CHAPTER 27 COST OF CAPITAL AND CAPITAL STRUCTURE DECISIONS The cost of capital is defined as the rate of return that is necessary to maintain the market value of the firm (or price of the firm’s stock).CFOs must know the cost of capital (the minimum required rate of return) in (1) making capital budgeting decisions, (2) helping to establish the optimal capital structure, and (3) making decisions such as leasing, bond refunding, and working capital management. The cost of capital is used either as a discount rate under the NPV method or as a hurdle rate under the IRR method. The cost of capital is computed as a weighted average of the various capital components, which are items on the right-hand side of the balance sheet such as debt, preferred stock, common stock, and retained earnings. How do you compute individual costs of capital? Each element of capital has a component cost that is identified by: k i = before-tax cost of debt k d = k i (1 − t) = after-tax cost of debt, where t = tax rate k p = cost of preferred stock k s = cost of retained earnings (or internal equity) k e = cost of external equity, or cost of issuing new common stock k o = firm’s overall cost of capital, or a weighted average cost of capital COST OF DEBT The before-tax cost of debt can be found by determining the internal rate of return (or yield to maturity) on the bond cash flows. 515 516 Cost of Capital a nd Capital Structure Decisions However, the following shortcut formula may be used for approximating the yield to maturity on a bond: k i = I + (M − V)/n (M + V)/2 where I = annual interest payments in dollars M = par or face value, usually $1,000 per bond V = market value or net proceeds from the sale of a bond n = term of the bond n years Since the interest payments are tax-deductible, the cost of debt must be stated on an after-tax basis. The after-tax cost of debt is: k d = k i (1 − t) where t is the tax rate. EXAMPLE 27.1 Assume that the Carter Company issues a $1,000, 8 percent, 20-year bond whose net proceeds are $940. The tax rate is 40 percent. Then, the before-tax cost of debt, k i ,is: k i = I + (M − V)/n (M + V)/2 = $80 + ($1,000 − $940)/20 ($1,000 + $940)/2 = $83 $970 = 8.56% Therefore, the after-tax cost of debt is: k d = k i (1 − t) = 8.56%(1 − 0.4) = 5.14% COST OF PREFERRED STOCK The cost of preferred stock, k p , is found by dividing the annual preferred stock dividend, d p , by the net proceeds from the sale of the preferred stock, p, as follows. k p = d p p Since preferred stock dividends are not a tax-deductible expense, these dividends are paid after taxes. Conse- quently, no tax adjustment is required. Cost of Equity Capital 517 EXAMPLE 27.2 Suppose that the Carter Company has preferred stock that pays a $13 dividend per share and sells for $100 per share in the market. The flotation (or underwrit- ing) cost is 3 percent, or $3 per share. Then the cost of preferred stock is: k p = d p P = $13 $97 = 13.4% COST OF EQUITY CAPITAL The cost of common stock, k e , is generally viewed as the rate of return investors require on a firm’s common stock. Two techniques for measuring the cost of common stock equity capital are widely used: (1) t he Gordon’s growth model and (2) the capital asset pricing model (CAPM) approach. The Gordon’s growth model is: P o = D 1 r − g where P o = value (or market price) of common stock D 1 = dividend to be received in one year r =investor’s required rate of return g = rate of growth (assumed to be constant over time) Solving the model for r results in the formula for the cost of common stock: r = D 1 P o + g or k e = D 1 P o + g Note that the symbol r is changed to k e to show that it is used for the computation of cost of capital. EXAMPLE 27.3 Assume that the market price of the Carter Company’s stock is $40. The dividend to be paid at the end of the coming year is $4 per share and is expected to grow at a constant annual rate of 6 percent. Then the cost of this common stock is: 518 Cost of Capital a nd Capital Structure Decisions EXAMPLE 27.3 (continued) k e = D 1 P o + g = $4 $40 + 6% = 16% The cost of new common stock, or external equity capital, is higher than the cost of existing common stock because of the flotation costs involved in selling the new common stock. Flotation costs, sometimes called issuance costs, are the total costs of issuing and selling a security that include printing and engraving, legal fees, and accounting fees. If f is flotation cost in percent, the formula for the cost of new common stock is: k e = D 1 P o (1 − f) + g EXAMPLE 27.4 Assume the same data as in Example 27.3, except the firm is trying to sell new issues of stock A and its flotation cost is 10 percent Then: k e = D 1 P o (1 − f) + g = $4 $40(1 −0.1) + 6% = $4 $36 + 6% = 11. 