CH12

Chapter 12Capital Budgeting: Decision Criteria

TopicsOverview MethodsNPVIRR, MIRRProfitability IndexPayback, discounted paybackUnequal livesEconomic life

Capital Budgeting:Analysis of potential projectsLong-term decisionsLarge expendituresDifficult/impossible to reverseDetermines firms strategic direction

Steps in Capital BudgetingEstimate cash flows (Ch 13)Assess risk of cash flows (Ch 13)Determine r = WACC for project (Ch10)Evaluate cash flows Chapter 12

Independent versus Mutually Exclusive ProjectsIndependent:The cash flows of one are unaffected by the acceptance of the otherMutually Exclusive:The acceptance of one project precludes accepting the other

Cash Flows for Projects L and S

CH12 TOOLKIT

3/19/09

Chapter 12. Tool Kit for Basics of Capital Budgeting: Decision Criteria

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 both tabular and a time line formats. Spreadsheet analyses can be set up vertically, i

Expected after-tax

net cash flows (CFt)

Year (t)Project SProject L

0($1,000)($1,000)

1500100

2400300

3300400

4100600

Figure 12-1: Net Cash Flows and Selected Evaluation Criteria for Projects S and L (CFt)

Panel A: Project Cash Flows and Cost of Capital

Project S:01234

|||||

-$1,000$500$400$300$100

Project L:01234

|||||

-$1,000$100$300$400$600

Project cost of capital = r =10%

Panel B: Summary of Selected Evaluation Criteria

Project

SL

NPV:$78.82$49.18

IRR:14.5%11.8%

MIRR:12.1%11.3%

PI:1.081.05

NET PRESENT VALUE (NPV) (Section 12.2)

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.

r =10%

Project S

Time period:01234Notice 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 re

Cash flow:(1,000)500400300100

Disc. cash flow:(1,000)45533122568

NPV(S) =$78.82= Sum disc. CF's.or$78.82= Uses NPV function.

Project L

Time period:01234

Cash flow:(1,000)100300400600

Disc. cash flow:(1,000)91248301410

NPV(L) =$49.18$49.18= Uses NPV function.

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 manag

INTERNAL RATE OF RETURN (IRR) (Section 12.2)

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

Expected after-tax



0($1,000)($1,000)The IRR function assumes

1500100IRR S =14.49%payments occur at end of

2400300IRR L =11.79%periods, so that function does

3300400not have to be adjusted.

4100600

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 th

COMPARISON OF THE NPV AND IRR METHODS (Section 12.4)

NPV Profiles

NPV profiles graph the relationship between projects' NPVs and the cost of capital. To create NPV profiles for Projects S and L, we create data tables of NPV at different costs of capital.

Net Cash Flows

YearProject SProject LWACC =10.0%

0-$1,000-$1,000Project SProject L

1$500$100NPV =$78.82$49.18

2$400$300IRR =14.49%11.79%

3$300$400Crossover =7.17%

4$100$600

Data Table used to make graph:

Project NPVs

SL

WACC$78.82$49.18

0%$300.00$400.00

5%$180.42$206.50

7.17%$134.40$134.40

10%$78.82$49.18

11.79%$46.10$0.00

14.49%$0.00-$68.02

15.0%-$8.33-$80.14

20%-$83.72-$187.50

25%-$149.44-$277.44

Points about the graphs:

1. In Panel a, we see that if WACC < IRR, then NPV > 0, and vice versa.

2. Thus, for "normal and independent" projects, there can be no conflict between NPV and IRR rankings.

3. However, if we have mutually exclusive projects, conflicts can occur. In Panel b, we see that IRRS is

always greater than IRRL, but if WACC < 11.56%, then IRRL > IRRS, in which case a conflict occurs.

4. Summary: a. For normal, independent projects, conflicts can never occur, so either method can be used.

b. For mutually exclusive projects, if WACC > Crossover, no conflict, but if WACC < Crossover,

then there will be a conflict between NPV and IRR.

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 project profiles (S and L) intersect the x-axis at costs of capi

Looking further at the NPV profiles, we see that the two project profiles intersect at a point we shall call the crossover point. We observe that at costs of capital greater than the crossover point, the project with the greater IRR (Project S, in this c

Expected after-taxAlternative: Use Tools > Goal Seek to find WACC when NPV(S) =

net cash flows (CFt)Cash flowNPV(L). Set up a table to show the difference in NPV's, which we

Year (t)Project SProject Ldifferentialwant to be zero. The following will do it, getting WACC = 7.17%.

0($1,000)($1,000)0

1500100400Trial project cost of capital, r =7.17%

2400300100NPV S (based on trial r)=$134.40

3300400(100)NPV L (based on trial r) =$134.40

4100600(500)S - L =$0.00

IRR =Crossover rate =7.17%

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

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

MULTIPLE IRRS (Section 12.5)

Because of the mathematics involved, it is possible for some (but not all) projects that have more than one change of signs in the set of cash flows to have more than one IRR. If you attempted to find the IRR with such a project using a financial calcul

Consider the case of Project M.

