

The capital pricing model is used in calculation of the investment risks and the return one should expect after an investment. It is not possible to work in an environment that is fully risk free. Investors set a rate that compensates them for the risks that they take (Nicholas 2011). In CAMP, there are two risks that an investment faces; the systematic risk and unsystematic risk. The systematic risks are those risks that are un-diversifiable (Nicholas 2011). They include the interest rates, war and recession. The unsystematic risks, on the other hand are those risks that can be diversified. This is done when the numbers of stocks in a portfolio are increased by an investor. The CAPM as a technique that analyzes the volatility of assets shows that the beta of the summation of individual stocks is equal to the beta in the portfolio of assets.

The portfolio of assets means that various types of assets are combined together in order to diversify the risks. When the sources of finance are put together, their risks are best analyzed through the beta function (Nicholas 2011). Just as the assets of individual assets translate to the beta of the asset portfolio, the sources of finance are translated in the same way. In a case where there is a risk in investing in debt due to the risk of default, this risk is factored in the overall business through getting the average weight of the beta of the debt. The weighted average of the debt together with other average weighted are added together.

The Weighted Average Cost of Capital (WACC)

The weighted average cost of capital is the calculation of the cost of capital in a firm where each category of financing is proportionally weighted (Loffler 2002). The financing categories include the preferred stock, common stock, bonds and other long term debt. It represents the company’s overall cost of capital. The company is usually financed through these sources which include both the equity and debt. The WACC determines the interest that the company has to pay in order to cater for the cost (Lo%u0308Ffler 2002).

            WACC is developed from the basic accounting equation:

Assets = Equity + Debt.

 Its main focus is on the right hand of this equation where the cost of acquiring the sources of financing are determined. The average weight of each constituent source of financing is calculated (Lo%u0308Ffler 2002).

The WACC equation;

                            WACC   = (E/V)*Re + (D/V)*Rd (1 – Tc)

Where;

Re    = cost of equity

Rd    =cost of debt

D      = market value of the firm’s debt

E      =market value of firm’s equity

V     = D + E

E/V = percentage of financing that equity

D/V = percentage financing that debt

Tc   = Corporate tax rate

Before the WACC is determined, the firm’s equity value, preference and debt value are calculated so as to determine the value of the firm. The cost of equity and the cost of debt are also determined in each category of financing. The cost of equity is determined through the use of either the divided growth approach or the capital asset pricing model (CAPM).

Dividend Growth Approach

The dividend growth approach is valuation technique that takes into consideration the dividend per share and the expected growth in dividend at a constant rate or at perpetuity. This technique is not commonly used by many companies (Husmann 2001). Most of the companies do not have a constant growth rate in dividend. This makes it difficult in estimation of the value of the stock hence biased information can be given.

The formula:

Po   = D1 / (Re - g)

Where;

Po    = the current stock price or the price of the stock in period 0

D1    = the dividend in period 1

Re     = the cost of Equity

g        = dividend growth rate 

The equation can be rearranged to get the cost of equity;

Re   = D1/ P0 + g

The second approach, CAPM was advanced in 1990 by an economist and a Nobel Prize winner Sharpe.

The formulae

Re   = Rf + beta (Rm – Rf)

Where;

Re    = return on equity

Rm   = market return

Rf     = risk free rate

The CAPM is the most commonly used technique in determination of the cost of equity. This is because many stocks do not have a stable dividend history. The cost of debt is determined through the bond pricing technique. The equation is illustrated below;

P =   C × (1 – 1/(1 +r)ˆt)/r + F × 1(/1 + r)ˆt.

It is rational for companies to have lower cost of debt to cost of equity (Husmann 2001). This is because of the profit maximization nature of the businesses. After the determination of the cost of equity and cost of debt, the next step is the determination of the value of the firm.

The value of the firm is the total summation of the equity and the debt;

V = E + D

Where;

V is the Firm’s market value 

E is the equity

D is the debt

The subsequent process involves the determination of the weight of the equity and the debt.  They weight of equity is the quotient of the equity to the value of the firm; E/V whereas the weight of debt is the quotient of debt to the total value of the firm; D/V (Husmann 2001).

The final stage is the determination of WACC, which is given by the summation of the product of the cost of equity and weight of equity to the product of cost of the debt and weight of the debt (Husmann 2001).

                            WACC   = (E/V)*Re + (D/V)*Rd (1 – Tc)

The determination of the WACC serves to provide the managers with information about the business performance. For any project to be feasible, it is required that it generates higher returns than the cost of raising the funds (Keef 2011). The WACC provides this information that investors need in order to ensure that they set out policies that would ensure that positive returns are acquired in the business.  Most companies prefer the use of more debt in their capital structure because it reduces the WACC (Keef 2011). This is because of the tax shield which is incorporated when calculating the WACC. The company becomes shielded from taxation which lowers the WACC (Husmann 2001)

During the process of evaluating the WACC of a company there is much estimation that is made (Holland 2008). It is therefore necessary to account for these kinds of risks that comes about through estimation as they may affect the projects in a firm. Irrational decisions may be made which affect the performance of the company (Keef 2011). Most companies account for this through addition of risk factor of 1.5%. It is usually reflected by the beta which a provision of the risk in the environment.

