4/22/2006

Chapter 12. Mini Case

Situation

Expected Franchise Snet cash flows

Year (t) Franchise S Franchise L 0 1 2 3 0 ($100) ($100) (100) 70 50 20 1 70 10 2 50 60 Franchise L3 20 80

0 1 2 3 (100) 10 60 80

Depreciation, salvage values, net working capital requirements, and tax effects are all included in these cash flows.

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

Payback Period

Franchise STime period: 0 1 2 3

Cash flow: (100) 70 50 20 Cumulative cash flow: (100) (30) 20 40

% of year required for payback: 1.000 0.600 0.000

Payback: 1.60

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 $300,000 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 sell off your investment and 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 Wonderful 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 three-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. Here are the net cash flows (in thousands of dollars):

You also have made subjective risk assessments of each franchise, and concluded that both franchises have risk characteristics that require a return of 10 percent. You must now determine whether one or both of the projects should be accepted.

a. What is capital budgeting? Answer: See Chapter 12 Mini Case Show

b. What is the difference between independent and mutually exclusive projects? Answer: See Chapter 12 Mini Case Show

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 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.

If payback doesn't occur by year end, the entire year is needed. If it occurs by year end, calculate the fraction of the year needed.

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Alternative calculation: 1.60 uses a complicated IF function.

Franchise LTime period: 0 1 2 3

Cash flow: (100) 10 60 80 Cumulative cash flow: (100) (90) (30) 50

% of year required for payback: 1.000 1.000 0.375

Payback: 2.375

(3.) What is the difference between the regular and discounted payback periods?

If payback doesn't occur by year end, the entire year is needed. If it occurs by year end, calculate the fraction of the year needed.Use the sum function to calculate the total number of years to payback.

(2.) What is the rationale for the payback method? According to the payback criterion, which franchise or franchises should be accepted if the firm's maximum acceptable payback is 2 years, and if Franchise L and S are independent? If they are mutually exclusive? Answer: See Chapter 12 Mini Case Show

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Discounted Payback Period

WACC = 10%

Franchise STime period: 0 1 2 3

Cash flow: (100) 70 50 20 Disc. cash flow: (100) 64 41 15 Cash Flows Discounted back at 10%.

Disc. cum. cash flow: (100) (36) 5 20 % of year required for payback: 1.000 0.880 0.000

Discounted Payback: 1.9

Franchise LTime period: 0 1 2 3 4

Cash flow: (100) 10 60 80 0 Disc. cash flow: (100) 9 50 60 0

Disc. cum. cash flow: (100) (91) (41) 19 19 % of year required for payback: 1.000 1.000 0.688

Discounted Payback: 2.7

d. (1.) Define the term net present value (NPV). What is each franchise's NPV?

Net Present Value (NPV)

WACC = 10%

Franchise STime period: 0 1 2 3

Cash flow: (100) 70 50 20 Disc. cash flow: (100) 64 41 15

NPV(S) = $19.98 = Sum disc. CF's. or $19.98 = Uses NPV function.

Franchise LTime period: 0 1 2 3

Cash flow: (100) 10 60 80 Disc. cash flow: (100) 9 50 60

NPV(L) = $18.78 $ 18.78 = Uses NPV function.

Discounted payback period uses the project's cost of capital to discount the expected cash flows. The calculation of discounted payback period is identical to the calculation of regular payback period, except you must base the calculation on a new row of discounted cash flows. Note that both projects have a cost of capital of 10%.

(4.) What is the main disadvantage of discounted payback? Is the payback method of any real usefulness in capital budgeting decisions?

The inherent problem with both paybacks is that they ignore cash flows that occur after the payback period mark. 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 and risk.

To calculate the NPV, we find the present value of the individual cash flows and find the sum of those discounted cash flows. This value represents the value the project add to shareholder wealth.

(2.) What is the rationale behind the NPV method? According to NPV, which franchise or franchises should be accepted if they are independent? Mutually exclusive?

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100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134

e. (1.) Define the term internal rate of return (IRR). What is each franchise's IRR?

Internal Rate of Return (IRR)

Expected net cash flows

Year (t) Franchise S Franchise L0 ($100) ($100)1 70 10 23.56%2 50 60 18.13%3 20 80

(3.) Would the franchises' IRRs change if the cost of capital changed?

(4.) How is the IRR on a project related to the YTM on a bond?

Constant Cash Flows

Year (t) Cash Flow

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 12 Mini Case Show

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 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 IRR's for Project S and L are shown below, along with the data entry for Project S.

IRR S =The IRR function assumes payments occur at end of periods, so that function does not have to be adjusted.

IRR L =

(2.) What is the logic behind the IRR method? According to IRR, which franchise should be accepted if they are independent? Mutually exclusive?

