i need responses to the attached problem. i also have attached excel toolkit to assist with that problem

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i need responses to the attached problem. i also have attached excel toolkit to assist with that problem

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QUESTION-2 Your employer, a mid-sized human resources management company, is considering expansion into related fields, including the acquisition of Temp Force Company, an employment agency that supplies word processor operators and computer programmers to businesses with temporary heavy workloads. Your employer is also considering the purchase of Bigger- staff & McDonald (B&M), a privately held company owned by two friends, each with 5 million shares of stock. B&M currently has free cash flow of $24 million, which is expected to grow at a constant rate of 5%. B&M’s financial statements report short-term investments of $100 million, debt of $200 million, and preferred stock of $50 million. B&M’s weighted average cost of capital (WACC) is 11%. Answer the following questions. a. Describe briefly the legal rights and privileges of common stockholders. b. What is free cash flow (FCF)? What is the weighted average cost of capital? What is the free cash flow valuation model? c. Use a pie chart to illustrate the sources that comprise a hypothetical company’s total value. Using another pie chart, show the claims on a company’s value. How is equity a residual claim? d. Suppose the free cash flow at Time 1 is expected to grow at a constant rate of gL forever. If gL WACC, what is a formula for the present value of expected free cash flows when discounted at the WACC? If the most recent free cash flow is expected to grow at a constant rate of gL forever (and gL WACC), what is a formula for the present value of expected free cash flows when discounted at the WACC? e. Use B&M’s data and the free cash flow valuation model to answer the following questions. (1) What is its estimated value of operations? (2) What is its estimated total corporate value? (This is the entity value.) (3) What is its estimated intrinsic value of equity? (4) What is its estimated intrinsic stock price per share? f. You have just learned that B&M has undertaken a major expansion that will change its expected free cash flows to −$10 million in 1 year, $20 million in 2 years, and $35 million in 3 years. After 3 years, free cash flow will grow at a rate of 5%. No new debt or preferred stock was added; the investment was financed by equity from the owners. Assume the WACC is unchanged at 11% and that there are still 10 million shares of stock outstanding. (1) What is the company’s horizon value (i.e., its value of operations at Year 3)? What is its current value of operations (i.e., at Time 0)? (2) What is its estimated intrinsic value of equity on a price-per-share basis g. If B&M undertakes the expansion, what percent of B&M’s value of operations at Year 0 is due to cash flows from Years 4 and beyond? (Hint: Use the horizon value at t 3 to help answer this question.) h. Based on your answer to the previous question, what are two reasons why managers often emphasize short-term earnings? i. YouremployeralsoisconsideringtheacquisitionofHatfieldMedicalSupplies.Youhave gathered the following data regarding Hatfield, with all dollars reported in millions: (1) most recent sales of $2,000; (2) most recent total net operating capital, OpCap $1,120; (3) most recent operating profitability ratio,OP NOPAT Sales 45%;and (4) most recent capital requirement ratio, CR OpCap Sales 56%. You estimate that the growth rate in sales from Year 0 to Year 1 will be 10%, from Year 1 to Year 2 will be 8%, from Year 2 to Year 3 will be 5%, and from Year 3 to Year 4 will be 5%. You also estimate that the long-term growth rate beyond Year 4 will be 5%. Assume the operating profitability and capital requirement ratios will not change. Use this information to forecast Hatfield’s sales, net operating profit after taxes (NOPAT), OpCap, free cash flow, and return on invested capital (ROIC) for Years 1 through 4. Also estimate the annual growth in free cash flow for Years 2 through 4. The weighted average cost of capital (WACC) is 9%. How does the ROIC in Year 4 compare with the WACC? j. What is the horizon value at Year 4? What is the total net operating capital at Year 0? How does the value of operations compare with the current total net operating capital? k. What are value drivers? What happens to the ROIC and current value of operations if expected growth increases by 1 percentage point relative to the original growth rates (including the longterm growth rate)? What can explain this? (Hint: Use Scenario Manager.) l. Assume growth rates are at their original levels. What happens to the ROIC and current value of operations if the operating profitability ratio increases to 5.5%? Now assume growth rates and operating profitability ratios are at their original levels. What happens to the ROIC and current value of operations if the capital requirement ratio decreases to 51%? Assume growth rates are at their original levels. What is the impact of simultaneous improvements in operating profitability and capital requirements? What is the impact of simultaneous improvements in the growth rates, operating profitability, and capital requirements? (Hint: Use Scenario Manager.) m. What insight does the free cash flow valuation model provide regarding possible reasons for market volatility? (Hint: Look at the value of operations for the combinations of ROIC and gL in the previous questions n. (1) Write out a formula that can be used to value any dividend-paying stock, regardless of its dividend pattern. (2) What is a constant growth stock? How are constant growth stocks valued? (3) What happens if a company has a constant gL that exceeds its rs? Will many stocks have expected growth greater than the required rate of return in the short run (i.e., for the next few years)? In the long run (i.e., forever)? o. Assume that Temp Force has a beta coefficient of 1.2, that the risk-free rate (the yield on Tbonds) is 7.0%, and that the market risk premium is 5%. What is the required rate of return on the firm’s stock? p. Assume that Temp Force is a constant growth company whose last dividend (D0, which was paid yesterday) was $2.00 and whose dividend is expected to grow indefinitely at a 6% rate. (1) What is the firm’s current estimated intrinsic stock price? (2) What is the stock’s expected value 1 year from now? (3) What are the expected dividend yield, the expected capital gains yield, and the expected total return during the first year? q. Now assume that the stock is currently selling at $30.29. What is its expected rate of return? r. Now assume that Temp Force’s dividend is expected to experience nonconstant growth of 30% from Year 0 to Year 1, 25% from Year 1 to Year 2, and 15% from Year 2 to Year 3. After Year 3, dividends will grow at a constant rate of 6%. What is the stock’s intrinsic value under these conditions? What are the expected dividend yield and capital gains yield during the first year? What are the expected dividend yield and capital gains yield during the fourth year (from Year 3 to Year 4)? s. What is the market multiple method of valuation? What are its strengths and weaknesses? t. What are the advantages of the free cash flow valuation model relative