Cost of Capital

A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 B C D E F G 8/23/2004 H Chapter 9. Tool Kit for the Cost of Capital The cost of capital is a vital element in the capital budgeting process. For a project to be accepted, it must provide a return that exceeds its cost of capital, or hurdle rate. The cost of capital also serves three other purposes: (1) It is used to help determine the EVA, (2) Managers use the cost of capital when deciding between buying and leasing, and (3) the cost of capital is used in the regulation of electric, gas, and telephone companies. The cost of capital is the weighted average cost of the debt, preferred stock, and common equity that the firm uses to finance its assets, or its WACC. There is an overall, or corporate, WACC which reflects the average riskiness of all the firm's assets. However, since different assets may have more or less risk than the average, the overall WACC must be adjusted up or down to reflect the riskiness of different proposed capital budgeting projects. COST OF DEBT, rd The relevant cost of debt is the after-tax cost of new debt, taking account of the tax deductibility of interest. The after-tax calculated by multiplying the interest rate (or the before-tax cost of debt) times one minus the tax rate. PROBLEM Find the after-tax cost of debt for a company that pays 11% interest on debt and is subject to a 40% marginal tax rate. B-T rd Tax rate A-T rd = A-T rd = A-T rd = 11% 40% (1-Tax rate) 60% 6.6% x x (B-T rd) 11% COST OF PREFERRED STOCK, rps The cost of preferred stock is simply the preferred dividend divided by the price the company will receive if it issues new preferred stock. No tax adjustment is necessary, as preferred dividends are not tax deductible. PROBLEM What is the cost of preferred stock for a company that pays a preferred dividend of $10 per share if the company could sell new preferred for $97.50 per share? Pref. Dividend Pref. Price $10.00 $97.50 ÷ ÷ Pref. Price $97.50 rps = Pref. Dividend rps = $10.00 rps = 10.3% A 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 B C D E F G H COST OF EQUITY (INTERNAL), rs There are two sources of equity capital, internal equity and external equity. External equity is raised when the firm issues new stock. Mature firms (other than utilities) rarely issue new equity, for two main reasons. First, there are considerable commissions and fees, called flotation costs, when a firm issues new equity. Second, investors perceive issuing equity as a negative signal with respect to the true value of the company's stock; i.e., managers know best the company's future prospects, and they are most likely to issue new stock when they think the current stock price is higher than the true value of the stock. We explain how to incorporate flotation costs later in this spreadsheet. Firms raise internal equity when they choose to reinvest net income rather than pay it out as dividends. The cost of this internal equity is simply an opportunity cost equal to the return investors could have earned if they had received dividends and used the dividends to purchase stock in the company. This is the expected return on the firm's stock, rs. Several procedures frequently are used to find the cost of equity. These include the CAPM approach (described in Chapter 5), the DCF approach (described in Chapter 7), and a bond-yield-plus-risk-premium approach. The CAPM Approach rs = risk-free rate + (Market risk premium) (Beta) rs = rrf + (RPm) bi (Note: RPM is the expected return on the market minus the risk-free rate.) PROBLEM Assuming the risk-free rate (i.e., the current yield on a long-term Treasury bond) equals 8%, the market risk 75 premium is 6%, and the firm's beta is 1.1, what is the company's cost of equity from internal funds? 76 77 78 Risk-free rate 8% 79 Market risk premium 6% 80 Beta 1.1 81 82 rs = rrf + (RPm) (bi) 83 rs = 8.0% + 6.0% 1.1 rs = 84 8.0% + 6.6% rs = 85 14.6% 86 87 PROBLEM 88 What if the above firm had a beta of 0.7? 89 90 Beta 0.7 91 rs = 92 12.2% 93 94 What if the above firm had a beta of 1.5? 