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 projects have IRR's that exceed the cost of capital (10%) and both should be accepted, if they are independent. If, however, the projects are mutually exclusive, we would chose Project 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 agree.

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.

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.

C142:C145C153:C156

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0 ($100) 0 1 2 3 1 40 (100) 40 40 40 2 40 3 40

IRR = 9.70% Note: You can use the Rate function ifpayments are constant.

Similarity to a bond:

0 1 2 3 4 5 6 7 8 (1,134) 90 90 90 90 90 90 90 90

IRR = 7.08%

NPV Profilesf. Draw NPV profiles for Franchises L and S. At what discount rate do the profiles cross?

Franchise S Franchise LWACC $19.98 WACC $18.78

0% 40.00 0% 50.00 2% 35.53 2% 42.86 4% 31.32 4% 36.21 6% 27.33 6% 30.00 8% 23.56 8% 24.21

10% 19.98 10% 18.78 12% 16.60 12% 13.70 14% 13.38 14% 8.94 16% 10.32 16% 4.46 18% 7.40 18% 0.26 20% 4.63 20% (3.70)22% 1.98 22% (7.43)24% (0.54) 24% (10.95)

(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 than 23.6 percent?

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 IRR's 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 IRR of a project is defined as the point at which its profile intersects the x-axis.

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

(20.00)

(10.00)

0.00

10.00

20.00

30.00

40.00

50.00

60.00

NPV Profile of Franchises S and L

Project SProject L

Cost of Capital

NPV

Franchise L- IRR

Franchise S- IRR

Crossover Rate = 8.7%

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g. (1.) What is the underlying cause of ranking conflicts between NPV and IRR?

Expected net cash flows Cash flow

Year (t) Franchise S Franchise L differential0 ($100) ($100) 0 1 70 10 60 2 50 60 (10)3 20 80 (60)

IRR = Crossover rate = 8.68%

Modified Internal Rate of Return (MIRR)

h. (1.) Define the term modified IRR (MIRR). Find the MIRRs for Franchise L and S.

WACC = 10% 16.89%Franchise S 16.50%

10%0 1 2 3

(100) 70 50 20

Franchise L

0 1 2 3 (100) 10 60 80

66 12.1

P V : (100) TV = 158

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 IRR's 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 IRR of a project is defined as the point at which its profile intersects the x-axis.

(2.) What is the "reinvestment rate assumption," and how does it affect the NPV versus IRR conflict? Answer: See Chapter 12 Mini Case Show

(3.) Which method is the best? Why? Answer: See Chapter 12 Mini Case Show

Looking further at the NPV profiles, we see that the two franchises profiles intersect at a point we shall call the crossover point. We observe that at costs of capital greater than the crossover point, 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 point, 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 appears to occur at approximately 8.7%. Luckily, there is a more precise way of determining crossover. To find crossover, we will find the difference between the two franchises' cash flows in each year, and then find the IRR of this series of differential cash flows.

The intuition behind the relationship between the NPV profile and the crossover rate is as follows: (1) Distant cash flows are heavily penalized by high discount rates--the denominator is (1+r)t, and it increases geometrically, hence gets very large at high values of t. (2) Long-term projects like L have most of their cash flows coming in the later years, when the discount penalty is largest, hence they are most severely impacted by high capital costs. (3) 'Therefore, Franchise L's NPV profile is steeper than that of S. (4) Since the two profiles have different slopes, they cross one another.

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. Or, you can solve using the MIRR function.

MIRRS =

MIRRL =

B294:E294

B287

B287

B305:E305

B296

B296

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Multiple IRR's

Project M: 0 1 2 (800.0) 5,000 (5,000)

The project is estimated to be of average risk, so its cost of capital is 10 percent.

(2.) What is Project P's NPV? What is its IRR? Its MIRR?

25.0% MIRR = 5.6%

400%

(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 WACC, and IRR at the IRR.

i. As a separate project (Project P), you are considering sponsoring a pavilion at the upcoming World's Fair. The pavilion would cost $800,000, and it is expected to result in $5 million of incremental cash inflows during its 1 year of operation. However, it would then take another year, and $5 million of costs, to demolish the site and return it to its original condition. Thus, Project P's expected net cash flows look like this (in millions of dollars):

(1.) What are normal and nonnormal cash flows? Answer: See Chapter 12 Mini Case Show

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%. Notice, that the first IRR calculation is exactly as it was above.

IRR M 1 =

IRR M 2 =

The two solutions to this problem tell us that this project will have a positive NPV for all costs of capital between 25% and 400%. We illustrate this point by creating a data table and a graph of the project NPVs.

