fundamental of corporate finance,chpt9

8/3/2019 Fundamental of Corporate Finance,chpt9

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Chapter 9

Net Present Value and Other

Investment Criteria

Prepared and Taught by Lecturer : YIN SOKHNG

E-mail: [email protected]

Tel:(855) 16889872 / 17989972

Chapter Outline

9.1 Net Present Value (NPV)

9.2 The Payback Rule (PR)

9.3 The Discounted Payback Period Rule (DPR)

9.4 The Average Accounting Return (AAR)

9.5 The Internal Rate of Return (IRR)

9.6 The Profitability Index (PI)

9.7 The Practice of Capital Budgeting

2Instructed by YIN SOKHENG, Master in Finance

3

Accepting positive NPV projects benefits

shareholders.NPV uses cash flows

NPV uses all the cash flows of the project

NPV discounts the cash flows properly

The difference between the market value of aproject and its cost

How much value is created from undertakingan investment?

9.1 Net Present Value

Instructed by YIN SOKHENG, Master in Finance


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The Net Present Value (NPV) Rule

Net Present Value (NPV) =Initial Investment (costs)

+ PV of future CFs

Estimating NPV: 1. Estimate initial costs

2. Estimate future cash flows: how much? and when?

3. Estimate discount rate

Minimum Acceptance Criteria: Accept if NPV > 0

Ranking Criteria: Choose the highest NPV


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Good Attributes of the NPV Rule

1. Uses cash flows

2. Uses ALL cash flows of the project

3. Discounts ALL cash flows properly

Reinvestment assumption: the NPV rule

assumes that all cash flows can be reinvested

at the discount rate.


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For example of NPV

Year Cash flow (net income)

0 $9,0001 6,000

2 4,000

3 3,000

4 2,000

Initial cash flow = $9,000; IR = 10%; Do you

Recommend this project?



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For example of NPV

PV = 6,000 /(1.1) + 4,000 /(1.1)2 + 3,000

/(1.1)3 + 2,000 /(1.1)4 = $12,377

NPV = $12,3779,000 = $3,377

EX2: IBM Company has two projects to invest:

1. Project (A) is initial cost of $350,000 and

cash inflow in year one is $400,000

2. Project (B) invests in treasury bill with 7%

of interest rate, Do you recommend?


8

For example of NPV

PV of Project (B)= 400,000 / (1.07) =

$373,832

NPV = $373,832350,000 = $23,832

Invest in project (A) is best


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9.2 The Payback Period

How long does it take the project to pay

back its initial investment?

Computation

Estimate the cash flows

Subtract the future cash flows from the initial cost

until the initial investment has been recovered

Payback Period = number of years to recover

initial costs



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The Payback Period Rule

Decision RuleAccept if the payback

period is less than some preset limit Minimum Acceptance Criteria:

set by management

Ranking Criteria:

set by management


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The Payback Period Rule

Disadvantages:

Ignores the time value of money

Ignores cash flows after the payback period

Biased against long-term projects

Requires an arbitrary acceptance criteria

A project accepted based on the payback criteriamay not have a positive NPV

Advantages:

Easy to understand Biased toward liquidity


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Computing Payback For The

Project

Assume we will accept the project if it pays

back within two years.

Year 1: 165,00063,120 = 101,880 still to recover

Year 2: 101,88070,800 = 31,080 still to recover

Year 3: 31,08091,080 = -60,000project pays

back in year 3

Do we accept or reject the project?



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Payback Period

Assume ABC Co. plans to invest in a project

that has a $50,000 initial outlay. It is estimatedthat the project will provide regular cashinflows of $30,000 in year 1, $20,000 in year 2,

$10,000 in year 3, and $5,000 in year 4.

Payback period = 2 years


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For example of Payback period

Year A B C D E

0 -100 -200 -200 -200 -50

1 30 40 40 100 100

2 40 20 20 100 -50,000

3 50 10 10 10 -200

4 60 130 200


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For example of Payback period

Payback period (A) = 2 years + (10070 )/ 50 = 2.6 years

Payback period (B) = Never payback

Payback period ( C) = 4 years

Payback period (D) = 2 years

Payback period (E) = 6 months



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9.3 The Discounted Payback

Period Rule

How long does it take the project to pay

back its initial investment taking the timevalue of money into account?

By the time you have discounted the cash

flows, you might as well calculate the NPV.


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9.4 The Average Accounting Return Rule

Another attractive but fatally flawed approach.

Ranking Criteria and Minimum Acceptance Criteriaset by management

Disadvantages: Ignores the time value of money

Uses an arbitrary benchmark cutoff rate

Based on book values, not cash flows and market values

Advantages: The accounting information is usually available

Easy to calculate


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InvestentofValueBookAverage

IncomeNetAverageAAR

Book value is a started investment

Average book value of Investment

= a stated investment / 2

Decision Rule: Accept the project if the AARis greater than a preset rate.



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Computing AAR For The Project

Assume we require an average accounting

return of 25%

Average Net Income:

(13,620 + 3,300 + 29,100) / 3 = 15,340

AAR = 15,340 / 72,000 = .213 = 21.3%

Do we accept or reject the project?


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Example of AAR

Assume we require an average accounting return of25%

Assume that net earnings for the next 4 years areestimated to be $10,000, 15,000, $20,000, and$30,000, respectively. If the initial investment is$100,000, find the average rate of return

Average net earnings = 10,000 + 15,000 + 20,000 +30,000 / 4 = $18,750

Average Book value = 100,000 / 2 = $50,000

AAR = $18,750 / $50,000 = 37.5% Do we accept or reject the project?