Project M:Year:012

CF:(1.6)10(10)

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 300%. Notice, that the first IRR calculation is exactly as it was above.

IRR M 1 =25.0%

IRR M 2 =400%

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.

Project M:Year:012

CF:(1.6)10(10)

r =25.0%

NPV =0.00

NPV

r$0.0

0%(1.60)

25%0.00

50%0.62

75%0.85

100%0.90Max.

125%0.87

150%0.80

175%0.71

200%0.62

225%0.53

250%0.44

275%0.36

300%0.28

325%0.20

350%0.13

375%0.06

400%0.00

425%(0.06)

450%(0.11)

475%(0.16)

500%(0.21)

525%(0.26)

550%(0.30)

MODIFIED INTERNAL RATE OF RETURN (MIRR) (Section 12.6)

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 inf

WACC =10%

Project SMIRRS =12.11%

10%MIRRL =11.33%

01234

(1,000)500400300100

Project L

01234

(1,000)100300400600

440.0

363.0

133.1

P V :(1,000)Terminal Value:1,536.1

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 proj

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 negativ

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 differe

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 lik

Project S

WACC =10%

01234

(1,000)500400300100

330.0

484.0

665.5Reinvestment at WACC = 10%

PV outflows-$1,000.00Terminal Value:1,579.5

PV of TV$1,078.82

NPV$78.82Thus, we see that the NPV is consistent with reinvestment at WACC.

Now repeat the process using the IRR as the discount rate.

Project S

IRR =14.49%

01234

(1,000)500400300100

343.5

524.3

750.3Reinvestment at IRR = 14.49%


PV of TV$1,000.00

NPV$0.00Thus, if compounding is at the IRR, NPV is zero. Since the

definition of IRR is the rate at which NPV = 0, this demonstrates

that the IRR assumes reinvestment at the IRR.

PROFITABILITY INDEX (PI) (Section 12.7)

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 project S:

PI(S) =PV of future cash flowsInitial cost

PI(S) =$1,078.82$1,000.00

PI(S) =1.079

For project L:

PI(L) =PV of future cash flowsInitial cost

PI(L) =$1,049.18$1,000.00

PI(L) =1.049

PAYBACK METHODS (Section 12.8)

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

Figure 12-4. Payback Periods for Projects S and L

Project SYear:01234

|||||

Cash flow:-1,000500400300100

Cumulative cash flow:-1,000-500-100200300

Percent of year required for payback:1.001.000.330.00

Payback =2.33

Project LYear:01234

|||||

Cash flow:-1,000100300400600

Cumulative cash flow:-1,000-900-600-200400


Payback =3.33

Discounted Payback Period

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

WACC =10%

Figure 12-5. Projects S and L: Discounted Payback Period (r = 10%)

Project SYear:01234

|||||

Cash flow:-1,000500400300100

Discounted cash flow:-1,000454.5330.6225.468.3

Cumulative discounted CF:-1,000-545.5-214.910.578.8


Discounted Payback:2.95

Project LYear:01234

|||||

Cash flow:-1,000100300400600


Cumulative discounted CF:-1,000-909.1-661.2-360.649.2



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

SPECIAL APPLICATIONS OF CASH FLOW EVALUATION (Section 12.11)

PROJECTS WITH UNEQUAL LIVES

If two mutually exclusive projects have different lives, and if the projects can be repeated, then it is necessary to deal explicitly with those unequal lives. We use the replacement chain (or common life) approach. This procedure compares projects of un

r =11.5%

Figure 12-6 Analysis of Projects C and F (r = 11.5%)

Project C:

Year (t)0123456

CFt for C-$40,000$8,000$14,000$13,000$12,000$11,000$10,000

NPVC =$7,165IRRC =17.5%

Project F:

Year (t)0123

CFt for F-$20,000$7,000$13,000$12,000

NPVF =$5,391IRRF =25.2%

Common Life Approach with F Repeated (Project FF):

Year (t)0123456

CFt for F-$20,000$7,000$13,000$12,000

CFt for F-$20,000$7,000$13,000$12,000

CFt for FF-$20,000$7,000$13,000-$8,000$7,000$13,000$12,000

NPVFF =$9,281IRRFF =25.2%

On the basis of this extended analysis, it is clear that Project F is the better of the two investments (with both the NPV and IRR methods).

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).

NPVC=7,165

NPVF=5,391

2.Convert the NPV into an annuity payment with a life equal to the life of the project.

EEAC=1,718Note: we used the Function Wizard for the PMT function.

EEAF=2,225

Project F has a higher EEA, so it is a better project.

ECONOMIC LIFE VS. PHYSICAL LIFE

Sometimes an asset has a physical life that is greater than its economic life. Consider the following asset which has a physical life of three years. During its life, the asset will generate operating cash flows. However, the project could be terminate

YearOperating Cash FlowSalvage Value

0($4,800)$4,800

1$2,000$3,000

2$2,000$1,650

3$1,750$0

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 =Intial Cost+PV of Operating Cash Flow+PV of Salvage Value

=($4,800.00)+$4,785.88+$0.00

3-Year NPV =($14.12)

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.


