Capital Budgeting Criteria for Investments Projects Mutually Exclusive versus Independent Project

Jacoby, Stangeland and Wajeeh, 2000

1

Capital Budgeting Criteria for Investments Projects

Mutually Exclusive versus Independent Project

Mutually Exclusive Projects: only ONE of several potential projects can be chosen, e.g. acquiring an accounting system.

RANK all alternatives and select the best one.

Independent Projects: accepting or rejecting one project does not affect the decision of the other projects.

Must exceed a MINIMUM acceptance criteria.

Chapter 6


2

The Net Present Value (NPV) Rule

Net Present Value (NPV) =

Total PV of future CF’s - Initial Investment

Estimating NPV: 1. Estimate future cash flows: how much? and when? 2. Estimate discount rate 3. Estimate initial costs

Minimum Acceptance Criteria:

Accept if: NPV > 0

Ranking Criteria: Choose the highest NPV


3

NPV - An Example

Assume you have the following information on

Project X:

Initial outlay -$1,100 Required return = 10%

Annual cash revenues and expenses are as follows:

Year Revenues Expenses

1 $1,000 $500

2 2,000 1,300

3 2,200 2,700

4 2,600 1,400

Draw a time line and compute the NPV of project X.

4

The Time Line & NPV of Project X0 1 2

Initial outlay($1,100)

Revenues $1,000Expenses 500

Cash flow $500

Revenues $2,000Expenses 1,300

Cash flow $700

– $1,100.00

+454.54

+578.51

-375.66

+819.62

1$500 x 1.10

1$700 x 1.10

2

3


Cash flow (500)

1- $500 x 1.10

3

4


Cash flow $1,200

1$1,200 x 1.10

4

NPV = -C0 + PV0(Future CFs)= -C0 + C1/(1+r) + C2/(1+r)2 + C3/(1+r)3 + C4/(1+r)4

= - + + + +

= $377.02 > 0

5

First, clear previous data, and check that your calculator is set to 1 P/YR:NPV in your HP 10B Calculator

CFj

I/YR

Key in CF0

Key in CF4

Key in r

Key in CF3 +/- CFj500

1,200

CFjKey in CF1500

CFjKey in CF2700

+/- CFj1,100

The display should show: 1 P_YrInput data (based on above NPV example)

Display should show: CF 0





PRCNPV

Compute NPVDisplay should show:

377.01659723

10

Yellow

YellowC

C ALL


6

The Payback Period Rule

How long does it take the project to “pay back” its initial investment?

Payback Period = # of years to recover costs of project

Minimum Acceptance Criteria: set by management

Ranking Criteria: set by management


7

Discounted Payback - An Example

Initial outlay -$1,000r = 10%

PV of Year Cash flow Cash flow 1 $ 200 $ 182 2 400 331 3 700 526 4 300 205

Accumulated Year discounted cash flow 1 $ 182 2 513 3 1,039 4 1,244

Discounted payback period is just under 3 years


8

Average Accounting Return (AAR)

You want to invest in a machine that produces squash balls. The machine costs $90,000.

The machine will ‘die’ after 3 years (assume straight line depreciation, the annual depreciation is $30,000).

You estimate for the life of the project:

Year 1 Year 2 Year 3

Sales 140 160 200

Expenses 120 100 90

EBD 20 60 110


9

Year 1 Year 2 Year 3

Sales 140 160 200

Expenses 120 100 90

E.B.D.

Depreciation

E.B.T.

Taxes (40%)

NI:

Calculating Projected NI


10

We calculate:

(i) Average NI =

(ii) Average book value (BV) of the investment (machine):

time-0 time-1 time-2 time-3

BV of investment: 90 60 30 0

=> Average BV = (divide by 4 - not 3)

(iii) The Average Accounting Return:

AAR = = 44.44%

Conclusion: If target AAR < 44.44% => accept

If target AAR > 44.44% => reject

203

603

48186

454

0306090

4520


11

The Internal Rate of Return (IRR) Rule

IRR: the discount rate that sets the NPV to zero Minimum Acceptance Criteria:

Accept if: IRR > required return

Ranking Criteria: Select alternative with the highest IRR

Reinvestment assumption: the IRR calculation assumes that all future cash flows are reinvested at the IRR

Disadvantages: Does not distinguish between investing and financing IRR may not exist or there may be multiple IRR Problems with mutually exclusive investments

Advantages: Easy to understand and communicate


12

Internal Rate of Return - An Example

Initial outlay = -$2,200

Year Cash flow

1 800 2 900 3 500 4 1,600

Find the IRR such that NPV = 0

0 = - + + + + (1+IRR)1 (1+IRR)2 (1+IRR)3 (1+IRR)4

Or:

800 900 500 1,600

2,200 = + + + (1+IRR)1 (1+IRR)2 (1+IRR)3 (1+IRR)4


13

First, clear previous data, and check that your calculator is set to 1 P/YR:IRR in your HP 10B Calculator

CFj

CFj500

1,600

CFj800

CFj900

+/- CFj2,200







CSTIRR/YR

Compute IRRDisplay should show:

23.29565668%Yellow

Key in CF0

Key in CF4

Key in CF3

Key in CF1

Key in CF2

YellowC

C ALL


14

The NPV Profile

Discount rates NPV

0% $1,600.00

5% 1,126.47

10% 739.55

15% 419.74

20% 152.62

25% -72.64

IRR is between 20% and 25% -- about 23.30%

If required rate of return (r) is lower than IRR => accept the project (e.g. r = 15%)

