economic analysis

BAKR FAHAD AL-HAJRISenior Project EngineerSaudi Aramco CompanyMobile: 054-‐241-‐9000

e-‐mail: [email protected]

Bakr holds BS and MEG degrees in Architectural Engineering from KFUPM. He is accredited by theSaudi Council of Engineers as a Consultant Engineer (CE-‐SCE). Also, Bakr is a Project ManagementProfessional (PMP), a Certified Cost Engineer (CCE) and an Associate Value Specialist (AVS).

Bakr has more than 33 years of professional experience in areas of engineering and projectmanagement. Since 1983, he has been an Architect, Engineering Office Manager, Project Engineer,Lead Project Engineer and Senior Project Engineer. He worked with Zamil & Turbag / Brown & Root,Saudi Arabian Bechtel Company, Bakr Al-‐Hajri Engineering, Saudi Consulting Services and SaudiChevron Phillips Company. Currently Bakr is working as a Senior Project Engineer in Community andIndustrial Projects Division, Saudi Aramco, responsible for Project Management of Plants InfrastructureProjects.

Bakr is an active member of AACEI-‐Arabian Gulf Section and served the association as Director ofPublic Relations (2007-‐08), Vice President –Technical (2008-‐09), President (2009-‐10) and currently he isa member of the current AACEI-‐AGS Board . In addition, Bakr is a photographer and a writer.

Prepared, Compiled & Presented byBakr Fahad Al-‐Hajri, CE-‐SCE PMP CCP AVS

November 2013 Revision

Outline

Objectives /Introduction /SymbolsEquivalence & ConventionsInterestDiscount FactorsEquivalent WorthCash Flow AnalysisMultiple AlternativesIncremental AnalysisTax Consideration

20 March 2015 Economic Analysis 5

Objectives

§ Calculate simple and compounded interest rates and solve interest problems using basic single payments, uniform series, and gradientformulas.

§ Calculate present value, future value, and equivalent uniform annual value of cash flow series.

§ Determine the discounted rate of return of a cash flow series.

§ Evaluate and select the best alternative using present value, future value, equivalent uniform annual value and discounted rate of return.

§ Compare alternatives using the benefit-cost ratio.

Equivalence & Conventions Interest Discount

FactorsEquivalentWorth

Cash Flow Analysis

Multiple Alternatives

Incremental Analysis

Tax Considerations


Introduction

§ Engineers are confronted with two important interconnected environments, the physical and the economics.

§ Select from among multiple alternatives.

§ Need arises to quantify alternatives objectively and equate them in some numerical value such as money.

§ Economic selection criteria will be either:§ Maximization of benefit.§ Minimization of cost.§ or Maximization of the net profit.

Alternative 3

Alternative 2

Alternative 1



Cash Flow Analysis



Tax Considerations


Symbols

A Annual amount or Annuity

B Benefits or income

C Cost or expenses

e The base of natural logarithms ( 2.71828)

EOY End-‐of-‐year, usually followed by a number indicating which year

EUAB Equivalent uniform annual benefits

EUAC Equivalent uniform annual cost

EUAW Equivalent uniform annual worth

F Future value

G Uniform or arithmetic gradient amount

i Interest rate per period

k Number of compounding periods per year

MARR Minimum attractive rate of return

n Total number of compounding period, or life of assets

P Present value

r Nominal annual interest rate

ROR Rate of return

Sn Expected salvage value at end of year n

Ø Effective interest rate (r/k)



Cash Flow Analysis



Tax Considerations

Equivalence & Convention


Equivalence

§ An essential concept in engineering economic analysis is that of equivalence or the ability to compare cash flows at different points in time. Equivalence is based on the time value of money, and the cardinal rule is that two cash flows or alternatives only can be compared at a common interest rate.

§ The model used for engineering economic analysis is based on the conversion of an existing cash flow to an equivalent cash flow at a particular interest rate through the application of predefined factors.

§ The conversion factors are called discount factors and are readily available in either algebraic form or in tables.



Cash Flow Analysis



Tax Considerations


Conventions

§ Cash Flow Representation

§ Cash flow occurs whenever cash or something of monetary value flows from one party to another.

§ It can be either cash flow in, for example cash receipts, or when payments or disbursements are made, which is a cash flow out.

§ It can be shown in tabular format or cash flow diagram.



Cash Flow Analysis



Tax Considerations


Conventions

§ Salvage Value

§ Residual value resulting in income at the end of the useful life of an alternative.

