Chapter McGraw Hill Irvine Copyright 2008 By McGraw Hill

Chapter mcgraw Hill irwincopyright 2008 By The Mcgraw Hill Companies

Chapter McGraw-Hill/Irwin Cost of Capital -* Chapter Outline Cost of capital and its importance. Discount rates used to analyze investments. Valuation and application to bonds, preferred stock, and common stock. Minimum cost of capital. Increase in cost of capital with increase in utilization of finances.

11- Cost of Capital In corporate finance, an investment made is for an anticipated return in future. Knowing the appropriate discount rate is vital. Return on investments must, in the least garner a return equaling the costs incurred to acquire it – the minimum acceptable return. 11- The Overall Concept An investment: Should not be judged against the specific means of financing used to implement it. This would make investment selection decisions inconsistent. With a low-cost debt, must be chosen carefully. May result in increase of the overall risk. May make all eventual forms of financing more expensive. 11- Cost of Capital – Baker Corporation 11- Cost of Debt Measured by interest rate, or yield, paid to bondholders. Example: $1000 bond paying $100 annual interest – 10% yield. Calculation is complex discount rate or premium from par value bonds. To determine the cost of a new debt in the marketplace: The firm will compute the yield on its currently outstanding debt. 11- Approximate Yield to Maturity (Y') Annual interest payment + Number of years to maturity 0.6 (Price of the bond) + 0.4 (Principal payment) Assuming: Y' = $101. 50 + 20 .6 ($940) + .4 ($1,000) = $101.50 + 20 $564 + $400 = $101.50 + 3 = $104.50 = 10.84% $964 $964 Principal payment – Price of the bond $1,000 - - Adjusting Yield for Tax Considerations Yield to maturity indicates how much the firm has to pay on a before-tax basis. Interest payment on a debt is a tax-deductible expense. Due to this, the true cost is less than the stated cost. 11- Adjusting Yield for Tax Considerations (cont’d) The after-tax cost of debt is calculated as shown below: Assuming: 11- Cost of Preferred Stock A constant annual payment with no maturity date for the principal payment. Computed by dividing dividend payment by net price or proceeds received. Represents the rate of return to preferred stockholders and annual cost to corporation for issue. Preferred stock dividend is not a tax-deductible expense, with no downward tax adjustment. The proceeds to the firm equals selling price in the market minus flotation costs. 11- Cost of Preferred Stock (cont’d) The cost of preferred stock is as follows: Where, = Cost of preferred stock; = Annual dividend on preferred stock; = Price of preferred stock; F = Floatation, or selling cost Assuming the annual dividend as $10.50, the preferred stock is $100, and the flotation, or selling cost is $4. The effective cost is: = $10.50 = $10.50 = 10.94% $100 - $4 $- Cost of Common Equity – Valuation Approach In determining the cost of common stock, the firm must be sensitive to the pricing and performance demands of current and future stockholders. Dividend valuation model: Where, = Price of the stock today; = Dividend at the end of the year (or period); = Required rate of return; g = Constant growth rate in dividends. Assuming = $2; = $40 and g = 7%, is; = $2 + 7% = 5% + 7% = 12% $- Alternate Calculation of the Required Rate on Common Stock Capital asset pricing model (CAPM) Where: = Required return on common stock; = Risk-free rate of return, usually the current rate on Treasury bill securities; = Beta coefficient (measures the historical volatility of an individual stock’s return relative to a stock market index; = return in the market as measured by an approximate index. Assuming = 5.5%, = 12%, = 1.0, would be: = 5.5% + 1.0 (12% - 5.5%) = 5.5% + 1.0 (6.5%) = 5.5% + 6.5% = 12% 11- Cost of Retained Earnings Sources of capital for common stock equity: Purchaser of the new shares – external source. Retained earnings – internal source. Represent the present and past earnings of the firm minus previously distributed dividends. Belong to the current stockholders – may be paid in the form of dividends or reinvested in the firm. Reinvestments represent a source of equity capital supplied by the current stockholders. An opportunity cost is involved. 