Chapter 6: An Economic Appraisal Technique: PBP and ARR

Chapter 6: An Economic Appraisal Technique: PBP and ARR

23年 4月 21日 1Kim, GT IE of Chosun University

The Purpose of An Economic Appraisal

• An economic appraisal is a vein to accomplish a corporate objective.•In other words, it is commensurate with evaluating the corporate strategies so as to improve stockholders’ wealth by implementing a most desirable projects.•The types of investment projects; i) service (cost) projects: those which are with regard to reducing costs. (ex. A power plant may need to decide one fuel resource to generate electricity between gas and oil.)• ii) revenue projects: those which are concerned with increasing a firm’s revenue.(ex. A company may need to decide which one to produce to increase its profit or revenue between a HD and plain tv)•All projects need cash outflows at the outset and generates cash inflows in the following times.


Depending on whether or not the interest concept is involved.

- Appraisal techniques without interest involved.

(1) payback period(PB)

(2) accounting rate of return(ARR)

- Appraisal techniques with interest involved.

(1) net present value(NPV)

(2) annual equivalent value(AE)

(3) internal rate of return(IRR)

Appraisal Techniques


Depending on the final value of the results which are provided by the appraisal techniques

- appraisal techniques with an absolute value

i) conventional & discounted PB

ii) NPV

iii) AE

- appraisal techniques with a relative value

i) ARR

ii) IRR

Appraisal Techniques


Tech. %*Firm Size PER Debt Dividend Industry Ownership

Avg Small Big G NG H L Y N M NM L H

IRR 75.61 3.09 2.87 3.41 3.36 3.36 2.85 3.36 3.43 2.68 3.19 2.94 3.34 2.85

NPV 74.93 3.08 2.83 3.42 3.30 3.27 2.84 3.39 3.35 2.76 3.23 2.82 3.35 2.77

PB 56.74 2.53 2.72 2.25 2.55 2.41 2.58 2.46 2.46 2.63 2.68 2.33 2.39 2.70

MARR 56.94 2.48 2.13 2.95 2.78 2.87 2.27 2.63 2.84 2.06 2.60 2.29 2.70 2.12

SA 51.54 2.31 1.58 2.56 2.35 2.41 2.10 2.56 2.42 2.17 2.35 2.24 2.37 2.18

DPB 29.45 1.56 1.47 1.55 1.52 1.67 1.49 1.64 1.54 1.62 1.61 1.50 1.49 1.76

ROA 26.59 1.47 1.34 1.57 1.31 1.55 1.50 1.41 1.37 1.52 1.49 1.45 1.40 1.52

ARR 20.29 1.34 0.95 1.25 1.43 1.19 1.34 1.32 1.40 1.27 1.36 1.34 1.30 1.44

SA** 13.66 0.95 0.85 1.22 0.84 0.86 0.78 1.10 1.04 0.82 0.95 0.92 0.95 0.86

APV 10.78 0.85 0.83 0.72 0.97 0.69 0.87 0.80 0.91 0.78 0.92 0.79 0.99

PI 11.87 0.83 0.75 0.73 0.81 0.74 0.81 0.83 0.90 0.76 0.81 0.98

The Utilization of the Appraisal Techniques

PER: price-earning ratio, G: growth, NG: no-growth, H: hight, L: low, Y: yes, N: no, M: a manufacturing industry, NM: a non-manufacturing industry, IRR: internal rate of return, NPV: net present value, PB: payback period, MARR: minimum attractive of return, SA: sensitivity analysis, DPB: discounted payback period,ROA: real options approach, ARR: accounting rate of return, SA**: simulation analysis,APV: adjusted present value, PI: profitability index


Principle - To be a period of time spent to fully recover the initial investment cost

Method - It is determined based on the cumulative amount of cash flows.

A PB is found to be one which satisfies the equation above.

Decision Criteria - If A PB is less than the predetermined period of time, undertake the project and perform

the following sophisticated evaluation techniques. Otherwise, reject it.

The Types of PB i) Traditional payback period(TPBP): no interest concept considered. ii) Discounted payback period (DPB): interest concept considered.

Payback Period


00

tCFn

n

Traditional Payback Period

N CF CCF 012345

-30,0009,0009,0009,0009,0009,000

-30,000-21,000-12,000-3,0006,000

15,000

A TPBP is determined between 3 and 4 years. TPBP= 3.33 years

(unit: 000 won)


A Conventional Payback Period

A TPBP based on the a real cash flowA TPBP based on a nominal cash

flow

n Real CF CCF Nominal CF CCF

012345

-300,00090,00090,00090,00090,00090,000

-300,000-210,000

-12,000-3,0006,000

15,000

-300,0009,900

10,89011,97913,17714,495

-300,000-20,100

-9,2102,769

15,94630,441

(unit: 000 won)


A Conventional Payback Period

Ex 6.1] Determine a TPBP

Given] The initial investment costs of project A and B: 120 m won and 150 m won

A project life of A and B are 3 and 7 years

n A B

CF CCF CF CCF01234567

-120,00060,00060,00060,000

-120,000-60,000

060,000

-150,00050,00050,00050,00050,00050,00050,00050,000

-150,000-100,000

-50,0000

50,000100,000150,000200,000

IRR 23.4% 27%


Principle - TPBP + Interest Concept Employed

Decision Criteria - To be one which makes a cumulative cash flow zero - NPV=0

Equation

Discounted Payback Period

0

0(1 )

ntt

t

CF

i

DPBP


Ex 6.2] Determine a discounted payback period for the project for an automatic machining center