§ The resale or salvage value may be associated with the anticipated market value of the asset at that point in time.

§ It is shown as an upward arrow on the cash flow diagram.

§ Any significant costs associated with disposal at the end of useful life also can be shown on the diagram as a downward arrow.



Cash Flow Analysis



Tax Considerations


Conventions

§ Example:

§ An investor bought an equipment and paid an advance payment of $ 20,000.

§ He is required to pay annual operation cost of $ 500 at the end of each year.

§ He is required to pay maintenance cost of $0, $100, $200, $300, and $400 at the end year 1, 2, 3, 4 and 5 respectively.

§ He is expecting a revenue of $5,000 at the end of each year from renting the equipment to outside users.

§ At the end of the fifth year he is planning to sell it for $10,000.



Cash Flow Analysis



Tax Considerations


Conventions

YEAR INCOME EXPENSE

0 0 $20,000

1 $5,000 $500

2 $5,000 $600

3 $5,000 $700

4 $5,000 $800

5 $15,000 $900



Cash Flow Analysis



Tax Considerations


Conventions

CASH IN : INCOME/ BENEFITS / RECEIPTS / SALVAGE

$15,000

$5,000 $5,000 $5,000 $5,000

0 1 2 3 4 5

$500 $600$700 $800

$900

$20,000

CASH OUT : COST / EXPENDITURE / DISBURESMENTS

Time Line Time Line



Cash Flow Analysis



Tax Considerations


Conventions


$10,000

$5,000 $5,000 $5,000 $5,000 $5,000

0 1 2 3 4 5

$500 $500 $500 $500 $500

$100$200 $300

$400

$20,000


Time Line Time Line



Cash Flow Analysis



Tax Considerations


Conventions


S = $10,000A = $5,000

0 1 2 3 4 5

A = $500

G = $100

$20,000


Time Line Time Line



Cash Flow Analysis



Tax Considerations

Interest


Interest

§ Time Value of Money

§ There is usually a cost associated with the use of the money. Since money is a valuable asset, people are willing to pay to have it available for their immediate use. With money, the charge for its use is called interest.

§ Interest Types:§ Simple Interest

§ Compound Interest

§ Nominal Interest Rate

§ Effective Interest Rate

§ Continuous Compounding

§ Minimum Attractive Rate of Return (MARR)



Cash Flow Analysis



Tax Considerations


Interest

§ Simple Interest

§ The interest due is proportional to the length of time the principal is outstanding and does not accrue or compound on previous interest. Each subsequent interest payment is calculated based on the total principal, ignoring accumulated interest to date.

SIMPLE INTEREST (i = 10%)

Principal $1,000

Interest accrued EOY1 $100


Total at EOY2 $1,200



Cash Flow Analysis



Tax Considerations


Interest

§ Compound Interest

§ The interest is considered an increased increment of principal earning additional interest with time. Each subsequent interest payment is calculated based on total principal plus accumulated interest to date.

COMPOUND INTEREST (i = 10%)

Principal $1,000


New principal with accrued interest $1,100


Total at EOY2 $1,210



Cash Flow Analysis



Tax Considerations


Interest

§ Nominal Interest Rate

§ The annual interest rate, r, disregarding the effects of compounding periods that are more frequent than annually.

§ Common practice is to express interest rates at the nominal rate even though there is compounding such as quarterly, monthly, or daily.

§ The nominal rate, r, is not the same as the annual rate, i, except in the case of annual compounding.



Cash Flow Analysis



Tax Considerations


Interest

§ Effective Interest Rate

§ If the effective interest rate per period, φ, is given, it can be converted easily to the effective annual interest rate, i, which includes the effects of compounding over k periods per year.

§ In general, it can be assumed that the rate given in a problem is annual unless stated otherwise. If compounding is annual, the rate given is the effective rate. If compounding is anything other than annual, the rate given is the nominal rate.

i = ( 1 + r/k)k -‐ 1 (equation 27.1)

i = ( 1 + φ ) k -‐ 1 (equation 27.2)



Cash Flow Analysis



Tax Considerations


Interest

Q1: If a monthly interest rate is compounded to yield an effective 12% annual rate of return, then that monthly interest rate must be:

a. More than 1%b. Equal to1%c. Less than 1%d. None of the above is correct

A1: C, The monthly interest rate must be less than 1. Were it 1% per month and not compounded at all, then the annual return would be 12 X 1% = 12%, which the stated effective rate. But the monthly rate is compounded in this case, so the annual rate would exceed 12%, if the monthly rate were 1%. Since the effective annual rate is 12%, not more, then the compounded monthly rate must be less than 1%.



