Ch10 13ed CapitalBudget MinicMaster

8/12/2019 Ch10 13ed CapitalBudget MinicMaster

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A B C D E F G H I J K

1/1/2012

Capital Budgeting Decisions

Situation

Fr anchise S

Year (t) Franchise S Franchise L 0 1 2 3

0 ($100) ($100) (100) 70 50 20

1 70 10

2 50 60 Fr anchise L

3 20 80

0 1 2 3

(100) 10 60 80

Net Present Value (NPV)

WACC = 10%

Fr anchise S

Time 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.

b. What is the difference between independent and mutually exclusive projects? Answer: See Chapter 10 Mini Case Show

Chapter 10. Mini Case

Expected

Net Cash Flows

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.

Here are the net cash flows (in thousands of dollars):

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.

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

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

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

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.

a. What is capital budgeting? Answer: See Chapter 10 Mini Case Show


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Fr anchise L


Cash flow: (100) 10 60 80

Disc. cash flow: (100) 9 50 60

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

Internal Rate of Return (IRR)

Year (t) Franchise S Franchise L

0 ($100) ($100)

1 70 10 IRRS= 23.56%

2 50 60 IRRL= 18.13%

3 20 80

Constant Cash Flows

Year (t) Cash Flow

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 if

payments are constant.

Similarity to a bond:

0 1 2 3 4 5 6 7 8 9 10

(1,134) 90 90 90 90 90 90 90 90 90 1,090

IRR = 7.08%

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

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.

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

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

net cash flows

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

they

The IRR function

assumes payments occur

at end of periods, so that

function does not have to

be adjusted.

Expected

Notice that for IRR you mustspecify all cash flows,including the time zero cashflow. This is in contrast tothe NPV function, in whichyou specify only the futurecash flows.


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NPV Profiles

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

Franchise S Franchise L

WACC $19.98 WACC $18.78

0% 40.00 0% 50.002% 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)

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

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.

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

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

(2.) Look at your NPV profile graph without referring to the actual NPVs and IRRs. Which franchise or franchises should

beaccepted if they are independent? Mutually exclusive? Explain. Are your answers correct at any cost of capital less

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.

(3.) What is the logic behind the IRR method? According to IRR, which franchises should be accepted if they are

independent?

(20)

(10)

0

10

20

30

40

50

60

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

NPV ($)

Cost of Capital

NPV Profile of Franchises S and L

Project L

Project S

Franchise L- IRR

FranchiseS- IRR

Crossover Rate =8.7%


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Cash Flow

Year (t) Franchise S Franchise L Differential

0 ($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)

WACC = 10% MIRRS = 16.89%

Fr anchise S MIRRL = 16.50%

10%

0 1 2 3

(100) 70 50 20

Fr anchise L

0 1 2 3

(100) 10 60 80

66

12.1

P V : (100) TV = 158.1

(3.) Which method is the best? Why? Answer: See Chapter 10 Mini Case Show

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 .

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.

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.

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

Expected

Net Cash Flows

,

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

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, it gets very large athigh 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.

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.

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

the IRR of this series of differential cash flows. This IRR is the crossover rate.

(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?


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PROFITABILITY INDEX

h. 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

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

Payback Period

Fr anchise S


Cash flow: (100) 70 50 20

Cumulative cash flow: (100) (30) 20 40

Payback: 1.600

Fr anchise L


Cash flow: (100) 10 60 80

Cumulative cash flow: (100) (90) (30) 50

Payback: 2.375

Discounted Payback Period

WACC = 10%

Fr anchise S


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

Discounted Payback: 1.9

(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

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.

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%.

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

e pay ac per o s e ne as t e expecte num er o years requ re to recover t e nvestment, an t was t e rst ormamethod 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

payback period, the better the investment.


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Fr anchise L

Time 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

Discounted Payback: 2.7

Multiple IRRs

Project M : 0 1 2

(800) 5,000 (5,000)

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

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

NPVM= ($386.78)

IRRM1= 25.0% MIRR = 5.6%

IRRM2= 400%

0 1 2

(800.0) 5,000 (5,000)

j. 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

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.

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.

(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 and neither

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

and risk.

(1.) What are normal and nonnormal cash flows? Answer: See Chapter 10 Mini Case Show


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r = 25.0%

NPV = 0.00

NPV

r $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% 31.02400% 0.00

425% (29.02)

450% (56.20)

475% (81.66)

500% (105.56)

525% (128.00)

550% (149.11)

PROJECTS WITH UNEQUAL LIVES

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

Year Project S Project L

0 ($100,000) ($100,000)

1 60,000 33,500

2 60,000 33,5003 33,500

4 33,500

Proj ect L WACC: 10.0%

0 1 2 3 4

($100) $33.5 $33.5 $33.5 $33.5

NPV $6.19

Project S

0 1 2 3 4

($100) $60 $60

NPV $4.13

End of Period:

End of Period:

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.

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

(1.) What is each projects initial NPV without replication?

-1,000

-800

-600

-400

-200

0

200

400

600

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

NPV ($)

Cost of Capital

Multiple Rates of Return


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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

Proj ect S

0 1 2 3

($100) $60 $60

($100) $60 $60

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

NPV $7.55

Proj ect S

0 1 2 3

($100) $60 $60

($105) $60 $60

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

NPV $3.42

ECONOMIC LIFE VS. PHYSICAL LIFE

Year

Operating

Cash Flow

Salvage

Value

0 ($5,000) $5,000

1 $2,100 $3,100

2 $2,000 $2,000

3 $1,750 $0

3-Year NPV = Initial Cost +

PV of

Operating

Cash Flow

+

PV of

Salvage

Value

= ($5,000.00) + $4,876.78 + $0.00

3-Year NPV = ($123.22)

2-Year NPV = Initial Cost +

PV of

Operating

Cash Flow

+

PV of

Salvage

Value

= ($5,000.00) + $3,561.98 + $1,652.892-Year NPV = $214.88

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

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.

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

End of Period:

End of Period:

(2.) What is each projects equivalent annual annuity?

(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?

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

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


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1-Year NPV = Initial Cost +PV of

Operating+

PV of

Salvage

= ($5,000.00) + $1,909.09 + $2,818.18

1-Year NPV = ($272.73)

The project's NPV will only be positive when it is operated for 2 years. Therefore, the project's economic life is 2 years.

m. 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: S ee Chapter 10 Mini Case Show

(4.) What is the projects optimal (economic) life?

(3.) At the end of Year 1?


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L M N O P Q R S T U

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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L M N O P Q R S T U


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Ch10 13ed CapitalBudget MinicMaster

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Transcript of Ch10 13ed CapitalBudget MinicMaster