=($4,800.00)+$3,471.07+$1,363.64

2-Year NPV =$34.71


=($4,800.00)+$1,818.18+$2,727.27

1-Year NPV =($254.55)

CH12 TOOLKIT

0

0

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0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

Multiple Rates of Return

TimeLines-NPV

00

00

00

00

00

00

00

00

00

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.

Project S

WACC

NPV

Project S's NPV Profile

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

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NPVs

Project S

Project L

WACC

NPV

Both Projects' Profiles

TimeLines -IRR

NPV for Project S

10%

t =01234

S's CFs-1000500400300100

-1000

454.55

330.58

225.39

68.30

$78.82

NPV for Project L

10%

t =01234

L's CFs-1000100300400600

-1000

90.91

247.93

300.53

409.81

$49.18

NPVs

NPVL

Crossover = 7.17%

IRRS = 14.49%

%

Accept

Reject

Conflict

No conflict

The NPV, if k=25%.

PROFILES

IRR for Project S

?%

t =01234

S's CFs-1000500400300100

-1000

PV(1)

PV(2)

PV(3)

PV(4)

NPV =$0.00

IRR for Project L

?%

t =01234

L's CFs-1000100300400600

-1000

PV(1)

PV(2)

PV(3)

PV(4)

NPV =$0.00

MIRR

rNPV (S)NPV(L)

0$300.00$400.00

5%$180.42$206.50

10%$78.82$49.18

15%($8.33)($80.14)

20%($83.72)($187.50)

IRR14.5%11.8%

tSLDiff

0-1000-10000

1500100400

2400300100

3300400-100

4100600-500

7.2%

PROF INDEX

MIRR for Project S

r = 10%

t =01234

S's CFs-1000500400300100

330

484

665.5

-1000.00MIRR12.1%1579.5

PV OutflowsTV Inflows

MIRR for Project L

?%

t =01234

L's CFs-1000100300400600

-1000

$0.00

PAYBACK

PV of Inflows for Project S

10%

t =01234

S's CFs-1000500400300100

454.55

330.58

225.39

68.30

$1,078.82

PV of Inflows for Project L

10%

t =01234

L's CFs-1000100300400600

90.91

247.93

300.53

409.81

$1,049.18

DC PAYBACK

Payback for Project S

t =01234

S's CFs-1000500400300100

Cumulative-1000-500-100200300

Payback =2.33

Payback for Project L

t =01234

L's CFs-1000100300400600

Cumulative-1000-900-600-200400

Payback =3.33

ECON LIFE

Discounted Payback for Project S

r = 10%01234

S's CFs-1000500400300100

Discounted CFs-1000454.55330.58225.3968.30

Cumulative-1000-545.45-214.8810.5278.82

Discounted Payback =2.95

Discounted Payback for Project L

r = 10%01234

L's CFs-1000100300400600

Discounted CFs-100090.91247.93300.53409.81

Cumulative-1000-909.09-661.16-360.6349.18


12.2

ECONOMIC vs. PHYSICAL LIFEr =10%

CFs if Terminated in Year

YRCFSV321

0-$4,800$4,800-$4,800-$4,800-$4,800

1$2,000$3,000$2,000$2,000$5,000

2$2,000$1,650$2,000$3,650

3$1,750$0$1,750

NPV($14.12)$34.71($254.55)

12.3

SECTION 12.2

SOLUTIONS TO SELF-TEST

3 A project has the following expected cash flows: CF0 = -$500, CF1 = $200, CF2 = $200, and CF3 = $400. If the project cost of capital is 9 percent, what is the NPV?

WACC9%

Expected After-Tax Net Cash Flows, CFt

Year (t)

0-$500

1$200

2$200

3$400

NPV =$160.70

12.5

SECTION 12.3


3 A project has the following expected cash flows: CF0 = -$500, CF1 = $200, CF2 = $200, and CF3 = $400. What is the IRR?


Year (t)

0-$500

1$200

2$200

3$400

IRR =24.1%

12.6

SECTION 12.5


2 A project has the following cash flows: CF0 = $1,100, CF1 = $2,100, CF2 = $2,100, and CF3 = $3,600. How many positive IRRs might this project have? If you set the starting trial value to 10 percent in either your calculator of Excel, what is the IR

Project

Year (t)CFs

0-$1,100

1$2,100

2$2,100

3-$3,600

IRR with starting trial at 10%:18.2%


NPV with r = 0%:($500.00)

12.7

SECTION 12.6


3 A project has the following expected cash flows: CF0 = -$500, CF1 = $200, CF2 = $200, and CF3 = $400. Using a 10 percent discount rate and reinvestment rate, what is the MIRR?

