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Chapter 10. Mini Case Capital Budgeting Decisions Situation You have just graduated from the MBA program of a large university, and one of your favorite courses was "Today's Entrepreneurs." In fact, you enjoyed it so much you have decided you want to "be your own boss." While you were in the master's program, your grandfather died and left you $1 million to do with as you please. You are not an inventor, and you do not have a trade skill that you can market; however, you have decided that you would like to purchase at least one established franchise in the fast-foods area, maybe two (if profitable). The problem is that you have never been one to stay with any project for too long, so you figure that your time frame is three years. After three years you will go on to something else.

You have narrowed your selection down to two choices: (1) Franchise L, Lisa's Soups, Salads, & Stuff, and (2) Franchise S, Sam's Fabulous Fried Chicken. The net cash flows shown below include the price you would receive for selling the franchise in Year 3 and the forecast of how each franchise will do over the 3-year period. Franchise L's cash flows will start off slowly but will increase rather quickly as people become more health conscious, while Franchise S's cash flows will start off high but will trail off as other chicken competitors enter the marketplace and as people become more health conscious and avoid fried foods. Franchise L serves breakfast and lunch, while Franchise S serves only dinner, so it is possible for you to invest in both franchises. You see these franchises as perfect complements to one another: You could attract both the lunch and dinner crowds and the health conscious and not so health conscious crowds without the franchises directly competing against one another. 18 Here are the net cash flows (in thousands of dollars): 19 20 21 Expected Franchise S 22 Net Cash Flows 23 Year (t) Franchise S Franchise L 0 1 2 3 24 0 ($100) ($100) (100) 70 50 20 25 1 70 10 26 2 50 60 Franchise L 27 3 20 80 28 0 1 2 3 29 (100) 10 60 80 30 31 Depreciation, salvage values, net working capital requirements, and tax effects are all included in these cash flows. 32 33 You also have made subjective risk assessments of each franchise and concluded that both franchises have risk characteristics 34 that require a return of 10%. You must now determine whether one or both of the franchises should be accepted. 35 36 a. What is capital budgeting? Answer: See Chapter 10 Mini Case Show 37 38 b. What is the difference between independent and mutually exclusive projects? Answer: See Chapter 10 Mini Case Show 39 40 c. (1.) Define the term net present value (NPV). What is each franchise's NPV? 41 42 Net Present Value (NPV) 43 To calculate the NPV, we find the present value of the individual cash flows and find the sum of those discounted cash flows. 44 This value represents the value the project add to shareholder wealth. 45 46 WACC = 10% 47 48 Franchise S 49 Time period: 0 1 2 3 50 Cash flow: (100) 70 50 20 51 Disc. cash flow: (100) 64 41 15 52 53 NPV(S) = $19.98 = Sum disc. CF's. or $19.98 = Uses NPV function. 54

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A Franchise L

B Time period: Cash flow: Disc. cash flow:

NPV(L) =

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0 (100) (100)

1 10 9

2 60 50

3 80 60

$18.78

$18.78

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10 1,090

= Uses NPV function.

(2.) What is the rationale behind the NPV method? According to NPV, which franchise or franchises should be accepted if they The NPV method of capital budgeting dictates that all independent projects that have positive NPV should accepted. The rationale behind that assertion arises from the idea 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 NPV). Hence, if considering the above two projects, you would accept both projects if they are independent, and you would only accept Project S if they are mutually exclusive. (3.) Would the NPVs change if the cost of capital changed? Answer: See Chapter 10 Mini Case Show d. (1.) Define the term internal rate of return (IRR). What is each franchise's IRR? Internal Rate of Return (IRR) 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. It is the discount rate that forces the PV of the inflows to equal the initial cost. 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 IRR's for Franchises S and L are shown below, along with the data entry for Franchise S.

Year (t) 0 1 2 3

Expected net cash flows Franchise S Franchise L ($100) ($100) 70 10 50 60 20 80

IRR S = IRR L =

23.56% The IRR function 18.13% assumes payments occur at end of periods, so that function does not have to be adjusted. Notice that for IRR you must specify all cash flows, including the time zero cash flow. This is in contrast to the NPV function, in which you specify only the future cash flows.

(2.) How is the IRR on a project related to the YTM on a bond? Constant Cash Flows Year (t) 0 1 2 3

Cash Flow ($100) 40 40 40

0 (100)

IRR =

1 40

9.70%

2 40

3 40

Note: You can use the Rate function if payments are constant.

