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A B C D E F G H I J K 1 12/24/2007 2 3 Chapter 10. Tool Kit for Basics of Capital Budgeting: Evaluating Cash Flows 4 5 In this file we use Excel to do most of the calculations explained in the textbook. First, we analyze Projects S and L, 6 whose cash flows are shown immediately below in both tabular and a time line formats. Spreadsheet analyses can be set 7 up vertically, in a table with columns, or horizontally, using time lines. For short problems, with just a few years, we 8 generally use the time line format because rows can be added and we can set the problem up as a series of income statements. For long problems, it is often more convenient to use a tabular layout. 9 10 11 Expected after-tax 12 net cash flows (CFt) 13 Year (t) Project S Project L 14 0 ($1,000) ($1,000) 15 1 500 100 16 2 400 300 17 3 300 400 18 4 100 600 19 20 Figure 10-1: Net Cash Flows and Selected Evaluation Criteria for 21 Projects S and L (CFt) 22 23 Panel A: Project Cash Flows and Cost of Capital 24 25 Project S: 0 1 2 3 4 26 | | | | | 27 -$1,000 $500 $400 $300 $100 28 29 Project L: 0 1 2 3 4 30 | | | | | 31 -$1,000 $100 $300 $400 $600 32 33 Project cost of capital = r = 10% 34 35 Panel B: Summary of Selected Evaluation Criteria 36 37 Project 38 S L 39 NPV: $78.82 $49.18 40 IRR: 14.5% 11.8% 41 MIRR: 12.1% 11.3% 42 PI: 1.08 1.05 43 44 45 46 47 48 NET PRESENT VALUE (NPV) (Section 10.2) 49 50 To calculate the NPV, we find the present value of the individual cash flows and find the sum of those discounted cash 51 flows. This value represents the value the project add to shareholder wealth. 52 53 r = 10% 54 55 Project S 56 Time period: 0 1 2 3 4 57 Cash flow: (1,000) 500 400 300 100 A B C D E F G H I J K 58 Disc. cash flow: (1,000) 455 331 225 68 59 60 NPV(S) = $78.82 = Sum disc. CF's. or $78.82 = Uses NPV function. 61 62 Project L 63 Time period: 0 1 2 3 4 64 Cash flow: (1,000) 100 300 400 600 65 Disc. cash flow: (1,000) 91 248 301 410 66 67 NPV(L) = $49.18 $ 49.18 = Uses NPV function. 68 A B C D E F G H I J K 69 The NPV method of capital budgeting dictates that all independent projects that have positive NPV should accepted. 70 The rationale behind that assertion arises from the idea that all such projects add wealth, and that should be the overall 71 goal of the manager in all respects. If strictly using the NPV method to evaluate two mutually exclusive projects, you 72 would want to accept the project that adds the most value (i.e. the project with the higher NPV). Hence, if considering 73 the above two projects, you would accept both projects if they are independent, and you would only accept Project S if 74 they are mutually exclusive. 75 76 77 78 INTERNAL RATE OF RETURN (IRR) (Section 10.2) 79 80 The internal rate of return is defined as the discount rate that equates the present value of a project's cash inflows to its 81 outflows. In other words, the internal rate of return is the interest rate that forces NPV to zero. The calculation for 82 IRR can be tedious, but Excel provides an IRR function that merely requires you to access the function and enter the 83 array of cash flows. The IRR's for Project S and L are shown below, along with the data entry for Project S. 84 85 86 Expected after-tax 87 net cash flows (CFt) 88 Year (t) Project S Project L 89 0 ($1,000) ($1,000) The IRR function assumes 90 1 500 100 IRR S = 14.49% payments occur at end of 91 2 400 300 IRR L = 11.79% periods, so that function does 92 3 300 400 not have to be adjusted. 93 4 100 600 94 95 96 Notice that for IRR you must 97 specify all cash flows, including 98 the time zero cash flow. This 99 is in contrast to the NPV 100 function, in which you specify 101 only the future cash flows. 102 103 104 105 106 107 108 109 The IRR method of capital budgeting maintains that projects should be accepted if their IRR is greater than the cost of 110 capital. Strict adherence to the IRR method would further dictate that mutually exclusive projects should be chosen on 111 the basis of the greatest IRR. In this scenario, both projects have IRR's that exceed the cost of capital (10%) and both 112 should be accepted, if they are independent. If, however, the projects are mutually exclusive, we would chose Project S. 113 Recall, that this was our determination using the NPV method as well. The question that naturally arises is whether or 114 not the NPV and IRR methods will always agree. 