Capital Components and Cost of Capital in Finance

Basic Definitions Capital refers to the long-term funds used by a firm to finance its assets. Capital components the specific types of capital used by a firm Long-term debt Equity Cost of capital the cost associated with (price of) the various types of capital used by the firm, which is based on the rate of return required by the investors who provide the funds to the firm. 1

COST OF CAPITAL Component costs of capital: o Debt o Equity Preferred stock Common equity Retained earnings New issues of common stock 2

Basic Definitions Weighted average cost of capital, WACC the average percentage cost, based on the proportion of each type of capital, of all the funds used by the firm to finance its assets. Capital structure the mix of the types of capital used by the firm to finance its assets. Optimal capital structure the mix of capital that minimizesthe firm s WACC, thus maximizes its value. 3

COSTOF CAPITAL ^ ^ ^ ^ ^ ^ CF1 CF1 CF2 CF2 CFn CFn Asset Asset Value Value + + + + = = + + (1 + r)1 (1 + r)1 (1 + r)2 (1 + r)2 (1 + r)n (1 + r)n r = firm s required rate of return, which represents the return investors receive for providing funds to the firm. r = the firm s cost of capital for new funds 4

Weighted Average Cost of Capital (WACC)Logic Costs associated with different types of capital (funds) usually are not the same e.g., for a particular firm, debt generally is cheaper than equity. The average cost of each dollar should be a weighted average of the cost of each type of fund the firm uses. Example: Following is a firm s capital structure: Cost Debt rdebt = 8% Equity rstock = 12% Proportion 10% 90% The average cost of each dollar of financing is: Weighted average = 8%(0.1) + 12%(0.9) = 11.6% 5

Cost of Debt, rdT rd the before-tax cost of debt is simply the yield to maturity (YTM) of the debt YTM = bondholders required rate of return = rd rdT the after-tax cost of debt Bondholder required s' Tax savings = r dT rate of return associated with debt = = r r T r (1 T) d d d T = marginal tax rate 6

Cost of Debt, rdTExample A firm has debt with the following characteristics: Maturity value, M $1,000.00 Coupon rate, C Years to maturity Market price $1,099.50 Marginal tax rate 8.0% (paid semiannually) 6 yrs 40.0% Based on this information, we know that the following relationship exists: $40 + $40 + $1,040 r + $1,099.50 = = + + + V d 1 2 12 ) (1 ) (1 ) (1 r r d d d Solving for rd gives the YTM for this bond 7

Cost of Debt, rdTExample A firm has debt with the following characteristics: Maturity value, M $1,000.00 Coupon rate, C Years to maturity Market price $1,099.50 Marginal tax rate 8.0% (paid semiannually) 6 yrs 40.0% 12 ? -1,099.50 40 1,000 N I/Y PV PMT FV 3.0 I/Y = 3.0% = 6-month rate = rd/2 YTM = 3.0% x 2 = 6.0% per year = rd= Before- tax cost of debt 8

Cost of Debt, rdTTax Deductibility of Interest Example: Suppose the firm issues a new $1,000 face value bond with a 6 percent coupon rate, thus interest equal to $60 is paid each year. If the firm s taxable income before considering the interest payment is $500 and its marginal tax rate is 40 percent. Tax without interest = $500(0.40) Tax with interest = ($500 - $60)( 0.40) = $176 = $200 Savings = $24 = $60(0.4) Net interest after tax savings = $60 - $24 = $36 After-tax cost of the new bond = $36/$1,000 = 3.6% rdT = rd x (1 T) = 6% x (1 0.4) = 3.6% 9

Cost of Debt, rdT rdT = rd x (1 T) = YTM x (1 T) = 6%(1 0.4) = 3.6% rd = before-tax cost of debt = YTM T = marginal tax rate 10

Cost of Equity The cost of equity is based on the rate of return required by the firm s stockholders. Cost of preferred stock dividends received by preferred stockholders represent an annuity Cost of retained earnings (internal equity) return common stockholders require the firm to earn on the funds it has retained, thus reinvested in the firm, rather than paid out as dividends (no flotation costs) Cost of new (external) equity rate of return required by common stockholders after considering the cost associated with issuing new stock (flotation costs) 11