Cash Flow Analysis



Tax Considerations


Interest

Q2: Given the interest rate of 12%, find the effective and annual rate for yearly, semi annual, and monthly compounding.

A2: i = (1 + φ)k – 1 where φ = r/k

The nominal rate (r) = 12%

For yearly compounding:k = 1 &φ = 0.12/1 = 0.12i = (1 + 0.12)1 -1 = 1.120 – 1 = 12%

For semi-annual compounding:k = 2 &φ = 0.12/2 = 0.06i = (1 + 0.06)2 -1 = 1.124 – 1 = 12.4%

For monthly compounding:k = 12 &φ = 0.12/12 = 0.01i = (1 + 0.01)12 -1 = 1.127 – 1 = 12.7%



Cash Flow Analysis



Tax Considerations


Interest

§ Continuous Compounding

§ Discrete compounding occurs when interest payments are made at the end of finite compounding periods such as annually, monthly, quarterly, or daily.

§ As the duration of the interest period becomes infinitely short, the number of compounding periods per year becomes infinite and is referred to as continuous compounding.

i = e r -‐ 1 (equation 27.3)



Cash Flow Analysis



Tax Considerations


Interest

§ Minimum Attractive Rate of Return (MARR)

§ The interest rate used in feasibility studies is often called the minimum attractive rate of return, or MARR. This represents the minimum rate of return at which the owner is willing to invest.

§ The selection of a suitable rate of return can be quite complex and could vary from problem to problem. Simply stated, it involves the analysis and selection of the highest one of the following:

§ Cost of borrowed money from banks, insurance companies, etc.§ Cost of capital or the composite value for the capital structure of the firm§ Opportunity cost or the rate-of-return of the best project that is rejected

§ When there is risk or uncertainty in a project, a commonly used method is to increase the MARR, thus diminishing the effect of future costs and benefits.



Cash Flow Analysis



Tax Considerations

Discount Factors


Discount Factors

FACTOR CONVERTS

NOTATION FORMULA

Single PaymentCompound Amount

P to F (F/P, i, n) (1 + i)n

Single PaymentPresent Worth

F to P (P/F, i, n) (1 + i)-n

Uniform seriesSinking Fund

F to A (A/F, i, n) i / ( (1 + i)n – 1)

Uniform Series Capital Recovery

P to A (A/P, i, n) i (1 + i)n / ( (1 + i)n – 1)

Uniform SeriesCompound Amount

A to F (F/A, i, n) ( (1 + i)n – 1) / i

Uniform Series Present worth

A to P (P/A, i, n) ( (1 + i)n – 1)/ ( i (1 + i)n )

Arithmetic GradientUniform Series

G to A (A/G, i, n) ( 1 / i) – ( n / ((1 +i)n – 1)

Arithmetic GradientPresentWorth

G to P (P/G, i, n) ( ( (1 + i)n – 1)/ ( i2 (1 + i)n ) ) – ( n / ( i (1 + i)n )