115 116 117 COMPARISON OF THE NPV AND IRR METHODS (Section 10.4) 118 119 NPV Profiles 120 121 NPV profiles graph the relationship between projects' NPVs and the cost of capital. To create NPV profiles for Projects 122 S and L, we create data tables of NPV at different costs of capital. 123 124 Net Cash Flows 125 Year Project S Project L WACC = 10.0% 126 0 -$1,000 -$1,000 Project S Project L 127 1 $500 $100 NPV = $78.82 $49.18 128 2 $400 $300 IRR = 14.49% 11.79% 129 3 $300 $400 Crossover = 7.17% 130 4 $100 $600 A B C D E F G H I J K 131 Data Table used to make graph: 132 133 Project S's Both Projects' Profiles NPV Profile 134 WACC 135 $400 $600 0% Conflict 136 NPVs No conflict 5% $300 $400 NPVL 137 7.17% Accept Reject 138 $200 10% 139 $200 11.79% NPV NPV 140 $100 14.49% $0 141 15.0% $0 142 -$200 20% Crossover 143 -$100 IRRS = 14.49% = 7.17% 25% 144 -$400 145 -$200 0% 5% 10% 15% 20% 25% 146 0% 5% 10% 15% 20% 25% WACC WACC 147 148 149 150 Points about the graphs: 151 1. In Panel a, we see that if WACC < IRR, then NPV > 0, and vice versa. 152 2. Thus, for "normal and independent" projects, there can be no conflict between NPV and IRR rankings. 153 3. However, if we have mutually exclusive projects, conflicts can occur. In Panel b, we see that IRRS is 154 always greater than IRRL, but if WACC < 11.56%, then IRRL > IRRS, in which case a conflict occurs. 155 4. Summary: a. For normal, independent projects, conflicts can never occur, so either method can be used. 156 b. For mutually exclusive projects, if WACC > Crossover, no conflict, but if WACC < Crossover, 157 then there will be a conflict between NPV and IRR. 158 A B C D E F G H I J K 159 160 Previously, we had discussed that in some instances the NPV and IRR methods can give conflicting results. First, we 161 should attempt to define what we see in this graph. Notice, that the two project profiles (S and L) intersect the x-axis at 162 costs of capital of 14% and 12%, respectively. Not coincidently, those are the IRR's of the projects. If we think about 163 the definition of IRR, we remember that the internal rate of return is the cost of capital at which a project will have an 164 NPV of zero. Looking at our graph, it is a logical conclusion that the IRR of a project is defined as the point at which its 165 profile intersects the x-axis. 166 167 Looking further at the NPV profiles, we see that the two project profiles intersect at a point we shall call the crossover 168 point. We observe that at costs of capital greater than the crossover point, the project with the greater IRR (Project S, 169 in this case) also has the greater NPV. But at costs of capital less than the crossover point, the project with the lesser 170 IRR has the greater NPV. This relationship is the source of discrepancy between the NPV and IRR methods. By 171 looking at the graph, we see that the crossover appears to occur at approximately 7%. Luckily, there is a more precise 172 way of determining crossover. To find crossover, we will find the difference between the two projects cash flows in each 173 year, and then find the IRR of this series of differential cash flows. 174 175 Expected after-tax Alternative: Use Tools > Goal Seek to find WACC when NPV(S) = 176 net cash flows (CFt) Cash flow NPV(L). Set up a table to show the difference in NPV's, which we 177 Year (t) Project S Project L differential want to be zero. The following will do it, getting WACC = 7.17%. 178 0 ($1,000) ($1,000) 0 179 1 500 100 400 Trial project cost of capital, r = 7.17% 180 2 400 300 100 NPV S (based on trial r)= $ 134.40 181 3 300 400 (100) NPV L (based on trial r) = $ 134.40 182 4 100 600 (500) S-L= $ 0.00 183 184 185 186 IRR = Crossover rate = 7.17% 187 188 189 190 191 192 193 194 The intuition behind the relationship between the NPV profile and the crossover rate is as follows: (1) 195 Distant cash flows are heavily penalized by high discount rates--the denominator is (1+r)t, and it 196 increases geometrically, hence gets very large at high values of t. (2) Long-term projects like L have most 197 of their cash flows coming in the later years, when the discount penalty is largest, hence they are most 198 severely impacted by high capital costs. (3) Therefore, Project L's NPV profile is steeper than that of S. 199 (4) Since the two profiles have different slopes, they cross one another. 