unit 11 capital budgeting tool kit

8/8/2019 Unit 11 Capital Budgeting Tool Kit

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A B C D E F G H I J K L M N O P Q R S T U V W

Unit 11

Project S

Year (t) Project S Project L 0 1 2 3 4

0 ($1,000) ($1,000) (1,000) 500 400 300 100

1 500 100

2 400 300 Project L

3 300 4004 100 600 0 1 2 3 4

(1,000) 100 300 400 600

Capital Budgeting Decision Criteria

Payback Period

Project S

Time period: 0 1 2 3 4

Cash flow: (1,000) 500 400 300 100

Cumulative cash flow: (1,000) (500) (100) 200 300 Click fx > Logical > AND > OK to get dialog box.

FALSE FALSE FALSE TRUE FALSE Use Logical "AND" to determine Then specify you want TRUE if cumulative CF > 0 but the previous CF < 0.

0.00 0.00 0.00 2.33 0.00 the first positive cumulative CF.There will be one TRUE.

Payback: 2.33 Use Logical IF to find the PaybackClick fx > Logical > IF > OK. Specify that if true, the payback is the previous year plus a fraction, if false, then 0.

Use Statistical Max function to Click fx > Statistical > MAX > OK > and specify range to find Payback.

Alternative calculation: 2.33 display payback.

Project L


Cash flow: (1,000) 100 300 400 600

Cumulative cash flow: (1,000) (900) (600) (200) 400

Payback: 3.33 Uses IF statement.

In this file we use Excel to do most of the calculations explained in Chapter 10. 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, in a table with columns, or horizontally, using time lines. For short problems, with just a few years,

we generally use the time line format because rows can be added and we can set the problem up as a series of income

statements. For long problems, it is often more convenient to use a tabular layout.

Here are the five key methods used to evaluate projects: (1) payback period, (2) discounted payback period, (3) net

present value, (4) internal rate of return, and (5) modified internal rate of return. Using these criteria, financial

'analysts seek to identify those projects that will lead to the maximization of the firm's stock price.

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 i n 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.

Tool Kit for The Basics of Capital Budgeting: Evaluating Cash Flows

Expected after-tax

net cash flows (CF t)


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Discounted Payback Period

WACC = 10%

Project S


Cash flow: (1,000) 500 400 300 100

Disc. cash flow: (1,000) 455 331 225 68 Cash Flows Discounted back at 10%.

Disc. cum. cash flow: (1,000) (545) (215) 11 79

Discounted Payback: 2.95 Uses IF statement.

Project L


Cash flow: (1,000) 100 300 400 600

Disc. cash flow: (1,000) 91 248 301 410

Disc. cum. cash flow: (1,000) (909) (661) (361) 49

Discounted Payback: 3.88 Uses IF statement.

Net Present Value (NPV)

WACC = 10%

Project S


Cash flow: (1,000) 500 400 300 100

Disc. cash flow: (1,000) 455 331 225 68

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

Project L


Cash flow: (1,000) 100 300 400 600

Disc. cash flow: (1,000) 91 248 301 410

NPV(L) = $49.18 49.18$ = 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%.

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.

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 wouldonly accept Project S if they are mutually exclusive.

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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Internal Rate of Return (IRR)

Year (t) Project S Project L

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

1 500 100 IRR S = 14.49% payments occur at end of

2 400 300 IRR L = 11.79% periods, so that function does

3 300 400 not have to be adjusted.4 100 600

Expected after-tax

The internal rate of return is defined as the discount rate that equates the present value of a project's cash inflows to

its outflows. In other words, the internal rate of return is the interest rate that forces NPV to zero. The calculation

for IRR can be tedious, but Excel provides an IRR function that merely requires you to access the function and

enter the array of cash flows. The IRR's for Project S and L are shown below, along with the data entry for Project

S.

net cash flows (CF t)

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 project s should bechosen 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 mustspecify all cashflows, including the time zerocash flow. This is in contrastto the NPV function, in whichyou specify only the futurecash flows.


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Multiple IRR's

Consider the case of Project M.

Project M: 0 1 2

(1.6) 10 (10)

IRR M1

= 25.0%

IRR M2

= 400%

Project M: 0 1 2

(1.6) 10 (10)

r = 25.0%NPV = 0.00

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.

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 calculator,

you would get an error message. The HP-10B says "Error - Soln", the HP-17B says '"Many/No Solutions, and the HP12C says

Error 3; Key in Guess" when such a project is evaluated. The procedure for correcting the problem isto store in a guess for the

IRR, and then the calculator will report the IRR that is closest to your guess. You can then use a different "guess" value, and

you should be able to find the other IRR. However, the nature of the mathematics creates a scenario in which one IRR is quite

extraordinary (often a few hundred percent).

We will solve this IRR twice, the first time using the default guess of 10%, and the second time we will enter a guessof 300%. Notice, that the first IRR calculation is exactly as it was above.


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NPV

r $0.0

0% (1.60)

25% 0.00

50% 0.62

75% 0.85

100% 0.90 Max.

125% 0.87

150% 0.80

175% 0.71

200% 0.62

225% 0.53

250% 0.44

275% 0.36300% 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)

NPV Profiles

Y ea r P ro jec t S P ro je ct L WACC = 10.0%

0 -$1 ,0 00 -$1 ,0 00 Project S Project L

1 $500 $100 NPV = $78.82 $49.182 $400 $300 IRR = 14.49% 11.79%

3 $300 $400 Crossover 7.17%

4 $100 $600

Data Table used to make graph:

S L

WACC $78.82 $49.18

0% $ 30 0.00 $ 40 0.00

5% $ 18 0.42 $ 20 6.50

7.17% $ 13 4.40 $ 13 4.40

10% $78.82 $49. 18

11.79% $46.10 $0.00

14.49% $ 0. 00 - $6 8. 02

15.0% - $8 .3 3 - $8 0. 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, conflict s 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.

