Based Financial Analysis of Projects

A 12 13 14 15 16 17 18 19 20 21 B C D E F G In this file we use Excel to do most of the calculations explained in the textbook. First, we analyze Projects S and L, whose cash flows are shown immediately below in time line formats. Spreadsheet analyses can be set up vertically, in a table with columns, or horizontally, using time lines. For short problems, with just a few years, we 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 vertical layout. Figure 10-1. Net Cash Flows (CFt) and Selected Evaluation Criteria for Projects S and L 22 23 Panel A: Project Cash Flows and Cost of Capital 24 25 26 Project cost of capital, r, for each project: 10% After-Tax, End of Year, Project Cash Flows, CFt 27 Initial Cost 28 0 -$10,000 1 $5,000 2 $4,000 3 $3,000 4 $1,000 -$10,000 $1,000 $3,000 $4,000 $6,750 29 30 31 32 Project S Project L Panel B: Summary of Selected Evaluation Criteria 33 34 Project S NPV IRR MIRR PI Payback Discounted Payback 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 $788.20 14.49% 12.11% 1.08 2.95 Project L $1,004.03 13.55% 12.66% 1.10 3.30 3.78 Figure 10-2. Finding the NPV for Projects S and L To calculate the NPV, we find the present value of the individual cash flows and then sum those discounted cash flows. The sum is the value the project adds to or subtracts from shareholder wealth. 50 r = 10% 51 52 53 54 Year = Project S 55 56 57 58 59 0 (r = 10%) -10,000.00 4,545.45 3,305.79 2,253.94 1 5,000 2 4,000 3 3,000 4 1,000 683.01 NPVS = $788.20 Long way: Sum the PVs of the CFs to find NPV 60 61 H Year = 0 (r = 10%) 1 2 3 4 A 62 B Project L C -10,000.00 1,000 D E F 3,000 4,000 6,750 G H 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 NPVL = $1,004.03 Short way: Use Excel's NPV function =NPV(B51,C62:F62)+B62 The NPV criterion says that all independent projects that have positive NPV should accepted. The rationale for this is that all such projects add wealth, and that should be the overall goal of the manager in all respects. If strictly using the NPV method to evaluate two mutually exclusive projects, you would want to accept the project that adds the most value (i.e. the project with the higher positive NPV). Hence, if considering the above two projects, you would accept both projects if they are independent, and you would only accept Project L if they are mutually exclusive. INTERNAL RATE OF RETURN (IRR) (Section 10.3) The internal rate of return is defined as the discount rate that equates the present value of a project's cash inflows to its outflows. In other words, the internal rate of return is the interest rate that forces NPV to zero. The calculation for IRR can be tedious, but Excel provides an IRR function that merely requires you to access the function and enter the array of cash flows. The IRRs for Project S and L are shown below, along with the data entry for Project S. 84 85 86 Figure 10-3. Finding the IRR 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 r = 14.49% Year = Project S Sum of PVs = IRRS 0 1 2 3 4 -10,000.00 4,367.24 3,051.64 1,999.09 582.03 $0.00 5,000 4,000 3,000 1,000 = 14.49% Year = Project L 0 -10,000.00 IRRL = 13.55% = NPV at r = 14.489%. NPV = 0, so IRR = 14.489%. =IRR(B90:F90) using IRR function 1 1,000 2 3,000 3 4,000 4 6,750 =IRR(B100:F100) using IRR function The IRR method of capital budgeting maintains that projects should be accepted if their IRR is greater than the cost of capital. Strict adherence to the IRR method would further dictate that mutually exclusive projects should be chosen on the basis of the greater IRR. In our example, each project has an IRR that exceeds the cost of capital (10%) so both projects should be accepted if they are independent. If, however, the projects are mutually exclusive, we would choose Project S because it has the higher IRR. Recall that this differs from our conclusion when using the NPV method. So, we have a conflict between the NPV and the IRR methods for ranking Projects S and L. MULTIPLE IRRS (Section 10.4) A 115 116 117 118 119 120 121 122 123 B C D E F G 124 Figure 10-4. Graph for Multiple IRRs: Project M (Millions of Dollars) 125 126 127 0 1 2 Year = 128 -1.60 10 -10 Project M 129 130 r = 10% NPV = -$0.774 131 132 133 134 NPV (Mil$0.900 lions) NPV = −$1.6 + $10/(1+r) + (−$10)/(1+r)2 135 136 137 $0.700 138 139 $0.500 140 141 142 $0.300 143 IRR #1 = 25% IRR #2 = 400% 144 $0.100 145 146 147 0% 50% 100% 150% 200% 250% 300% 350% 400% 450% 500% -$0.100 148 149 150 -$0.300 Cost of Capital (%) 151 152 153 Note: 154 The table shown below calculates Project M's NPV at the rates shown in the left column. These data are plotted to 155 form the graph shown above. Notice that NPV = 0 at both 25% and 400%. Since the definition of the IRR is the 156 rate at which the NPV = 0, there are two IRRs. 157 158 r NPV 159 160 0% -$1.600 161 10% 25% 110% -$0.774 $0.000 $0.894 400% 500% $0.000 -$0.211 162 163 164 165 166 167 168 H Because of the mathematics involved, it is possible for some (but not all) projects that have more than one change of signs in the cash flows to have more than one IRR. If you attempted to find the IRR with such a project using a financial calculator, you would get an error message. The HP-10B says "Error - Soln", the HP-17B says '"Many/No Solutions, and the HP12C says Error 3; Key in Guess." The procedure for correcting the problem is to store in a guess for the IRR, and then the calculator will report the IRR that is closest to your guess. You can then use a different "guess" value, and you should be able to find the other IRR. However, the nature of the mathematics creates a scenario in which one IRR is quite extraordinary (often, several hundred percent). = IRR #1 = 25% = IRR #2 = 400% A B C D E F G H 169 REINVESTMENT RATE ASSUMPTIONS (Section 10.5) 170 171 172 The IRR approach assumes that cash flows can be reinvested at the IRR, but it is more realistic to asssume that cash flows only can be reinvested at the cost of capital. For this reason, NPV is a better decision criterion than IRR. 173 174 175 MODIFIED INTERNAL RATE OF RETURN, MIRR (Section 10.6) 176 177 The modified internal rate of return is the discount rate that causes a project's cost (or cash outflows) to equal the 178 present value of the project's terminal value. The terminal value is defined as the sum of the future values of the 179 project's cash inflows, compounded at the project's cost of capital. To find MIRR, calculate the PV of the outflows 180 and the FV of the inflows, and then find the rate that equates the two. Alternatively, you can solve using Excel's 181 MIRR function. 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 One advantage of using the MIRR, relative to the IRR, is that the MIRR assumes that cash flows received are reinvested at the cost of capital, not the IRR. Since reinvestment at the cost of capital is more likely, the MIRR is a better indicator of a project's profitability. Moreover, it solves the multiple IRR problem, as a set of cash flows can have but one MIRR. Also, note that Excel's MIRR function allows for discounting and reinvestment to occur at different rates. Generally, MIRR is defined as reinvestment at the WACC, though Excel allows the calculation of MIRR where reinvestment is likely to occur at a different rate than WACC. As is stated in the text, NPV is superior to the IRR because (1) the NPV assumes that cash flows are reinvested at the cost of capital whereas the IRR assumes reinvestment at the IRR, and (2) it is more likely, in a competitive world, that the actual reinvestment rate will be the cost of capital than the IRR, especially if the IRR is quite high. The MIRR setup can be used to prove that NPV indeed does assume reinvestment at the WACC and IRR at the IRR. If negative cash flows occur in years beyond Year 1, those cash flows should be discounted at the cost of capital and added to the Year 0 cost to find the total PV of costs. If both positive and negative flows occurred in a given year, the negative flows