• Author / Uploaded
• Rimpy Sondh

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A 12 13 14 15 16 17 18 19 20 21

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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:

27

Initial Cost

28 29 30 31 32 33

0 -$10,000 -$10,000

Project S Project L

After-Tax, End of Year, Project Cash Flows, CFt 1 $5,000 $1,000

2 $4,000 $3,000

3 $3,000 $4,000

4 $1,000 $6,750

Panel B: Summary of Selected Evaluation Criteria Project S

34 35 36 37 38 39

10%

NPV IRR MIRR PI Payback Discounted Payback

$788.20 14.49% 12.11% 1.08

Project L $1,004.03 13.55% 12.66% 1.10 3.30 3.78

40 2.95 41 42 43 44 45 46 Figure 10-2. Finding the NPV for Projects S and L 47 48 To calculate the NPV, we find the present value of the individual cash flows and then sum those discounted cash 49 flows. The sum is the value the project adds to or subtracts from shareholder wealth. 50 51 r = 10% 52 53 Year = 0 (r = 10%) 1 2 3 4 54 Project S -10,000.00 5,000 4,000 3,000 1,000

A

B

55

D

E

F

G

4,545.45 3,305.79 2,253.94 683.01

56 57 58 59

C

NPVS =

$788.20

Long way: Sum the PVs of the CFs to find NPV

60 61

Year =

62

Project L

-10,000.00

NPVL =

$1,004.03

0 (r = 10%)

1

2

3

4

1,000

3,000

4,000

6,750

63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83

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 87 88 89 90 91 92 93 94 95 96

Figure 10-3. Finding the IRR r = 14.49% Year = Project S

Sum of PVs =

0 -10,000.00 4,367.24 3,051.64 1,999.09 582.03 $0.00

1 5,000

2 4,000

3 3,000

4 1,000

= NPV at r = 14.489%. NPV = 0, so IRR = 14.489%.

97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114

A IRRS

=

B 14.49%

Year = Project L

0 -10,000.00

IRRL

=

13.55%

C D =IRR(B90:F90) using IRR function 1 1,000

2 3,000

E

F

3 4,000

4 6,750

G

=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)

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115 116 117 118 119 120 121 122 123

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).

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Figure 10-4. Graph for Multiple IRRs: Project M (Millions of Dollars)

125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160

Year = Project M

0 -1.60

r =

1 10

10%

NPV =

2 -10

-$0.774

NPV (Millions)

NPV = −$1.6 + $10/(1+r) + (−$10)/(1+r)2

$0.90 $0.70 $0.50 $0.30

IRR #1 = 25%

IRR #2 = 400%

$0.10 -$0.10 0%

50% 100% 150% 200% 250% 300% 350% 400% 450% 500%

-$0.30 Cost of Capital (%)

Note: The table shown below calculates Project M's NPV at the rates shown in the left column. These data are plotted to form the graph shown above. Notice that NPV = 0 at both 25% and 400%. Since the definition of the IRR is the rate at which the NPV = 0, there are two IRRs. r

NPV

0%

-$1.600

A 161 162 163 164 165

B

C

10% 25% 110% 400% 500%

-$0.774 $0.000 $0.894 $0.000 -$0.211

D

E

F

G

= IRR #1 = 25% = IRR #2 = 400%

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

REINVESTMENT RATE ASSUMPTIONS (Section 10.5) 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. MODIFIED INTERNAL RATE OF RETURN, MIRR (Section 10.6) The modified internal rate of return is the discount rate that causes a project's cost (or cash outflows) to equal the present value of the project's terminal value. The terminal value is defined as the sum of the future values of the project's cash inflows, compounded at the project's cost of capital. To find MIRR, calculate the PV of the outflows and the FV of the inflows, and then find the rate that equates the two. Alternatively, you can solve using Excel's MIRR function. 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.