to the dividend growth model? u. What is preferred stock? Suppose a share of preferred stock pays a dividend of $2.10 and investors require a return of 7%. What is the estimated value of the preferred stock? I HAVE ATTACHED EXCEL TOOL KIT TO ASSIST WITH THIS QUESTION A 1 2 3 4 5 B C Tool Kit D E F Chapter 7 Corporate Valuation and Stock Valuation 7-4 Valuing Common Stocks—Introducing the Free Cash Flow (FCF) Valuation Model 6 7 Data for B&B Corporation (Millions) 8 9 Constant free cash flow (FCF) = $10 10 Weighted average cost of capital (WACC) = 10% 11 Short-term investments = $2 12 Debt = $28 13 Preferred stock = $4 14 Number of shares of common stock = 5 15 16 17 The first step is to estimate the value of operations, which is the present value of all expected free cash flows. Because the FCF's are 18 expected to be constant, this is a perpetuity. The present value of a perpetuity is the cash flow divided by the cost of capital: 19 Value of operations (Vop) = FCF/WACC 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 50 51 Value of operations (Vop) = $100,00 million B&B's total value is the sum of value of operations and the short-term investments: Value of operations + ST investments Estimated total intrinsic value $100 $2 $102 The next step is to estimate the intrinsic value of equity, which is the remaining total value after accounting for the claims of debtholders and preferred stockholders: Value of operations + ST investments Estimated total intrinsic value − All debt − Preferred stock Estimated intrinsic value of equity $100 $2 $102 $28 $4 $70 The final step is to estimate the intrinsic common stock price per share, which is the estimated intrinsic value of equity divided by the number of shares of common stock: Value of operations + ST investments Estimated total intrinsic value − All debt − Preferred stock Estimated intrinsic value of equity ÷ Number of shares Estimated intrinsic stock price = The figure below shows a summary of the previous calculations. $100 $2 $102 $28 $4 $70 5 $14,00 A B C D E F 52 53 54 Figure 7-2 55 B&B Corporation's Sources of Value and Claims on Value (Millions of Dollars except Per Share Data) 56 57 Inputs: Valuation Analysis 58 Constant free cash flow (FCF) = $10 Value of operations 59 Weighted average cost of capital (WACC) = 10% + ST investments 60 Short-term investments = $2 Estimated total intrinsic value 61 Debt = $28 62 Preferred stock = $4 − Preferred stock 63 Number of shares of common stock = 5 Estimated intrinsic value of equity 64 ÷ Number of shares 65 Estimated intrinsic stock price 66 67 68 Sources of Value Short-term Claims on Value 69 investments = 70 $2 71 72 73 74 Debt = $28 75 76 77 78 79 Estimated equity Value of 80 value = $70 operations = 81 $100 82 83 84 85 86 87 88 89 7-5 The Constant Growth Model: Valuation when Expected Free Cash Flow Grows at a Constant Rate 90 91 Case 1: The expected free cash flow at t=1 and the expected constant growth rate after t=1 are known. 92 First expected free cash flow (FCF1) = 93 $105 94 95 Weighted average cost of capital (WACC) = Constant growth rate (gL) = 9% 5% 96 97 When free cash flows are expected to grow at a constant rate, the value of operations is: 98 99 𝐅𝐂𝐅𝟏 100 𝐕𝐨𝐩 = 𝐖𝐀𝐂𝐂 − 𝐠 𝐋 101 102 103 104 A B C D Value of operations (Vop) = FCF1 / [WACC-gL] 105 Value of operations (Vop) = E $2.625 106 107 108 Case 2: Constant growth is expected to begin immediately. 109 Most recent free cash flow (FCF0) = 110 $200 111 112 12% 7% Weighted average cost of capital (WACC) = Constant growth rate (gL) = F 113 114 When free cash flows are expected to grow at a constant rate, the value of operations is: 115 116 𝐅𝐂𝐅𝟎 (𝟏 + 𝐠 𝐋 ) 117 𝐕𝐨𝐩 = 𝐖𝐀𝐂𝐂 − 𝐠 𝐋 118 119 120 Value of operations (Vop) = [FCF0(1+gL)]/[WACC-gL] 121 122 Value of operations (Vop) = $4.280 123 124 125 7-6 The Multi-Stage Model: Valuation when Expected Short-Term Free Cash Flow Grows at a Nonconstant Rate 126 127 Thurman Corporation's expected free cash flows are shown below. 128 129 Year 0 1 2 3 4 130 FCF −$20 $80 $100 $110 Growth in FCF 131 25% 10% 132 133 134 Free cash flows are expected to grow at a 5% rate starting at Year 4 and to continue growing at a 5% rate for 135 the foreseeable future. We know the free cash flow at Year 4 and we know that FCF grows at a constant rate 136 after Year 4. Therefore, we set the horizon date at Year 4. 137 138 Free cash flow at beginning of the constant growth phase (FCF 4) = 139 $110 140 141 142 143 144 145 146 147 148 149 Weighted average cost of capital (WACC) = Constant growth rate (gL) = 𝐇𝐕𝟒 = 𝐕𝐨𝐩, 𝐚𝐭 𝟒 = 𝐅𝐂𝐅𝟒 (𝟏 + 𝐠 𝐋 ) 𝐖𝐀𝐂𝐂 − 𝐠 𝐋 HV4 = Vop, at 4 = [FCF4 (1+gL)]/ [WACC-gL] HV4 = Vop, at 4 = $1.155 150 151 152 Thurman's time line of expected free cash flows and horizon value is shown below. 153 15% 5% A 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 Year FCF Horizon value B 0 C 1 −$20 D 2 $80 E 3 $100 Present value of HV4 = $660,375 Present value of free cash flows = Total value of operations at Year 0, Vop, at t=0 = $171,745 $832,120 F 4 $110 $1.155 There is more than one correct way to find the present value of the FCFs and the horizon value. For example, you could find the total cash flows, as shown below, which are equal to the free cash flows except for the last period, when they are equal to the sum of the free cash flow and the horizon value. (It is as though you received the FCF at Year 4 and then "sold" the operations and received cash equal to the horizon value.) You could then find present value of the combined free cash flows and horizon value. Year FCF Horizon value Combined FCF and HV 0 1 −$20 2 $80 3 $100 −$20,00 $80,00 $100 PV of combined FCF and HV = Total value of operations at Year 0, Vop, at t=0 = 4 $110 $1.155 $1.265 $832,12 Here is a third way to find the present value of the FCFs and the horizon value. The basic idea is to find the value of operations at each date. For the last date, the value of operations is the horizon value. For the previous date, the value of operations is equal to the present value of the sum of the next date's value of operations and FCF. For example, if you sell the operations immediately after receiving the FCF at Year 3, then the purchaser would receive the FCF at Year 4 plus the value of operations at Year 4 (which is the present value of all cash flows beyond Year 4). Year FCF Horizon value Vop,t = (FCFt+1 + Vop,t+1)/ (1+WACC) 2018 2019 −$20,00 2020 $80,00 2021 $100,00 2022 $110,00 $1.155 $832,12 $976,94 $1.043,48 $1.100,00 $1.155,00 Optional Material. You may have noticed that we could have defined the horizon date at Year 3 because we have an estimate of the Year 4 free cash flow, which is expected to grow at a constant rate thereafter. However, we recommend defining the horizon date as the last date in the forecast period even if growth becomes constant at or prior to this date because we have found that this leads to fewer errors. But we illustrate this approach below for the interested reader. Free cash flow at beginning of the constant growth phase (FCF 4) = $110 Weighted average cost of capital (WACC) = 15% A B C 205 D Constant growth rate (gL) = 206 HV3 = Vop, at 3 = FCF4 / [WACC-gL] 207 HV3 = Vop, at 3 = E F 5% $1.100 208 209 210 Thurman's time line of expected free cash flows and horizon value is shown below. 