Cost of EquityPreferred Stock Most preferred stocks pay constant dividends, thus the dividend stream represents a perpetuity. Valuing preferred stock as a perpetuity gives: D P = ps 0 ps r Solving for the required rate of return, rps, gives: D ps = ps r P 0 Because flotation (issuing) costs must be paid when preferred stock is issued, rps is: D NP 0 0 F D NP0 = net proceeds from issue = flotation costs (percent) ps ps = = r ps P (1 - F) 12

Cost of Preferred StockExample A firm has preferred stock with the following characteristics: Market price, P0 Dividend, Dps Flotation cost, F $75.00 $5.76 4.0% $5.76 $5.76 rps= = = 0.08 = 8.0% $75.00(1 0.04) - $72.00 No tax adjustment, because dividends are not a tax-deductible expense. 13

Cost of EquityRetained Earnings, rs The firm must earn a return on reinvested earnings that is sufficient to satisfy common stockholders investment demands. If the firm does not earn a sufficient return using retained earnings, then the earnings should be paid out as dividends so that stockholders can invest the funds outside the firm to earn an appropriate rate. 14

Cost of EquityRetained Earnings, rs Assuming the stock market is at or near equilibrium, we know that the following relationship exists: Required rate Expected rate = of return of return D 1 r = + = = + g r (r ) RF r RF r s s s M P 0 D rRF = risk-free rate rM = market return s= stock s beta coefficient = next expected dividend g = constant growth rate 1 15

Cost of Retained Earnings, rs CAPM Approach = + r r (r r ) s s RF M RF If rRF = 4%, rM = 9%, and s = 1.4 rs = 4% + (9% - 4%)1.4 = 11.0% Assumes the firm s stockholders are very well diversified. rRF generally is associated with Treasury securities 16

Cost of Retained Earnings, rs Discounted Cash Flow (DCF) Approach If the firm is expected to grow at a constant rate, then we have the following relationship: = + = = yield P 0 D Dividend Capital 1 r + r g s s gain Example: The firm, which is growing at a constant rate of 5 percent, just paid a dividend equal to $1.20; its stock currently sells for $18. $1.20(1.05) r 0.05= $18.00 $1.26 $18.00 = + + 0.05 s = 0.07 + 0.05 = 0.12 = 12.0% 17

Cost of Retained Earnings, rs Bond-Yield-Plus-Risk-Premium Approach Studies have shown that the return on equity for a particular firm is approximately 3 to 5 percentage points higher than the return on its debt. As a general rule of thumb, firms often compute the YTM, or rd, for their bonds and then add 3 to 5 percent. In the current example, rd = 6.0%. As a rough estimate, then, we might say the cost of retained earnings is rs rd + 4% = 6% + 4% = 10.0% 18

Cost of Retained Earnings, rs The three approaches we used to determine the cost of retained earnings give three different results. The approaches are based on different assumptions: o CAPM approach assumes investors are extremely well diversified. o DCF approach assumes the firms grows at a constant rate. o Bond-yield-plus-risk-premium approach assumes that the return on equity is related to the return on the firm s debt. Ideally all three approaches should give the same result; if not, however, we might average the results: rs = (11% + 10% + 12%)/3 = 11% 19

Cost of EquityNewly Issued Common Stock, re The same as rs, except the costs associated with issuing new stock (flotation costs) must be considered. Because the firm has to provide the same gross return to new stockholders as existing stockholders, when the flotation costs associated with a common stock issue are considered, the cost of new common stock always must be greater than the cost of retained earnings. Modify the DCF approach for computing the cost of retained earnings to include flotation costs 20

Cost of EquityNewly Issued Common Stock, re D D 1 1 = + = + r g g e P (1 F) NP 0 0 NP0 = net proceeds from the sale of the stock If flotation costs equal 6 percent, then re in our example is $1.26 $1.26 = 0.05 + re = 0.05 + 0.06) $18(1 $16.92 0.1245 = 12.45% = 21