Cash Flow Analysis



Tax Considerations


Discount Factors

Discrete Compound Interest Table with i = 5%

n F/P P/F A/F A/P F/A P/A A/G P/G

1 1.0500 0.9524 1.0000 1.0500 1.0000 0.9524 0.0000 0.0000

2 1.1025 0.9070 0.4878 0.5378 2.0500 1.8594 0.4878 0.9070

3 1.1576 0.8638 0.3172 0.3672 3.1525 2.7232 0.9675 2.6347

4 1.2155 0.8227 0.2320 0.2820 4.3101 3.5460 1.4391 5.1028

5 1.2763 0.7835 0.1810 0.2310 5.5256 4.3295 1.9025 8.2369

6 1.3401 0.7462 0.1470 0.1970 6.8019 5.0757 2.3579 11.9680

7 1.4071 0.7107 0.1228 0.1728 8.1420 5.7864 2.8052 16.2321

8 1.4775 0.6768 0.1047 0.1547 9.5491 6.4632 3.2445 20.9700

9 1.5513 0.6446 0.0907 0.1407 11.0266 7.1078 3.6758 26.1268

10 1.6289 0.6139 0.0795 0.1295 12.5779 7.7217 4.0991 31.6520



Cash Flow Analysis



Tax Considerations


Discount Factors

Discrete Compound Interest Table with i = 6%


1 1.0600 0.9434 1.0000 1.0600 1.0000 0.9434 0.0000 0.0000

2 1.1236 0.8900 0.4854 0.5454 2.0600 1.8334 0.4854 0.8900

3 1.1910 0.8396 0.3141 0.3741 3.1836 2.6730 0.9612 2.5692

4 1.2625 0.7921 0.2286 0.2886 4.3746 3.4651 1.4272 4.9455

5 1.3382 0.7473 0.1774 0.2374 5.6371 4.2124 1.8836 7.9345

6 1.4185 0.7050 0.1434 0.2034 6.9753 4.9173 2.3304 11.4594

7 1.5036 0.6651 0.1191 0.1791 8.3938 5.5824 2.7676 15.4497

8 1.5938 0.6274 0.1010 0.1610 9.8975 6.2098 3.1952 19.8416

9 1.6895 0.5919 0.0870 0.1470 11.4913 6.8017 3.6133 24.5768

10 1.7908 0.5584 0.0759 0.1359 13.1808 7.3601 4.0220 29.6023



Cash Flow Analysis



Tax Considerations


Discount Factors

§ The functional notation illustrates a standardized notation that simplifies the calculation and permits the use of tabulated factors.

§ The notation is in the form (X/Y, i, n) which can be read as “to find the equivalent amount X given amount Y, interest rate i, and the number of discounting or compounding periods n.”



Cash Flow Analysis



Tax Considerations


Discount Factors

§ The functional notation illustrates a standardized notation that simplifies the calculation and permits the use of tabulated factors.

§ The notation is in the form (X/Y, i, n) which can be read as “to find the equivalent amount X given amount Y, interest rate i, and the number of discounting or compounding periods n.”

Time Line0 1 2 3 4 5EOY

$1,000 (F/P ,5% ,5) F = $1,000 X 1.2763 = $1,276

P = $1,276 X 0.7835 = $1,000 $1,276 (P/F ,5% ,5)



Cash Flow Analysis



Tax Considerations

Equivalent Worth


Equivalent Worth

§ In most types of engineering economic problems, the primary calculation is determining the present worth or equivalent uniform annual cost of a cash flow to provide a basis for analysis.

§ Present Worth: The present worth of a cash flow can be compared given a lump-sum future value, a uniform series, or an arithmetic gradient series.

§ Future Worth : The future worth method uses the end of the planning horizon as a reference point.

§ Annual Worth : The basis of this method is the conversion of all cash flows to an equivalent uniform annual worth (EUAW).



Cash Flow Analysis



Tax Considerations


Equivalent Worth

§ A contractor is considering the acquisition of a piece of equipment with anticipated financial impact as shown in the table below.

YEAR EXPENSE INCOME

0 $38,000 0

1 0 $11,000

2 $1,000 $11,000

3 $2,000 $11,000

4 $3,000 $11,000



Cash Flow Analysis



Tax Considerations


Equivalent Worth

§ If the contractor’s minimum attractive rate of return (MARR) is 6 percent, should the investment be made?

§ Use the Present worth.§ By computing the present value of the net cash flow for each year.§ By using the cash flow diagram.

§ Use the Future worth.§ By computing the future value of the net cash flow for each year.§ By using the cash flow diagram.

§ Use the Annual worth.§ By using the cash flow diagram.§ By computing the Annual value of the net present value.§ By computing the Annual value of the net future value.



Cash Flow Analysis



Tax Considerations


Equivalent Worth

Cash Flow Table

YEAR EXPENSE INCOME NET

0 $38,000 0 ($38,000)

1 0 $11,000 $11,000

2 $1,000 $11,000 $10,000

3 $2,000 $11,000 $9,000

4 $3,000 $11,000 $8,000

TOTALS $44,000 $44,000 0



Cash Flow Analysis



Tax Considerations


Equivalent Worth

Cash Flow Diagram

Time Line0 1 2 3 4EOY

$38,000

G = $1,000

A = $11,000



Cash Flow Analysis



Tax Considerations


Equivalent Worth

Present Worth Calculations – Using Annual Net Present Worth

YEAR EXPENSE INCOME NET NOTATION FACTOR PW

0 $38,000 0 ($38,000) 1.0000 ($38,000)

1 0 $11,000 $11,000 F (P/F, 6%, 1) 0.9434 $10,377

2 $1,000 $11,000 $10,000 F (P/F, 6%, 2) 0.8900 $8,900

3 $2,000 $11,000 $9,000 F (P/F, 6%, 3) 0.8396 $7,556

4 $3,000 $11,000 $8,000 F (P/F, 6%, 4) 0.7921 $6,337

TOTALS $44,000 $44,000 0 ($4,829)