200 201 When dealing with independent projects, the NPV and IRR methods will always yield the same 202 accept/reject result. However, in the case of mutually exclusive projects, NPV and IRR can give 203 conflicting results. One shortcoming of the internal rate of return is that it assumes that cash flows 204 received are reinvested at the project's internal rate of return, which is not usually true. We explain how 205 to modify IRR to accommodate this shortcoming in a later section. 206 207 208 MULTIPLE IRRS (Section 10.5) 209 A B C D E F G H I J K 210 211 Because of the mathematics involved, it is possible for some (but not all) projects that have more than one 212 change of signs in the set of cash flows to have more than one IRR. If you attempted to find the IRR with 213 such a project using a financial calculator, you would get an error message. The HP-10B says "Error - 214 Soln", the HP-17B says '"Many/No Solutions, and the HP12C says Error 3; Key in Guess" when such a 215 project is evaluated. The procedure for correcting the problem isto store in a guess for the IRR, and then 216 the calculator will report the IRR that is closest to your guess. You can then use a different "guess" 217 value, and you should be able to find the other IRR. However, the nature of the mathematics creates a 218 scenario in which one IRR is quite extraordinary (often, a few hundred percent). 219 220 221 222 Consider the case of Project M. 223 224 Project M: Year: 0 1 2 225 CF: (1.6) 10 (10) 226 227 We will solve this IRR twice, the first time using the default guess of 10%, and the second time we will 228 enter a guess of 300%. Notice, that the first IRR calculation is exactly as it was above. 229 230 231 1 232 IRR M = 25.0% 233 234 235 236 237 238 239 240 241 2 242 IRR M = 400% 243 244 245 246 247 248 249 250 251 252 253 254 255 256 The two solutions to this problem tell us that this project will have a positive NPV for all costs of capital 257 between 25% and 400%. We illustrate this point by creating a data table and a graph of the project 258 NPVs. 259 260 Project M: Year: 0 1 2 261 CF: (1.6) 10 (10) 262 263 264 265 266 r = 25.0% 267 NPV = 0.00 268 A B C D E F G H I J K 269 NPV 270 r $0.0 Multiple Rates of Return 271 0% (1.60) 272 25% 0.00 $1.50 273 50% 0.62 274 75% 0.85 $1.00 275 100% 0.90 Max. 276 125% 0.87 $0.50 277 150% 0.80 278 175% 0.71 $0.00 279 200% 0.62 -100% 0% 100% 200% 300% 400% 500% 280 225% 0.53 -$0.50 281 250% 0.44 282 275% 0.36 -$1.00 283 300% 0.28 284 325% 0.20 -$1.50 285 350% 0.13 286 375% 0.06 -$2.00 287 400% 0.00 288 425% (0.06) 289 450% (0.11) 290 475% (0.16) 291 500% (0.21) 292 525% (0.26) 293 550% (0.30) 294 295 296 MODIFIED INTERNAL RATE OF RETURN (MIRR) (Section 10.6) 297 298 The modified internal rate of return is the discount rate that causes a project's cost (or cash outflows) to 299 equal the present value of the project's terminal value. The terminal value is defined as the sum of the 300 future values of the 'project's cash inflows, compounded at the project's cost of capital. To find MIRR, 301 calculate the PV of the outflows and the FV of the inflows, and then find the rate that equates the two. 302 Or, you can solve using the MIRR function. 303 304 305 306 A B C D E F G H I J K 307 WACC = 10% 308 Project S MIRRS = 12.11% 309 10% MIRRL = 11.33% 310 0 1 2 3 4 311 (1,000) 500 400 300 100 312 313 Project L 314 315 0 1 2 3 4 316 (1,000) 100 300 400 600 317 440.0 318 363.0 319 133.1 320 PV: (1,000) Terminal Value: 1,536.1 321 322 The advantage of using the MIRR, relative to the IRR, is that the MIRR assumes that cash flows received 323 are reinvested at the cost of capital, not the IRR. Since reinvestment at the cost of capital is more likely, 324 the MIRR is a better indicator of a project's profitability. Moreover, it solves the multiple IRR problem, 325 as a set of cash flows can have but one MIRR . 