Cost of Retained Earnings, rs, versus Cost of Newly Issued Common Stock, re Cost of retained earnings, rs D P $1.26 $18 1 = + = + = = r g 0.05 0.012 12.0% s 0 Cost of new common equity, re D $1.26 1 = + = + r g 0.05 e P (1 F) $18(1 0.06) 0 $1.26 $16.92 = + = = 0.05 0.1245 12.45% 22

WEIGHTED AVERAGE COSTOF CAPITAL (WACC) To make decisions about capital budgeting projects, we need to combine the various component costs of capital into a single required rate of return. Weighted average cost of capital, WACC the weighted average of the component costs of capital using as the weights the proportion each type of financing makes up of the total financing of the firm. % preferred % After - tax Cost of common % Cost of = WACC + + debt stock cost of debt preferred stock equity common equity = + + w r w r w (r or r ) d dT ps ps s s e 23

WACC Suppose our illustrative firm has the following capital structure: Percent Type of Financing of total Type of Financing of total Percent After-Tax Cost, r Debt, d Preferred stock, ps Common equity, s If the firm can use retained earningsto finance new projects 40.0 10.0 50.0 100.0 11.0 OR 12.45 3.6% 8.0 WACC = 0.4(3.6%) + 0.1(8.0%) + 0.5(11.0%) = 7.74% If the firm has to issue new common stockto finance new projects WACC = 0.4(3.6%) + 0.1(8.0%) + 0.5(12.45%) = 8.47% 24

Marginal Cost of Capital, MCC The WACC differs depending on the amount of funds the firm needs. MCC = WACC of raising additional funds, which means there is more than one WACC. Generally, MCC increases as more funds are raised, because the o firm s risk increases, which causes investors to require a higher rate of return. o costs of issuing new funds increase. MCC schedule a graph that shows the average cost of funds at various levels of new financing 25

MCC ScheduleExample * Firm expects to generate $200,00 in retained earnings MCC = r (%) 9.0 WACC2 = 8.4 8.0 WACC1 = 7.7 7.0 Total Funds Raised ($000) 0 100 200 300 400 500 BP1 = 400 Break point 26

MCC ScheduleBreak Points Break points occur when WACC increases, which is caused by an increase in any of the component costs of capital Costs of funds often increase as the firm uses significantly higher amounts risk increases. 27

MCC ScheduleBreak Points ( ) ( ) Total amount of funds needed ( source of funds Proportion of source of funds in capital structure Amount of a particular source of funds Proportion of source of funds in capital structure ) ) = Amount of a particular Total amount of= funds needed ( Total amount of a given type of lower the at capital cost Break= point Proportion of this type of capital the in capital structure Retained earnings $200,000 = = $400,000 = Proportion of common equity 0.50 This computation translates a break point caused by a specific component of capital into the equivalent amount of total funds. 28

MCC Schedule Break PointsExample Assume the firm faces the following situation this year: Debt (40%): Amount of Funds $ 1 - $100,000 100,001 - 200,000 200,001 - Preferred Stock (10%): rps = 8.0%, no matter the amount needed Common Equity (50%): o Retained earnings generated during the year = $200,000 o Cost of retained earnings (internal equity), rs = 11.0% o Cost of new common stock (external equity), re = 12.4%, no matter how much is needed Cost of Debt, rd 6.0% 7.0 7.5 29

MCC Schedule Break PointsExample Debt (40%): Amount of Funds Cost of Debt, rd 6.0% $ 1 - $100,000 100,001 - 200,000 7.0 200,001 - 7.5 $100,000 Break If the firm needs total funds equal to $250,000, 40%, or $100,000 would be debt. = $250,000 = Point 0.40 debt1 $200,000 Break If the firm needs total funds equal to $500,000, 40%, or $200,000 would be debt. = $500,000 = Point 0.40 debt2 30

MCC Schedule Break PointsExample Preferred Stock (10%): rps = 8.0%, no matter the amount needed Constant cost no break point due to preferred stock Common Equity (50%): Retained earnings generated during the year = $200,000 o Cost of retained earnings (internal equity), rs = 11.0% Cost of new common stock (external equity), re = 12.4%, no matter how much is needed o o If the firm needs total funds equal to $400,000, 50%, or $200,000 would be RE. $200,000 Break = $400,000 = Point 0.50 RE 31