95 96 Beta 1.5 97 rs = 98 17.0% A 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 B C D E F G H We could use an Excel Data Table to calculate rs at different betas and risk-free rates: Beta 0.00 0.50 1.00 1.50 2.00 rs 17.0% 8.0% 11.0% 14.0% 17.0% 20.0% 25.0% Cost of Equity Effect of beta on Cost of Equity 20.0% 15.0% 10.0% 5.0% 0.0% 0.00 0.50 1.00 Beta 1.50 2.00 The CAPM seems to produce a precise cost of equity value, but neither beta nor the market risk premium can be measured with precision, so the cost of equity may be incorrect. Also, it is not certain that the CAPM theory is completely correct. THE DISCOUNTED CASH FLOW APPROACH The simplest DCF model assumes that growth is expected to remain constant, and in this case: rs = D1/P0 + g. The next expected dividend is easy to estimate, and the stock price can be determined readily. However, it is not easy to determine the marginal investor's expected future growth rate. Three approaches are commonly used: (1) historical growth rates, (2) retention growth model, and (3) analysts' forecasts. A B C D E F G 129 1. Historical Growth Rates (See the Ch 09 Web Extension for a detailed discussion of the 130 techniques shown below.) 131 132 Here are the historical data for earnings per share (EPS) and dividends per share (DPS). 133 Natural log of Natural log of Year EPS DPS EPS DPS 134 1991 $2.08 $1.20 0.73 0.18 135 1992 $2.23 $1.30 0.80 0.26 136 1993 $2.38 $1.33 0.87 0.29 137 1994 $2.26 $1.40 0.82 0.34 138 1995 $2.21 $1.40 0.79 0.34 139 1996 $2.40 $1.40 0.88 0.34 140 1997 $2.00 $1.40 0.69 0.34 141 1998 $3.02 $1.43 1.11 0.36 142 1999 $3.56 $1.54 1.27 0.43 143 2000 $3.40 $1.64 1.22 0.49 144 2001 $4.65 $1.72 1.54 0.54 145 2002 $5.12 $1.95 1.63 0.67 146 2003 $5.14 $2.20 1.64 0.79 147 2004 $4.05 $2.20 1.40 0.79 148 2005 $5.73 $2.30 1.75 0.83 149 150 151 152 153 154 155 $10.00 156 157 158 159 EPS 160 161 DPS 162 163 164 165 $1.00 166 167 1990 1995 2000 2005 2010 168 Year 169 170 171 172 173 Compound Growth Rate, Point-to-Point 174 Use the Rate function to calculate the growth rates from point-to-point. 175 EPS DPS Average 176 177 Point-to-point (2000-2005) 11.0% 7.0% 9.0% 178 Point-to-point (1999-2004) 2.6% 7.4% 5.0% 179 Point-to-point (1991-2005) 7.5% 4.8% 6.1% 180 181 Notice that the point-to-point estimates are quite different, depending on the starting and finishing dates. 182 H Semilog Plot of Earnings per Share and Dividends per Share Semilog of EPS and DPS (Dollars) A B C 183 Compound Growth Rate, Average-to-Average 184 185 186 187 188 189 190 191 192 193 D E F G H First, find the average of three data points: the year before the interval, the year the interval starts, and the year after the interval starts. Use this as the starting point. Second, find the average of three other data points: the year before the interval ends, the year the interval ends, and the year after the interval ends. Use this as the ending point. Use the Rate function to calculate the growth rates from point-to-point, based on the averages (note: you can use the Average function within the Rate function). EPS 8.4% 6.9% DPS 7.8% 4.8% Average 8.1% 5.8% Average-to-average (1999-2005) Average-to-average (1992-2004) 194 Least Squares Regression (Log-linear regression). 195 Run a regression with the Year as the x-variable and the natural log of the EPS (or DPS) as the y-variable. This is 196 a log-linear regression, so called because the y-variable is a log and the x-variable is linear. This is better than the 197 previous methods because it gives equal consideration to all points, and is not unduly influenced by the starting or 198 ending points. The slope of the regression, b, is the annual growth rate over the period, assuming continuous 199 compounding. Since we need a growth rate assuming annual compounding, we need to convert the continuosly 200 compounded growth rate, b, by raising e to the b; i.e., eb. This gives 1+g, where g is the annual average growth 201 rate, assuming annual compounding. 202 203 Because we only need the slope coefficient, we will not actually run a regression. Instead, we will use the SLOPE 204 function. The result is the average growth rate, assuming continuous compounding. 205 Regression Slope Coefficient (Continuously 206 compounded growth rate) EPS DPS 207 See screen shot at right for the 208 Least squares regression (2000-2005) 6.3% 7.3% 209 Least squares regression (1991-2005) 7.6% 4.5% SLOPE function. 