Similarity to a bond: 0 (1,134)

1 90 IRR =

2 90 7.08%

3 90

4 90

5 90

6 90

7 90

8 90

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A B C D E F G H (3.) What is the logic behind the IRR method? According to IRR, which franchises should be accepted if they are independent? (4.) Would the franchises' IRRs change if the cost of capital changed?

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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 greatest IRR. In this scenario, both franchises have IRRs that exceed the cost of capital (10%) and both should be accepted, if they are independent. If, however, the franchises are mutually exclusive, we would choose Franchise S. Recall, that this was our determination using the NPV method as well. The question that naturally arises is whether or not the NPV and IRR methods will always arrive at the same conclusion. When dealing with independent projects, the NPV and IRR methods will always yield the same accept/reject result. However, in the case of mutually exclusive projects, NPV and IRR can give conflicting results. One shortcoming of the internal rate of return is that it assumes that cash flows received are reinvested at the project's internal rate of return, which is not usually true. The nature of the congruence of the NPV and IRR methods is further detailed in a latter section of this model. NPV Profiles e. Draw NPV profiles for Franchises L and S. At what discount rate do the profiles cross?

WACC 0% 2% 4% 6% 8% 10% 12% 14% 16% 18% 20% 22% 24%

Franchise S $19.98 40.00 35.53 31.32 27.33 23.56 19.98 16.60 13.38 10.32 7.40 4.63 1.98 (0.54)

Franchise L $18.78 50.00 42.86 36.21 30.00 24.21 18.78 13.70 8.94 4.46 0.26 (3.70) (7.43) (10.95)

WACC 0% 2% 4% 6% 8% 10% 12% 14% 16% 18% 20% 22% 24%

NPV Profile of Franchises S and L

NPV ($) 60 50

Project L

40

Crossover Rate = 8.7%

30

20

Project S

10 0 (10) 0%

2%

4%

6%

8%

10%

12%

14%

16%

18%

20%

22%

24%

Franchise S- IRR

(20) Cost of Capital

Franchise L- IRR

(2.) Look at your NPV profile graph without referring to the actual NPVs and IRRs. Which franchise or franchises should be accepted if they are independent? Mutually exclusive? Explain. Are your answers correct at any cost of capital less Previously, we had discussed that in some instances the NPV and IRR methods can give conflicting results. First, we should attempt to define what we see in this graph. Notice, that the two franchises' profiles (S and L) intersect the X-axis at costs of capital of 18.13% and 23.56%, respectively. Not coincidently, those are the IRRs of the franchises. If we think about the definition of IRR, we remember that the internal rate of return is the cost of capital at which a project will have an NPV of zero. Looking at our graph, it is a logical conclusion that the project IRR is defined as the point at which its profile intersects the f. (1.) What is the underlying cause of ranking conflicts between NPV and IRR? (2.) What is the "reinvestment rate assumption," and how does it affect the NPV versus IRR conflict? Answer: See Chapter

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A B C D E F (3.) Which method is the best? Why? Answer: See Chapter 10 Mini Case Show

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Looking further at the NPV profiles, we see that the two franchises profiles intersect at a point we shall call the crossover rate. We observe that at costs of capital greater than the crossover rate, the franchise with the greater IRR (Franchise S, in this case) also has the greater NPV. But at costs of capital less than the crossover rate, the franchise with the lesser IRR has the greater NPV. This relationship is the source of discrepancy between the NPV and IRR methods. By looking at the graph, we see that the crossover rate appears to occur at approximately 8.7%. Luckily, there is a more precise way of determining the crossover rate. To find the crossover rate, we will find the difference between the two franchises' cash flows in each year, and then find 196 the IRR of this series of differential cash flows. This IRR is the crossover rate. 197 Expected 198 Net Cash Flows Cash Flow 199 Year (t) Franchise S Franchise L Differential 200 0 ($100) ($100) 0 201 1 70 10 60 202 2 50 60 (10) 203 3 20 80 (60) 204 205 IRR = Crossover rate = 8.68% 206 207 The intuition behind the relationship between the NPV profile and the crossover rate is as follows: (1) Distant cash flows are 208 heavily penalized by high discount rates--the denominator is (1 + r)t, and it increases geometrically; hence, it gets very large at 209 high values of t. (2) Long-term projects like L have most of their cash flows coming in the later years, when the discount 210 penalty is largest; hence, they are most severely impacted by high capital costs. (3) Therefore, Franchise L's NPV profile is 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

steeper than that of S. (4) Since the two profiles have different slopes, they cross one another. Modified Internal Rate of Return (MIRR) g. (1.) Define the term modified IRR (MIRR). Find the MIRRs for Franchises L and S. 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 discount rate that equates the two. Or, you can solve using Excel's MIRR function. WACC =

10%

MIRRS = MIRRL =

Franchise S 10% 0 (100)

1 70

2 50

16.89% 16.50%

3 20

Franchise L 0 (100)

PV:

(100)

1 10

2 60

3 80 66 12.1

TV =

158.1

(2.) What are the MIRR's advantages and disadvantages vis-a-vis the regular IRR? What are the MIRR's advantages and disadvantages vis-a-vis the NPV? The 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 . Note that if negative cash flows occur in years beyond Year 1, those cash flows would 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 some year, the negative flow should be discounted, and the positive one compounded, rather than just dealing with the net cash flow. This makes a difference. 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 a special MIRR where reinvestment occurs at a different rate than WACC.