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Figure 10-5. Finding the MIRR for Projects S and L

205 206 r= 10% 207 208 Year = 0 (r = 10%) 1 2 3 209 Project S -10,000 5,000 4,000 3,000 210 211 212 213 -10,000 Terminal Value (TV) = 214 215 Calculator: N = 4, PV = -10000, PMT = 0, FV = 15795. Press I/YR to get:

4 1,000 $3,300 $4,840 $6,655 $15,795 MIRRS =

12.11%

216 Excel Rate function--Easier:

=RATE(F208,0,B209,F213)

MIRRS =

12.11%

217 Excel MIRR function--Easiest:

=MIRR(B209:F209,B206,B206)

MIRRS =

12.11%

218 219 220

Year = Project L

0 (r = 10%) -10,000

1

2

3

4

1,000

3,000

4,000

6,750

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

=MIRR(B220:F220,B206,B206) = MIRRL =

For Project L, using the MIRR function:

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 104, 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

2

3

4

5,000

4,000

3,000

1,000

A 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291

C

D E NPVS $3,000.00 1,804.24 788.20 0.00 NPV = $0, so IRR = 14.489% -83.30 -837.19

r 0% 5% 10% 14.489% 15% 20%

F

G

Net Present Value for S PROJECT S's NPV PROFILE

$2,000

0%

NPVS = 0, so IRR = 14.489%

2%

4%

6%

8%

10%

12%

14%

16%

18%

20%

Cost of Capital (%) -$1,000

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 293 294

B

0

1

2

3

-$10,000 -10,000

$5,000 1,000

$4,000 3,000

$3,000 4,000

$0

IRR D = 11.975%

$4,000

$1,000

4

-$1,000

$1,000 6,750 -$5,750

A

B

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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 5% 1,804.24 2,682.06 301 302 10% 788.20 1,004.03 303 Crossover = 11.975% 428.38 428.38 NPVS = NPVL IRRL = 13.549% 304 156.40 0.00 NPVL = 0 IRRS = 14.489% 305 0.00 -243.65 NPVS = 0 20% -$837.19 -$1,513.31 306 307 308 $5,000 NPV 309 L 310 311 Crossover: Conflict if WACC is to 312 left of crossover, no conflict if $4,000 313 WACC is to right. Since WACC = 10%, which is left of the crossover 314 rate, there IS a conflict: NPVL > 315 S NPVS, but IRRS > IRRL. 316 $3,000 317 At WACC: 318 NPV L > NPVS 319 320 $2,000 321 322 323 324 $1,000 325 326 IRRS > IRRL 327 NPVS at WACC 328 $0 329 Cost of Capital 30% 0% 10% 20% 330 331 332 IRRL 333 -$1,000 334 335 336 337 -$2,000 338 339 340 341 342 PROFITABILITY INDEX (PI) (Section 10.8) 343 344 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.

A B C D 345 per dollar of investment. 346 347 348 349 Figure 10-8. Profitability Index (PI) 350 PIS = PV of future cash flows ÷ 351 Project S: 352

PIS =

$10,788.20

353

PIS =

1.0788

÷

E

F

G

Initial cost $10,000

354 355 Project L:

PIL = PV of future cash flows ÷

356

PIL =

357

PIL =

358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383

$11,004.03

÷

Initial cost $10,000

1.1004 Notes: 1. If Projects L and S are independent, both should be accepted as both have PI greater than 1.0. However, if they are mutually exclusive, Project L should be chosen as it has the higher PI. 2. PI and NPV rankings will be consistent if the projects have the same cost, as is true for S and L. However, if they differ in size, conflicts can occur. In the event of a conflict, the NPV ranking should be used.

PAYBACK PERIOD (Section 10.9) 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.

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.

A 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429

B

C

D

E

F

G

0 -10,000 -10,000 -

1 5,000 -5,000 -

2 4,000 -1,000 -

3 3,000 2,000 2.33

4 1,000 3,000 5.00

Figure 10-9. Payback Period Years = Project S Cash flow Cumulative cash flow Intermediate calculation for payback

Intermediate calculation:

Manual calculation of Payback S = 2 + $1,000/$3,000 = Excel calculation of Payback S =

Project L

Years Cash flow Cumulative cash flow

0 -10,000 -10,000

2.33 2.33 1 1,000 -9,000

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

=IF(F388>0,E386+ABS(E388/F387),"-") 2.33 2 3,000 -6,000

3 4,000 -2,000

4 6,750 4,750

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 = 0 Project S 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 = Years 0 Project L Cash flow -10,000.00 Discounted cash flow -10,000.00 Cumulative discounted CF -10,000.00 Discounted Payback L = 3 + $3,606.31/$4,610.34 =

1 5,000.00 4,545.45 -5,454.55 2.95 2.95 1 1,000.00 909.09 -9,090.91 3.78

2 4,000.00 3,305.79 -2,148.76

3 3,000.00 2,253.94 105.18

4 1,000.00 683.01 788.20

Payback is between negative and positive cumulative discounted cash flow. 2 3,000.00 2,479.34 -6,611.57

3 4,000.00 3,005.26 -3,606.31

4 6,750.00 4,610.34 1,004.03

Payback is between negative and positive cumulative discounted cash flow.