should be discounted, and the positive ones compounded, rather than just dealing with the net cash flow. This can make a difference. Figure 10-5. Finding the MIRR for Projects S and L 205 206 r= 10% 207 208 1 2 3 Year = 0 (r = 10%) 209 -10,000 5,000 4,000 3,000 Project S 210 211 212 213 -10,000 Terminal Value (TV) = 214 215 Calculator: N = 4, PV = -10000, PMT = 0, FV = 15795. Press I/YR to get: 216 Excel Rate function--Easier: =RATE(F208,0,B209,F213) 217 Excel MIRR function--Easiest: 4 1,000 $3,300 $4,840 $6,655 $15,795 MIRRS = MIRRS = MIRRS = =MIRR(B209:F209,B206,B206) 218 219 Year = 0 (r = 10%) 1 2 3 4 12.11% 12.11% 12.11% A 220 B Project L -10,000 C D E F 1,000 3,000 4,000 6,750 G H 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 For Project L, using the MIRR function: =MIRR(B220:F220,B206,B206) = MIRRL = 12.66% Notes: 1. In Figure 10-5 we find the discount rate that forces the present value of the terminal value to equal the project's cost. That discount rate is defined as the MIRR. $10,000 =TV/(1+MIRR)N = $15,795/(1+MIRR)4 . We can find the MIRR with a calculator or Excel. 2. If S and L are independent, both should be accepted as both MIRRs exceed the cost of capital. If they are mutually exclusive, then L should be chosen because it has the higher MIRR. NPV PROFILES (Section 10.7) An NPV profile shows how a project's NPV declines as the WACC used to calculate the NPV increases. Figure 10-4, for the multiple IRR example, shows a NPV profile. Normally, though, the cash flows change sign only once--a negative for the Time = 0 cash flow and then positive cash flows thereafter, so normally NPV profiles look like the one in Figure 10-6. Figure 10-6. NPV Profile for Project S Cost of capital = 10.00% Year = Project S 0 -10,000.00 1 5,000 3 3,000 4 1,000 NPVS r 0% 5% 10% 14.489% 15% 20% Net Present Value for S 2 4,000 $3,000.00 1,804.24 788.20 0.00 NPV = $0, so IRR = 14.489% -83.30 -837.19 PROJECT S's NPV PROFILE $2,000.00 NPVS = 0, so IRR = 14.489% 0% 2% 4% 6% 8% 10% 12% 14% Cost of Capital (%) 16% 18% 20% A 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 B D Cost of Capital (%) E F G -$1,000.00 The Crossover Rate The crossover rate is the rate at which the NPV of Project S is equal to the NPV of Project L. The easiest way to find the crossover rate is to subtract one project's cash flows from the others and find the IRR of this differential cash flow stream. Year = Project S Project L 292 D = CFS − CFL 0 -$10,000 1 $5,000 2 $4,000 3 $3,000 -10,000 1,000 3,000 4,000 293 294 295 296 C IRR D = 11.975% $0 $4,000 $1,000 -$1,000 4 $1,000 6,750 -$5,750 H A B C D E F G 297 Figure 10-7. NPV Profiles for Projects S and L: Shows Why Conflict Occurs 298 NPVS NPVL 299 Cost of Capital 0% $3,000.00 $4,750.00 300 301 5% 1,804.24 2,682.06 302 10% 788.20 1,004.03 303 Crossover = 11.975% 428.38 428.38 NPVS = NPVL IRRL = 304 13.549% 156.40 0.00 NPVL = 0 IRRS = 305 14.489% 0.00 -243.65 NPVS = 0 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 20% -$837.19 -$1,513.31 $5,000.00NPV L Crossover: Conflict if WACC is to left of crossover, no conflict if WACC is to right. Since WACC = 10%, which is left of the crossover rate, there IS a conflict: NPVL > NPVS, but IRRS > IRRL. $4,000.00 $3,000.00 S At WACC: NPVL > NPVS $2,000.00 $1,000.00 IRRS > IRRL NPVS at WACC $0.00 0% 10% 20% Cost of Capital 30% IRRL -$1,000.00 -$2,000.00 PROFITABILITY INDEX (PI) (Section 10.8) The profitability index is the present value of all future cash flows divided by the intial cost. It measures the PV per dollar of investment. Figure 10-8. Profitability Index (PI) 351 Project S: PIS = PV of future cash flows ÷ 352 PIS = $10,788.20 Initial cost ÷ $10,000 H A B C PIS = 353 D E F G H 1.0788 354 355 Project L: PIL = PV of future cash flows ÷ 356 PIL = $11,004.03 357 PIL = 1.1004 Initial cost ÷ $10,000 358 Notes: 359 1. If Projects L and S are independent, both should be accepted as both have PI greater than 1.0. 