211 212 Year 0 1 2 3 213 FCF −$20 $80 $100 214 Horizon value $1.100 215 216 Present value of HV4 = 217 $723,268 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 Present value of free cash flows = Total value of operations at Year 0, Vop, at t=0 = $108,852 $832,120 Following is a summary of the steps used in estimating Thurman Corporation's value of operations. Figure 7-3 Thurman Corporation's Value of Operations (Millions of Dollars) INPUTS: gL = 5% Projections WACC = 15% Year 0 1 2 FCF −$20,00 $80,00 ↓ ↓ FCF1 FCF2 3 $100,00 ↓ FCF3 4 $110,00 ↓ FCF4 235 ────── ────── ────── ────── 236 237 (1+WACC)1 ↓ ↓ ↓ ↓ ⟵ ⟵⤶ ⟵⟵⟵⟵ ⟵⟵⟵⟵ ⟵⟵⟵⟵ ⟵⟵⟵⟵ (1+WACC)2 ↓ ↓ ↓ ↓ ↓ (1+WACC)3 ↓ ↓ ↓ ↓ ↓ ↓ ⟵⤶ ⟵⟵⟵⟵ ⟵⟵⟵⟵ (1+WACC)4 ↓ ↓ ↓ ↓ ↓ ↓ ↓ ⟵⤶ $1.155,000 238 239 240 241 242 243 244 245 −$17,391 $60,491 $65,752 $62,893 $660,375 PVs of FCFs PV of HV 246 247 Vop = ⟵⤶ ⟵⟵⟵⟵ ⟵⟵⟵⟵ ⟵⟵⟵⟵ ↓ $832,12 248 249 250 251 252 253 254 7-7 Application of the FCF Valuation Model to MicroDrive = ────── (1+WACC)4 255 256 257 258 259 260 261 262 263 264 265 266 267 268 A B C D E We begin with MicroDrive's most recent financial statements and selected additional data. Figure 7-4 MicroDrive’s Most Recent Financial Statements (Millions, Except for Per Share Data) INCOME STATEMENTS BALANCE SHEETS 2015 2016 Assets Net sales $ 4.760 $ 5.000 Cash $ COGS (excl. depr.) 3.560 3.800 ST Investments Depreciation 170 200 Accounts receivable Other operating expenses 480 500 Inventories EBIT $ 550 $ 500 Total CA $ Interest expense 100 120 Net PP&E Pre-tax earnings $ 450 $ 380 Total assets $ 269 Taxes (40%) 270 NI before pref. div. 271 Preferred div. 272 Net income 273 274 275 276 277 278 279 280 281 Other Data Common dividends Addition to RE Tax rate Shares of common stock Price per share $ $ 180 270 8 262 $48 $214 40% 50 $40,00 $ $ 152 228 Liabilities and Equity 8 Accounts payable 220 Accruals $50 $170 40% 50 $27,00 Notes payable Total CL Long-term bonds Total liabilities Preferred stock Common stock Retained earnings Total common equity Total liabs. & equity $ 2015 60 40 380 820 1.300 1.700 3.000 190 280 130 600 1.000 $ 1.600 100 500 800 $ 1.300 $ 3.000 $ F $ $ $ $ $ $ 2016 50 0 500 1.000 1.550 2.000 3.550 200 300 280 780 1.200 1.980 100 500 970 1.470 3.550 $ $ Weighted average 10,50% 10,97% 282 cost of capital (WACC) 283 284 285 The first step is to calculate the key performance measures that determine free cash flows. 286 287 Figure 7-5 288 Key Performance Measures for MicroDrive (Millions of Dollars) 289 MicroDrive 290 2015 2016 291 Calculating Net Operating Profit after Taxes (NOPAT) 292 NOPAT = EBIT(1 − T) $330 $300 293 Calculating Net Operating Working Capital (NOWC) 294 Operating current assets $1.260 $1.550 295 − Operating current liabilities $470 $500 296 NOWC $790 $1.050 297 Calculating Total Net Operating Capital (OpCap) 298 NOWC $790 $1.050 299 + Net PP&E $1.700 $2.000 300 OpCap $2.490 $3.050 301 Investment in operating capital $560 302 Calculating Free Cash Flow (FCF) 303 FCF = NOPAT – Investment in operating capital −$260 304 Calculating Return on Invested Capital (ROIC) 305 ROIC = NOPAT/Total net operating capital 13,25% 9,84% 306 Calculating the Operating Profitability Ratio (OP) 307 OP = NOPAT/Sales 6,93% 6,00% 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 A B C Calculating the Capital Requirement Ratio (CR) CR = (Total net operating capital)/Sales D E 52,31% F 61,00% The next step is to forecast sales, NOPAT, and total net operating capital. We do this by estimating future sales' growth rates, operating profitability ratios, and capital requirement ratios, as shown in Panel A in the Figure below. Yearly sales are forecast by letting the previous year's sales increase by the forecasted sales growth rate. Operating profitability and total net operating capital in a forecasted year are assumed to be proportional to sales in that year. Figure 7-6 MicroDrive's Forecast of Operations for the Selected Scenario (Millions of Dollars, Except for Per Share Data) Status Quo Industry MicroDrive MicroDrive Panel A: Actual Actual Forecast Operating Ratios 2016 2015 2016 2017 2018 g = Sales growth rate 15% 5% 10% 8% OP = NOPAT/Sales 6,92% 6,9% 6% 6% 6% CR = OpCap/Sales 46,0% 52,3% 61% 61% 61% Tax rate 40% 40% 40% 40% 40% Panel B: Actual Forecast Operating Items 2016 2017 2018 Net sales $5.000 $5.500 $5.940 Net operating profit after taxes $300 $330 $356 Total net operating capital (OpCap) $3.050 $3.355 $3.623 FCF = NOPAT – Investment in OpCap −$260 $25 $88 Growth in FCF 252% ROIC = NOPAT/OpCap 9,84% 9,84% 9,84% Note: Numbers in the figure are shown as rounded for clarity in reporting. However unrounded values are used for all calculations. The next step is to estimate the horizon value and the value of operations, beginning with the horizon value. Free cash flow at beginning of the constant growth phase (FCF 2021) = $216,892 Weighted average cost of capital (WACC) = Constant growth rate (gL) = 10,97% 5% 𝐇𝐕𝟐𝟎𝟐𝟏 = 𝐕𝐨𝐩, 𝟐𝟎𝟐𝟏 = 𝐅𝐂𝐅𝟐𝟎𝟐𝟏 (𝟏 + 𝐠 𝐋 ) 𝐖𝐀𝐂𝐂 − 𝐠 𝐋 HV2021 = Vop, 2021 = [FCF2021 (1+gL)]/ [WACC-gL] HV2021 = Vop, 2021 = $3.814,678 358 359 360 MicroDrive's time line of expected free cash flows and horizon value is shown below. A 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 Year FCF Horizon value B C D E F 2016 2017 $25,000 2018 $88,000 2019 $127,710 2020 $206,564 Present value of HV = Present value of free cash flows = Total value of operations at Year 0, Vop, at t=0 = The figure below shows a summary of these calculations. Figure 7-7 MicroDrive Inc.'s Value of Operations (Millions of Dollars) INPUTS: Scenario: gL = 5% WACC = 10,97% Year 2016 2017 2018 FCF $25,000 $88,000 ↓ ↓ FCF2017 FCF2018 ────── 383 384 395 396 PVs of FCFs PV of HV $22,529 $71,461 $93,456 $136,217 $128,889 $2.266,887 Status Quo Projections 2019 $127,710 ↓ FCF2019 ────── 1 385 386 387 388 389 390 391 392 393 394 $2.266,887 $452,552 $2.719,439 (1+WACC) ↓ ↓ ↓ ↓ ⟵⤶ ⟵⟵⟵⟵ ⟵⟵⟵⟵ ⟵⟵⟵⟵ ⟵⟵⟵⟵ ⟵⟵⟵⟵ (1+WACC) ↓ ↓ ↓ ↓ ↓ 2020 $206,564 ↓ FCF2020 ────── 2 ⟵⤶ ⟵⟵⟵⟵ ⟵⟵⟵⟵ ⟵⟵⟵⟵ ⟵⟵⟵⟵ ────── 3 (1+WACC) (1+WACC)4 ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ⟵⤶ ↓ ⟵⟵⟵⟵ ⟵⤶ ⟵⟵⟵⟵ ⟵⟵⟵⟵ ⟵⟵⟵⟵ ⟵⟵⟵⟵ ↓ Vop = $2.719,44 397 398 Note: Numbers in the figure are shown as rounded for clarity in reporting. However unrounded values are used for all calculations. 399 400 401 402 403 Estimating MicroDrive's Intrinsic Stock Price per Share 404 405 Value of operations = $2.719,44 406 Weighted average cost of capital (WACC) = 10,97% 407 Short-term investments = $0 408 Short-term debt (notes payable) = $280 409 Long-term debt (bonds) = $1.200 410 Preferred stock = $100 411 Number of shares of common stock = 50 A 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 B C D E F MicroDrive's total value is the sum of value of operations and the short-term investments: Value of operations + ST investments Estimated total intrinsic value $2.719,44 $0 $2.719,44 The next step is to estimate the intrinsic value of equity, which is the remaining total value after accounting for the claims of debtholders and preferred stockholders: Value of operations + ST investments Estimated total intrinsic value − All debt − Preferred stock Estimated intrinsic value of equity $2.719 $0 $2.719,44 $1.480 $100 $1.139,44 The final step is to estimate the intrinsic common stock price per share, which is the estimated intrinsic value of equity divided by the number of shares of common stock: Value of operations + ST investments Estimated total intrinsic value − All debt − Preferred stock Estimated intrinsic value of equity ÷ Number of shares Estimated intrinsic stock price = $2.719,44 $0 $2.719,44 $1.480 $100 $1.139,44 50 $22,79 The figure below shows a summary of the previous calculations. Figure 7-8 MicroDrive Inc.'s Intrinsic Stock Price (Millions, Except for Per Share Data) INPUTS: gL = 5% WACC = 10,97% Year = 2017 2018 2019 Projected FCF = $25 $88,0 $127,71 448 449 450 2020 2021 451 $206,564 $216,892 452 453 Horizon Value: Value of operations 454 + ST investments 𝐅𝐂𝐅𝟐𝟎𝟐𝟏 (𝟏+𝐠 𝐋 ) 𝐇𝐕𝟐𝟎𝟐𝟏 = 455 = $3.815 Estimated total intrinsic value (𝐖𝐀𝐂𝐂 − 𝐠 𝐋 ) 456 − All debt 457 Value of Operations: − Preferred stock 458 Present value of HV $2.266,89 Estimated intrinsic value of equity 459 + Present value of FCF $452,55 ÷ Number of shares 460 Value of operations = $2.719,44 Estimated intrinsic stock price = 461 462 Note: Numbers in the figure are shown as rounded for clarity in reporting. However unrounded values are used for all calculations. 