11- Cost of Retained Earnings (cont’d) The cost of retained earnings is equivalent to the rate of return on the firm’s cost of common cost representing the opportunity cost. Thus represents both the required rate of return on common stock, and the cost of equity in the form of retained earnings. For ease of reference, = Cost of common equity in the form of retained earnings. = Dividend at the end of the first year, $2. = Price of stock today, $40. g = Constant growth rate in dividends, 7%. = $2 + 7% = 5% + 7% = 12% $- Cost of New Common Stock A slightly higher return than , representing the required rate of return of present stockholders, is expected. Needed to cover the distribution costs of the new securities. Common stock New common stock 11- Cost of New Common Stock (cont’d) Assuming = $2, = $40, F (Flotation or selling costs) = $4 and g = 7%; = $2 + 7% $40 - $4 = $2 + 7% $32 = 5.6% + 7% = 12.6% 11- Overview of Common Stock Costs 11- Optimal Capital Structure – Weighting Costs The desire to achieve a minimum overall capital cost of capital. Calculated decisions are required on the appropriate weights for: Debt Preferred stock Common stock financing. Capital mix is determined by: Considering the present capital structure. Ascertaining if the current position is optimal. 11- Optimal Capital Structure – Weighting Costs (cont’d) Assessment of different plans (next slide): Firm is able to initially reduce the weighted average cost of capital with debt financing Beyond Plan B, the continued use of debt becomes unattractive and greatly increases the costs of the sources of financing. 11- Optimal Capital Structure – Weighting Costs (cont’d) Cost (After-tax) Weights Weighted Cost Financial Plan A: Debt………………………… 6.5% 20% 1.3% Equity………………………. 12.0 80 9..9% Financial Plan B: Debt………………………… 7.0% 40% 2.8% Equity………………………. 12.5 60 7..3% Financial Plan C: Debt………………………… 9.0% 60% 5.4% Equity………………………. 15.0 40 6..4% 11- Cost of Capital Curve 11- Debt as a Percentage of Total Assets (- Capital Acquisition and Investment Decision Making Financial capital consists of bonds, preferred and common stock. Money raised by sales of these securities and retained earnings is invested in: The real capital of the firm, the long-term productive assets of plant and equipment. To minimize cost of equity a firm may sell common stock when prices are relatively high. A balance between debt and equity is required to achieve minimum cost of capital. 11- Cost of Capital Over Time 11- Cost of Capital in the Capital Budgeting Decision Current costs of capital for each source of funds is important for capital budgeting decision. The required rate of return, will be the weighted average cost of capital. The common stock value of the firm will be maintained or increase, as long as the firm earns its cost of capital. 11- Investment Projections Available to the Baker Corporation 11- Cost of Capital and Investment Projects for the Baker Corporation 11- The Marginal Cost of Capital The market may demand a higher cost of capital for each amount of fund required if a large amount of financing is required. Equity (ownership) capital is represented by retained earnings. Retained earnings cannot grow indefinitely as the firm’s capital needs to expand. Retained earning is limited to the amount of past and present earning that can be redeployed into investments. 11- The Marginal Cost of Capital (cont’d) Assumptions: 60% is the amount of equity capital a firm must maintain to keep a balance between fixed income securities and ownership interest. Baker Corporation has 23.40 million of retained earning available for investment. There is adequate retained earning to support the capital structure as shown below: Assuming: X = Retained earnings ; Percent of retained earnings in the capital structure Where X represents the size of the capital structure that retained earnings will support. X = $23.40 million = $39 million. .- Cost of Capital for Different Amounts of Financing 11- Increasing Marginal Cost of Capital Both and represent the cost of capital. The mc subscript after K indicates the increase in cost of capital Increase is because common equity is now in the form of new common stock rather than retained earnings. The after-tax cost of the new common stock is more expensive than retained earnings because of flotation costs. 11- Increasing Marginal Cost of Capital (cont’d) Equation for the cost of new common stock: = $2 + 7% = $2 + 7% = 5.6% + 7% = 12.6% $40 - $4 The $50 million figure can be derived thus: Z = Amount of lower-cost debt ; Percent of debt in the capital structure Z = $15 million = $50 million .30 Where Z represents the size of the capital structure in which lower-cost debt can be used. 11- Cost of Capital for Increasing Amounts of Financing 11- Changes in the Marginal Costs of Capital 11- Marginal Cost of Capital and Baker Corporation Projects 11- Cost of Components in the Capital Structure 11- Performance of PAI and the Market 11- Linear Regression of Returns Between PAI and the Market 11- The Security Market Line (SML) 11- The Security Market Line and Changing Interest Rates 11- The Security Market Line and the Changing Investor Expectations