Cash Flow Analysis



Tax Considerations


Equivalent Worth

Present Worth Calculations – Using Cash Flow Diagram

P NET NOTATION FACTOR PW

P0 ($38,000) 1.0000 ($38,000)

P1 ($1,000) G (P/G, 6%, 4) 4.9455 ($4,946)

P2 $11,000 A (P/A, 6%, 4) 3.4651 $38,116

TOTALS P = P0 + P1 + P2 = ($4,829)



Cash Flow Analysis



Tax Considerations


Equivalent Worth

Future Worth Calculations – Using Annual Net Future Worth

YEAR EXPENSE INCOME NET NOTATION FACTOR FW

0 $38,000 0 ($38,000) P (F/P, 6%, 4) 1.2625 ($47,975)

1 0 $11,000 $11,000 P (F/P, 6%, 3) 1.1910 $13,101

2 $1,000 $11,000 $10,000 P (F/P, 6%, 2) 1.1236 $11,236

3 $2,000 $11,000 $9,000 P (F/P, 6%, 1) 1.0600 $9,540

4 $3,000 $11,000 $8,000 1.0000 $8,000

TOTALS $44,000 $44,000 0 ($6,098)



Cash Flow Analysis



Tax Considerations


Equivalent Worth

Future Worth Calculations – Using Cash Flow Diagram

F NET NOTATION FACTOR FW

F0 ($38,000) 1.2625 ($47,975)

F1 ($1,000) G (P/G, 6%, 4) (F/P, 6%, 4) 4.9455 X 1.2625 = 6.2437 ($6,244)

F2 $11,000 A (F/A, 6%, 4) 4.3746 $48,121

TOTALS F = F0 + F1 + F2 = ($6,098)



Cash Flow Analysis



Tax Considerations


Equivalent Worth

Annual Worth Calculations – Using Cash Flow Diagram

A NET NOTATION FACTOR AW

A0 ($38,000) P (A/P, 6%, 4) 0.2886 ($10,967)

A1 ($1,000) G (A/G, 6%, 4) 1.4272 ($1,427)

A2 $11,000 1.0000 $11,000

TOTALS A = A0 + A1 + A2 = ($1,394)



Cash Flow Analysis



Tax Considerations


Equivalent Worth

Annual Worth Calculations – Using Present / Future Values

PW NOTATION FACTOR AW

($4,829) P (A/P, 6%, 4) 0.2886 ($1,394)

FW NOTATION FACTOR AW

($6,098) F (A/F, 6%, 4) 0.2286 ($1,394)



Cash Flow Analysis



Tax Considerations


Equivalent Worth


$4,829 $6,098

A = $1,394



Cash Flow Analysis



Tax Considerations


Equivalent Worth

Q1: The following chart shows ending of period cash flows for expenses. The interest rate is 10%:

YEAR EXPENSE

1 $100

2 $100

3 $100

4 $100

5 $100

What is the net present worth (value) of this cash flow?a. $500b. $269c. $316.99d. $379.08

A1: NPW = $100 (P/A,10%,5)

= $100 (3.7908)

= $379.08



Cash Flow Analysis



Tax Considerations


Equivalent Worth

Q2: You are evaluating an alternative that requires an initial investment of $50,000. The following chart shows ending of period cash flows of annual savings. The interest rate is 10%.YEAR SAVINGS

1 $2,667

2 $14,292

3 $19,181

4 $13,114

What is the net present worth (value) of this investment alternative at end of year 4?

a. $746b. $5,223c. $9,296d. $12,397

A2:NPW = -$50,000 + $2,667 (P/F,10%,1) + $14,292 (P/F,10%,2) + $19,181 (P/F,10%,3) + $13,114 (P/F,10%,4)

= -$50,000 + $2,667 ( 0.9091) + $14,292 (0.8264) + $ 19,181 (0.7513) + $13,114 ( 0.6830)

= -$50,000 + $2,424.57 + $11,810.91 + $14,410.69 + $8,956.86

= -$12,396.97



Cash Flow Analysis



Tax Considerations

Cash Flow Analysis


Cash Flow Analysis

§ There are two fundamental approaches to the analysis of a given cash flow: equivalent worth, and rate-of-return.

§ Equivalent Worth

§ The equivalent worth method simply converts to one of the basic forms, i.e., the equivalent present worth, or annual worth, using previously-developed techniques and the required MARR as learned in last session.