Discount rate = reinvestment rate =10%


Year (t)

0-$500

1$200

2$200

3$400

MIRR =19.9%

12.8

SECTION 12.7


2 A project has the following expected cash flows: CF0 = -$500, CF1 = $200, CF2 = $200, and CF3 = $400. If the project cost of capital is 9 percent, what is the PI?

WACC9%


Year (t)

0-$500

1$200

2$200

3$400

PI =1.32

SECTION 12.8


3 A project has the following expected cash flows: CF0 = -$500, CF1 = $200, CF2 = $200, and CF3 = $400. If the project's cost of capital is 9%, what are the project's payback period and discounted payback period?

Year:0123

Cash flow:(500)200200400

Cumulative CF:(500)(300)(100)300

Percent of year required for payback:1.001.000.25


r =9%

Year:0123

Cash flow:(500)200200400

Discounted cash flow:(500)183.49168.34308.87

Cumulative discounted CF:(500)(316.51)(148.18)160.70



NPV: Sum of the PVs of all cash flows.Cost often is CF0 and is negativeNOTE: t=0

Project Ss NPV

Chapter

3/19/09



Expected after-tax


0($1,000)($1,000)

1500100

2400300

3300400

4100600


Project S:01234

|||||

-$1,000$500$400$300$100

Project L:01234

|||||

-$1,000$100$300$400$600



Project

SL

NPV:$78.82$49.18

IRR:14.5%11.8%

MIRR:12.1%11.3%

PI:1.081.05


r =10%

Project S


Cash flow:(1,000)500400300100

Disc. cash flow:(1,000)45533122568


Project L

Time period:01234

Cash flow:(1,000)100300400600

Disc. cash flow:(1,000)91248301410




Expected after-tax



150010014.49%payments occur at end of

240030011.79%periods, so that function does


4100600


NPV Profiles


Net Cash Flows



1$500$100NPV =$78.82$49.18

2$400$300IRR =14.49%11.79%

3$300$400Crossover =7.17%

4$100$600


Project NPVs

SL

WACC$78.82$49.18

0%$300.00$400.00

5%$180.42$206.50

7.17%$134.40$134.40

10%$78.82$49.18

11.79%$46.10$0.00

14.49%$0.00-$68.02

15.0%-$8.33-$80.14

20%-$83.72-$187.50

25%-$149.44-$277.44










Cash flowNPV(L). Set up a table to show the difference in NPV's, which we


0($1,000)($1,000)0




4100600(500)S - L =$0.00





Project M:Year:012

CF:(1.6)10(10)


25.0%

400%


Project M:Year:012

CF:(1.6)10(10)

r =25.0%

NPV =0.00

NPV

r$0.0

0%(1.60)

25%0.00

50%0.62

75%0.85

100%0.90Max.

125%0.87

150%0.80

175%0.71

200%0.62

225%0.53

250%0.44

275%0.36

300%0.28

325%0.20

350%0.13

375%0.06

400%0.00

425%(0.06)

450%(0.11)

475%(0.16)

500%(0.21)

525%(0.26)

550%(0.30)


WACC =10%

Project S12.11%

10%11.33%

01234

(1,000)500400300100

Project L

01234

(1,000)100300400600

440.0

363.0

133.1






Project S

WACC =10%

01234

(1,000)500400300100

330.0

484.0



PV of TV$1,078.82



Project S

IRR =14.49%

01234

(1,000)500400300100

343.5

524.3



PV of TV$1,000.00





For project S:


PI(S) =$1,078.82$1,000.00

PI(S) =1.079

For project L:


PI(L) =$1,049.18$1,000.00

PI(L) =1.049

Payback Period



Project SYear:01234

|||||

Cash flow:-1,000500400300100



Payback =2.33

Project LYear:01234

|||||

Cash flow:-1,000100300400600



Payback =3.33



WACC =10%


Project SYear:01234

|||||

Cash flow:-1,000500400300100





Project LYear:01234

|||||

Cash flow:-1,000100300400600








r =11.5%


Project C:

Year (t)0123456

-$40,000$8,000$14,000$13,000$12,000$11,000$10,000

$7,16517.5%

Project F:

Year (t)0123

-$20,000$7,000$13,000$12,000

$5,39125.2%


Year (t)0123456

-$20,000$7,000$13,000$12,000

-$20,000$7,000$13,000$12,000

-$20,000$7,000$13,000-$8,000$7,000$13,000$12,000

$9,28125.2%





NPVC=7,165

NPVF=5,391



EEAF=2,225





0($4,800)$4,800

1$2,000$3,000

2$2,000$1,650

3$1,750$0



=($4,800.00)+$4,785.88+$0.00

3-Year NPV =($14.12)



=($4,800.00)+$3,471.07+$1,363.64

2-Year NPV =$34.71


=($4,800.00)+$1,818.18+$2,727.27

1-Year NPV =($254.55)