463 464 A B C D E F 465 466 7-8 Do Stock Prices Reflect Long-Term or Short-Term Cash Flows? 467 468 Managers often claim that stock prices are "short-term" in nature in the sense that they reflect what is happening in the near-term and 469 ignore the long-term. We can use MicroDrive's results to shed light on this claim. 470 471 472 We previously estimated MicroDrive's current value of operations. We also estimated MicroDrive's horizon value at Year 5 and 473 calculated its present value. If we divide the present value of the horizon value, we can estimate how much of MicrDrive's value is due to cash flows occurring beyond Year 5. In other words, we can determine how much of MicroDrive's value is due to long-term cash flows 474 and how much is due to short-term cash flows. 475 476 Inputs: 477 478 479 480 481 482 483 484 485 486 487 Weighted average cost of capital = Horizon year = Horizon value at Year 5 (HV5) = 10,97% 5 $3.814,678 Value of operations at Year 0 (Vop,0) = $2.719,439 Present value of the horizon value = Value of operations at Year 0 = $2.266,887 $2.719,439 Analysis: Results: Percent of current value due to long-term cash flows (i.e., PV of HV 5) = 488 489 Percent of current value due to short-term cash flows = 490 491 For most stocks, the percentage of the current price that is due to long-term cash flows is over 80%. 83% 17% 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 7-9 Using the Free Cash Flow Valuation Model to Identify Value Drivers We can use the free cash flow valuation model we developed previously for MicroDrive to determine how the inputs (sales growth, operating profitability, and capital requirements) affect the value of operations and intrinsic stock price. It is very easy to do this in Excel by using the Scenario Manager feature. Following is an explantion of how to use this feature. The Scenario Manager allows you to specify values for particular cells and then save those values as a "scenario." If you later change the values in the cells, perhaps to see the impact that the change has on an output, the Scenario Manager allows you to restore the saved scenario without having to re-input the original values. You can create numerous different scenarios, and you can even have the Scenario Manager create a summary that shows the values of the input cells and the values of the output cells for each scenario that you created. To create a scenario, go to the Data tab in the menu, look in the Data Tools section for What-If Analysis, and then select Scenario Manager. This will open a dialog box that shows seven existing scenarios. If you select the button for "Add…", you will get another dialog box asking you to give the scenario a name and to specify the "Changing cells." The "Changing cells" are the cells with values that you want the Scenario Manager to save. For example, we want to save the values for MicroDrive's estimated sales growth rates, operating profitabiltiy ratio, and capital requirement ratio. To create a scenario, go to the Data tab in the menu, look in the Data Tools section for What-If Analysis, and then select Scenario Manager. This will open a dialog box that shows seven existing scenarios. If you select the button for "Add…", you will get another dialog box asking you to give the scenario a name and to specify the "Changing cells." The "Changing cells" are the cells with values that you want the Scenario Manager to save. For example, we want to save the values for MicroDrive's estimated sales growth rates, operating profitabiltiy ratio, and capital requirement ratio. A B C D E F 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 After specifying the "Changing cells", click "Ok" and you will get a new dialog box asking you to input the values into the changing cells that you want for this scenario. There will already be values shown, which are the values currently in those cells. So if you have already put the values into the cells in the Excel workbook, you won't have to re-enter them in the dialog box, you can simply click "Ok" and you will have created a new scenario. The original dialog box gives you several options, including adding a scenario, deleting a scenario, and editing a scenario. It also give you the option to run a "Summary." If you select the "Summary" button, you get a dialog box asking you to specify some "Results" cells. For example, we specified the cells in this worksheet that have the value of operations, the intrinsic stock price, and the return on invested capital for the last year in the forecast horizon. After selecting the "Results" cells, you can click "Ok" and the Scenario Manager will create a new worksheet named "Scenario Summary". This new sheet contains the name of each scenario, the values in the "Changing cells", and the values in the "Results cells. We copied the information from the "Scenario Summary" into the table below and then formatted the table to make it a bit more reader-friendy. Figure 7-9 Value Drivers for MicroDrive Inc. (Millions, Except for Per Share Data) (1) Status Quo (2) Higher Sales Growth (Only) Scenario (3) Higher (4) Operating Better Capital Profitabilit Utilization y (Only) (Only) Inputs 545 546 547 548 Sales growth in 1st year Sales growth in 2nd year Sales growth in 3rd year Long-term sales growth (gL) 10% 8% 7% 5% 11% 9% 8% 6% 10% 8% 7% 5% 10% 8% 7% 5% 549 550 Operating profitability (OP) Capital requirement (CR) Weighted average cost of capital (WACC) 6% 61% 6% 61% 7% 61% 6% 52% 10,97% 10,97% 10,97% 10,97% $2.719 $22,79 $2.713 $22,67 $3.682 $42,04 $3.576 $39,91 551 552 Results Value of operations Intrinsic stock price Return on invested capital (ROIC) 553 554 555 9,84% 9,84% 11,48% 556 557 558 To better understand why growth doesn't always add value, we can express the horizon value as: 559 560 561 562 L T op(at HorizonYear T ) T 563 V 11,54%  (1+ g )ROIC − WACC = OpCap 1+  WACC − g L   564 565 566 567 568 569 570 571 572 573 574 575  (1+ g L )ROICT − WACC V = OpCap  T 1+ A op(at HorizonYear B T) C D E F WACC − g L   If the numerator in the fraction in brackes, (1+gL) ROIC − WACC, is negative, then the value of operations will be less than the total net operation capital, OpCapT. If ROIC < WACC/(1+WACC), then growth hurts value. The 2-way data table below show the difference between the value operations and the amount of operating capital for different combinations of growth and ROIC. For input values, we use values similar to those of MicroDrive's at the horizon. OpCap = gL = 576 577 578 579 580 ROIC = WACC = 581 Vop − OpCap = 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 9,84% 10,97% Output from equation above in yellow. $3.815 -$460 A Two-Way Data Table Showing How Combinations of Growth and ROIC Affect the Value of Operations Minus the Value of Operating Capital Combinations of growth and ROIC that have Vop < OpCap are shown in pink. Notice that for very low values of ROIC, such as the first row with ROIC = 9.7%, growth reduces value (you can see this by looking across the row. For very high values of ROIC, such as the last row with ROIC = 11%, growth adds value. For other combinations, it depends on the relative values of growth, ROIC, and WACC. gL ROIC 582 583 584 585 586 587 588 589 590 591 592 593 Vop = Input Values (Base Case) $4.274 5,0% −$460 9,70% 9,80% 9,84% 9,90% 10,00% 10,10% 10,20% 10,30% 10,40% 10,50% 10,60% 10,70% 10,80% 10,90% 11,00% 0,0% -$495 -$456 -$442 -$417 -$378 -$339 -$300 -$261 -$222 -$183 -$144 -$105 -$66 -$27 $12 2,5% -$519 -$467 -$448 -$415 -$363 -$312 -$260 -$208 -$156 -$105 -$53 -$1 $50 $102 $154 613 7-11 Valuing Common Stocks with the Dividend Growth Model 614 615 The Discounted Dividend Approach 5,0% -$562 -$487 -$460 -$412 -$337 -$261 -$186 -$111 -$36 $39 $115 $190 $265 $340 $415 7,5% -$668 -$536 -$488 -$403 -$271 -$139 -$6 $126 $259 $391 $524 $656 $788 $921 $1.053 A 616 617 618 619 620 621 622 623 624 625 B E D1 D2 + ( 1 + rs ) ( 1 + rs ) + Valuing a Constant Growth Stock In the constant growth model, we assume that the dividend and stock will grow forever at a constant growth rate. Naturally, assuming a consta growth rate for the rest of eternity is a rather bold assumption. However, considering the implications of imperfect information, information asymmetry, and general uncertainty, the assumption of constant growth is often reasonable. It is reasonable to guess that a given stock will experience ups and downs throughout its life. By assuming constant growth, we are trying to find the average of the good times and the bad ti and we assume that we will see both scenarios over the firm's life. In addition to a constant growth rate, we also need the estimated long-term required return for the stock, and it too must be constant. If these variables are constant, our price equation for common stock simplifies to th following expression: D1 ( rs – g L ) Generally speaking, the long-run growth rate of a firm is likely to fall between 5% and 8% a year. Example: Value of a Constant Growth Stock A firm just paid a $1.15 dividend and its dividend is expected to grow at a constant rate of 8%. What is its stock price, assuming it has a requir return of 13.4%? 654 655 656 D0 = 657 gL = 8% 658 659 rs = 13,4% P0 = $1,15 D1 ( rs – g L ) 661 662 663 664 . . . . 2 The dividend stream theoretically extends on out forever, i.e., to N = infinity. Obviously, it would not be feasible to deal with an infinite stream dividends, but fortunately, a relatively simple equation has been developed that can be used to find the PV of the dividend stream, provided it growing at a constant rate. 645 P0 = 660 F Here is the basic dividend valuation equation: 627 646 647 648 649 650 651 652 653 D The value of any financial asset is the present value of the future cash flows provided by the asset. When an investor buys a share of stock, he o typically expects to receive cash in the form of dividends and then, eventually, to sell the stock and to receive cash from the sale. However, the price the first investor receives is dependent upon the dividends the next investor expects to earn, and so on for different generations of inves Thus, the stock's value ultimately depends on the cash dividends the company is expected to provide and the discount rate used to find the pre value of those dividends. 626 P0 = 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 C P0 = $23,00 = D0 (1 + gL) = ( rs – g L ) A B C D E F 665 666 667 Expected Rate of Return on a Constant Growth Stock 668 669 Using the constant growth equation introduced earlier, we can re-work the equation to solve for r s. In doing so, we are now solving for an expe 670 return. The expression we are left is: 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 D1 𝐫ො = gL + P0 This expression tells us that the expected return on a stock comprises two components. First, it consists of the expected dividend yield, which simply the next expected dividend divided by the current price. The second component of the expected return is the expected capital gains yie The expected capital gains yield is the expected annual price appreciation of the stock, and is given by g L. This shows us the dual role of gL in t constant growth rate model. Not only does g indicate expected dividend growth, but it is also the expected stock price growth rate. Example: Expected Rate of Return on a Constant Growth Stock You buy a stock for $23, and you expect the next annual dividend to be $1.242. Furthermore, you expect the dividend to grow at a constant rat 8%. What is the expected rate of return on the stock, and what is the dividend yield of the stock? Inputs: 689 P0 $23,00 690 D1 $1,242 691 692 693 gL 8% 𝐫ො = 13,40% 694 695 Dividend yield = 5,40% 696 697 698 What is the expected price of this stock in 1 year? 699 700 Application of Constant Growth Model at t=1 701 D2 702 P1 = ( rs – g L ) 703 704 705 D2 = 1,34136 P1 = $24,84 706 707 708 709 Valuing Nonconstant Growth Stocks 710 711 712 For many companies, it is unreasonable to assume that they grow at a constant growth rate. Hence, valuation for these companies proves a lit 713 more complicated. The valuation process, in this case, requires us to estimate the short-run nonconstant growth rate and predict future divid Then, we must estimate a constant long-term growth rate at which the firm is expected to grow. Generally, we assume that after a certain poin time, all firms begin to grow at a rather constant rate. Of course, the difficulty in this framework is estimating the short-term growth rate, how the short-term growth will hold, and the long-term growth rate. For many companies, it is unreasonable to assume that they grow at a constant growth rate. Hence, valuation for these companies proves a lit more complicated. The valuation B process, in this to estimate the short-run nonconstant A C case, requires us D E F growth rate and predict future divid 714 Then, we must estimate a constant long-term growth rate at which the firm is expected to grow. Generally, we assume that after a certain poin 715 time, all firms begin to grow at a rather constant rate. Of course, the difficulty in this framework is estimating the short-term growth rate, how 716 the short-term growth will hold, and the long-term growth rate. 717 718 719 720 Figure 7-10 721 Illustrative Dividend Growth at Different Rates 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 $2,65 $1,65 Constant Growth: 8% $1,15 Zero Growth $0,65 Declining Growth: 8% 0 1 2 3 4 5 Specifically, we will predict as many future dividends as we can and discount them back to the present. Then we will treat all dividends to be received after the convention of constant growth rate with the Gordon constant growth model described above. The point in time when the dividend begins to grow constantly is called the horizon date. When we calculate the constant growth dividends, we solve for the horizon valu (also called a terminal value or a continuing value) as of the horizon date. The horizon value can be summarized as: 751 HVT = 752 753 754 755 756 757 758 759 760 761 762 763 764 Long-Term Growth: 8% $2,15 737 738 739 740 741 742 743 744 745 746 747 748 749 750 End of Nonconstant Growth Period PT = DT+1 = ( rs – g L ) DT (1 + g) ( rs – g L ) This condition holds true, where T is the horizon date. The horizon value can be described as the expected value of the stock at the time perio corresponding to the horizon date. A company's stock just paid a $1.15 dividend, which is expected to grow at 30% the first year, 20% the second year, and 10% the third year. Af three years the dividend is expected to grow constantly at 8% forever. The stock's required return is 13.4%; what is the price of the stock tod Figure 7-11 Process for Finding the Value of a Nonconstant Growth Stock INPUTS: A D0 = B $1,15 C D Last dividend the company paid. 766 rs = 13,4% Stockholders' required return. 