If required rate of return (r) is higher than IRR => reject the project (e.g. r = 25%)

Internal Rate of Return and the NPV Profile


15

Year Cash flow

0 – $2,200 1 800 2 900 3 500 4 1,600

The Net Present Value Profile

Discount rate2% 6% 10

%14% 18%

1,600.00

1,126.47

739.55

419.74

Net present value

159.62

– 72.64 22%

IRR=23.30%

0


16

IRR: Investment vs. Financing Project

Initial outlay = $4,000

Year Cash flow

1 -1,200 2 -800 3 -3,500

Find the IRR such that NPV = 0

0 = + + + (1+IRR)1 (1+IRR)2 (1+IRR)3

Or:

-1,200 -800 -3,500

- 4,000 = + + (1+IRR)1 (1+IRR)2 (1+IRR)3


17

The NPV Profile of a Financing Project:

Discount rates NPV

0% -$1,500.00

5% -891.91

10% -381.67

15% 50.2

20% 418.98

IRR is between 10% and 15% -- about 14.37%

For a Financing Project, the required rate of return is the cost of financing, thus

If required rate of return (r) is lower than IRR => reject the project (e.g. r = 10%)

If required rate of return (r) is higher than IRR => accept the project (e.g. r = 15%)

Internal Rate of Return and the NPV Profile for a Financing Project

18

The NPV Profile for a Financing Project

-$2,000.00

-$1,500.00

-$1,000.00

-$500.00

$0.00

$500.00

$1,000.00

$1,500.00

$2,000.00

0% 5% 10% 15% 20% 25% 30% 35% 40% 45%

Rate of Return (%)

NP

V (

$)


19

Assume you are considering a project for which the cash flows are as follows:

Year Cash flows

0 -$900

1 1,200

2 1,300

3 -1,200

Multiple Internal Rates of Return

Example 1

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-$1,000.00

-$800.00

-$600.00

-$400.00

-$200.00

$0.00

$200.00

$400.00

$600.00

-60% -40% -20% 0% 20% 40% 60% 80% 100% 120% 140%

Rate of Return (%)

NP

V (

$)Multiple IRRs and the NPV Profile - Example 1

IRR2=72.25%IRR1=-29.35%

21

First, clear previous data, and check that your calculator is set to 1 P/YR:Multiple IRRs in your HP 10B Calculator

CFj1,200

CFj1,200

CFj1,300

+/- CFj900






CSTIRR/YR

Compute 1st IRRDisplay should show:

72.252175%Yellow

+/-

CSTIRR/YR

Compute 2nd IRR by guessing it first

Display should show: -29.352494%

Yellow30 +/- RCLSTO

Yellow

Key in CF0

Key in CF3

Key in CF1

Key in CF2

YellowC

C ALL


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Year Cash flows

0 -$260

1 250

2 300

3 20

4 -340


Example 2

23

-$80.00

-$70.00

-$60.00

-$50.00

-$40.00

-$30.00

-$20.00

-$10.00

$0.00

$10.00

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Rate of Return (%)

NP

V (

$)Multiple IRRs and the NPV Profile - Example 2

IRR1=11.52%IRR2=29.84%


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Year Cash flows

0 $660

1 -650

2 -750

3 -50

4 850


Example 3


25

-$50.00

$0.00

$50.00

$100.00

$150.00

$200.00

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Rate of Return (%)

NP

V($

)Multiple IRRs and the NPV Profile - Example 3

IRR1=8.05%IRR2=33.96%


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-200

-150

-100

-50

0

50

100

150

200

0% 5% 10% 15% 20% 25% 30% 35% 40% 45%

Rate of Return (%)

NP

V (

$)

Project A Project B

IRR, NPV, and Mutually Exclusive Projects

Year

0 1 2 3

4

Project A: – $350 50 100 150 200

Project B: – $250 125 100 75 50%80.17BIRR

%91.12AIRR


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-200

-150

-100

-50

0

50

100

150

200

0% 5% 10% 15% 20% 25% 30% 35% 40% 45%

Rate o Return (%)

NP

V (

$)

Project A Project B Incremental (A-B)

IRR, NPV, and the Incremental Project Year

0 1 2 3

4

Project A: – $350 50 100 150 200

Project B: – $250 125 100 75 50

(A-B):

The Crossover Rate = IRRA-B = 8.07%


28

The Profitability Index (PI) Rule PI =

Total Present Value of future CF’s / Initial Investment Minimum Acceptance Criteria: Accept if PI > 1 Ranking Criteria: Select alternative with highest PI Disadvantages:

Problems with mutually exclusive investments Advantages:

May be useful when available investment funds are limited Easy to understand and communicate Correct decision when evaluating independent projects


29

Profitability Index - An Example

Consider the following information on Project Y:

Initial outlay -$1,100

Required return = 10%

Annual cash benefits:

Year Cash flows

1 $ 500

2 1,000

What’s the NPV? What’s the Profitability Index (PI)?


30

The NPV of Project Y is equal to:

NPV = (500/1.1) + (1,000/1.12) - 1,100 = ($454.54 + 826.45) - 1,100

= $1,280.99 - 1,100 = $180.99.

PI = PV Cashflows/Initial Investment

=

This is a good project according to the PI rule. Can you explain why?

Capital Budgeting Criteria for Investments Projects Mutually Exclusive versus Independent Project

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