§ Rate of Return (ROR)

§ The ROR is the interest rate at which benefits are equivalent to costs.

§ Thus the cash flow is solved for the unknown value, i.



Cash Flow Analysis



Tax Considerations


Cash Flow Analysis

§ A $10,000 investment returned $2,342 per year over a 5-year period. What was the rate of return on this investment?

YEAR INCOME EXPENSE

0 $10,000

1 $2,342

2 $2,342

3 $2,342

4 $2,342

5 $2,342

0 1 2 3 4 5EOY

$10,000

A = $2,342



Cash Flow Analysis



Tax Considerations

1. Set present worth (PW) of benefits equal to the present worth (PW) of costs.

Benefits PW = Cost PW

Benefits PW = $2,342 (P/A, I, 5)

Cost PW = $10,000

$2,342 (P/A, i, 5) = $10,000

(P/A, i, 5) = $10,000 / $2,342

(P/A, i, 5) = 4.270


Cash Flow AnalysisEquivalence & Conventions Interest Discount


Cash Flow Analysis



Tax Considerations

2. Look at the compound interest factors tables and read the factor value where the P/A column intersect with the row where n = 5 for a factor equal to or around the value of 4.270.


Cash Flow Analysis

I = 5%n F/P P/F A/F A/P F/A P/A A/G P/G

5 1.2763 0.7835 0.1810 0.2310 5.5256 4.3295 1.9025 8.2369


5 1.3382 0.7473 0.1774 0.2374 5.6371 4.2124 1.8836 7.9345



Cash Flow Analysis



Tax Considerations

3. Since there is no exact factor with that amount, then we need to interpolate between 2 values in order to get the value of i.


Cash Flow Analysis

i (P/A, i, 5)

i1 = 5.0% F1 = 4.379

i = ? Fi = 4.270

i2= 6.0% F2 = 4.212

By interpolation i = 5.5%



Cash Flow Analysis



Tax Considerations



§ Many projects will require a selection from among several mutually-exclusive alternatives. The selection of one alternative will preclude the selection of any other alternative. Two simple rules will help identify the preferred alternative:

§ Compute the net present worth of each alternative at the required minimum attractive rate of return (MARR).

§ Select the alternative having the highest net worth



Cash Flow Analysis



Tax Considerations



§ Given the following mutually-exclusive alternatives and a minimum attractive rate of return (MARR) of 5 percent, which one would be chosen?

YEAR ALTERNATIVE A ALTERNATIVE B ALTERNATIVE C

0 -‐$2,500 -‐$2,700 -‐$3,000

1 0 $650 0

2 0 $650 $350

3 0 $650 $700

4 0 $650 $1050

5 $3,100 $650 $1400

TOTAL $600 $550 $500



Cash Flow Analysis



Tax Considerations



1. Compute the Present Worth for each alternative.

2. Select the alternative with the highest value.

ALTERNATIVE NOTATION FACTOR NPW

A -‐ $2,500 + $3,100 (P/F, 5%, 5) 0.7835 -‐$71

B -‐ $2,700 + $650 (P/A, 5%, 5) 4.3295 $114

C -‐ $3,000 + $350 (P/G, 5%, 5) 8.2369 -‐$117


5 1.2763 0.7835 0.1810 0.2310 5.5256 4.3295 1.9025 8.2369



Cash Flow Analysis



Tax Considerations



§ Analysis Period

§ When comparing alternatives using present worth methods, it is necessary to analyze over a common planning horizon.

§ In the event that alternatives do not have equal lives, consideration must be given to the difference. A common technique is to select an analysis period equal to the least common multiple of the alternative lives.

§ Another approach is to select an analysis period and determine the salvage value for each alternative at that point in time.

§ When using annual worth methods there is no need to establish equal lives.



Cash Flow Analysis



Tax Considerations



§ Capitalized Cost

§ Problems occasionally arise involving extremely long analysis periods. For example, in governmental analysis of permanent structures such as roads, dams, and pipelines, the required maintenance can be spread over an infinite period (n = ∝). In these cases the analysis is called capitalized cost.

§ Simply stated, capitalized cost is the present sum of money that would have to be set aside now, at a given interest rate, to provide a perpetual uniform cash flow.



Cash Flow Analysis



Tax Considerations

§ Assume that you have the following two alternatives. Which one would you select?



ALTERNATIVE ROR

A 100%

B 20%



Cash Flow Analysis



Tax Considerations

§ What if the investment on alternatives is as shown on the table below:

§ Will you change your decision after this new data?