Chapter

-1.6

0

0.6222222222

0.8489795918

0.9

0.8691358025

0.8

0.7140495868

0.6222222222

0.5301775148

0.4408163265

0.3555555556

0.275

0.1993079585

0.1283950617

0.0620498615

0

-0.0580498866

-0.1123966942

-0.1633270321

-0.2111111111

-0.256

-0.2982248521


Sheet1

300400

180.4237946123206.5034630632

134.4046591185134.4046591185

78.819752749149.1769687863

46.10444213440.000000002

0-68.0175364364

-8.3297300967-80.1419377432

-83.7191358025-187.5

-149.44-277.44


Project S

WACC

NPV


0

0.05

0.0716727998

0.1

0.1179055563

0.1448884428

0.15

0.2

0.25

300

180.4237946123

134.4046591185

78.8197527491

46.1044421344

0

-8.3297300967

-83.7191358025

-149.44

NPVs

Project S

Project L

WACC

NPV


12.2

NPV for Project S

10%

01234

S's CFs-1000500400300100

-1000

454.55

330.58

225.39

68.30

$78.82

NPV for Project L

10%

01234

L's CFs-1000100300400600

-1000

90.91

247.93

300.53

409.81

$49.18

NPVs

NPVL

Crossover = 7.17%

IRRS = 14.49%

%

Accept

Reject

Conflict

No conflict

The NPV, if k=25%.

12.3

SECTION 12.2


WACC9%

Year (t)

0-$500

1$200

2$200

3$400

NPV =$160.70

12.5

SECTION 12.3


Year (t)

0-$500

1$200

2$200

3$400

IRR =24.1%

12.6

SECTION 12.5


Project

Year (t)CFs

0-$1,100

1$2,100

2$2,100

3-$3,600



NPV with r = 0%:($500.00)

12.7

SECTION 12.6



Year (t)

0-$500

1$200

2$200

3$400

MIRR =19.9%

12.8

SECTION 12.7


WACC9%

Year (t)

0-$500

1$200

2$200

3$400

PI =1.32

SECTION 12.8


Year:0123

Cash flow:(500)200200400

Cumulative CF:(500)(300)(100)300



r =9%

Year:0123

Cash flow:(500)200200400





CH12 TOOLKIT

3/19/09



Expected after-tax



0($1,000)($1,000)

1500100

2400300

3300400

4100600



Project S:01234

|||||

-$1,000$500$400$300$100

Project L:01234

|||||

-$1,000$100$300$400$600



Project

SL

NPV:$78.82$49.18

IRR:14.5%11.8%

MIRR:12.1%11.3%

PI:1.081.05



r =10%

Project S


Cash flow:(1,000)500400300100

Disc. cash flow:(1,000)45533122568


Project L

Time period:01234

Cash flow:(1,000)100300400600

Disc. cash flow:(1,000)91248301410





Expected after-tax







4100600



NPV Profiles


Net Cash Flows



1$500$100NPV =$78.82$49.18

2$400$300IRR =14.49%11.79%

3$300$400Crossover =7.17%

4$100$600


Project NPVs

SL

WACC$78.82$49.18

0%$300.00$400.00

5%$180.42$206.50

7.17%$134.40$134.40

10%$78.82$49.18

11.79%$46.10$0.00

14.49%$0.00-$68.02

15.0%-$8.33-$80.14

20%-$83.72-$187.50

25%-$149.44-$277.44














0($1,000)($1,000)0




4100600(500)S - L =$0.00







Project M:Year:012

CF:(1.6)10(10)


IRR M 1 =25.0%

IRR M 2 =400%


Project M:Year:012

CF:(1.6)10(10)

r =25.0%

NPV =0.00

NPV

r$0.0

0%(1.60)

25%0.00

50%0.62

75%0.85

100%0.90Max.

125%0.87

150%0.80

175%0.71

200%0.62

225%0.53

250%0.44

275%0.36

300%0.28

325%0.20

350%0.13

375%0.06

400%0.00

425%(0.06)

450%(0.11)

475%(0.16)

500%(0.21)

525%(0.26)

550%(0.30)



WACC =10%


10%MIRRL =11.33%

01234

(1,000)500400300100

Project L

01234

(1,000)100300400600

440.0

363.0

133.1






Project S

WACC =10%

01234

(1,000)500400300100

330.0

484.0



PV of TV$1,078.82



Project S

IRR =14.49%

01234

(1,000)500400300100

343.5

524.3



PV of TV$1,000.00






For project S:


PI(S) =$1,078.82$1,000.00

PI(S) =1.079

For project L:


PI(L) =$1,049.18$1,000.00

PI(L) =1.049


Payback Period



Project SYear:01234

|||||

Cash flow:-1,000500400300100



Payback =2.33

Project LYear:01234

|||||

Cash flow:-1,000100300400600



Payback =3.33



WACC =10%


Project SYear:01234

|||||

Cash flow:-1,000500400300100





Project LYear:01234

|||||

Cash flow:-1,000100300400600









r =11.5%


Project C:

