Reading 37 – Cost of Capital

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http://www.docertifications.com/r37_l1

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a. Calculate and interpret the weighted average cost of capital (WACC) of a company

b. Describe how taxes affect the cost of capital from different capital sources

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1. Cost of Capital – It is the rate of return which suppliers of capital (equity and debt) require on their contributed capital to the firm
   1. It is also opportunity cost of funds for suppliers of capital. One will not invest in a firm if he/she can get better returns on opportunities with comparable risk
   2. Marginal Cost – Cost at which additional funds for a project can be raised
   3. Component cost of capital – cost of capital for various sources (for e.g., common equity, preferred equity, long term debt etc.)
2. 2. WACC (Weighted Average Cost of Capital) – Marginal cost of each source is computed and then weighted average of these costs is computed to estimate WACC
   1. Weight for a component is the proportion of total required capital that is funded by a particular component
   2. For e.g., if total fund required is $100 and if it is funded with $20 equity and $80 debt, then weight for equity component is 0.2 and that for debt is 0.8

3. Where,

1. R_e is rate of return required by common equity investors
2. R_d is the rate of return required by debt investors
3. R_p is the rate of return required by preferred equity investors
4. W_e is the proportion of total capital which is supplied by equity investors
5. W_d is the proportion of total capital which is supplied by debt investors
6. W_p is the proportion of total capital which is supplied by preferred equity investors
7. t is company’s marginal tax rate

Effect of taxes on various sources of capital

1. Interest on debt financing is tax deductible, hence cost of debt is multiplied by (1-t)
2. Dividend and other payments to equity holders are not tax deductible, hence Cost of equity is not multiplied by (1-t)

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c. Explain alternative methods of calculating the weights used in the WACC, including the use of the company’s target capital structure

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Target capital structure approach

1. Target capital structure is the capital structure which a company is striving to obtain
2. If a company has a target capital structure (proportion of equity and debt) and generally raises capital which is consistent with this target, then this capital structure can be used to determine weights

If target capital structure if it is not known, one of these approaches can be used

1. Use market value of components (debt and equity) of the firm to determine weights
2. Use average of comparable firm’s capital structure as target capital structure
   1. Generally un-weighted simple average is used for simplicity
3. Infer target capital structure from management discussion and trends which can be seen in annual reports

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d. Explain how the marginal cost of capital and the investment opportunity schedule are used to determine the optimal capital budget

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1. Investment opportunity schedule is a plot of return Vs. amount of new capital available. While marginal cost of capital is a plot cost of capital Vs. amount of new capital available
2. Marginal cost of capital is a positively sloped curve while investment opportunity schedule has a negative slope
3. Optimal capital budget is a point where marginal cost of capital and investment opportunity schedule meet
4. This graph indicates that all the projects with return greater than cost of capital should be undertaken

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e. Explain the marginal cost of capital’s role in determining the net present value of a project

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1. As the risk of a project increases, return required by investors also increases
2. WACC is appropriate cost of capital only for projects which have approximately same level of risk as that of firm’s existing projects
3. For projects with risk higher than average risk of firm’s existing projects, cost of capital should be greater than WACC. Similarly, for projects with lower risk than average risk of firm’s existing projects, cost of capital should be lower than WACC
4. If WACC is used as cost of capital for a project, then it is implicitly assumed that firm’s capital structure will not change during lifetime of the project

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f. Calculate and interpret the cost of fixed rate debt capital using the yield-to maturity approach and the debt-rating approach

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Yield To Maturity Approach

1. Cost of debt is equal to after tax value of interest rate at which firm can issue new debt
2. Consider market interest rate on new debt issued and not that of existing debt
3. Cost of debt = K_d * (1-t)

Debt Rating Approach

1. If debt is not publicly traded then rating and maturity of firm’s existing debt can be used to compute pre-tax cost of debt. Interest rate can be estimated by finding a bond with comparable rating as that of firm and maturity equal to that of existing debt
2. Covenants and other characteristics of new debt should be considered while determining comparable debt rating and yield

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g. Calculate and interpret the cost of non-callable, nonconvertible preferred stock

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Cost of preferred stock = Preferred dividends / Market price of preferred stock

For e.g., if annual preferred dividends paid is equal to $10 and market value of preferred stock is equal to $100, then cost of capital is 10%

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h. Calculate and interpret the cost of equity capital using the capital asset pricing model approach, the dividend discount model approach, and the bond-yield-plus risk-premium approach

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Capital asset pricing model (CAPM) – Expected return on stock is equal to sum of risk free rate and a premium for bearing stock’s market risk