11% + 6% = 17.11% CAPITAL ASSET PRICING MODEL (CAPM)APPROACH An alternative approach to measuring the cost of common stock is to use the CAPM, which involves these four steps: 1. Estimate the risk-free rate, r f , generally taken to be the United States Treasury bill rate. 2. Estimate the stock’s beta coefficient, b,whichis an index of systematic (or nondiversifiable market) risk. 3. Estimate the rate of return on the market portfolio, r m , such as the Standard & Poor’s 500 Stock Composite Index or Dow Jones 30 Industrials. 4. Estimate the required rate of return on the firm’s stock, using the CAPM equation: k e = r f + b(r m − r f ) Again, note that the symbol r j is changed to k e . Cost of Retained Earnings 519 EXAMPLE 27.5 Assuming that r f is 7 percent, b is 1.5, and r m is 13 percent, then: k e = r f + b(r m − r f ) = 7% + 1.5 (13% − 7%) = 16% This 16 percent cost of common stock canbe viewed as consisting of a 7 percent risk-free rate plus a 9 percent risk premium, which reflects t hat the firm’s stock price is 1.5 times more volatile than the market portfolio to the factors affecting nondiversifiable, or systematic risk. COST OF RETAINED EARNINGS The cost of retained earnings, k s is closely related to the cost of existing common stock, since the cost of equity obtained by retained e arnings is the same as the rate of return investors require on the firm’s common stock. Therefore, k e = k s How is the overall cost of capital determined? The firm’s overall cost of capital is the weighted average of the individual capital costs, with the weights being the proportions of each type of capital used. Let k o be the overall cost of capital. k o =  (percentage of the total capital structure supplied by each source of capital × cost of capital for each source) =  w d k d + w p k p + w e k e + w s k s where w d = % of total capital supplied by debts w p = % of total capital supplied by preferred stock w e = % of total capital supplied by external equity w s = % of total capital supplied b y retained e arnings (or internal equity) The weights can be historical, target, or marginal. 520 Cost of Capital a nd Capital Structure Decisions HISTORICAL WEIGHTS Historical weights are based on a firm’s existing capital structure. The use of these weights is based on the assumption that the firm’s existing capital structure is optimal and therefore should be maintained in the future. Two types of historical weights can be used: book value weights and market value weights. Book Value Weights The use of book value weights in calculating the firm’s weighted cost of capital assumes that new financing will be raised employing the same method the firm used for its present capital structure. The weights are determined by dividing the book value of each capital component by t he sum o f the book values of all the long-term capital sources. The computation of overall cost of capital is illustrated in Example 27.6. EXAMPLE 27.6 Assume the follo wing capital structure and cost of each source of financing for the Carter Company: Source Cost Mortgage bonds ($1,000 par) $20,000,000 5.14% (Example 27.1) Preferred stock ($100 par) 5,000,000 13.40% (Example 27.2) Common stock ($40 par) 20,000,000 17.11% (Example 27.3) Retained earnings 5,000,000 16.00% (Example 27.4) $50,000,000 The book value weights and the overall cost of capital are computed as: Source Book value Weights Cost Weighted cost Debt $20,000,000 40% a 5.14% 2.06% b Preferred stock 5,000,000 10 13.40% 1.34 Common stock 20,000,000 40 17.11% 6.84 Retained earnings 5,000,000 10 16.00% 1.60 $50,000,000 100% 11.84 Overall cost of capital = k o = 11.84% a $20,000,000/$50,000,000 = 0.40 = 40% b 5.14% × 40% = 2.06% Historical Weights 521 Market Value Weights Market value weights are determined by dividing the market value of each source by the sum of the market val- ues of all sources. The use of market value weights forcom- puting a firm’s weighted average cost of capital is theoret- ically more appealing than the use of book value weights because the market values of the securities closely approx- imate the actual dollars to be received from their sale. EXAMPLE 27.7 In addition to the data from Example 27.6, assume that the security market prices are: Mortgage bonds = $1,100 per bond Preferred stock = $90 per share Common stock = $80 per share The firm’s number of securities in each category is: Mortgage bonds = $20,000,000 $1,000 = 20,000 Preferred stock = $5,000,000 $100 = 50,000 Common stock = $20,000,000 $40 = 500,000 Therefore, the market value weights are: Source Number of Price Market Securities Value Debt 20,000 $1,100 $22,000,000 Preferred stock 50,000 $ 90 4,500,000 Common stock 500,000 $ 80 40,000,000 $66,500,000 The $40 million common stock value must be split in the ratio of 4 to 1 (the $20 million common stock versus the $5 million retained earnings in the origi- nal capital structure), since the market value of the retained earnings has been impounded into the com- mon stock. The firm’s cost of capital is: Source Market Value Weights Cost Weighted Average Debt $22,000,000 33.08% 5.14% 1.70% Preferred stock 4,500,000 6.77 13.40% 0.91 522 Cost of Capital a nd Capital Structure Decisions EXAMPLE 27.7 (continued) Source Market Value Weights Cost Weighted Common stock 32,000,000 48.12 17.11% 8.23 Retained earnings 8,000,000 12.03 16.00% 1.92 $66,500,000 100.00% 12.76% Overall cost of capital = k o = 12.76% TARGET WEIGHTS If the firm has a target capital structure (desired debt- equity mix) that is maintained over the long term, then that capital structure and associated weights can be used in calculating the firm’s weighted cost of capital. MARGINAL WEIGHTS Marginal weights involves use of the actual financial mix used in financing the proposed investments. In using tar- get weights, the firm is concerned with what it believes to be the optimal capital structure o r target percentage. In using marginal weights, the firm is concerned with the actual dollar amounts of each type of financing to be needed for a given investment project. This approach, though attractive, presents a problem. The cost of cap- ital for the individual sources depends on the firm’s financial risk, which is affected by the firm’s financial mix. If the company alters its present capital structure, the individual costs will change, which makes it more difficult to compute the weighted cost of capital. The important assumption needed is that the firm’s financial mix is relatively stable and that these weights will closely approximate future financing practice. EXAMPLE 27.8 The Carter Company is considering raising $8 million for plant expansion. The CFO estimates using the following mix for financing this project: Debt $4,000,000 50% Common stock 2,000,000 25% Retained earnings 2,000,000 25% $8,000,000 100% EBIT-EPS Approach to Capital Structure Decisions 523 EXAMPLE 27.8 (continued) The company’s cost of capital is computed as: Source Marginal Cost Weighted Weights Cost Debt 50% 5.14% 2.57% Common stock 25 17.11% 4.28 Retained earnings 25 16.00% 4.00 100% 10.85% Overall cost of capital = k o = 10.85% How do you determine the firm’s optimal capital structure? The concepts to be covered in this chapter relate closely to the cost of capital and also to the crucial problem of determining the firm’s optimal capital structure. We will cover three methods that show how to build an appropriate financing mix. EBIT-EPS APPROACH TO CAPITAL STRUCTURE DECISIONS This analysis is a practical tool that enables the CFO to evaluate alternative financing plans by investigating their effect on EPS over a range of EBIT levels. Its primary objective is to determine the EBIT breakeven, or indif- ference, points between the various alternative financing plans. The indifference point identifies the EBIT level at which the EPS will be the same regardless of the financing plan chosen by the CFO. This indifference point has major implications for cap- ital structure decisions. At EBIT amounts in excess of the EBIT indifference level, the more heavily levered financing plan will generate a higher EPS. At EBIT amounts below the EBIT indifference level, the financing plan involving less leverage will generate a higher EPS. Therefore, it is of critical importance for the CFO to know the EBIT indif- ference level. The indifference points between any two methods of financing can be determined by solving for EBIT in this equality: (EBIT − I)(1 − t) − PD S 1 = (EBIT − I)(1 − t) − PD S 2 where t = tax rate PD = preferred stock dividends 524 Cost of Capital a nd Capital Structure Decisions S 1 and S 2 = number of shares of common stock outstanding after financing for plan 1 and plan 2, respectively EXAMPLE 27.9 Assume that ABC Company, with long-term capital- ization consisting entirely of $5 million in stock, wants to raise $2 million for the acquisition of special equip- ment by (1) selling 40,000 shares of common stock at $50 each, (2) selling bonds at 10 percent interest, or (3) issuing preferred stock with an 8 percent dividend. The present EBIT is $800,000, the income tax rate is 50 percent, and 100,000 shares of common stock are now outstanding. To compute the indifference points, we begin by calculating EPS at a projected EBIT level of $1 million. All All Debt All Common Preferred EBIT $1,000,000 $1,000,000 $1,000,000 Interest 200,000 Earnings before taxes (EBT) $1,000,000 $ 800,000 $1,000,000 Taxes 500,000 400,000 500,000 Earnings after taxes (EAT) $ 500,000 $ 400,000 $ 500,000 Preferred stock dividend 160,000 Earnings available to common stockholders $ 500,000 $ 400,000 $ 340,000 Number of shares 140,000 100,000 100,000 EPS $3.57 $4.00 $3.40 Now connect the EPSs at the level of EBIT of $1 million with the EBITs for each financing alternative on the horizontal axis to obtain the EPS-EBIT graphs. We plot the EBIT necessary to cover all fixed financial costs for each financing alternative on the horizontal axis. For the common stock plan, there are no fixed costs, so the intercept on the horizontal axis is zero. For the debt plan, there must be an EBIT of $200,000 to cover interest charges. For the preferred stock plan, there must be an EBIT of $320,000 [$160,000/(1 – 0.5)] to cover $160,000 in preferred stock dividends at a 50 percent income tax rate; thus, $320,000 becomes the horizontal axis intercept. (See Exhibit 27.1.) In this example, the indifference point between all common and all debt is: [...]