360 However, if they are mutually exclusive, Project L should be chosen as it has the higher PI. 361 2. PI and NPV rankings will be consistent if the projects have the same cost, as is true for S and L. 362 However, if they differ in size, conflicts can occur. In the event of a conflict, the NPV ranking 363 should be used. 364 365 366 PAYBACK PERIOD (Section 10.9) 367 368 369 370 371 372 373 374 The payback period is defined as the expected number of years required to recover the investment, and it was the first formal method used to evaluate capital budgeting projects. First, we identify the year in which the cumulative cash inflows exceed the initial cash outflows. That is the payback year. Then we take the previous year and add to it the unrecovered balance at the end of that year divided by the following year's cash flow. Generally speaking, the shorter the payback period, the better the investment. 375 376 377 378 379 380 381 It's easy to calculate the payback manually--calculate cumulative cash flows and look to see when the cumulative CF turns positive, and recognize that the payback year is the prior year plus a fraction equal to the shortfall divided by the CF in the next year. However, it would be useful to have an automated procedure if you were calculating many paybacks or if you wanted to do sensitivity analysis for a given project, but this is more complicated. You can see the formula below, and the procedure is explained in detail in our Excel Tutorial. We use the formula only if we must do a number of payback calculations--for just one or two, the manual approach is much easier. 382 383 A B C D E F G 384 Figure 10-9. Payback Period 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 Years = Project S Cash flow Cumulative cash flow Intermediate calculation for payback 0 -10,000 -10,000 - 1 5,000 -5,000 - 2 3 4,000 -1,000 - 4 3,000 2,000 2.33 1,000 3,000 5.00 Intermediate calculation: Manual calculation of Payback S = 2 + $1,000/$3,000 = Excel calculation of Payback S = Years Project L Cash flow Cumulative cash flow 0 -10,000 -10,000 2.33 2.33 =IF(F388>0,E386+ABS(E388/F387),"-") 2.33 1 2 3 4 1,000 -9,000 3,000 -6,000 4,000 -2,000 6,750 4,750 Manual calculation of Payback L = 3 + $2,000/$6,750 = 3.30 Alternative Excel calculation of Payback L = =PERCENTRANK(C397:G397,0,6)*G395 = 3.30 Payback is between negative and positive cumulative cash flow. The regular payback has two major flaws. First, it does not take account of any cash flows that occur past the payback year, no matter how large those flows might be. Second, the payback does not take account of the time value of money. This second problem is addressed with the discounted payback as discussed below, but the failure to consider beyond-payback cash flows is a problem for both payback methods. Figure 10-10. Discounted Payback WACC = 10% Years = Project S 0 Cash flow -10,000.00 Discounted cash flow -10,000.00 Cumulative discounted CF -10,000.00 Discounted Payback S = 2 + $2,148.76/$2,253.94 = Excel calculation of Discounted Payback S = =PERCENTRANK(C418:G418,0,6)*G415 = 1 2 3 5,000.00 4,545.45 -5,454.55 4,000.00 3,305.79 -2,148.76 3,000.00 2,253.94 105.18 2.95 2.95 4 1,000.00 683.01 788.20 Payback is between negative and positive cumulative discounted cash flow. Years 0 1 2 3 4 425 Cash flow -10,000.00 1,000.00 3,000.00 4,000.00 6,750.00 Project L 909.09 2,479.34 3,005.26 4,610.34 426 Discounted cash flow -10,000.00 427 Cumulative discounted CF -10,000.00 -9,090.91 -6,611.57 -3,606.31 1,004.03 428 429 Discounted Payback L = 3 + $3,606.31/$4,610.34 = 3.78 Payback is between negative 430 Excel calculation of Discounted Payback L = and positive cumulative 431 =PERCENTRANK(C427:G427,0,6)*G424 = 3.78 discounted cash flow. 432 433 434 435 CONCLUSIONS ON CAPITAL BUDGETING METHODS (Section 10.10) 436 437 NPV is the single best criterion because it provides a direct measure of the value a project adds to shareholder H A B C D 438 wealth. However, all methods provide helpful information. 439 440 441 DECISION CRITERIA USED IN PRACTICE (Section 10.11) 442 443 NPV and IRR are the most widely used methods. 