Finally, it is stated in the text, when the IRR versus the NPV is discussed, that the NPV is superior 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 is more likely to 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 252 WACC, and IRR at the IRR.

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PROFITABILITY INDEX h. What does the profitability index (PI) measure? What are the PI's for Franchises S and L? 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. For Franchise S: PI(S) = PV of future cash flows PI(S) = $119.98 PI(S) = 1.1998

÷ ÷

Initial cost

PI(L) = PV of future cash flows PI(L) = $118.78 PI(L) = 1.1878

÷ ÷

Initial cost

$100

For Franchise L: $100

i. (1.) What is the payback period? Find the paybacks for Franchises L and S.

Payback Period 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 fraction calculated as the unrecovered balance at the end of that year divided by the following year's cash flow. Generally speaking, the shorter the 276 payback period, the better the investment. 277 278 Franchise S 279 Time period: 0 1 2 3 280 Cash flow: (100) 70 50 20 281 Cumulative cash flow: (100) (30) 20 40 282 283 284 Payback: 1.600 285 286 287 288 Franchise L 289 Time period: 0 1 2 3 290 Cash flow: (100) 10 60 80 291 Cumulative cash flow: (100) (90) (30) 50 292 293 294 Payback: 2.375 295 (2.) What is the rationale for the payback method? According to the payback criterion, which franchise or franchises 296 297 should 298 be accepted if the firm's maximum acceptable payback is 2 years, and if Franchise L and S are independent? If they 299 300 (3.) What is the difference between the regular and discounted payback periods? 301 302 Discounted Payback Period 303 Discounted payback period uses the project's cost of capital to discount the expected cash flows. The calculation of discounted 304 payback period is identical to the calculation of regular payback period, except you must base the calculation on a new row of 305 discounted cash flows. Note that both projects have a cost of capital of 10%. 306 307 WACC = 10% 308 309 Franchise S 310 Time period: 0 1 2 3 311 Cash flow: (100) 70 50 20 312 Disc. cash flow: (100) 64 41 15 Cash Flows Discounted back at 10%. 313 Disc. cum. cash flow: (100) (36) 5 20 314 315 316 Discounted Payback: 1.9 317

A B C D E F G H I 318 Franchise L 319 Time period: 0 1 2 3 4 320 Cash flow: (100) 10 60 80 0 321 Disc. cash flow: (100) 9 50 60 0 322 Disc. cum. cash flow: (100) (91) (41) 19 19 323 324 325 Discounted Payback: 2.7 326 327 (4.) What is the main disadvantage of discounted payback? Is the payback method of any real usefulness in capital budgeting 328 decisions? 329 330 The inherent problem with both paybacks is that they ignore cash flows that occur after the payback period mark and neither 331 provides a specific acceptance rule. While the discounted method accounts for timing issues (to some extent), it still falls short of fully analyzing projects. However, all else equal, these two methods do provide some information about projects' liquidity 332 and risk. 333 334 Multiple IRRs 335 j. As a separate project (Project P), you are considering sponsoring a pavilion at the upcoming World's Fair. The pavilion 336 would cost $800,000, and it is expected to result in $5 million of incremental cash inflows during its 1 year of operation. However, 337 338 it 339 340 Project M: 0 1 2 341 (800) 5,000 (5,000) 342 343 The project is estimated to be of average risk, so its cost of capital is 10%. 344 345 (1.) What are normal and nonnormal cash flows? Answer: See Chapter 10 Mini Case Show 346 347 (2.) What is Project P's NPV? What is its IRR? Its MIRR? 348 349 We will solve this IRR twice, the first time using the default guess of 10%, and the second time we will enter a guess of 200%. 350 Notice, that the first IRR calculation is exactly as it was above. 351 352 NPVM = ($386.78) 353 1 354 IRR M = 355 356 357 358