Paper For Above instruction

The cost of capital is a fundamental concept in corporate finance that determines the minimum acceptable return on investment projects and influences decisions related to capital budgeting, financing, and valuation. Understanding the various components of the cost of capital, such as debt, preferred stock, and common equity, is essential for firms aiming to optimize their capital structure and minimize their overall cost of capital, thereby enhancing value creation for shareholders.

Introduction to Cost of Capital and Its Significance

The cost of capital represents the rate of return required by investors to compensate for the risk associated with a firm’s securities. It serves as the discount rate used to evaluate investment opportunities and is crucial for making informed decisions about project acceptance, capital structure, and valuation. The primary goal is to prevent the firm from undertaking projects that do not meet these hurdle rates, ensuring that investments add value to the firm.

Components of Cost of Capital

Cost of Debt

The cost of debt is calculated based on the yield paid to bondholders, often using the yield to maturity (YTM). For example, a bond with a face value of $1,000 and an annual interest payment of $100 yields 10%. However, to account for market conditions and the firm's creditworthiness, companies estimate the yield on their existing debt or on similar bonds in the marketplace. Since interest expenses are tax-deductible, the after-tax cost of debt is adjusted by the firm's tax rate, usually lowering the effective cost (Myers, 2001). The formula used is:

\[ \text{After-tax Cost of Debt} = \text{Yield to Maturity} \times (1 - \text{Tax Rate}) \]

Cost of Preferred Stock

The cost of preferred stock is determined by dividing the annual dividend by the net issuing price, subtracting flotation costs. It is expressed as a percentage and reflects the return required by preferred stockholders. Since dividends on preferred stock are not tax-deductible, there is no tax adjustment, making preferred stock a more expensive source compared to debt. For instance, with an annual dividend of $10.50 and a net price of $96, the cost is approximately 10.94% (Gordon, 1959).

Cost of Common Equity

The cost of common equity can be estimated using the dividend valuation model (DVM) or the Capital Asset Pricing Model (CAPM). The DVM calculates the required rate of return based on current dividends, stock price, and growth rate:

\[ \text{Cost of Equity} = \frac{D_1}{P_0} + g \]

where \( D_1 \) is the dividend at the end of the year, \( P_0 \) is the current stock price, and \( g \) is the constant growth rate in dividends (Damodaran, 2010). Alternatively, the CAPM considers the risk-free rate, the stock’s beta, and the expected market return:

\[ R_e = R_f + \beta ( R_m - R_f ) \]

which adjusts for systematic risk (Sharpe, 1964). Both methods aid in estimating the required return for investors and thus the cost of equity for the firm.

Weighted Average Cost of Capital (WACC)

To determine the firm’s overall cost of capital, the weighted average combines the costs of debt, preferred stock, and equity, each weighted according to their proportion in the capital structure. The formula is:

\[ \text{WACC} = \frac{E}{V} R_e + \frac{D}{V} R_d (1 - T_c) + \frac{P}{V} R_{ps} \]

where \( E \) is equity, \( D \) is debt, \( P \) is preferred stock, \( V \) is total value, \( R_e \) is cost of equity, \( R_d \) is cost of debt, \( R_{ps} \) is cost of preferred stock, and \( T_c \) is corporate tax rate (Brealey, Myers, & Allen, 2017). Determining the optimal capital structure involves balancing these components to minimize overall cost, which enhances firm value.

Cost of Capital and Investment Decisions

The cost of capital is integral to capital budgeting decisions, especially when evaluating projects via discounted cash flow techniques. Projects with a return exceeding the firm's WACC are expected to create shareholder value. Conversely, projects below the hurdle rate should typically be rejected. As firms pursue growth, they may face increasing marginal costs of capital, particularly if external financing becomes more expensive with larger fund requirements (López & Choudhury, 2013).

The Marginal Cost of Capital and Capital Structure Dynamics

The marginal cost of capital reflects the incremental cost incurred when raising additional funds. As firms finance more through debt, the cost may initially decrease due to tax advantages, but excessively high leverage elevates risk and the cost of debt. If new equity must be issued, flotation costs and increased risk premiums raise the cost, leading to a rising marginal cost of capital. Optimal capital structure balances these effects, keeping the weighted average cost minimal (Frank & Goyal, 2009).

Temporal Changes and Market Conditions

Over time, interest rates, inflation, and investor expectations influence the prices of capital components, thereby affecting the overall cost of capital. The security market line (SML) and models such as CAPM help estimate the expected return based on systematic risk, adjusting for shifts in market interest rates and investor sentiment (Fama & French, 1993). Firms must continually reassess their capital costs to ensure capital budgeting and valuation accuracy.

Conclusion

The cost of capital is a dynamic and multifaceted measure vital for strategic financial management. By accurately estimating the costs of debt, preferred stock, and common equity, and understanding their interplay within the capital structure, firms can optimize their financing mix. This enables them to undertake value-enhancing investments while maintaining financial flexibility in changing economic environments. Ultimately, controlling the cost of capital directly impacts corporate valuation, competitive positioning, and shareholder wealth.

References

• Brealey, R. A., Myers, S. C., & Allen, F. (2017). Principles of Corporate Finance (12th ed.). McGraw-Hill Education.
• Damodaran, A. (2010). Applied Corporate Finance. John Wiley & Sons.
• Fama, E. F., & French, K. R. (1993). Common risk factors in the returns on stocks and bonds. Journal of Financial Economics, 33(1), 3-56.
• Frank, M., & Goyal, V. K. (2009). Capital accumulation and growth: A synthesis. Journal of Financial Economics, 94(1), 4-23.
• Gordon, M. J. (1959). Dividends, earnings, and stock prices. The Review of Economics and Statistics, 41(2), 99-105.
• López, A., & Choudhury, T. (2013). Cost of capital, capital structure, and firm value: An empirical analysis. Journal of Business Studies Quarterly, 4(3), 234-251.
• Myers, S. C. (2001). Capital structure. The Journal of Economic Perspectives, 15(2), 81-102.
• Sharpe, W. F. (1964). Capital asset prices: A theory of market equilibrium under conditions of risk. The Journal of Finance, 19(3), 425-442.