444 E F G H Web Extension 10A: The Accounting Rate of Return ACCOUNTING RATE OF RETURN (ARR) The ARR is the second oldest criterion, after the regular payback. We have seen several versions of the ARR, one we've seen most often is shown below. In the example we assume that the projects both have $2,500 of dep per year. Figure 10A-1. Accounting Rate of Return ARR = Average annual cash inflows – Average annual depreciation Average Investment Project S $3,250 $2,500 4 $10,000 $5,000 Average CF Average Depreciation Years Investment Avg. Investment Project L $3,687.50 $2,500 4 $10,000 $5,000 ARRS = $750 $5,000 = 15.00% ARRL = $1,187.50 $5,000 = 23.75% We don't like the ARR, primarily because it ignores the time value of money and also because the IRR and the provide much more reasonable rate of return estimates. We include it here strictly for completeness. 4/11/2010 but the preciation e MIRR SECTION 10.2 SOLUTIONS TO SELF-TEST Projects SS and LL have the following cash flows: WACC = r = SS LL 10% 0 -700 -700 1 500 100 2 300 300 3 100 600 If a 10% cost of capital is appropriate for both of them, what are their NPVs? SS LL NPV $77.61 $89.63 4. What project or set of projects would be in your capital budget if SS and LL were (a) independent or (b) mutually exclusive? If the projects are independent, accept both. If the projects are mutually exclusive, accept Project LL. SECTION 10.3 SOLUTIONS TO SELF-TEST The cash flows for Projects SS and LL are as follows: WACC = r = SS LL 10% 0 -700 -700 1 500 100 2 300 300 3 100 600 What are the two projects’ IRRs, and which one would the IRR method select if the firm has a 10% cost of capital and the projects are (a) independent or (b) mutually exclusive? SS LL IRR 18.0% 15.6% If the two projects are independent, accept both. If the two projects are mutually exclusive, accept Project LL. SECTION 10.4 SOLUTIONS TO SELF-TEST QUESTIONS Project MM has the following cash flows: r= 10% 0 -$1,000 1 $2,000 2 $2,000 3 -$3,350 Calculate MM’s NPV at discount rates of 0%, 10%, 12.2258%, 25%, 122.1470%, and 150%. What are MM's IRRs? If the cost of capital were 10%, should the project be accepted or rejected? NPV = -$45.83 WACC: 0% 10% 12.2258% 25% 122.1470% 150% -$45.83 -$350.00 -$45.83 $0.00 $164.80 $0.00 -$94.40 $200.00 $100.00 $0.00 0% -$100.00 -$200.00 -$300.00 -$400.00 20% 40% 60% 80% 100% 120% 140% 160% SECTION 10.6 SOLUTIONS TO SELF-TEST Projects A and B have the following cash flows: A B 0 -$1,000 -$1,000 1 $1,150 $100 2 $100 $1,300 Their cost of capital is 10%. What are the projects’ IRRs, MIRRs, and NPVs? Which project would each method select? WACC = A B 10% IRR 23.1% 19.1% MIRR 16.8% 18.7% NPV $128.10 $165.29 We used Excel functions to calculate these values. See the Tutorial for instructions on the NPV, IRR, and MIRR functions. SECTION 10.8 SOLUTIONS TO SELF-TEST 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 is the PI? WACC = r = 9% 0 -$500 PI = PI = 1 $200 PV of future cash flows $660.70 1.321391 2 $200 3 $400 ¸ ¸ Initial cost $500 SECTION 10.9 SOLUTIONS TO SELF-TEST Project P has a cost of $1,000 and cash flows of $300 per year for 3 years plus another $1,000 in Year 4. The project’s cost of capital is 15%. What are P’s regular and discounted paybacks? Regular payback Years 0 | Cash Flow -1,000 Cumulative Cash Flow -1,000 Regular payback = 1 | 300 -700 2 | 300 -400 3 | 300 -100 4 | 1,000 900 3 | 300 197 -315 4 | 1,000 572 257 3.10 Discounted payback WACC 15% Years 0 | Cash Flow -1,000 Discounted Cash Flow -1,000 Cumulative Discounted CF -1,000 Discounted payback = 1 2 | 300 261 -739 | 300 227 -512 3.55 If the company requires a payback of 3 years or less, would the project be accepted? The payback rule of 3 years leads to a reject decision. Would this be a good accept/reject decision, considering the NPV and/or the IRR? NPV = IRR = $256.72 24.78% The payback rule conflicts with both the NPV and IRR criteria, which would suggest accepting the project.