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

Project NPVs

-$2.00

-$1.50

-$1.00

-$0.50

$0.00

$0.50

$1.00

$1.50

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

Multiple Rates of Return

-$200

-$100

$0

$100

$200

$300

$400

0% 5% 10% 15% 20% 25%

NPV

WACC

Project S'sNPV Profile

-$400

-$200

$0

$200

$400

$600

0% 5% 10% 15% 20% 25%

NPV

WACC

Both Projects' Profiles

NPVsNPVL

Crossover= 7.17%IRRS = 14.49%

Accept Reject

ConflictNo conflict


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Expected after-tax

net cash flows (CF t) Cash flow Alternative: Use Tools > Goal Seek to find WACC when NPV(S) =

Year (t) Project S Project L differential NPV(L). Set up a table to show the difference in NPV's, which we

0 ($1,000) ($1,000) 0 want to be zero. The following will do it, getting WACC = 7.17%.

1 500 100 400 Look at B57 for the answer, then restore B57 to 10%.

2 400 300 100 NPV S = 78.82$

3 300 400 (100) NPV L = 49.18$4 100 600 (500) S - L = 29.64$

IRR = Crossover rate = 7.17%

Modified Internal Rate of Return (MIRR)

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 capital of 14% and 12%, respectively. Not coincidently, those are the IRR's of the projects. 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.

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 case) also has the greater NPV. But at costs of capital less than the crossover point, the

project 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 7%.

Luckily, there is a more precise way of determining crossover. To find crossover, we will find the difference betweenthe two projects 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, Project 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.

G277


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WACC = 10% MIRRS = 12.11%

Project S MIRRL = 11.33%

10%

0 1 2 3 4

(1,000) 500 400 300 100

Project L

0 1 2 3 4

(1,000) 100 300 400 600

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 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 indeeddoes assume reinvestment at the WACC, and IRR at the IRR.

B304:F304

B300

B300


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Project S

WACC = 10%

0 1 2 3 4

(1,000) 500 400 300 100

330.0

484.0 Reinvestment at WACC = 10%

665.5PV outflows -$1,000.00 Terminal Value: 1,579.5

PV of TV $1,078.82NPV 78.82$ Thus, we see that the NPV is consistent with reinvestment at WACC.

Now repeat the process using the IRR, which is G118 as the discount rate.

Project S

IRR = 14.49%

0 1 2 3 4

(1,000) 500 400 300 100

343.5

524.3 Reinvestment at IRR = 14.49%

750.3

PV outflows -$1,000.00 Terminal Value: 1,718.1

PV of TV $1,000.00NPV $0.00 Thus, 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)

For project S:

PI(S) = PV of future cash flows Initial costPI(S) = 1,078.82$ 1,000.00$

PI(S) = 1.079

For project L:

PI(L) = PV of future cash flows Initial cost

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

PI(L) = 1.049

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

unequal lives by equalizing their lives by assuming that each project can be repeated as many times as necessary to reach a

common life span. The NPVs over this life span are then compared, and the project with the higher common life NPV is chosen.

To illustrate, suppose a firm is considering two mutually exclusive projects, either a conveyor system (Project C) or a fleet of

forklift trucks (Project F) for moving materials. The firm's cost of capital is 12%. The cash flow timelines are shown below,

'along with the NPV and IRR for each project.

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.


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Project C WA CC : 1 1. 5%

0 1 2 3 4 5 6

($40,000) $8,000 $14,000 $13,000 $12,000 $11,000 $10,000

NPV $7,165

IRR 17.5%

Project F

0 1 2 3

($20,000) $7, 000 $13,000 $12,000

NPV $5,391IRR 25.2%

Common Life Approach

Project C

0 1 2 3 4 5 6

($40,000) $8,000 $14,000 $13,000 $12,000 $11,000 $10,000

NPV $7,165IRR 17.5%

Project F

0 1 2 3 4 5 6

($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

NPV $9,281IRR 25.2%

Equivalent Annual Annuity (EAA) Approach (See the Chapter 10 Web Extension for details.)

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.

EE AC = 1 ,7 18 No te : w e us ed t he F unc ti on W iza rd f or t he P MT f unc ti on.

EEAF= 2,225

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

ECONOMIC LIFE VS. PHYSICAL LIFE

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).

Initially, it would appear that Project C is the better investment, based upon its higher NPV. However, if the firm chooses

Project F, it would have the opportunity to make the same investment three years from now. Therefore, we must reevaluate

Project F 'using extended common life of 6 years. The time lines are shown below. Note that only F's is changed.

End of Period:

End of Period:

End of Period:

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 terminated and the asset sold at the end of any year. The following table

shows the operating cash flows and the salvage value for each year-- all values are shown on an after-tax

basis.


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Year

Operating

Cash Flow

Salvage

Value

0 ( $4 ,8 00 ) $4 ,8 00

1 $2,000 $3,000

2 $2,000 $1,650

3 $1,750 $0

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)


PV of

Operating

Cash Flow+

PV of

Salvage

Value

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

2-Year NPV = $34.71


PV of

Operating

Cash Flow+

PV of

Salvage

Value

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

1-Year NPV = ($254.55)

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.

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

unit 11 capital budgeting tool kit

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