326 327 Note that if negative cash flows occur in years beyond Year 1, those cash flows would be discounted at the 328 cost of capital and added to the Year 0 cost to find the total PV of costs. If both positive and negative 329 flows occurred in some year, the negative flow should be discounted, and the positive one compounded, 330 rather than just dealing with the net cash flow. This makes a difference. 331 332 Also note that Excel's MIRR function allows for discounting and reinvestment to occur at different rates. 333 Generally, MIRR is defined as reinvestment at the WACC, though Excel allows the calculation of a 334 special MIRR where reinvestment occurs at a different rate than WACC. 335 336 Finally, it is stated in the text, when the IRR versus the NPV is discussed, that the NPV is superior 337 because (1) the NPV assumes that cash flows are reinvested at the cost of capital whereas the IRR assumes 338 reinvestment at the IRR, and (2) it is more likely, in a competitive world, that the actual reinvestment rate 339 is more likely to be the cost of capital than the IRR, especially if the IRR is quite high. The MIRR setup 340 can be used to prove that NPV indeed does assume reinvestment at the WACC, and IRR at the IRR. 341 A B C D E F G H I J K 342 343 Project S 344 WACC = 10% 345 0 1 2 3 4 346 (1,000) 500 400 300 100 347 330.0 348 484.0 349 665.5 Reinvestment at WACC = 10% 350 PV outflows -$1,000.00 Terminal Value: 1,579.5 351 PV of TV $1,078.82 352 NPV $ 78.82 Thus, we see that the NPV is consistent with reinvestment at WACC. 353 354 355 Now repeat the process using the IRR as the discount rate. 356 357 Project S 358 IRR = 14.49% 359 0 1 2 3 4 360 (1,000) 500 400 300 100 361 343.5 362 524.3 363 750.3 Reinvestment at IRR = 14.49% 364 PV outflows -$1,000.00 Terminal Value: 1,718.1 365 PV of TV $1,000.00 366 NPV $0.00 Thus, if compounding is at the IRR, NPV is zero. Since the 367 definition of IRR is the rate at which NPV = 0, this demonstrates 368 that the IRR assumes reinvestment at the IRR. 369 370 PROFITABILITY INDEX (PI) (Section 10.7) 371 372 The profitability index is the present value of all future cash flows divided by the intial cost. It measures 373 the PV per dollar of investment. 374 375 For project S: 376 PI(S) = PV of future cash flows ÷ Initial cost 377 PI(S) = $ 1,078.82 ÷ $ 1,000.00 378 PI(S) = 1.079 379 380 For project L: 381 PI(L) = PV of future cash flows ÷ Initial cost 382 PI(L) = $ 1,049.18 ÷ $ 1,000.00 383 PI(L) = 1.049 384 385 386 387 PAYBACK METHODS (Section 10.8) 388 389 Payback Period 390 The payback period is defined as the expected number of years required to recover the investment, and it was the first 391 formal method used to evaluate capital budgeting projects. First, we identify the year in which the cumulative cash 392 inflows exceed the initial cash outflows. That is the payback year. Then we take the previous year and add to it 393 unrecovered balance at the end of that year divided by the following year's cash flow. Generally speaking, the shorter 394 the payback period, the better the investment. 395 396 Figure 10-4. Payback Periods for Projects S and L 397 398 Project S Year: 0 1 2 3 4 399 | | | | | 400 Cash flow: -1,000 500 400 300 100 A B C D E F G H I J K 401 Cumulative cash flow: -1,000 -500 -100 200 300 Percent of year required 402 for payback: 1.00 1.00 0.33 0.00 403 Payback = 2.33 404 405 Project L Year: 0 1 2 3 4 406 | | | | | 407 Cash flow: -1,000 100 300 400 600 408 Cumulative cash flow: -1,000 -900 -600 -200 400 Percent of year required 409 for payback: 1.00 1.00 1.00 0.33 410 Payback = 3.33 411 412 413 A B C D E F G H I J K 414 Discounted Payback Period 415 Discounted payback period uses the project's cost of capital to discount the expected cash flows. The 416 calculation of discounted payback period is identical to the calculation of regular payback period, except 417 you must base the calculation on a new row of discounted cash flows. Note that both projects have a cost 418 of capital of 10%. 