767 g0,1 = 30% Growth rate for Year 1 only. 768 g1,2 = 20% Growth rate for Year 2 only. 769 g2,3 = 770 771 772 773 774 gL = 10% 8% Growth rate for Year 3 only. Constant long-run growth rate for all years after Year 3. 765 Year Growth rate Dividend Dt 775 776 777 0 D0 $1,15 778 779 782 783 784 785 786 787 788 789 3 10% D2(1+g1,2) $1,495 ↓ D1 $1,794 ↓ D2 $1,973 ↓ D3 ────── ────── ────── 2 (1+rs) ↓ ↓ ↓ ↓ ↓ PVs of Dividends ෡𝟑 PV of 𝐏 790 791 Projections 2 20% D1(1+g1,2) (1+rs) 781 ⟵⤶ $27,065 ⟵⟵⟵⟵ ⟵⟵⟵⟵ Vop = $31,13 ⟵⟵⟵⟵ ⟶∞ 8% ෡𝟑 HV3 = 𝐏 3 (1+rs) ↓ ↓ ↓ ↓ ↓ ↓ $1,318 ⟵⤶ $1,395 ⟵⟵⟵⟵ $1,353 ⟵⟵⟵⟵ ↓ F 1 30% D0(1+g0,1) 1 780 E ↓ ↓ ↓ ↓ ↓ ↓ ↓ ⟵⤶ ↓ D3(1+gL) ─────── (rs− gL) ෡𝟑 = 𝐏 ෡𝟑 = 𝐏 ෡𝟑 = 𝐏 ↓ $2,131 5,400% ↓ $39,468 $39,468 = ────── ⟵⟵⟵⟵ (1+0.134)3 792 793 Note: Numbers in the figure are shown as rounded for clarity in reporting. However unrounded values are used for all 794 calculations. 795 796 797 7-12 Market Multiple Analysis 798 799 Use the following data in the market multiple approach to estimate the stock price per share. 800 801 Forecasted earnings per share (EPS) = $7,70 802 Average peer price/earnings (P/E) ratio = 12 803 804 Estimated stock price: $92,40 805 806 807 808 7-14 Preferred Stock 809 810 Consider an issue of preferred stock that pays an $8 dividend and has a required return of 8%. What is the value of this preferred stock? 811 812 813 814 815 A Vps = B Dps C ÷ D rps = $8,00 ÷ 8,00% = $100,00 E F 816 817 818 Some preferred stock has a maturity date. Consider a firm whose preferred stock matures in 50 years, pays a $8 annual dividend, has a par va 819 of $100, and has a required return of 6%. What is the price of this preferred stock? 820 821 822 823 Years to Maturity (N): 824 Annual Dividend (PMT): 825 Par value (FV): 826 Required return, rd (I/YR): 50 $8 $100 6% 827 828 829 Vps = $131,52 G 1 2 H 10/27/2015 3 4 5 6 7 8 9 10 11 12 13 14 15 16 xpected free cash flows. 17 Because the FCF's are cash flow divided by the 18 cost of capital: 19 20 21 22 23 24 25 26 27 28 value after accounting 29for the claims of debtholders 30 31 32 33 34 35 36 37 38 estimated intrinsic value 39 of equity divided by the 40 41 42 43 44 45 46 47 48 49 50 51 I J K L M N G H 52 53 54 55 56 57 Value 58of operations $100 + 59 ST investments $2 Estimated total60 intrinsic value $102 61 − All debt $28 − 62 Preferred stock $4 Estimated intrinsic63 value of equity $70 ÷ Number 64 of shares 5 Estimated intrinsic 65 stock price $14,00 66 67 68 69 70 71 72 73 74$28 75 76 77 78 Preferred stock = $4 79 80 81 82 83 84 85 86 87 88 h Flow Grows at a89 Constant Rate 90 91 92 93 94 95 is: 96 97 98 99 100 101 102 103 I J K L M N Data for Pie Charts Short-term investments = Value of operations = Total = $2 $100 $102 Debt = Preferred stock = Estimated equity value = Total = $28 $4 $70 $102 G H 104 105 106 107 108 109 110 111 112 is: 113 114 115 116 117 118 119 120 121 122 123 124 ee Cash Flow Grows 125 at a Nonconstant Rate 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 I J K L M N G 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 H I J K L M N G H 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 of operations. 220 221 222 223 224 225 226 227 228 229 230 231 232 ⟶ ⟶ ⟶ ↴ ↓ 233 HV = Vop(t=4) 234 ↓ 235 FCF4(1+gL) 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 ───────── (WACC− g L) ↓ $115,500 10,00% ↓ $1.155,000 ↓ ⟵⟵⟵⤶ I J K L M N G data. 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 Industry 2016 15,04% 6,92% H I J K L M N G H 308 309 46,00% 310 311 312 313 by estimating future sales' 314 growth rates, operating below. 315 316 317 ed sales growth rate. Operating profitability and 318 es in that year. 319 320 321 322 323 324MicroDrive 325 Forecast 326 2019 2020 327 7% 5% 328 6% 6% 329 61% 61% 330 40% 40% 331 Forecast 332 2019 2020 333 $6.356 $6.674 334 $381 $400 335 $3.877 $4.071 336 $128 $207 337 45,1% 61,7% 338 9,84% 9,84% 339 340 unrounded values are used for all calculations. 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 I 2021 5% 6% 61% 40% 2021 ####### ####### ####### ####### 5,0% 9,84% J K L M N ons G 361 362 2021 363 $216,892 364 $3.814,678 365 366 367 368 369 H I 370 371 372 373 374 375 376 377 378 379 2021 380 $216,892 381 ↓ FCF2021 382 383 ────── 384 (1+WACC)5 ↓ 385 386 ↓ ↓ 387 388 ↓ ↓ 389 ↓ 390 391 ↓ 392 ↓ 393 ⟵⤶ 394 $3.814,678 ⟶ ↴ ↓ ↓ HV = Vop(2021) ↓ FCF2021(1+gL) ───────── (WACC− g L) ↓ $227,736 0,0597 ↓ $3.814,678 ↓ ⟵⟵⤶ 395 = ────── 5 396 (1+WACC) 397 398 unrounded values are used for all calculations. 399 400 401 402 403 404 405 406 407 408 409 410 411 J K L M N G H 412 ents: 413 414 415 416 417 418 value after accounting 419 for the claims of debtholders 420 421 422 423 424 425 426 427 428 estimated intrinsic value 429 of equity divided by the 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 $2.719 454 $0 455 $2.719 456 $1.480 457 $100 458 $1.139 459 50 460 $22,79 461 462 unrounded values are used for all calculations. 463 464 I J K L M N G H 465 466 467 468 ey reflect what is happening in the near-term and 469 470 471 472 d MicroDrive's horizon value at Year 5 and an estimate how much of MicrDrive's value is due to 473 MicroDrive's value is due to long-term cash flows 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 ve to determine how the inputs (sales growth, 497 ntrinsic stock price. It is very easy to do this in Excel 498 eature. 499 500 501 those values as a "scenario." If you later change the 502 enario Manager allows you to restore the saved 503 erent scenarios, and 504 you can even have the Scenario the output cells for each 505scenario that you created. 506 507 508 r What-If Analysis, and then select Scenario 509 t the button for "Add…", 510you will get another dialog hanging cells" are the cells with values that you 511 oDrive's estimated sales 512 growth rates, operating 513 I J K L M N r What-If Analysis, and then select Scenario t the button for "Add…", you will get another dialog hanging cells" are the cells with values that you oDrive's estimated sales growth rates, operating G H I 514 515 516 ing you to input the values into the changing cells 517 lues currently in those cells. So if you have already 518 n the dialog box, you can simply click "Ok" and you 519 520 521 522 ng a scenario, and editing a scenario. It also give you 523 ox asking you to specify some "Results" cells. For 524 he intrinsic stock price, and the return on invested 525 526 527 528 reate a new worksheet named "Scenario Summary". 