Year (t)0123456

CFt for C-$40,000$8,000$14,000$13,000$12,000$11,000$10,000

NPVC =$7,165IRRC =17.5%

Project F:

Year (t)0123

CFt for F-$20,000$7,000$13,000$12,000

NPVF =$5,391IRRF =25.2%


Year (t)0123456

CFt for F-$20,000$7,000$13,000$12,000

CFt for F-$20,000$7,000$13,000$12,000

CFt for FF-$20,000$7,000$13,000-$8,000$7,000$13,000$12,000

NPVFF =$9,281IRRFF =25.2%





NPVC=7,165

NPVF=5,391



EEAF=2,225





0($4,800)$4,800

1$2,000$3,000

2$2,000$1,650

3$1,750$0



=($4,800.00)+$4,785.88+$0.00

3-Year NPV =($14.12)



=($4,800.00)+$3,471.07+$1,363.64

2-Year NPV =$34.71


=($4,800.00)+$1,818.18+$2,727.27

1-Year NPV =($254.55)

CH12 TOOLKIT

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0


TimeLines-NPV

00

00

00

00

00

00

00

00

00


Project S

WACC

NPV


0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

NPVs

Project S

Project L

WACC

NPV


TimeLines -IRR

NPV for Project S

10%

t =01234

S's CFs-1000500400300100

-1000

454.55

330.58

225.39

68.30

$78.82

NPV for Project L

10%

t =01234

L's CFs-1000100300400600

-1000

90.91

247.93

300.53

409.81

$49.18

NPVs

NPVL

Crossover = 7.17%

IRRS = 14.49%

%

Accept

Reject

Conflict

No conflict

The NPV, if k=25%.

PROFILES

IRR for Project S

?%

t =01234

S's CFs-1000500400300100

-1000

PV(1)

PV(2)

PV(3)

PV(4)

NPV =$0.00

IRR for Project L

?%

t =01234

L's CFs-1000100300400600

-1000

PV(1)

PV(2)

PV(3)

PV(4)

NPV =$0.00

MIRR

rNPV (S)NPV(L)

0$300.00$400.00

5%$180.42$206.50

10%$78.82$49.18

15%($8.33)($80.14)

20%($83.72)($187.50)

IRR14.5%11.8%

tSLDiff

0-1000-10000

1500100400

2400300100

3300400-100

4100600-500

7.2%

PROF INDEX

MIRR for Project S

r = 10%

t =01234

S's CFs-1000500400300100

330

484

665.5

-1000.00MIRR12.1%1579.5

PV OutflowsTV Inflows

MIRR for Project L

?%

t =01234

L's CFs-1000100300400600

-1000

$0.00

PAYBACK

PV of Inflows for Project S

10%

t =01234

S's CFs-1000500400300100

454.55

330.58

225.39

68.30

$1,078.82

PV of Inflows for Project L

10%

t =01234

L's CFs-1000100300400600

90.91

247.93

300.53

409.81

$1,049.18

DC PAYBACK

Payback for Project S

t =01234

S's CFs-1000500400300100

Cumulative-1000-500-100200300

Payback =2.33

Payback for Project L

t =01234

L's CFs-1000100300400600

Cumulative-1000-900-600-200400

Payback =3.33

ECON LIFE

Discounted Payback for Project S

r = 10%01234

S's CFs-1000500400300100

Discounted CFs-1000454.55330.58225.3968.30

Cumulative-1000-545.45-214.8810.5278.82


Discounted Payback for Project L

r = 10%01234

L's CFs-1000100300400600

Discounted CFs-100090.91247.93300.53409.81

Cumulative-1000-909.09-661.16-360.6349.18


12.2

ECONOMIC vs. PHYSICAL LIFEr =10%

CFs if Terminated in Year

YRCFSV321

0-$4,800$4,800-$4,800-$4,800-$4,800

1$2,000$3,000$2,000$2,000$5,000

2$2,000$1,650$2,000$3,650

3$1,750$0$1,750

NPV($14.12)$34.71($254.55)

12.3

SECTION 12.2


3 A project has the following expected cash flows: CF0 = -$500, CF1 = $200, CF2 = $200, and CF3 = $400. If the project cost of capital is 9 percent, what is the NPV?

WACC9%


Year (t)

0-$500

1$200

2$200

3$400

NPV =$160.70

12.5

SECTION 12.3


3 A project has the following expected cash flows: CF0 = -$500, CF1 = $200, CF2 = $200, and CF3 = $400. What is the IRR?


Year (t)

0-$500

1$200

2$200

3$400

IRR =24.1%

12.6

SECTION 12.5


2 A project has the following cash flows: CF0 = $1,100, CF1 = $2,100, CF2 = $2,100, and CF3 = $3,600. How many positive IRRs might this project have? If you set the starting trial value to 10 percent in either your calculator of Excel, what is the IR

Project

Year (t)CFs

0-$1,100

1$2,100

2$2,100

3-$3,600



NPV with r = 0%:($500.00)

12.7

SECTION 12.6


3 A project has the following expected cash flows: CF0 = -$500, CF1 = $200, CF2 = $200, and CF3 = $400. Using a 10 percent discount rate and reinvestment rate, what is the MIRR?