25.0%

MIRR =

5.6%

2 359 IRR M = 400% 360 361 362 363 364 365 366 367 368 The two solutions to this problem tell us that this project will have a positive NPV for all costs of capital between 25% and 369 400%. We illustrate this point by creating a data table and a graph of the project NPVs. 370 371 0 1 2 372 (800.0) 5,000 (5,000) 373

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A B C D E F G H I (3.) Draw Project P's NPV profile. Does Project P have normal or nonnormal cash flows? Should this project be accepted? r = NPV = r 0% 25% 50% 75% 100% 125% 150% 175% 200% 225% 250% 275% 300% 325% 350% 375% 400% 425% 450% 475% 500% 525% 550%

25.0% 0.00 NPV $0.0 (800.00) 0.00 311.11 424.49 450.00 Max. 434.57 400.00 357.02 311.11 265.09 220.41 177.78 137.50 99.65 64.20 31.02 0.00 (29.02) (56.20) (81.66) (105.56) (128.00) (149.11)

Multiple Rates of Return NPV ($) 600 400

200 0 -100%

0%

100%

200%

300%

400%

500%

-200

Cost of Capital

-400 -600

-800 -1,000

PROJECTS WITH UNEQUAL LIVES k. In an unrelated analysis, you have the opportunity to choose between the following two mutually exclusive projects: Year 0 1 2 3 4

Project S ($100,000) 60,000 60,000

Project L ($100,000) 33,500 33,500 33,500 33,500

The projects provide a necessary service, so whichever one is selected is expected to be repeated into the foreseeable future. Both projects have a 10% cost of capital. (1.) What is each project’s initial NPV without replication? Project L

WACC: 10.0% End of Period:

0 ($100)

1 $33.5

NPV

$6.19

2 $33.5

3 $33.5

4 $33.5

3

4

Project S End of Period: 0 ($100)

1 $60

NPV

$4.13

2 $60

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A B C D (2.) What is each project’s equivalent annual annuity?

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Equivalent Annual Annuity (EAA) Approach Here are the steps in the EAA approach. 1. Find the NPV of each project over its initial life (we already did this in our previous analysis). NPVL = $6.19 NPVS = $4.13 2. Convert the NPV into an annuity payment with a life equal to the life of the project. EAAL = $1.95 Note: we used Excel's PMT function by using the function wizard. EAAS = $2.38 (3.) Now apply the replacement chain approach to determine the projects’ extended NPVs. Which project should be chosen? Project S End of Period: 0 ($100)

1 $60

($100)

$60

NPV

$7.55

2 $60 ($100) ($40)

3 $60 $60

$60 $60

(4.) Now assume that the cost to replicate Project S in 2 years will increase to $105,000 because of inflationary pressures. How should the analysis be handled now, and which project should be chosen? Project S End of Period: 0 ($100)

1 $60

($100)

$60

NPV

$3.42

2 $60 ($105) ($45)

3 $60 $60

$60 $60

ECONOMIC LIFE VS. PHYSICAL LIFE l. You are also considering another project which has a physical life of 3 years; that is, the machinery will be totally worn out after 3 years. However, if the project were terminated prior to the end of 3 years, the machinery would have a positive salvage

Year 0 1 2 3

Operating Cash Flow ($5,000) $2,100 $2,000 $1,750

Salvage Value $5,000 $3,100 $2,000 $0

(1.) Using the 10% cost of capital, what is the project's NPV If it is operated for the full 3 years?

3-Year NPV = Initial Cost

+

PV of Operating Cash Flow

+

PV of Salvage Value

485 486 = ($5,000.00) + $4,876.78 + $0.00 487 3-Year NPV = ($123.22) 488 489 The asset has a negative NPV if it is kept for three years. But even though the asset will last three years, it might be better to 490 operate the asset for either one or two years, and then salvage it. 491 492 (2.) Would the NPV change if the company planned to terminate the project at the end of Year 2? 493 PV of PV of Operating Salvage 2-Year NPV = Initial Cost + + Cash Flow Value 494 495 = ($5,000.00) + $3,561.98 + $1,652.89 496 2-Year NPV = $214.88 497

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PV of PV of 1-Year NPV = Initial Cost + + Operating Salvage 499 500 = ($5,000.00) + $1,909.09 + $2,818.18 501 1-Year NPV = ($272.73) 502 503 (4.) What is the project’s optimal (economic) life? 504 505 The project's NPV will only be positive when it is operated for 2 years. Therefore, the project's economic life is 2 years. 506 507 m. After examining all the potential projects, you discover that there are many more projects this year with positive NPVs 508 than in 509 a normal year. What two problems might this extra large capital budget cause? Answer: S ee Chapter 10 Mini Case Show

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Notice that the NPV function isn't really a Net present value. 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.

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