419 420 WACC = 10% 421 422 Figure 10-5. Projects S and L: Discounted Payback Period (r = 10%) 423 424 Project S Year: 0 1 2 3 4 425 | | | | | 426 Cash flow: (1,000) 500 400 300 100 427 Discounted cash flow: (1,000) 454.5 330.6 225.4 68.3 428 Cumulative discounted CF: (1,000) (545.5) (214.9) 10.5 78.8 Percent of year required 429 for payback: 1.00 1.00 0.95 0.00 430 Discounted Payback: 2.95 431 432 Project L Year: 0 1 2 3 4 433 | | | | | 434 Cash flow: (1,000) 100 300 400 600 435 Discounted cash flow: (1,000) 90.9 247.9 300.5 409.8 436 Cumulative discounted CF: (1,000) (909.1) (661.2) (360.6) 49.2 Percent of year required 437 for payback: 1.00 1.00 1.00 0.88 438 Discounted Payback: 3.88 439 440 441 The inherent problem with both paybacks is that they ignore cash flows that occur after the payback 442 period mark. While the discounted method accounts for timing issues (to some extent), it still falls short of 443 fully analyzing projects. However, all else equal, these two methods do provide some information about 444 projects' liquidity and risk. 445 446 447 SPECIAL APPLICATIONS OF CASH FLOW EVALUATION (Section 10.11) 448 449 PROJECTS WITH UNEQUAL LIVES 450 451 If two mutually exclusive projects have different lives, and if the projects can be repeated, then it is 452 necessary to deal explicitly with those unequal lives. We use the replacement chain (or common life) 453 approach. This procedure compares projects of unequal lives by equalizing their lives by assuming that 454 each project can be repeated as many times as necessary to reach a common life span. The NPVs over this 455 life span are then compared, and the project with the higher common life NPV is chosen. To illustrate, 456 suppose a firm is considering two mutually exclusive projects, either a conveyor system (Project C) or a 457 fleet of forklift trucks (Project F) for moving materials. The firm's cost of capital is 12%. The cash flow 458 timelines are shown below, along with the NPV and IRR for each project. 459 460 461 r= 11.5% 462 463 Figure 10-6 Analysis of Projects C and F (r = 11.5%) 464 465 Project C: 466 467 Year (t) 0 1 2 3 4 5 6 A B C D E F G H I J K 468 CFt for C ####### $8,000 $14,000 $13,000 $12,000 $11,000 $10,000 469 470 NPVC = $7,165 IRRC = 17.5% 471 472 Project F: 473 474 Year (t) 0 1 2 3 475 CFt for F ####### $7,000 $13,000 $12,000 476 477 NPVF = $5,391 IRRF = 25.2% 478 479 Common Life Approach with F Repeated (Project FF): 480 481 Year (t) 0 1 2 3 4 5 6 482 CFt for F ####### $7,000 $13,000 $12,000 483 CFt for F ($20,000) $7,000 $13,000 $12,000 484 CFt for FF ####### $7,000 $13,000 ($8,000) $7,000 $13,000 $12,000 485 486 NPVFF = $9,281 IRRFF = 25.2% 487 488 489 On the basis of this extended analysis, it is clear that Project F is the better of the two investments (with 490 both the NPV and IRR methods). 491 492 Equivalent Annual Annuity (EAA) Approach 493 494 Here are the steps in the EAA approach. 495 1. Find the NPV of each project over its initial life (we already did this in our previous analysis). 496 NPVC= 7,165 497 NPVF= 5,391 498 499 2. Convert the NPV into an annuity payment with a life equal to the life of the project. 500 EEAC= 1,718 Note: we used the Function Wizard for the PMT function. 501 EEAF= 2,225 502 503 Project F has a higher EEA, so it is a better project. 504 505 ECONOMIC LIFE VS. PHYSICAL LIFE 506 507 Sometimes an asset has a physical life that is greater than its economic life. Consider the following asset 508 which has a physical life of three years. During its life, the asset will generate operating cash flows. 509 However, the project could be terminated and the asset sold at the end of any year. The following table 510 shows the operating cash flows and the salvage value for each year-- all values are shown on an after-tax 511 basis. A B C D E F G H I J K 512 Operating Salvage 513 Year Cash Value 514 0 ($4,800) $4,800 515 1 $2,000 $3,000 516 2 $2,000 $1,650 517 3 $1,750 $0 518 519 The cost of 520 PV of PV of 3-Year NPV = Intial Cost + + Operating Salvage 521 Cash Flow Value 522 = ($4,800.00) + $4,785.88 + $0.00 523 3-Year NPV = ($14.12) 524 The asset has 525 a negative 526 527 PV of PV of 2-Year NPV = Intial Cost + + Operating Salvage 528 Cash Flow Value 529 = ($4,800.00) + $3,471.07 + $1,363.64 530 2-Year NPV = $34.71 531 PV of PV of 1-Year NPV = Intial Cost + + Operating Salvage 532 Cash Flow Value 533 = ($4,800.00) + $1,818.18 + $2,727.27 534 1-Year NPV = ($254.55) L M N O P Q 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 52 53 54 55 56 Notice that the NPV function isn't really a Net present value. 