Advantages of WACC

Everything that exist either living or non-living has its pros and cons. This puts the WACC at no exception. There are several advantages that the method of evaluation brings (Holland 2008). The WACC is an analysis tool that is used as a discounting rate during the appraisements of investments’.

WACC serves as a tool on which the risk that faces a business in course of its operations is factored in the formulae. The value of the beta serve to represent the risk the company has in course of its operations (Holland 2008).  The beta also serves to show the volatility of the assets. If the individual assets are very volatile it has to be more.

WACC serve to represent an overall cost of the cost of capital involved. This is done through evaluation of the weighted average of the constituent sources of finance that are involved in financing a project. The company can determine whether it is economical for the company to use the available sources of finance that is available.

Disadvantages of WACC

WACC can lead to an incorrect conclusion during appraisal of an investment. This is because it assumes that the investment projects do not change the financial risks or business risks. In the real world, the investment projects change both the financial risk and business risk of the company involved in investing (Nicholas 2011).

When using WACC as a discounting tool, a viable investment could be rejected because its internal rate of return is less than the WACC. The method is used in the determination of the NPV of an investment. When the WACC is discounted it gives the NPV. The future cash flows of the company can be determined with certainty (Nicholas 2011).

Equity

The cost of equity can be best calculated using the asset pricing model. The method provides for various components which include the free risk return, the market return and the beta. This method is used in evaluation of the risks that are involved in the business and the returns that the business accrues from the investments (Nicholas 2011). When the cost of equity increases, the company gears up. The shareholders’ returns become volatile as the returns increases. The extra risk is born by the high returns that the company benefits from.

Example on how to calculate cost of capital on equity;

Re   = Rf +  beta ( Rm – Rf)

Unlevered beta = 1.1

Capital structure to be 40% debt and 60% equity

Tax rate =40%

Risk free market rate =3%

Market return = 4%

Re =3+1.1(4 -3)

        =4.1%

A company has 60 million shares that cost $ 60 per share. The stock beta is 1.15, risk free rate is 4% and the market price risk premium is 9%.

The Cost of Equity

Re   = Rf  +  beta ( Rm – Rf)

= 4+ 1.15(9)

=14.35%

The cost of debt

 The cost of capital on the debt is evaluated using the bond pricing method.  The following method is used in the determination of the cost of the debt;

P =   C × (1 – 1/(1 +r)ˆt)/r + F × 1(/1 + r)ˆt.

The company has a debt of $ 1 Million.  The current price and the coupon rate of the debt are 120 and 9% respectively. The coupons have 15 years to maturity with semi-annual coupon payments and 15% tax rate. An assumption is made on the face value of the bond which is $ 1,000. The C= $50, t= 30, P= $ 1,200 F=$ 1,000 and r= 3.23.

Preference Share Capital

The preferred share capital is a class of ownership in a company where the claim in the assets of a company and earnings are higher than the common stock (Nicholas 2011). There is a dividend that is paid out to the shareholders who have preferred share capital. This type of capital, however, does not provide the shareholders with the voting rights (Nicholas 2011).

The method that is used in evaluation of the preference share capital is the dividend growth model (Nicholas 2011). The preference share capital pays a constant dividend in each year. The cash flow is constant. The company through the use of this method will benefit from the tax shield. The tax shield reduces the cost of debt.

Question Two

Part A

Beta is a measure of risk. It measures the sensitivity of an individual security to the market movement. It is a good indicator of the stock’s inherent risk and its sensitivity to the general market fluctuations. It is also referred to as financial elasticity. The stock analysts use it to get a better feel of the risk profile of a stock in the market. It provides stock analysts with price movements of a particular stock in comparison to the overall market. The expected returns increase linearly with beta. Stocks with betas greater than one tend to amplify the overall movement of the market. Aggressively or highly leveraged companies have high betas. Conversely, stocks with betas between 0 and 1 tend to move less than the market especially for conservative companies. Betas that are equal to one tend to imitate the market. Stock Beta values are also fairly easy to interpret too since from the experience of price movements of stock and greater stock volatility than the stock market return then the beta values will be greater than one.

However, if the stock price movements are less volatile than the market return then the beta values have a less than one value. An increase in stock volatility means an amplified and more risk to the investors, then it is fair to expect greater returns from stocks with beta values more than one. The reverse is true whereby beta values are less than one hence has less risk for the investors to bear and less stock volatility is expected and also lower overall returns are generated. Beta allows the investor to understand if the price of a stock is less or greatly volatile which is a good indicator to understand before adding any security to a portfolio.