C332:E332

200%

C343:E343

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0 1 2 (800.0) 5,000 (5,000)

(3.) Draw Project P's NPV profile. Does Project P have normal or nonnormal cash flows? Should this project be accepted?

r = 25.0%NPV = 0.00

NPVr $0.0

0% (800.00)25% 0.00 50% 311.11 75% 424.49 100% 450.00 Max.125% 434.57 150% 400.00 175% 357.02 200% 311.11 225% 265.09 250% 220.41 275% 177.78 300% 137.50 325% 99.65 350% 64.20 375% 31.02 400% 0.00 425% (29.02)450% (56.20)475% (81.66)500% (105.56)525% (128.00)550% (149.11)

PROFITABILITY INDEX

j. What does the profitability index (PI) measure? What are the PI's for Franchises S and L?

For Franchise S:PI(S) = PV of future cash flows ÷ Initial cost

PI(S) = $119.98 ÷ $100 PI(S) = 1.1998

For Franchise L:PI(L) = PV of future cash flows ÷ Initial cost

PI(L) = $118.78 ÷ $100 PI(L) = 1.1878

PROJECTS WITH UNEQUAL LIVES

k. In an unrelated analysis, you have the opportunity to choose between the following two mutually exclusive projects:

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.

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 percent cost of capital.

-100% 0% 100% 200% 300% 400% 500%

-$1,000.00

-$800.00

-$600.00

-$400.00

-$200.00

$0.00

$200.00

$400.00

$600.00

Multiple Rates of Return

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(1.) What is each project’s initial NPV without replication?

Project L WACC: 10.0%End of Period:

0 1 2 3 4 ($100) $33.5 $33.5 $33.5 $33.5

NPV $6.19

Project SEnd of Period:

0 1 2 3 ($100) $60 $60

NPV $4.13

(2.) Now apply the replacement chain approach to determine the projects’ extended NPVs. Which project should be chosen?

Project SEnd of Period:

0 1 2 3 ($100) $60 $60

($100) $60 $60 ($100) $60 ($40) $60 $60

NPV $7.55

(3.) Repeat the analysis using the equivalent annual annuity approach

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.EEAL= 1.95 Note: we used the Function Wizard for the PMT function.EEAS= 2.38

Project SEnd of Period:

0 1 2 3 ($100) $60 $60

($105) $60 $60 ($100) $60 ($45) $60 $60

NPV $3.42

projects have a 10 percent cost of capital.

(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?

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ECONOMIC LIFE VS. PHYSICAL LIFE

Year0 ($5,000) $5,000 1 $2,100 $3,100 2 $2,000 $2,000 3 $1,750 $0

(1.) The cost of capital is 10%. If the asset is operated for the entire three years of its life, its NPV is:

3-Year NPV = Initial Cost + +

= ($5,000.00) + $4,876.78 + $0.00 3-Year NPV = ($123.22)

(2.) Would the NPV change if the company planned to terminate the project at the end of Year 2?

2-Year NPV = Initial Cost + +

= ($5,000.00) + $3,561.98 + $1,652.89 2-Year NPV = $214.88

(3.) At the end of Year 1?

1-Year NPV = Initial Cost + +

= ($5,000.00) + $1,909.09 + $2,818.18 1-Year NPV = ($272.73)

(4.) What is the project’s optimal (economic) life?

m. 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 value. Here are the project’s estimated cash flows:

Operating Cash Flow

Salvage Value

PV of Operating Cash Flow

PV of Salvage Value

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 operate the asset for either one or two years, and then salvage it.

PV of Operating Cash Flow

PV of Salvage Value

PV of Operating Cash Flow

PV of Salvage Value

l. After examining all the potential projects, you discover that there are many more projects this year with positive NPVs than in a normal year. What two problems might this extra large capital budget cause? Answer: See Chapter 12 Mini Case Show

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Chapter 12. Mini Case

If payback doesn't occur by year end, the entire year is needed. If it occurs by year end, calculate the fraction of the year needed.

J K L M N O P Q R S123456789

101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

If payback doesn't occur by year end, the entire year is needed. If it occurs by year end, calculate the fraction of the year needed.Use the sum function to calculate the total number of years to payback.

J K L M N O P Q R S6162636465666768697071727374757677

Cash Flows Discounted back at 10%.

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.

B102

D106:F106

B113

D117:F117

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100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134

J K L M N O P Q R S135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194

9 10 90 1,090

J K L M N O P Q R S195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224225226227228229230231232233234235236237238239240241242243244245246247248249250251252253254

J K L M N O P Q R S255256257258259260261262263264265266267268269270271272273274275276277278279280281282283284285286287288289290291292293294295296297298299300301302303304305306307308309310311312313314

-100% 0% 100% 200% 300% 400% 500%

-$1,000.00

-$800.00

-$600.00

-$400.00

-$200.00

$0.00

$200.00

$400.00

$600.00

Multiple Rates of Return

J K L M N O P Q R S375376377378379380381382383384385386387388389390391392393394395396397398399400401402403404405406407408409410411412413414415416417418419

420421422423424

425426427428429430431432433