A 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444

B C Excel calculation of Discounted Payback L = =PERCENTRANK(C427:G427,0,6)*G424 =

D

E

3.78

F between negative G Payback is and positive cumulative discounted cash flow.

CONCLUSIONS ON CAPITAL BUDGETING METHODS (Section 10.10) NPV is the single best criterion because it provides a direct measure of the value a project adds to shareholder wealth. However, all methods provide helpful information.

DECISION CRITERIA USED IN PRACTICE (Section 10.11) NPV and IRR are the most widely used methods.

H 12 analyze Projects S and L, 13 can be set14 up vertically, ew years, we generally 15 ies of income statements. 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 hose discounted cash 49 50 51 52 53 54

H 55 56 57 58 59 60 61 62 63 64

65 66 67 ed. The rationale for this ll respects.68If strictly 69 that adds pt the project ove two projects, you 70 they are mutually 71 72 73 74 75 76 77 a project's78cash inflows PV to zero.79The es you to access the 80the data along with 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96

H 97 98 99 100 101 102 103 104 105 ater than the cost of capital. e chosen on106 the basis of the 107 be projects should Project S because it has the 108 a conflict between the NPV 109 110 111 112 113 114

H 115 an one change of signs in 116calculator, ng a financial utions, and117 the HP12C says and then 118 the calculator u should be able to find the 119 traordinary (often, several 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 hese data154 are plotted to 155IRR is the nition of the 156 157 158 159 160

H 161 162 163 164 165 166

167 168 169 170 171 listic to asssume that 172 ision criterion than IRR. 173 174 175 176 177 h outflows) to equal the he future 178 values of the 179the outflows e the PV of an solve using 180 Excel's 181 182 183 are h flows received ore likely,184 the MIRR is a as a set of185 cash flows can 186 187 different 188 rates. 189 where tion of MIRR 190 191 flows are 192 reinvested at 193 ely, in a competitive if the IRR194 is quite high. WACC and195 IRR at the 196 197 at the cost198 of capital and ccurred in199 a given year, st dealing200 with the net 201 202 203

H 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221

222 223 224 225 226 227 228 capital. If229 230 231 232 233 234 235 236 Figure 10V increases. hange sign237 only once--a V profiles238 look like the 239 240 241 242 243 244 245 246 247

H

248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 way to L. The easiest 285 RR of this differential 286 287 288 289 290 291 292 293 294

H

297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 t. It measures 344 the PV

H 345 346 347 348 349 350 351 352 353 354 355 356 357

358 han 1.0. 359 360 PI. 361 362 363 364 365 366 367 368 vestment,369 and it was the in which370 the cumulative previous year and add to 371 . Generally speaking, 372 373 374 375 see when the cumulative 376 al to the shortfall 377were edure if you ut this is more 378 r Excel Tutorial. We use 379 manual approach is 380 381 382 383

H 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399

400 401 402 403 404 405 that occur past the 406 ke account of the time 407 ed below, but the failure 408 409 410 411 412

413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 tween negative cumulative d cash flow.

H tween negative 430 cumulative d cash flow.431 432 433 434 435 436 437 adds to shareholder 438 439 440 441 442 443 444

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, but the one we've seen most often is shown below. In the example we assume that the projects both have $2,500 of depreciation 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 MIRR provide much more reasonable rate of return estimates. We include it here strictly for completeness.

4/11/2010

n

ns of the ARR, but the ve $2,500 of

he IRR and the MIRR eness.

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

$12 $10 $8 $6 $4 $2 $0 0%

20%

40%

60%

80%

100%

120%

140%

160%

Multiple IR Rs:Project MM

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: CF 0 = -$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

2 $200

PV of future cash flows $660.70 1.321391

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 Cash Flow Cumulative Cash Flow Regular payback =

0 | -1,000 -1,000

1 | 300 -700

2 | 300 -400

3 | 300 -100

4 | 1,000 900

0

1

2

3

4

| -1,000 -1,000 -1,000

| 300 261 -739

| 300 227 -512

| 300 197 -315

| 1,000 572 257

3.10

Discounted payback WACC

15% Years

Cash Flow Discounted Cash Flow Cumulative Discounted CF Discounted payback =

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.