529 , and the values in the530 "Results cells. We copied the he table to make it a bit 531more reader-friendy. 532 533 534 535 536 537 Scenario 538 539 (7) 540 (5) (6) Improve 541 Improve Improve Growth, 542 Growth and Growth and OP, and 543 OP CR CR 544 J K L M Additional information not in textbook (8) Status Quo (9) but Lower Better OP and WACC CR 545 546 547 548 11% 9% 8% 6% 11% 9% 8% 6% 11% 9% 8% 6% 10% 8% 7% 5% 10% 8% 7% 5% 549 550 7% 61% 6% 52% 7% 52% 6% 61% 7% 52% 551 552 10,97% 10,97% 10,97% 9,50% 10,97% 553 554 $3.880 $46,00 $3.751 $43,42 $4.918 $66,76 $3.690 $42,19 $4.538 $59,16 555 556 557 558 559 560 561 562 563 11,48% 11,54% 13,46% 9,84% 13,46% ROICT − WACC  WACC − g L  N ROICT − WACC G WACC − g L 564  H 565 566 567 value of operations will be less than the total net 568 2-way data table below show the difference between 569 of growth and ROIC. For input values, we use values 570 571 572 573 574 575 576 577 578 579 580 581 582 583 ct the Value of Operations Minus 584 585 586 587 at for very low values of ROIC, such as the first row 588 For very high values of ROIC, such as the last row 589 ive values of growth, ROIC, and WACC. 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 9,5% -$1.013 -$695 -$580 -$377 -$58 $260 $579 $897 $1.215 $1.534 $1.852 $2.171 $2.489 $2.807 $3.126 I J K L M N G H I 616 617 by the asset. When an investor buys a share of stock, he or she 618 the stock and to receive cash from the sale. However, the 619 pects to earn, and so on for different generations of investors. 620 ected to provide and the discount rate used to find the present 621 622 623 624 625 626 DN 627 ( 1 + rs ) N 628 sly, it would not be feasible to deal with an infinite stream of 629 be used to find the PV630 of the dividend stream, provided it is 631 632 633 634 635 er at a constant growth 636rate. Naturally, assuming a constant g the implications of imperfect information, information 637 onable. It is reasonable 638 to guess that a given stock will trying to find the average 639 of the good times and the bad times, nstant growth rate, we 640also need the estimated long-term tant, our price equation 641for common stock simplifies to the 642 643 644 645 646 647 d 8% a year. 648 649 650 651 te of 8%. What is its 652 stock price, assuming it has a required 653 654 655 656 657 658 659 660 $1,2420 661 662 0,0540 663 664 J K L M N G H I 665 666 667 668 to solve for r s. In doing 669so, we are now solving for an expected 670 671 672 673 674 675 ts. First, it consists of676 the expected dividend yield, which is ent of the expected return 677 is the expected capital gains yield. k, and is given by g L. 678 This shows us the dual role of gL in the it is also the expected679 stock price growth rate. 680 681 682 683 684 ermore, you expect the dividend to grow at a constant rate of 685 of the stock? 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 h rate. Hence, valuation 712 for these companies proves a little ort-run nonconstant 713 growth rate and predict future dividends. ed to grow. Generally, we assume that after a certain point of framework is estimating the short-term growth rate, how long J K L M N h rate. Hence, valuation for these companies proves a little ort-run nonconstant growth rate G and predictHfuture dividends. I J K L M N ed to grow. Generally, we assume that after a certain point of 714 framework is estimating 715 the short-term growth rate, how long 716 717 718 719 720 721 Data for figure: Growth Rates 722 Year Declining Zero Constant Nonconstant 723 1 -8% 0% 8% 30% 724 2 -8% 0% 8% 20% 725 Term Growth: 3 -8% 0% 8% 10% 726 8% 4 -8% 0% 8% 8% 727 5 -8% 0% 8% 8% 728 Dividend 729 Year Declining Growth: Zero Growth -8% Constant Growth: Long-Term 8% Growth: 8% 730 Growth: 8% Constant 0 $1,15 $1,15 $1,15 $1,15 731 1 $1,06 $1,15 $1,24 $1,50 732 2 $0,97 $1,15 $1,34 $1,79 733 3 $0,90 $1,15 $1,45 $1,97 734 Zero Growth 4 $0,82 $1,15 $1,56 $2,13 735 736 Growth: 5 $0,76 $1,15 $1,69 $2,30 Declining 737 8% 738 739 740 741 742 743 ack to the present. Then 744we will treat all dividends to be th model described above. 745 The point in time when the constant growth dividends, we solve for the horizon value 746 on value can be summarized as: 747 748 749 750 751 752 753 cribed as the expected value of the stock at the time period 754 755 756 757 rst year, 20% the second year, and 10% the third year. After 758 equired return is 13.4%; what is the price of the stock today? 759 760 761 762 763 764 G H 765 766 767 768 769 770 771 772 773 774 775 776 777 ෡𝟑 HV3 =778 779 ↓ 780D3(1+gL) ─────── 781 782(rs− gL) 783 ↓ $2,131 784 5,400% 785 786 ↓ $39,468 787 788 ↓ 789 ෡𝟑 𝐏 790 = ────── 791 (1+rs)3 792 unrounded values are793 used for all 794 795 796 er share. 797 798 799 800 801 802 803 804 805 806 807 808 809 810 urn of 8%. What is the value of this preferred stock? 811 812 I J K L M N G H I 813 814 815 816 817 818 atures in 50 years, pays a $8 annual dividend, has a par value 819 820 821 822 823 824 825 826 827 828 829 J K L M N O 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 50 51 P Q R S T U O 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 99 100 101 102 103 P Q R S T U O 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 P Q R S T U O 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 P Q R S T U O 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 P Q R S T U O 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 P Q R S T U O 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 P Q R S T U O 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 P Q R S T U O 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 P Q R S T U O 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 P Q R S T U O 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 P Q R S T U O 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 P Q R S T U O 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 P Q R S T U O 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 P Q R S T U O P Q R S T 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 Year Declining Growth: Zero -8% Growth Constant Growth: Long-Term 8% Growth: 8% 0 1,1500 1,1500 1,1500 1,1500 1 1,0580 1,1500 1,2420 1,4950 2 0,9734 1,1500 1,3414 1,7940 3 0,8955 1,1500 1,4487 1,9734 4 0,8239 1,1500 1,5646 2,1313 5 0,7579 1,1500 1,6897 2,3018 U Scenario Summary Current Values: Changing Cells: $A$324 Status Quo Status Quo $F$327 8% $G$327 7% $H$327 5% $E$327 10% $E$328 6% $E$329 61% $C$282 10,97% Result Cells: $B$396 $2.719,44 $G$460 $22,79 $I$338 9,84% Notes: Current Values column represents values of changing cells at time Scenario Summary Report was created. Changing cells for each scenario are highlighted in gray. Status Quo Higher Growth (Only) Higher Growth (Only) 8% 7% 5% 10% 6% 61% 10,97% 9% 8% 6% 11% 6% 61% 10,97% $2.719,44 $22,79 9,84% $2.713,27 $22,67 9,84% Higher OP (Only) Higher OP (Only) Better CR (Only) Better CR (Only) Improve Growth and OP Improve Growth and OP Improve Growth and CR Improve Growth and CR 8% 7% 5% 10% 7% 61% 10,97% 8% 7% 5% 10% 6% 52% 10,97% 9% 8% 6% 11% 7% 61% 10,97% 9% 8% 6% 11% 6% 52% 10,97% $3.681,78 $42,04 11,48% $3.575,63 $39,91 11,54% $3.879,93 $46,00 11,48% $3.751,25 $43,42 11,54% Improve Growth, OP, and CR Lower WACC (Only) Improve Growth, OP, and CR Lower WACC (Only) 9% 8% 6% 11% 7% 52% 10,97% $4.917,91 $66,76 13,46% Better OP and CR Better OP and CR 8% 7% 5% 10% 6% 61% 9,50% 8% 7% 5% 10% 7% 52% 10,97% $3.689,71 $42,19 9,84% $4.537,97 $59,16 13,46% SECTION 7-4 SOLUTIONS TO SELF-TEST A company expects a constant FCF of $240 million per year forever. If the WACC is 12%, what is the value of operations? Expected FCF WACC $240 12% Vop = $2.000,00 A company has a current value of operations of $800 million. The company has $100 million in short-term investments. If the company has $400 million in debt and has 10 million shares outstanding, what is the price per share? Vop $800 ST investments Total value Debt Value of equity Number of shares Price per share $100 $900 $400 $500 10 $50,00 SECTION 7-5 SOLUTIONS TO SELF-TEST A company expects to have a FCF in 1 year of $300, which is expected to grow at a constant rate of 3% forever. If the WACC is 11%, what is the value of operations? Expected FCF1 = $330 Expected gL = 3% WACC = 11% Vop = $4.125 A company's most recent free cash flow was $270. The company expects to have a FCF in 1 year of $300, which is expected to grow at a constant rate of 3% forever. If the WACC is 11%, what is the value of operations? Expected FCF1 = $300 Expected gL = 3% WACC = 11% Notice that the FCF of $270 at t = 0 is irrelevant to the value of operations, because it occurred in the past. The value of operations depends only on the future free cash flows. Vop = $3.750 A company's most recent free cash flow was $600 and is expected to grow at a constant rate of 4% forever. If the WACC is 10%, what is the value of operations? FCF0 = $600 Expected gL = 4% WACC = 10% Vop = $10.400 SECTION 7-6 SOLUTIONS TO SELF-TEST A company expects to have a FCF at Year 10 of $600, which is expected to grow at a constant rate of 8% thereafter. If the WACC is 8%, what is the value of operations at Year 10, HV 10? Expected FCF12 = $600 Expected gL = 4% WACC = 8% Vop = $15.600 A company expects a FCF of −$10 million at Year 1 and a FCF of $20 million at Year 2. FCF is expected to grow at a 5% rate after Year 2. If the WACC is 10%, what is the horizon value of operations; i.e., V op(Year 2)? What is the current value of operations; i.e., Vop(Year 0)? Long-term growth rate WACC 5% 10% Year 1 FCF1 Expected FCF -$10,00 Vop(Year 2) 2 FCF2 $20,00 $420,00 PV of expected FCF PV of expected Vop(Year 2) $7,44 $347,11 Vop(Year 0) $354,55 SECTION 7-7 SOLUTIONS TO SELF-TEST Cathey Corporation currently has sales of $1,000, which are expected to grow by 10% from Year 0 to Year 1 and by 4% from Year 1 to Year 2. The company currently has and operating profitability (OP) ratio of 7% and a capital requirement (CR) ratio of 50% and expects to maintain these ratios at their current levels. The current level of operating capital is $510. Use these inputs to forecast free cash flow (FCF) for Years 1 and 2. Hint: You must first forecast sales, net operating profit after taxes (NOPAT), and total net operating capital (OpCap) for each year. Sales0 = g0,1 = g1,2 = $1.000 10% 4% OP = NOPAT/Sales = CR = OpCap/Sales = OpCap0 = 7% 50% $510 Year Growth rate in sales Sales NOPAT OpCap Investment in OpCap FCF Growth in FCF 0 $1.000 $510 1 10% $1.100,00 $77,00 $550,00 $40,00 $37,00 2 4% $1.144,00 $80,08 $572,00 $22,00 $58,08 57,0% 3 4% $1.189,76 $83,28 $594,88 $22,88 $60,40 4,0% Cathey Corporation has a 12% weighted average cost of capital. Cathey's free cash flows, estimated in the previous question, are expected to grow at 4% beginning at Year 2 and continuing for the foreseeable future. What is the horizon value (use Year 2 for the horizon)? What is the current value of operations? Long-term growth rate WACC 4% 12% Year 1 FCF1 Expected FCF $37,00 HV2 = Vop(Year 2) 2 FCF2 $58,08 $755,04 PV of expected FCF PV of expected HV(Year 2) $79,34 $601,91 Vop(Year 0) $681,25 Cathey Corporation has $80 in short-term investments, $20 in short-term debt, $140 in long-term debt, $30 in preferred stock, and 10 shares of common stock outstanding. Use the value of operations from the previous question to estimate the intrinsic common stock price per share. Vop = ST investments = ST debt = Long-term debt = Preferred stock = $681,25 $80,00 $20,00 $140,00 $30,00 Number of shares = 10 Vop $681,25 ST investments Value of equity Number of shares $80,00 $761,25 $160,00 $30,00 $571,25 10,00 Price per share $57,13 Total value All debt Preferred stock SECTION 7-11 SOLUTIONS TO SELF-TEST If D1 = $3.00, P0 = $50, and the expected P at t=1 is equal to $52, what are the stock’s expected dividend yield, capital gains yield, and total return for the coming year? D1 $3,00 P0 $50,00 Expected P1 $52,00 Exp. dividend yield Exp. capital gains yield Exp. total return 6,0% =B6/B7 4,0% =(B8-B7)/B7 10,0% =C10+C11 A stock is expected to pay a dividend of $2 at the end of the year. The required rate of return is r s = 12%. What would the stock’s price be if the growth rate were 4%? D1 $2,00 gL 4% rs 12% Stock price $25,00 A stock is expected to pay a dividend of $2 at the end of the year. The required rate of return is r s = 12%. What would the stock’s price be if the growth rate were 0%? D1 $2,00 gL 0% rs 12% Stock price $16,67 If D0 = $4.00, rs = 9%, and g = 5% for a constant growth stock, what are the stock’s expected dividend yield and capital gains yield for the coming year? D0 $4,00 gL 5% rs 9% Expected D1 $4,20 Stock price $105,00 Expected dividend yield 4,00% Expected capital gains yield 5,00% Alternatively, you know that the capital gains yield is equal to the growth rate. Expected capital gains yield = growth rate = 5,00% Because the total return is rs, the dividend yield is rs minus the capital gains yield: Expected dividend yield = 4,00% Suppose D0 = $5.00 and rs = 10%. The expected growth rate from Year 0 to Year 1 (g 0 to 1) = 20%, the expected growth rate from Year 1 to Year 2 (g1 to 2) = 10%, and the constant rate beyond Year 2 is g L = 5%. What are the expected dividends for Year 1 and Year 2? What is the expected horizon value price at Year 2? What is the expected price at Time 0? D0 $5,00 g0 to 1 20% g1 to 2 10% gL 5% rs 10% Year 1 D1 Expected dividends 2 D2 $6,00 Expected HVP,2 $6,60 $138,60 PV of expected dividends PV of expected HVP,2 $10,91 $114,55 Expected price at Time 0 $125,45 SECTION 7-12 SOLUTIONS TO SELF-TEST Dodd Corporation is a private company that earned $4.00 per share for the most recent year. If the average P/E ratio of a group of comparable public companies is 11, what is an estimate of Dodd's stock value on a per share basis? Earnings per share = Average comparable P/E ratio = $4,00 11,0 Estimated price per share = $44,00 The company in the previous question, Dodd Corporation, has 100,000 shares of common stock owned by its founder. Dodd owes $1,300,000 to its bank. Dodd has 11,400 customers. If the average ratio of total entity value to customers is $500 for a group of comparable public companies, what is Dodd's estimated total entity value? What is its estimated stock value on a per share basis? Number of shares = Debt = Number of customers = 100.000 $1.300.000 11.400 Average comparable ratio of total entity value to number of customers = $500 Estimated entity value = − Debt Intrinsic equity value ÷ Number of shares $5.700.000 $1.300.000 4.400.000 100.000 Estimated price per share = $44,00 io of a group of der. Dodd owes or a group of comparable is? SECTION 7-14 SOLUTIONS TO SELF-TEST A preferred stock has an annual dividend of $5. The required return is 8%. What is the V ps? Dps rps Vps $5,00 8% $62,50
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