Given] Cash flows for the project, interest rate=15%

DPBP

0

62,500

33,982

33,726

33,205

33,135

82,013

n

Unit: ooo won

1 2 3 4 5


Sol] determine a DPBP

DPBP

N 0 1 2 3 4 5

NCF -62,500 33,982 33,726 33,205 33,135 82,013

CCF* -62,500 -28,518 -5,208 38,413 71,548 153,562

Interest Factor(P/F,15%,0)

=1(P/F,15%,1)

=0.870(P/F,15%,2)

=0.7561(P/F,15%,3)

=0.658(P/F,15%,4)

=0.572(P/F,15%,5)

=0.4971

Discounted CF -62,500 29,564 25,500 21,848 18,953 40,768**

CumDCF*** -62,500 -32,936 -7,436 14,412 33,365 74,134

*: Cumulative Cash Flow without considering an interest rate **: Discounted Cash Flow= NCF * Interest Factor***: Cumulative Discounted Cash Flow


A Relationship Between PB and ROR

i

0

P

A

1

A

2

A

3

A

4

A

N

…………………………

N

N

ii

i1AP

1

1

where, P: present value, A: equal amount of a cash flow

N: project life, i: interest rate


if a project life is infinite, i.e., “ ” ,

The equation above is called a capitalized equivalent (CE).

- A relationship between a PB and IRR

i

A

i

i1A

ii

i1AP

N

NN

N

N

/11lim

1

1lim

N

nnA

Ai

P

Ai

i

APnAP

1

PB Approx. IRR3 년 33%4 년 25%5 년 20%6 년 17%7 년 14%


A Relationship Between PB and ROR

Ex 6.3] A adequate Case for A Traditional Payback Period

Given] A investment cost for installing a heating and air conditioning system in the class: May=3.375m won, Jun=1.125m won, a cost saving of electricity: Jun. to Aug. =450, 000 won, Apr. to May & Sep to Oct=225,000 won, Nov. to Mar=337,000 won

Sol] Determine a traditional payback period

2009 2010

mo CF CCF CF CCF

5

6

7

8

9

10

11

12

1

2

3

4

-3,375

-1,125

450

450

225

225

337.5

337.5

337.5

337.5

337.5

225

-3,375

-4,500

-4,050

-3,600

-3,375

-3,150

-2,812.5

-2,475

-2,137.5

-1,800

-1,462.5

-1,237

225

450

450

450

-1,012.5

-562.5

-112.5

337.5

PBP 15.25months

When The Payback Period Technique Can Be Properly Used:

It is better to use for a case in which the project life is measured in a month rather than a year.

(unit: 000 won)


Ex 6.4] Measure Risk with a Payback PeriodGiven] A investment cost for installing a heating and air conditioning system in the class:

May=3.375m won, Jun=1.125m won, a cost saving of electricity: Jun. to Aug. =450, 000 won, Apr. to May & Sep to Oct=225,000 won, Nov. to Mar=337,000 won , Interest Rate =12%

Sol] Determine a discounted payback period

A Risk Measuring with A Payback Period

(unit: 000 won)

2009 2010

mo CF CCF CF CCF

5

6

7

8

9

10

11

12

1

2

3

4

-3,375

-1,125

450

450

225

225

337.5

337.5

337.5

337.5

337.5

225

-3,408.8

-4,579.1

-4,174.9

-3,766.6

-3,579.3

-3,390.1

-3,086.5

-2,780.0

-2,470.2

-2,157.4

-1,841.4

-1,634.8

225

450

450

450

225

225

337.5

-1,426.2

-990.5

-550.4

-106.0

118.1

344.3

685.2투자회수기간 16.47

개월

ttt CFiPBPB 11

Project Balance: PB


-5000

-4000

-3000

-2000

-1000

0

1000

1 2 3 4 5 6 7 8 9 10111213141516171819

월

누적현금흐름


A Risk Measuring with A Payback Period

Ex 6.6] Determine an ARR with an average investment capital

Given] I: 500 m won, life: 5 years, No salvage value at the end of year 5: 0, The relevant financial date

Accounting Rate of Return

ARR Af ter-Tax Average I ncomeAverage I nvestment Capi tal

n 1 2 3 4 5

Rev 433,333 450,000 266,667 200,000 133,333

Expenses 200,000 150,000 100,000 100,000 100,000

BTCF 233,333 300,000 166,667 100,000 33,333

Dep 100,000 100,000 100,000 100,000 100,000

BTI 133,333 200,000 66,667 0 -66,667

Tax(25%) 33,333 50,000 16,667 0 -16,667

NI 100,000 150,000 50,000 0 -50,000


- Step 1: derive an after-tax average income

- Step 2: determine an average investment capital

- Step 3: Determine an ARR

100,000 150,000 50,000 0 50,000 50 5

m won ATAI

500,000 400,000 300,000 200,000 100,000 0 250 5

m won Average I nvestment Capi tal

50,000 20%250,000

ARR


Accounting Rate of Return

Chapter 6: An Economic Appraisal Technique: PBP and ARR

Documents

Transcript of Chapter 6: An Economic Appraisal Technique: PBP and ARR