210 211 We convert the continuously compounded growth rate into a growth rate assuming annual compounding. Growth Rate 212 (Assuming Annual Compounding) EPS DPS Average 213 214 Least squares regression (2000-2005) 6.5% 7.6% 7.0% 215 Least squares regression (1991-2005) 7.9% 4.6% 6.2% 216 217 218 2. Retention Growth Model 219 220 Another method for finding the growth is utilizing the sustainable growth rate, found by multiplying the expected 221 future return on equity (ROE) times the expected future retention ratio (i.e., the percent of net income that is not 222 paid out as dividends). This is: g = (Retention rate) (ROE) = (1 - Payout rate) (ROE). 223 224 PROBLEM 225 Suppose a firm's expected ROE is 14.5% and it pays out 52% of its earnings. What is the firm's sustainable growth 226 rate? 227 228 Find g 229 230 Payout rate = 52% 231 ROE = 14.50% 232 233 g = (1-Payout rate) (ROE) 234 g= 48% 14.50% 235 g= 7.0% 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 A B 3. Analysts' Forecasts C D E F G H A third method for estimating the growth rate is to use analysts's forecasts. Value Line, IBES, Zach's, and many brokerage firms provide estimates of growth rates. These often have a forecast for the next five years and then a long-term forecast for the period after five years. This non-constant growth can be converted into an approximate estimate of constant growth by weighting the short-term growth and the long-term growth. Although it is somewhat arbitrary, it is common to assume a fifty year period and weight the growth over that period. For example, suppose an analyst's provides an estimate for short-term growth over the first five years and an estimate for long-term growth thereafter. You could weight the short-term growth by 10% = 5 years / 50 years, and weight the long-term growth by 90% = 45 years / 50 years. PROBLEM Suppose an analyst forecasts growth of 10.4% for the next five years and 6.5% thereafter. What is an approximation of a constant growth rate? Short-term growth = Short-term growth period= Long-term growth= Assumed long-term period= Results Short-term weight = Long-term weight= Approximate constant growth rate= 6.9% 10% 90% 10.40% 5 6.50% 50 APPLICATION OF THE DISCOUNTED CASH FLOW APPROACH PROBLEM Suppose a firm's stock trades at $32 and its dividend is $2.40. If the expected growth rate is 7%, what is the firm's cost of equity? P0 = D1 = g= $32.00 $2.40 7% rs = rs = rs = D1 $2.40 14.5% ÷ ÷ P0 $32.00 + + g 7% APPLICATION OF THE DISCOUNTED CASH FLOW APPROACH WHEN GROWTH IS NOT CONSTANT (See the Ch 09 Web Extension for a detailed discussion of the techniques shown below.) As we noted earlier, analysts often provide non-constant estimates of future growth. We can use a modification of the discounted cash flow valuation procedure for non-constant growth from Chapter 7 to estimate the cost of equity. PROBLEM Suppose the current dividend is $2.16 per share and the current actual price that we observe is $32.00 per share. Analysts forecast growth of 11 percent the first year, 10 percent the second year, 9 percent the third year, 8 percent the fourth year, and 7 percent thereafter. Estimate the cost of equity. 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 A B C D E F G Step 1: Create a time-line showing the expected future dividend payments. These are based on the current dividend and the estimated growth rates. Year Growth Dividend Step 2: Using the constant growth formula from Chapter 7 to estimate the price at Year 4: P 4 = D5 / (rs - g). Notice that D5 and g are given in the time-line above, but the estimate for rs is shown below. Price at Year 4 = $42.20 0 2.16 1 11% 2.40 2 10% 2.64 3 9% 2.87 4 8% 3.10 5 7% 3.32 H Step 3: Calclate the current price of the stock, based on the estimate of rs below. To do this, find the present value of the price at Year 4, P4, and then find the present value of the dividends from Year 1 through Year 4. Use the cost of 309 equity, rs, shown below, as the discount rate. 310 311 Calculated Current Price $32.00 312 313 Step 4: 314 Use Goal Seek to determine the cost of equity, rs, shown below. Click Tools, Goal Seek and set the value of the 315 Calculated Current Price, cell C311, equal to the actual current stock price of $32 by changing the cost of equity, 316 rs, in cell B318. 