1 southern illinois university“the nature of it outsourcing”april 2006 lecture 5-2: capital...

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Southern Illinois University “The Nature of IT Outsourcing” April 2006

Lecture 5-2: Lecture 5-2:

Capital Budgeting Techniques Capital Budgeting Techniques

Azerbaijan State Economic University

Principles of Finance

Instructor: Asif Shamilov

Spring 2010

Should we build this

plant?

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PF Lecture 5 “Capital Budgeting Techniques” Spring 2008

Profitability Index

• Profitability Index is the ratio of project PV to initial cost

or

.

Decision rule

Take the project if PI > 1

IO

PVPI IO

NPVPI 1

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Capital rationing

• Happens when the firm (or division) has a limited amount of capital to invest

• In the case of capital rationing, it is better to select projects based on the profitability index

• When funds are limited, a firm should choose those projects that give more for each dollar invested

• Rank projects based upon their PIs. Invest in the projects with the highest PIs until all capital is exhausted (provided PI > 1).

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Profitability Index Example

Suppose your division has been given a capital budget of $6,000. Which projects do you choose?

Project I NPV PI

A 1,000 600 1.6

B 4,000 2,000 1.5

C 6,000 2,400 1.4

D 3,000 600 1.2

E 5,000 500 1.1

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Profitability Index Example

• Suppose your budget increases to $7,000.

• Choosing projects in descending order of PIs no longer maximizes the aggregate NPV.

• Projects A and C provide the highest aggregate NPV = $3,000 and stay within budget.

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Strengths and Weaknesses of PI Method

• Strength- It measures the wealth created per dollar of initial outlay

• Weakness- It does not take into account any investments in future periods (PV index is better in this case)

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Example:

Project x Project y

Present value $25,000,000 $3,000

Initial cost $24,000,000 $1,000

PI 1.042 3

NPV $1,000,000 $2,000

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PI(x) < PI(y)

but

NPV(x) > NPV(y)

Example:

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IRR is the discount rate that forces PV of inflows equal to cost, and the NPV = 0:

In other words, IRR makes the present value of the

project equal to its initial cost.

n

0tt

t

) IRR 1 (CF

0

Internal Rate of Return (IRR)

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Decision rule:

Take the project If the IRR exceeds the required rate of return

If IRR > k, accept project.

If IRR < k, reject project.

• If projects are independent, accept both projects if IRR > k.

• If projects are mutually exclusive, accept one with the highest IRR

IRR Acceptance Criteria

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If IRR > the required rate of return, the

project’s rate of return is greater than its

costs. There is some return left over to boost

stockholders’ returns.

Rationale for the IRR method

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IRR Example

• Consider the company that has the opportunity to invest $100 million into the new equipment that will the following after-tax cash flows:

Then, the IRR is

Time 0 1 2 3-100.00 -50.00 30.00 200.00

NPV

IRR IRR IRR

100

50

1

30

1

200

102 3

IRR = 18.29%Therefore, accept the project if r<18.29%

IRR = 18.29%Therefore, accept the project if r<18.29%

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How is a project’s IRR similar to a bond’s YTM?

• They are the same thing.

• Think of a bond as a project. The YTM on the bond would be the IRR of the “bond” project.

• EXAMPLE: Suppose a 10-year bond with a 9% annual coupon sells for $1,134.20.

– Solve for IRR = YTM = 7.08%, the annual return for this project/bond.

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Strengths:• Many people find it a more intuitive measure than NPV• Usually gives the same signal as NPV

Weaknesses:• Reinvestment rate assumption is unrealistic (IRR method

assumes CFs are reinvested at IRR, whereas NPV method assumes CFs are reinvested at the required rate of return)

• Multiple IRR

Strengths and Weaknesses of IRR Method

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IRR Problems I:Borrowing or Lending?

• Consider the following two investment projects faced by a firm with k = 10%.

Both projects have an IRR = 40%, but only

project B is acceptable.– What is happening here?

Project 0 1 2 IRRB -5000 0 9800 40%C 5000 -9800 40%

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IRR Problems II: Multiple IRRs/No IRRs

Consider a firm with the following investment project and a discount rate of k= 25%.

Typical if investment at the end: a) Repair environmental damage b) Dismantling of machine

This project has two IRRs: one above k and the other below k. Which should be compared to the required rate of return?

Happens with the non-conventional cash flows

Year 0 1 2 IRR

A -5000 16000 -12000 100%, 20%

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IRR Problems III:Mutually Exclusive Projects with different time horizon

Consider the following two mutually exclusive projects.

The discount rate is k = 20%.

• Despite having a higher IRR, project A is less valuable than project B.

Project 0 1 2 IRR NPV(k=20%)

A -5,000 8,000 0 60% 1,667

B -5,000 0 9,800 40% 1,806

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• Consider the following two mutually exclusive projects:

– Project A has higher IRR– Project D has higher NPV at discount rates of 10%

or 20%

IRR Problems IV:Mutually Exclusive Projects with different scale

Project 0 1 2 IRR NPV @ 10% NPV @ 20%A -5000 8000 0 60% 2273 1667D -10000 15000 0 50% 3636 2500

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NPV Profiles

A graphical representation of project NPVs at various different costs of capital.

Year 0 1 2 3

Project L -100 10 60 80

Project S -100 70 50 20

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-10

0

10

20

30

40

50

60

0 5 10 15 20 23.6

NPV ($)

Discount Rate (%)

IRRL = 18.1%

IRRS = 23.6%

Crossover Point = 8.7%

k

0

5

10

15

20

NPVL

50

33

19

7

(4)

NPVS

40

29

20

12

5

S

L

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• If projects are independent, the two methods always lead to the same accept/reject decisions. If NPV says accept the IRR also says accept

• If projects are mutually exclusive …– If k > crossover point, the two methods lead to

the same decision and there is no conflict.– If k < crossover point, the two methods lead to

different accept/reject decisions.

Comparing the NPV and IRR methods

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• Size (scale) differences – the smaller project frees up funds at t = 0 for investment. The higher the opportunity cost, the more valuable these funds, so high k favors small projects.

• Timing differences – the project with faster payback provides more CF in early years for reinvestment. If k is high, early CF especially good, NPVS > NPVL.

Reasons why NPV profiles cross

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Conclusions

NPV has strong attractions:– based on cash flows– fully reflects time value of money– takes into account riskiness of project– gives clear go/no go answer

1 southern illinois university“the nature of it outsourcing”april 2006 lecture 5-2: capital...

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