MCC Schedule Break PointsExample Break Points 1. BP1 (Debt1) = $250,000 2. BP2 (RE) 3. BP3 (Debt2) = $500,000 = $400,000 WACC ranges 1. WACC1: $ 1 $250,000 2. WACC2: $250,001 $400,000 3. WACC3: $400,001 $500,000 4. WACC4: Greater than $500,000 32

MCC ScheduleExample Funds = $1 - $250,000 Debt Preferred Stock Common Equity Amount at $250,000 Weight x Cost, r = WACC $100,000 25,000 125,000 250,000 1.0 After-Tax 0.4 0.1 0.5 3.6 8.0 11.0 1.44 0.80 5.50 7.74%= WACC1 Funds = $250,001 - $400,000 Amount at $400,000 After-Tax Debt Preferred Stock Common Equity Weight x Cost, r = WACC 1.68 0.80 5.50 7.98%= WACC2 $160,000 40,000 200,000 400,000 0.4 0.1 0.5 1.0 4.2 8.0 11.0 33

MCC ScheduleExample Funds = $400,001 - $500,000 Debt Preferred Stock Common Equity Amount at $500,000 Weight x Cost, r = WACC $200,000 50,000 250,000 500,000 1.0 After-Tax 0.4 0.1 0.5 4.2 8.0 12.4 1.68 0.80 6.20 8.68%= WACC3 Funds = Above $500,000 Debt Preferred Stock Common Equity Amount at $600,000 After-Tax Weight x Cost, r = WACC 1.80 0.80 6.20 8.80%= WACC4 $240,000 60,000 300,000 600,000 0.4 0.1 0.5 1.0 4.5 8.0 12.4 34

MCC ScheduleExample MCC = r (%) WACC4 = 8.8 9.0 WACC3 = 8.7 WACC2 = 8.0 8.0 WACC1 = 7.7 7.0 Total Funds Raised ($000) 0 100 200 300 400 500 BP1 = 250 BP2 BP3 35

WACC EXAMPLE Suppose the firm s capital budgeting projects are: Project Cost IRR A $150,000 9.3% B 200,000 8.9 C 200,000 8.6 D 100,000 8.2 36

Investment Opportunity Schedule (IOS) IRR (%) 10.0 IRRA = 9.3 IRRB = 8.9 9.0 IRRC = 8.6 IRRD = 8.2 8.0 7.0 0 100 200 300 400 500 600 700 Total Funds Raised ($000) 37

IOS/MCC SchedulesMaking a Decision (%) 10.0 IRRA = 9.3 WACC4 = 8.8 IRRB = 8.9 9.0 WACC3 = 8.7 IRRC = 8.6 IRRD = 8.2 WACC2 = 8.0 8.0 WACC1 = 7.7 7.0 0 100 200 300 Optimal Capital Budget = 350 400 500 600 700 Total Funds Raised ($000) 38

WACC Investors determine the firm s costs of funds. The firm s costs of funds change when o conditions in the financial markets change. o investors general risk aversion changes. o firm s risk changes Relationships of Capital Components o Risk For the COMPANY debt is riskiest For the INVESTOR common equity is riskiest o Cost for a particular firm rdT < rd < rps < rs < re Common Equity Debt 39

CHAPTER 11 QUESTIONS 1. What types of capital do firms use to finance investments? 2. What is the cost of capital? 3. Why do funds generated through retained earnings have a cost? 4. How is the weighted average cost of capital (WACC) computed? 5. How is the weighted average cost of capital (WACC) used to make financial decisions? 6. Who determines a firm s cost of capital? 40

CHAPTER 11 SUPPLEMENTAL QUESTIONS 1. In what sense does the marginal cost of capital schedule represent a series of average costs? 2. What impact will investors expectations about inflation have on a firm s cost of debt? Will the firm s cost of equity be affected? Explain. 3. Explain why, for a particular firm, the cost of retained earnings, rs, will always be less than the cost of new equity, re. 4. Suppose a firm invests in projects that are much riskier than its average investments. Do you think the firm s weighted average cost of capital will be affected? Explain 41