1. Expected Return on stock = Risk free rate + Beta * (Expected return on market – Risk free rate)
2. Market risk premium = Expected return on market – Risk free rate
3. Beta = return sensitivity of stock to changes in market return
4. Risk free rate is an asset which has no default risk
   1. Yield on government bond is commonly considered as risk free rate
   2. For e.g., if a project has estimated life of 10 years, then 10 year government yield can be used as risk free rate

Dividend discount model

1. Cost of equity = Next year’s dividend / current value of stock price + g
2. g = firm’s expected constant growth rate = retention rate * return on equity
3. Next year’s dividend = Current year’s dividend * g
4. Equity risk premium – Realized equity risk premium observed over a long period of time is considered to be a good estimator of expected equity risk premium. So, past value of equity risk premium is used in CAPM equation

Bond yield plus risk premium approach

1. Cost of equity = pre-tax cost of debt + risk premium
2. Risk premium is added to compensate for additional risk of equity compared with that of debt

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i. Calculate and interpret the beta and cost of capital for a project

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1. A project’s beta is a measure of its systematic risk or market risk
2. However, a project is not publicly traded and hence beta cannot be directly computed
3. Pure-play method
   1. It is computed using beta of publicly traded firms with similar business line and comparable risk as that of project under consideration
   2. Since beta of a firm is affected by capital structure, hence unlevered cost of equity of firms should be used to compute cost of equity for a project
   3. Compute asset beta of publicly traded comparable firm by dividing equity beta of firm by [1 + (1-t) * D/E]. Where t is marginal tax rate and D/E is debt to equity ratio of comparable firm
   4. Compute equity beta of project by multiplying asset beta found in previous step by [1 + (1-t) * D/E]. Where t is marginal tax rate and D/E is debt to equity ratio of subject firm

Issues with pure-play method

1. Since beta is estimated using historical data, choice of length (5, 10 or 20 years) of past data and frequency (daily, weekly or annual) affects beta value
2. Estimate is affected by the choice of benchmark index (for example beta computed using DJIA or NASDAQ or MSCI world index)
3. Betas are expected to revert to 1 over long period. Such adjustment to project equity beta must be applied
4. Small firm beta should be adjusted for small firm risk premium. Small firms have higher chances of failure than large firms, hence risk premium for small firms should be higher

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j. Explain the country equity risk premium in the estimation of the cost of equity for a company located in a developing market

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Beta doesn’t adequately capture country risk premium in developing market. However, it is able to capture country risk premium in developed market. Country risk premium is added to market risk premium in CAPM equation to reflect increased risk in developing world

Modified CAPM Equation

1. Expected Return on stock = Risk free rate + Beta * Market risk premium
2. Market risk premium = Expected return on market – Risk free rate + country risk premium
3. CRP = Country Risk Premium
4. Sovereign Yield Spread = Difference between yields of government bonds in developing country and treasury bonds of similar maturities

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k. Describe the marginal cost of capital schedule, explain why it may be upward sloping with respect to additional capital, and calculate and interpret its breakpoints

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Marginal cost of capital schedule – As a company raises more funds, cost of capital for different sources of financing changes and accordingly value of WACC changes. Marginal cost of capital schedule shows value of WACC for different levels of financing.

Break Point – amount of capital at which WACC changes is called as a break point. Breakpoint changes when cost of capital of any component of WACC changes

Raising additional capital increases cost of capital

1. As more and more debt is raised, financial risk increases and thus cost of debt increases
   1. Covenants of existing debt may put more constraints on issuance of additional debt and this may lead to higher financing cost for new debt
   2. For e.g. if covenants of existing senior debt forbid issuance of additional senior debt, then company will have to pay higher interest on subordinate debt
2. Issuance of new equity is costlier than using retained earnings due to floatation cost associated with equity issuance

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l. Explain and demonstrate the correct treatment of flotation costs

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Floatation cost – It is the fees charged by investment bankers in raising of new equity. For debt and preferred shares, fee is not included as part of estimated cost of capital as the value is very small (typically less than 1%). For equity it ranges in between 2% to 7%

Correct treatment of flotation cost

1. Let total cost of project be X which is financed with Y equity and Z debt, with X = Y + Z
2. Let flotation cost be a%, then cost of flotation of equity is Y * a% = Y * a / 100
3. Compute NPV of project by considering flotation cost as cash outflow in period zero
4. For e.g. if a project with total cost of $10,000 is financed with 50% equity and 50% debt. Let flotation cost be 5%, after tax cost of debt be 4% and cost of equity be 10%. Let the life of project be equal to 2 years with annual cash inflow of $6,000
5. Flotation cost (cost of raising equity) = $10,000 * 50% * 5% = $250
6. Cost of capital = 0.5 * 4% + 0.5 * 10% = 7%
7. NPV = -10,000 – 250 + 6,000 / 1.07 + 6,000 / (1.07^2) = 598.11