317 See screen shot at right for rs= 318 14.9% GOAL SEEK. 319 320 Note that if rs is not equal to 14.9%, then the Calculated Current Price will not be equal to the actual current price 321 of $32. In other words, 14.9% is the only correct value for rs, given the current stock price, the expected future 322 dividends, and thelong-term constant growth rate of 7%. 323 A B C D E F G 324 THE BOND-YIELD-PLUS-RISK-PREMIUM APPROACH 325 326 This approach consists of adding a judgmental risk premium to the yield on the firm's own long-term debt. It is logical that a firm with risky, low-rated debt would also have risky, high-cost equity. Historically, we have 327 observed that risk premium for equity is in the range of 3 to 5 percentage points. This method provides a ballpark 328 estimate, and it is generally used as a check on the CAPM and DCF estimates. This method is used primarily in 329 utility rate case hearings. 330 331 PROBLEM 332 If the yield on a company's bonds is 11% and the appropriate equity premium is 3.7%, what is the cost of equity? 333 334 Equity RP = 3.7% 335 Bond yield = 11.0% 336 337 rs = (Equity RP) (Bond yield) rs = 338 3.7% 11.0% rs = 339 14.7% 340 341 342 THE COST OF EQUITY ESTIMATE 343 It is common to use several methods to estimate the cost of equity, and then find the average of these methods. 344 345 Method Cost of Equity 346 CAPM rs = 14.6% 347 Constant growth DCF rs = 14.5% 348 Bond-yield-plus-risk-premium rs = 14.7% 349 Average rs= 350 14.6% 351 352 353 THE WEIGHTED AVERAGE COST OF CAPITAL 354 355 The weighted average cost of capital (WACC) is calculated using the firm's target capital structure together with 356 its after-tax cost of debt, cost of preferred stock, and cost of common equity. 357 358 PROBLEM 359 A firm's target capital structure consists of 30 percent debt, 10 percent preferred stock, and 60 percent common 360 equity. Using the relevant costs calculated previously, what is the firm's weighted average cost of capital? 361 wd = rd = 362 30% 6.6% wp = rp = 363 10% 10.3% WACC = 11.76% 364 ws = 60% rs = 14.6% 365 366 The WACC is the marginal cost of capital, i.e., the cost of the last unit of capital raised during a given period, 367 usually one year. Note that the WACC will increase if the firm expands so rapidly that it exhausts all of its 368 reinvested earnings for the year and must issue new common stock. We show how to include flotation costs later in 369 this spreadsheet. 370 371 ADJUSTING THE COST OF CAPITAL FOR RISK 372 There is a relationship between the cost of capital and risk--the higher a project's risk, the higher its cost of capital. 373 When adjusting for risk, firms usually begin by estimating a divisional cost of capital, and then adjust this for the 374 risk of individual projects. 375 376 H 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 A B C D E F G PROBLEM Problem: Consider a company with a single division, steel production. The risk-free rate of interest is 7%, and the market risk premium is 6%. If the firm has a beta of 1.1, what is the firm's cost of equity? Risk-free rate Market risk premium Steel Beta 7% 6.0% 1.1 H rSteel = 13.6% PROBLEM Suppose the firm undertakes a new operation (a barge project). This average beta of companies that only have barge operations (I.e., pure-play companies) is 1.5. What is the cost of equity for the new division? Risk-free rate Market risk premium Barge Beta 7% 6.0% 1.5 rBarge = 16.0% PROBLEM Now suppose the firm undertakes a new low-risk operation (a distribution center). This average beta of companies that only have distribution centers (I.e., pure-play companies) is 0.5. What is the cost of equity for the new Risk-free rate Market risk premium Distribution Beta 7% 6.0% 0.5 rCenter = 10.0% PROBLEM After adding the two new divisions, the Steel division will make up 70% of the company's value, the Barge division will make up 20%, and the Distribution Center will make up 10%. What is the new beta for the entire company? (Hint: the beta of the firm is a weighted averge of the divisional betas.) What rate of return will equity holders require the firm as a whole to provide? Beta of Steel Division % of the firm Beta of Barge Division % of the firm Beta of Distribution Division % of the firm Risk-free rate Market risk premium Beta 1.1 70% 1.5 20% 0.5 10% 7% 6.0% 1.12 New