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9.5 The Internal Rate of Return (IRR)

Rule IRR: the discount that sets NPV to zero

Minimum Acceptance Criteria: Accept if the IRR exceeds the required return.

Ranking Criteria: Select alternative with the highest IRR

Reinvestment assumption: All future cash flows assumed reinvested at the IRR.

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

Advantages: Easy to understand and communicate



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The Internal Rate of Return:

ExampleConsider the following project:

0 1 2 3

$50 $100 $150

-$200

The internal rate of return for this project is 19.44%

32 )1(

150$

)1(

100$

)1(

50$0

IRRIRRIRRNPV


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The NPV Payoff Profile for This Example

Discount Rate NPV

0% $100.00

4% $71.04

8% $47.32

12% $27.79

16% $11.65

20% ($1.74)

24% ($12.88)

28% ($22.17)

32% ($29.93)36% ($36.43)

40% ($41.86)

If we graph NPV versus discount rate, we can see the

IRR as the x-axis intercept.

IRR = 19.44%

($60.00)($40.00)

($20.00)

$0.00

$20.00

$40.00

$60.00

$80.00

$100.00

$120.00

-1% 9% 19% 29% 39%

NPV

Discount rate


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Problems with the IRR Approach

Multiple IRRs. Are We Borrowing or Lending?

The Scale Problem

The Timing Problem



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Multiple IRRs

There are two IRRs for this project:

0 1 23

$200 $800

-$200 - $800

($150.00)

($100.00)

($50.00)

$0.00

$50.00

$100.00

-50% 0% 50% 100% 150% 200%

Discount rate

NPV

100% = IRR2

Which one

should we use?

0% = IRR1


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The Scale Problem

Would you rather make 100% or 50% on your

investments?

What if the 100% return is on a $1 investment

while the 50% return is on a $1,000

investment?


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The Timing Problem

0 1 2 3

$10,000 $1,000 $1,000

-$10,000

Project A

0 1 2 3

$1,000 $1,000 $12,000

-$10,000

Project B

The preferred project in this case depends on the discount rate, not

the IRR.



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The Timing Problem

($4,000.00)

($3,000.00)

($2,000.00)

($1,000.00)

$0.00

$1,000.00

$2,000.00

$3,000.00

$4,000.00

$5,000.00

0% 10% 20% 30% 40%

Discount rate

NPV

Project A

Project B10.55% = crossoverrate

16.04% = IRRA12.94% = IRRB


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Calculating the Crossover RateCompute the IRR for either project A-B or B-A

Year Project A Project B Project A-B Project B-A

0 ($10,000) ($10,000) $0 $0

1 $10,000 $1,000 $9,000 ($9,000)

2 $1,000 $1,000 $0 $0

3 $1,000 $12,000 ($11,000) $11,000

($3,000.00)($2,000.00)

($1,000.00)

$0.00

$1,000.00

$2,000.00

$3,000.00

0% 5% 10% 15% 20%

Discount rate

NPV A-B

B-A

10.55% = IRR


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Mutually Exclusive vs.

Independent Project

Mutually Exclusive Projects: only ONE of several

potential projects can be chosen, e.g. acquiring anaccounting system.

RANK all alternatives and select the best one.

Independent Projects: accepting or rejecting oneproject does not affect the decision of the otherprojects. Must exceed a MINIMUM acceptance criteria.



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IRR and Mutually Exclusive

Projects

Mutually exclusive projects

If you choose one, you cant choose the other

Example: You can choose to attend graduate

school next year at either Harvard or Stanford, but

not both

Intuitively you would use the following

decision rules:

NPVchoose the project with the higher NPV

IRRchoose the project with the higher IRR


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Example With Mutually Exclusive Projects

Period Project A Project B

0 -500 -400

1 325 325

2 325 200

IRR 19.43% 22.17%

NPV 64.05 60.74

The required

return for both

projects is 10%.

Which project

should you

accept and why?


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9.6 The Profitability Index (PI) Rule

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

InvestentInitial

FlowsCashFutureofPVTotalPI



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9.7 The Practice of Capital Budgeting

Varies by industry:

Some firms use payback, others use accounting

rate of return.

The most frequently used technique for large

corporations is IRR or NPV.


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Example of Investment Rules

Compute the IRR, NPV, PI, and payback period for the

following two projects. Assume the required return is

10%.

Year Project A Project B

0 -$200 -$150

1 $200 $50

2 $800 $100

3 -$800 $150


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Project A Project BCF0 -$200.00 -$150.00

PV0 of CF1-3 $241.92 $240.80

NPV = $41.92 $90.80

IRR = 0%, 100% 36.19%

PI = 1.2096 1.6053



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Payback Period:

Project A Project B

Time CF Cum. CF CF Cum. CF

0 -200 -200 -150 -150

1 200 0 50 -100

2 800 800 100 0

3 -800 0 150 150

Payback period for project B = 2 years.

Payback period for project A = 1 or 3 years?


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Relationship Between NPV and IRR

Discount rate NPV for A NPV for B

-10% -87.52 234.77

0% 0.00 150.00

20% 59.26 47.92

40% 59.48 -8.60

60% 42.19 -43.07

80% 20.85 -65.64

100% 0.00 -81.25120% -18.93 -92.52


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Project AProject B

($200)

($100)

$0

$100

$200

$300

$400

-15% 0% 15% 30% 45% 70% 100% 130% 160% 190%

Discount rates

N

PV

IRR 1(A) IRR (B)

NPV Profiles

Cross-over Rate

IRR 2(A)


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