Year (t)

0-$500

1$200

2$200

3$400

MIRR =19.9%

12.8

SECTION 12.7


2 A project has the following expected cash flows: CF0 = -$500, CF1 = $200, CF2 = $200, and CF3 = $400. If the project cost of capital is 9 percent, what is the PI?

WACC9%


Year (t)

0-$500

1$200

2$200

3$400

PI =1.32

SECTION 12.8


3 A project has the following expected cash flows: CF0 = -$500, CF1 = $200, CF2 = $200, and CF3 = $400. If the project's cost of capital is 9%, what are the project's payback period and discounted payback period?

Year:0123

Cash flow:(500)200200400

Cumulative CF:(500)(300)(100)300



r =9%

Year:0123

Cash flow:(500)200200400





Project Ls NPV

Chapter

3/19/09



Expected after-tax


0($1,000)($1,000)

1500100

2400300

3300400

4100600


Project S:01234

|||||

-$1,000$500$400$300$100

Project L:01234

|||||

-$1,000$100$300$400$600



Project

SL

NPV:$78.82$49.18

IRR:14.5%11.8%

MIRR:12.1%11.3%

PI:1.081.05


r =10%

Project S


Cash flow:(1,000)500400300100

Disc. cash flow:(1,000)45533122568


Project L

Time period:01234

Cash flow:(1,000)100300400600

Disc. cash flow:(1,000)91248301410




Expected after-tax



150010014.49%payments occur at end of

240030011.79%periods, so that function does


4100600


NPV Profiles


Net Cash Flows



1$500$100NPV =$78.82$49.18

2$400$300IRR =14.49%11.79%

3$300$400Crossover =7.17%

4$100$600


Project NPVs

SL

WACC$78.82$49.18

0%$300.00$400.00

5%$180.42$206.50

7.17%$134.40$134.40

10%$78.82$49.18

11.79%$46.10$0.00

14.49%$0.00-$68.02

15.0%-$8.33-$80.14

20%-$83.72-$187.50

25%-$149.44-$277.44










Cash flowNPV(L). Set up a table to show the difference in NPV's, which we


0($1,000)($1,000)0




4100600(500)S - L =$0.00





Project M:Year:012

CF:(1.6)10(10)


25.0%

400%


Project M:Year:012

CF:(1.6)10(10)

r =25.0%

NPV =0.00

NPV

r$0.0

0%(1.60)

25%0.00

50%0.62

75%0.85

100%0.90Max.

125%0.87

150%0.80

175%0.71

200%0.62

225%0.53

250%0.44

275%0.36

300%0.28

325%0.20

350%0.13

375%0.06

400%0.00

425%(0.06)

450%(0.11)

475%(0.16)

500%(0.21)

525%(0.26)

550%(0.30)


WACC =10%

Project S12.11%

10%11.33%

01234

(1,000)500400300100

Project L

01234

(1,000)100300400600

440.0

363.0

133.1






Project S

WACC =10%

01234

(1,000)500400300100

330.0

484.0



PV of TV$1,078.82



Project S

IRR =14.49%

01234

(1,000)500400300100

343.5

524.3



PV of TV$1,000.00





For project S:


PI(S) =$1,078.82$1,000.00

PI(S) =1.079

For project L:


PI(L) =$1,049.18$1,000.00

PI(L) =1.049

Payback Period



Project SYear:01234

|||||

Cash flow:-1,000500400300100



Payback =2.33

Project LYear:01234

|||||

Cash flow:-1,000100300400600



Payback =3.33



WACC =10%


Project SYear:01234

|||||

Cash flow:-1,000500400300100





Project LYear:01234

|||||

Cash flow:-1,000100300400600








r =11.5%


Project C:

Year (t)0123456

-$40,000$8,000$14,000$13,000$12,000$11,000$10,000

$7,16517.5%

Project F:

Year (t)0123

-$20,000$7,000$13,000$12,000

$5,39125.2%


Year (t)0123456

-$20,000$7,000$13,000$12,000

-$20,000$7,000$13,000$12,000

-$20,000$7,000$13,000-$8,000$7,000$13,000$12,000

$9,28125.2%





NPVC=7,165

NPVF=5,391



EEAF=2,225





0($4,800)$4,800

1$2,000$3,000

2$2,000$1,650

3$1,750$0



=($4,800.00)+$4,785.88+$0.00

3-Year NPV =($14.12)



=($4,800.00)+$3,471.07+$1,363.64

2-Year NPV =$34.71


=($4,800.00)+$1,818.18+$2,727.27

1-Year NPV =($254.55)