corp. beta = 1.12 New rs = 13.72% PROBLEM Use a data table and graph to demonstrate the relationship between divisional risk and the divisional cost of equity. Beta and the Cost of Equity 20.0% Cost of Equity Beta 0.00 0.50 1.10 1.50 2.00 10.0% 7.0% 10.0% 13.6% 16.0% 19.0% 18.0% 16.0% 14.0% 12.0% 10.0% 8.0% 6.0% 4.0% 2.0% 0.0% Acceptance Region Steel Center Barge Rejection Region A B C D 0.00 0.50 438 439 440 441 442 443 444 445 446 ADJUSTING THE COST OF CAPITAL FOR FLOTATION COSTS 447 E 1.00 F 1.50 2.00 G H Beta 448 Flotation costs are the fees charged by investment bankers plus the accounting and legal expenses associated with 449 the issuance of new securities. A company cannot use the entire proceeds of a new security issuance, because it 450 must use some of the proceeds to pay the flotation costs. 451 452 PROBLEM: Flotation Costs and the Cost of Debt 453 A company can issue a 30-year, $1,000 par value bond with a coupon rate of 10 percent, paid annually. The tax 454 rate is 40%, and the flotation costs are 1% of the value of the issue. Find the after-tax percentage cost of the bond 455 issue. 456 40% 457 Tax rate = 1% 458 Flotation percentage cost (F) = $1,000 459 Par value = $1,000 460 Maturity payment = $100 461 Pre-tax coupon payment = 462 463 First, calculate the after-tax coupon payments and the net proceeds after the flotation costs. 464 465 After-tax coupon payment = (Coupon pmt.) (1-Tax rate) $100 60% 466 After-tax coupon payment = 467 After-tax coupon payment = $60 468 (1-F) 469 Net proceeds after flotation costs = (Par value) $1,000 99% 470 Net proceeds after flotation costs = 471 Net proceeds after flotation costs = $990 472 473 Now find the rate that the company pays, based on its net proceeds after flotation costs and its after-tax payments. 474 475 Number of coupon payments = N= 30 476 After-tax coupon payment = PMT= 60 477 Net proceeds after flotation costs = PV= 990 478 Payment of face value at maturity= FV= 1000 A 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 B C D E 6.07% F G H After tax cost of debt = Rate = See screen shot at right for RATE function. Notice that this after-tax cost of debt is only slightly higher than the after-tax cost of debt for which flotation costs are ignored. Therefore, analysts often ignore the flotation costs of debt. PROBLEM: Flotation Costs and the Cost of New Equity A company's stock sells for $23 and its next dividend is expected to be $1.24, with constant growth of 8%. What is the cost of equity using the DCF model? P0 = D1 = g= $23.00 $1.24 8% rs = D1 ÷ P0 + g rs = 494 $1.24 ÷ $23.00 + 8% rs = 495 13.4% 496 497 If the firm in the preceding question incurred a flotation cost of 10% for issuing new stock, how much higher is its 498 cost of equity from new common stock? 499 10% 500 Flotation percentage cost (F) = $23.00 501 Stock price = 502 (1-F) 503 Net proceeds after flotation costs = (Stock Price) $23.00 90% 504 Net proceeds after flotation costs = 505 Net proceeds after flotation costs = $20.70 506 507 Net proceeds after flotation costs = $20.70 508 D1 = $1.24 509 g= 8% 510 511 rs = D1 ÷ Net Proceeds + g rs = 512 $1.24 ÷ $20.70 + 8% rs = 513 14.0% 514 515 Notice that this cost of stock is quite different than the cost of stock without flotation costs. To find the cost of 516 perpetual preferred stock, simply use the procedure above with g=0. If the preferred stock has a fixed maturity, 517 then use the same procedure as for debt, except that the preferred dividend is not tax deductible. I 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 J K L M N I 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 J K L M N I 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 J K L M N I 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 J K L M N I 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 J K L M N 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 I 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 J K L M N I 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 J K L M N I 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 J K L M N I 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 J K L M N I 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 J K L M N I 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 J K L M N