§ What if your MARR is 25%.

§ What if your MARR is 15%.



ALTERNATIVE INITIAL INVESTMENT ROR EOY PROFIT

A $100 100% $100

B $10,000 20% $2,000



Cash Flow Analysis



Tax Considerations



§ This illustrate the need for a procedure to evaluate the return on the increment of initial investment if one alternative requires a higher initial investment than the other.

§ This process should also apply to multiple alternatives. By examining the differences between alternatives, we can determine whether or not the differential costs are justified based on the differential benefits.



Cash Flow Analysis



Tax Considerations



§ Rate of Return

§ This technique is based on the paired comparison of alternatives. The following steps should be followed in an incremental rate-of-return analysis:1. Identify all alternatives. Be sure to consider the “do nothing” option.

2. Compute ROR for each alternative and discard any alternative with ROR < MARR.

3. Arrange remaining alternatives in ascending order of initial cost.

4. Calculate the ROR on the difference between the first two (lowest initial cost) alternatives. If this ΔROR ≥ MARR, retain the higher cost alternative, otherwise retain the lower cost alternative.

5. Take the retained alternative from the previous step and compare it to the next higher alternative.

6. Repeat this process until all alternatives have been evaluated.



Cash Flow Analysis



Tax Considerations



§ Given the following mutually-exclusive alternatives and a minimum attractive rate of return (MARR) of 5 percent, which one should be chosen? Use the incremental rate-of-return method and assume the “do nothing” alternative is not available.


0 -‐$2,500 -‐$2,738 -‐$3,000

1 0 $650 0

2 0 $650 $350

3 0 $650 $700

4 0 $650 $1,050

5 $3,190 $650 $1,400



Cash Flow Analysis



Tax Considerations



1. Identify all alternatives. Be sure to consider the “do nothing” option.

2. Compute ROR for each alternative and discard any alternative with ROR < MARR.

ALTERNATIVE NOTATION FACTOR i

A (P/F, i, 5) = $2,500 / $3,190 0.7835 5%

B (P/A, i, 5) = $2,738 / $650 4.2124 6%

C (P/G, i,5) = $3,000 / $350 8.5714 ROR<MARR

i = 5%n F/P P/F A/F A/P F/A P/A A/G P/G5 1.2763 0.7835 0.1810 0.2310 5.5256 4.3295 1.9025 8.2369




Cash Flow Analysis



Tax Considerations




4. Calculate the ROR on the difference between the first two (lowest initial cost) alternatives by setting present worth of benefits equal to present worth of cot. If this ΔROR ≥ MARR, retain the higher cost alternative, otherwise retain the lower cost alternative.

YEAR ALTERNATIVE A ALTERNATIVE B B -‐ A

0 -‐$2,500 -‐$2,738 -‐$238

1 0 $650 $650

2 0 $650 $650

3 0 $650 $650

4 0 $650 $650

5 $3,190 $650 -‐$2,540

$650 (P/A, i%, 4) = $238 + $2,540 (P/F, i%, 5)



Cash Flow Analysis



Tax Considerations



5. Since we have two unknown discount factors in this equation, it must be solved by trial and error by using the appropriate factors for varying values of i. The first try should be the MARR of 5 percent, which results in:

YEAR 0 COST -‐$238

YEAR 5 COST -‐2,540 X 0.7835 -‐$1,990

YEAR 1-‐4 BENEFITS $650 X 3.5460 $2,305

TOTAL BENEFITS LESS COST $77

i = 5%n F/P P/F A/F A/P F/A P/A A/G P/G4 1.2155 0.8227 0.2320 0.2820 4.3101 3.5460 1.4391 5.10285 1.2763 0.7835 0.1810 0.2310 5.5256 4.3295 1.9025 8.2369



Cash Flow Analysis



Tax Considerations



6. Since the benefits are greater than the costs, or in other words, the net present worth of the increment is greater than 0, the rate-of-return on the increment must be something greater than 5 percent and we therefore accept the increment and retain the higher cost alternative, B.



Cash Flow Analysis



Tax Considerations



§ Benefit-Cost Ratio

§ The incremental approach for the analysis of two or more alternatives will follow the same procedure as that for rate-of-return analysis.

1. Identify all alternatives. Be sure to consider the “do nothing” option.2. Compute Benefit/Cost ratio for each alternative and discard any alternative with B/C< 1.3. Arrange remaining alternatives in ascending order of initial cost.4. Calculate the ratio of the present worth of Benefits and Costs on the difference between the

first two (lowest initial cost) alternatives. If this B/C> 1, retain the higher cost alternative, otherwise retain the lower cost alternative.