... Structure Decisions 529 CAPITAL STRUCTURE DECISIONS How are capital structure decisions made in practice? How do companies decide in practice which route to go in raising capital? It is a complex decision, related to a company’s balance sheet, market conditions, outstanding obligations, and a host of other factors Many CFOs believe that these six factors influence capital structure: 1 2 3 4 5 6 Growth rate and. .. impact of financial leverage as a financing method Investment performance is crucial to the successful application of any leveraging strategy 526 Cost of Capital and Capital Structure Decisions Preferred Debt Common 4 $1,120 EPS ($) 3.57 3.40 3 $700 2 1 200 320 400 800 1,000 1,200 1,600 EBIT (thousands of dollars) Exhibit 27.1 EPS-EBIT GRAPH ANALYSIS OF CORPORATE CASH FLOWS A second tool of capital structure. .. rate and stability of future sales Competitive structure in the industry Asset makeup of the individual firm The business risk to which the firm is exposed Control status of owners and management Lenders’ attitudes toward the industry and the company Surveys indicate that the majority of CFOs of large firms believe in the concept of an optimal capital structure The optimal capital structure is approximated... best capital structure Coverage ratios are subject to certain limitations and, consequently, cannot be used as a sole means of determining the capital structure For one thing, the fact that EBIT falls below the debt-service burden does not spell immediate doom for the company Often alternative sources of funds, including renewal of a loan, are available, and these sources must be considered Capital Structure. .. analysis of cash flows When considering the appropriate capital structure, it is important to analyze the cash flow ability of the firm to service fixed charges, among other things The greater the dollar amount of debt and/ or preferred stock the firm issues and the shorter their maturity, the greater the fixed charges of the firm These charges include principal and interest payments on debt, lease payments, and. .. ratio of less than 1.0, a company may still 528 Cost of Capital and Capital Structure Decisions meet its obligations if it can renew some of its debt when it comes due The financial risk associated with leverage should be analyzed on the basis of the firm’s ability to service total fixed charges Although lease financing is not debt per se, its impact on cash flows is exactly the same as the payment of interest... a deterioration in coverage over time Another method of analyzing the appropriate capital structure for a company is to evaluate the capital structure of other companies having similar business risk Companies used in this comparison may be those in the same industry If the firm is contemplating a capital structure significantly out of line with that of similar companies, it is conspicuous to the marketplace... the exception of preferred stock dividends, may result in insolvency The greater and more stable the expected future cash flows of the firm, the greater the debt capacity of the company COVERAGE RATIOS A third tool is the calculation of comparative coverage ratios Among the ways we can gain insight into the debt capacity of a firm is through the use of coverage ratios In the computation of these ratios,... the use of debt The optimal capital structure for all companies in the industry might call for a higher proportion of debt to equity than the industry average As a result, the firm may well be able to justify more debt than the industry average Because investment analysts and creditors tend to evaluate companies by industry, however, the firm should be able to justify its position if its capital structure. .. computations and observing Exhibit 27.1, we can draw three conclusions: 1 At any level of EBIT, debt is better than preferred stock, since it gives a higher EPS 2 At a level of EBIT above $700,000, debt is better than common stock If EBIT is below $700,000, the reverse is true 3 At a level of EBIT above $1,120,000, preferred stock is better than common At or below that point, the reverse is true A Word of Caution . CHAPTER 27 COST OF CAPITAL AND CAPITAL STRUCTURE DECISIONS The cost of capital is defined as the rate of return that is necessary to maintain the market value of the firm (or price of the firm’s. stock k s = cost of retained earnings (or internal equity) k e = cost of external equity, or cost of issuing new common stock k o = firm’s overall cost of capital, or a weighted average cost of capital COST. individual costs of capital? Each element of capital has a component cost that is identified by: k i = before-tax cost of debt k d = k i (1 − t) = after-tax cost of debt, where t = tax rate k p = cost of