Beta calculations are based on the historical movements of price and hence calculations cannot accurately predict that the expected returns in the future will be the same for the newly issued stocks. This is a major disadvantage when calculating Beta. Also, even though Beta informs analysts about the historical past of a security it does not reveal to the investor the value or the attractiveness of that security today or in the future. Stock beta values are key variables when using the capital asset pricing model technique. When CAPM method is used, the required return on an asset can be calculated, the formula is as follows;

Ri = Rf + βi (Rm-Rf),

Where Ri is the expected return from asset I,

Rf is the risk free rate of return,

βi is the beta factor of asset i,

 Rm is the return from the market as a whole and (Rm-Rf) is the market premium.

 Using the above formula,

Ri =3.95%+1.06(6.01) =0.10321×100=10.32%

The required rate of return on the asset is 10.32%.

Calculate the debt to equity ratio which in this case is;

Total long term liabilities/total shareholder’s equity =

$15,000,000/$45,000,000 = 1/3

Using the asset beta formula;

Βeta asset=β equity (E/ (1-t) D+E) + β debt (1-t) D/1-t (D+E)

Where E= market value of equity,

D is the market value of debt and t is the rate of tax.

Applying the above formula gives the following solution,

β asset= 3÷($45,000,000÷(1-0.0485)$15,000,000+$45,000,000+1(1-0.0485)$15,000,000÷1-0.0485($60,000,000).

The solution =2.36+0.25=2.61/3.0

The beta for the assets of the comparable company is 3.0 which show that the stock is more volatile and reacts strongly to the variations in the market. This information is quite useful for the chief financial officer (CFO) in decision making for the firm since he can be able to determine the equity betas for companies under different debt amounts and also by using the capital asset pricing model he can accurately determine the effect on the stock prices if the company borrowed additional debt. A positive beta as in this case shows fluctuation of stock in comparison to the market trends and the more volatile will be the asset.

Part B

The market value of 35% of debt amounts to (35%×$15,000,000) =$5,250,000 and the market value of 65% of equity amounts to (65%×$45,000,000) =$29,250,000 and the tax rate is 5.45%.

Using the asset beta formula;

Βeta asset=β equity (E/ (1-t) D+E) + β debt (1-t) D/1-t (D+E)

Where E= market value of equity,

D is the market value of debt and t is the rate of tax.

The debt to equity ratio is given by,

Total long term liabilities/total shareholder’s equity=$5,250,000÷29,250,000=0.21:1.17

Beta asset= 1.17÷ ($29,250,000÷ (1-0.0545) $5,250,000+$29,250,000+0.21(1-0.0545) $5,250,000÷1-0.0545($34,500,000) =1.20

The beta for Coral Gable’s common stock is 1.20 which means that the stock is more volatile and that it will probably move 20% more than the market.

Part C

The weighted cost of capital (WACC) is the overall cost of using the various forms of funds. WACC is neither a cost incurred by the firm nor an expected return. It is an appropriate measure for the firm’s cost of capital. Calculation of WACC requires knowledge of the required rates of return on each source of capital since all capital sources assume different risks. WACC can also be referred to as the minimum returns expected by the company’s providers of capital from the existing asset base so that they are satisfied and are not interested in investing their capital elsewhere. A company has numerous sources of capital ranging from preferred equity, convertible debt, and common equity, straight debt, warrants, options, exchangeable debt, government subsidies and each capital category is weighted proportionately when calculating WACC. The different securities of finance sources give returns that are not similar. WACC is derived using the formula below,

WACC=E/V× Re +D/V ×Rd× (1-Tc).

Where E/V is the percentage of financing that is equity, Re is the cost of equity, D/V is the percentage of financing that is debt, Rd is the cost of debt, V is the value of the firm, Tc is the corporate tax rate, E and D are the market values of the equity and debt of the firm.

Cost of equity= Ri=Rf +βi (Rm-Rf),

Where Ri is the expected return from asset I

 Rf is the risk free rate of return

 βi is the beta factor of asset i

 Rm is the return from the market as a whole and;

 (Rm-Rf) is the market premium.

Cost of equity=3.95%+1.2(6.01%) =11.2%

The cost of debt= (Rf + credit risk rate) (1-t)

Where Rf is the risk free rate and;

T is the corporate tax rate which in this case is (3.95%+9.96%) (1-0.25)=0.104×100=10.4%

WACC=65%×11.2%+35%× 10.4% × (1-0.25) =0.65×0.112+0.35×0.104×0.75=0.0728+0.0273=0.1001

WACC=0.1001×100=10.01%

WACC is usually used by companies to arrive at meaningful investment decisions. WACC is also useful in that it is used to discount cash flows in the calculation of net present value and other valuations that are of major importance in investment analysis. WACC is also useful in representing the average risk faced by the organization in that it is adjusted upwardly for more risky projects than the company’s average risky projects and  also downwardly for the less risky projects compared to the average risky company projects. When the risk of an individual project is equal to that of the company as a whole, then WACC is the appropriate measure to use when finding a rate of return for an individual project. It is also useful as a measure to find out the best and optimal capital structure for a company and is a key variable in choosing the combination of debt and equity to be used to finance the operations of the firm.

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