Chapter

-1.6

0

0.6222222222

0.8489795918

0.9

0.8691358025

0.8

0.7140495868

0.6222222222

0.5301775148

0.4408163265

0.3555555556

0.275

0.1993079585

0.1283950617

0.0620498615

0

-0.0580498866

-0.1123966942

-0.1633270321

-0.2111111111

-0.256

-0.2982248521


Sheet1

300400

180.4237946123206.5034630632

134.4046591185134.4046591185

78.819752749149.1769687863

46.10444213440.000000002

0-68.0175364364

-8.3297300967-80.1419377432

-83.7191358025-187.5

-149.44-277.44


Project S

WACC

NPV


0

0.05

0.0716727998

0.1

0.1179055563

0.1448884428

0.15

0.2

0.25

300

180.4237946123

134.4046591185

78.8197527491

46.1044421344

0

-8.3297300967

-83.7191358025

-149.44

NPVs

Project S

Project L

WACC

NPV


12.2

NPV for Project S

10%

01234

S's CFs-1000500400300100

-1000

454.55

330.58

225.39

68.30

$78.82

NPV for Project L

10%

01234

L's CFs-1000100300400600

-1000

90.91

247.93

300.53

409.81

$49.18

NPVs

NPVL

Crossover = 7.17%

IRRS = 14.49%

%

Accept

Reject

Conflict

No conflict

The NPV, if k=25%.

12.3

SECTION 12.2


WACC9%

Year (t)

0-$500

1$200

2$200

3$400

NPV =$160.70

12.5

SECTION 12.3


Year (t)

0-$500

1$200

2$200

3$400

IRR =24.1%

12.6

SECTION 12.5


Project

Year (t)CFs

0-$1,100

1$2,100

2$2,100

3-$3,600



NPV with r = 0%:($500.00)

12.7

SECTION 12.6



Year (t)

0-$500

1$200

2$200

3$400

MIRR =19.9%

12.8

SECTION 12.7


WACC9%

Year (t)

0-$500

1$200

2$200

3$400

PI =1.32

SECTION 12.8


Year:0123

Cash flow:(500)200200400

Cumulative CF:(500)(300)(100)300



r =9%

Year:0123

Cash flow:(500)200200400





CH12 TOOLKIT

3/19/09



Expected after-tax



0($1,000)($1,000)

1500100

2400300

3300400

4100600



Project S:01234

|||||

-$1,000$500$400$300$100

Project L:01234

|||||

-$1,000$100$300$400$600



Project

SL

NPV:$78.82$49.18

IRR:14.5%11.8%

MIRR:12.1%11.3%

PI:1.081.05



r =10%

Project S


Cash flow:(1,000)500400300100

Disc. cash flow:(1,000)45533122568


Project L

Time period:01234

Cash flow:(1,000)100300400600

Disc. cash flow:(1,000)91248301410





Expected after-tax







4100600



NPV Profiles


Net Cash Flows



1$500$100NPV =$78.82$49.18

2$400$300IRR =14.49%11.79%

3$300$400Crossover =7.17%

4$100$600


Project NPVs

SL

WACC$78.82$49.18

0%$300.00$400.00

5%$180.42$206.50

7.17%$134.40$134.40

10%$78.82$49.18

11.79%$46.10$0.00

14.49%$0.00-$68.02

15.0%-$8.33-$80.14

20%-$83.72-$187.50

25%-$149.44-$277.44














0($1,000)($1,000)0




4100600(500)S - L =$0.00







Project M:Year:012

CF:(1.6)10(10)


IRR M 1 =25.0%

IRR M 2 =400%


Project M:Year:012

CF:(1.6)10(10)

r =25.0%

NPV =0.00

NPV

r$0.0

0%(1.60)

25%0.00

50%0.62

75%0.85

100%0.90Max.

125%0.87

150%0.80

175%0.71

200%0.62

225%0.53

250%0.44

275%0.36

300%0.28

325%0.20

350%0.13

375%0.06

400%0.00

425%(0.06)

450%(0.11)

475%(0.16)

500%(0.21)

525%(0.26)

550%(0.30)



WACC =10%


10%MIRRL =11.33%

01234

(1,000)500400300100

Project L

01234

(1,000)100300400600

440.0

363.0

133.1






Project S

WACC =10%

01234

(1,000)500400300100

330.0

484.0



PV of TV$1,078.82



Project S

IRR =14.49%

01234

(1,000)500400300100

343.5

524.3



PV of TV$1,000.00






For project S:


PI(S) =$1,078.82$1,000.00

PI(S) =1.079

For project L:


PI(L) =$1,049.18$1,000.00

PI(L) =1.049


Payback Period



Project SYear:01234

|||||

Cash flow:-1,000500400300100



Payback =2.33

Project LYear:01234

|||||

Cash flow:-1,000100300400600



Payback =3.33



WACC =10%


Project SYear:01234

|||||

Cash flow:-1,000500400300100





Project LYear:01234

|||||

Cash flow:-1,000100300400600









r =11.5%


Project C:

Year (t)0123456

CH12

Documents

Transcript of CH12