57 Instead, it is the present value of future cash flows. Thus, you specify only the future cash flows in the NPV function. To find the true NPV, you must add the time zero cash flow to the result of the NPV function. Notice that the NPV function isn't really a Net present value. L present value of future O flows. P Instead, it is the M N cash Thus, you Q 58 specify only the future cash flows in the NPV function. To find the 59 true NPV, you must add the time zero cash flow to the result of the 60 NPV function. 61 62 63 64 65 66 67 68 L M N O P Q 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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 L M N O P Q 131 Data Table used to make graph: 132 Project NPVs 133 S L 134 $78.82 $49.18 135 $300.00 $400.00 136 $180.42 $206.50 137 $134.40 $134.40 138 $78.82 $49.18 139 $46.10 $0.00 140 $0.00 -$68.02 141 -$8.33 -$80.14 142 -$83.72 -$187.50 143 -$149.44 -$277.44 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 L M N O P Q 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 L M N O P Q 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 L M N O P Q 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 L M N O P Q 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 SECTION 10.2 SOLUTIONS TO SELF-TEST 3 A project has the following expected cash flows: CF0 = -$500, CF1 = $200, CF2 = $200, and CF3 = $400. If the project of capital is 9 percent, what is the NPV? WACC 9% Expected After-Tax Net Cash Flows, CFt Year (t) 0 -$500 1 $200 2 $200 3 $400 NPV = $160.70 d CF3 = $400. If the project cost SECTION 10.3 SOLUTIONS TO SELF-TEST 3 A project has the following expected cash flows: CF0 = -$500, CF1 = $200, CF2 = $200, and CF3 = $400. What is the IRR? Expected After- Tax Net Cash Year (t) 0 -$500 1 $200 2 $200 3 $400 IRR = 24.1% and CF3 = $400. What SECTION 10.5 SOLUTIONS TO SELF-TEST 2 A project has the following cash flows: CF0 = −$1,100, CF1 = $2,100, CF2 = $2,100, and CF3 = −$3,600. How many positive IRRs might this project have? If you set the starting trial value to 10 percent in either your calculator of Excel, what is the IRR? If you set the starting trial value to 400%? What is the NPV of the project with a very low cost of capital, such as r = 0%? Does this suggest that the project should or should not be accepted? Project Year (t) CFs 0 -$1,100 1 $2,100 2 $2,100 3 -$3,600 IRR with starting trial at 10%: 18.2% IRR with starting trial at 300%: 106.7% NPV with r = 0%: ($500.00) and CF3 = −$3,600. 10 percent in either What is the NPV of e project should or SECTION 10.6 SOLUTIONS TO SELF-TEST 3 A project has the following expected cash flows: CF0 = -$500, CF1 = $200, CF2 = $200, and CF3 = $400. Using a 10 percent discount rate and reinvestment rate, what is the MIRR? Discount rate = reinvestment rate = 10% Expected After-Tax Net Cash Flows, CFt Year (t) 0 -$500 1 $200 2 $200 3 $400 MIRR = 19.9% and CF3 = $400. SECTION 10.7 SOLUTIONS TO SELF-TEST 2 A project has the following expected cash flows: CF0 = -$500, CF1 = $200, CF2 = $200, and CF3 = $400. If the project of capital is 9 percent, what is the PI? WACC 9% Expected After-Tax Net Cash Flows, CFt Year (t) 0 -$500 1 $200 2 $200 3 $400 PI = 1.32 nd CF3 = $400. If the project cost SECTION 10.8 SOLUTIONS TO SELF-TEST 3 A project has the following expected cash flows: CF0 = -$500, CF1 = $200, CF2 = $200, and CF3 = $400. If the project's cost of capital is 9%, what are the project's payback period and discounted payback period? Year: 0 1 2 3 Cash flow: (500) 200 200 400 Cumulative CF: (500) (300) (100) 300 Percent of year required for payback: 1.00 1.00 0.25 Discounted Payback: 2.25 r= 9% Year: 0 1 2 3 Cash flow: (500) 200 200 400 Discounted cash flow: (500) 183.49 168.34 308.87 Cumulative discounted CF: (500) (316.51) (148.18) 160.70 Percent of year required 1.00 1.00 0.48 Discounted Payback: 2.48