5. Take the retained alternative from the previous step and compare it to the next higher alternative.

6. Repeat this process until all alternatives have been evaluated.

PW of benefits -‐ PW of costs > 0 OR EUAB -‐ EUAC > 0

B/C = PW of benefits/ PW of Costs = EUAB/ EUAC > 1



Cash Flow Analysis



Tax Considerations



§ Given the following mutually-exclusive alternatives and a MARR of 5 percent, which one should be chosen? Use the benefit-cost method and assume the “do nothing” alternative is not available.


0 -‐$2,500 -‐$2,738 -‐$3,000

1 0 $650 0

2 0 $650 $350

3 0 $650 $700

4 0 $650 $1,050

5 $3,190 $650 $1,400



Cash Flow Analysis



Tax Considerations



1. Identify all alternatives. Be sure to consider the “do nothing” option.

2. Compute the benefit-cost ratio for each alternative and discard alternatives with B/C < 1.

ALTERNATIVE BENEFIT/COST RATIO NOTES

A $3,190 X (P/F, i, 5) / $2,500 = $3190 X 0.7835 / $2,500 = 1 Acceptable

B $650 X (P/A, i, 5) / $2,738 =$650 X 4.3295/ $2,738 = 1.03 Acceptable

C $350 X (P/G, i,5) / $3,000 =$350 X 8.2369/ $3,000 = 0.96

NotAcceptable




Cash Flow Analysis



Tax Considerations




4. Calculate Benefit/Cost ratio of the difference. If this B/C > 1, retain the higher cost alternative, otherwise retain the lower cost alternative.

YEAR ALTERNATIVE A ALTERNATIVE B B -‐ A

0 -‐$2,500 -‐$2,738 -‐$238

1 0 $650 $650

2 0 $650 $650

3 0 $650 $650

4 0 $650 $650

5 $3,190 $650 -‐$2,540

B/C = $650 X 3.5460/ ($238 + $2,540 X 0.7835) = 1.03



Cash Flow Analysis



Tax Considerations



5. Since the B/C > 1,the rate-of-return on the increment must be something greater than 5 percent and we therefore accept the increment and retain the higher cost alternative, B.



Cash Flow Analysis



Tax Considerations

Tax Consideration


Tax Consideration

§ The effects of taxes on investments are significant part of all real problems and should be considered.

§ Because taxes have been ignored in our analysis, the results are considered a before-tax cash flow.

§ If the consequences of income tax and other tax effects are incorporated into the economic analysis we will have an after-tax analysis.



Cash Flow Analysis



Tax Considerations


Tax Consideration

§ The following relationships are involved:§ before-tax cash flow

§ depreciation

§ taxable income = (before-tax cash flow) - (depreciation)

§ income taxes = (taxable income) x (incremental tax rate)

§ after-tax cash flow = (before-tax cash flow) - (income taxes)

§ Tax laws are complex and changing. All of the principles and techniques that have been developed can be applied to an after-tax analysis.



Cash Flow Analysis



Tax Considerations

AACE InternationalArabian Gulf Section

CCP CertificationExam Preparation Workshop


Discrete Compound Interest Table

i = 6%


FactorsEquivalent Worth

Cash Flow Analysis



Tax Consideration

Problem Solving


1 1.0600 0.9434 1.0000 1.0600 1.0000 0.9434 0.0000 0.0000

2 1.1236 0.8900 0.4854 0.5454 2.0600 1.8334 0.4854 0.8900

3 1.1910 0.8396 0.3141 0.3741 3.1836 2.6730 0.9612 2.5692

4 1.2625 0.7921 0.2286 0.2886 4.3746 3.4651 1.4272 4.9455

5 1.3382 0.7473 0.1774 0.2374 5.6371 4.2124 1.8836 7.9345

6 1.4185 0.7050 0.1434 0.2034 6.9753 4.9173 2.3304 11.4594

7 1.5036 0.6651 0.1191 0.1791 8.3938 5.5824 2.7676 15.4497

8 1.5938 0.6274 0.1010 0.1610 9.8975 6.2098 3.1952 19.8416

9 1.6895 0.5919 0.0870 0.1470 11.4913 6.8017 3.6133 24.5768

10 1.7908 0.5584 0.0759 0.1359 13.1808 7.3601 4.0220 29.6023


Uniform Gradient

Uniform Gradient



Cash Flow Analysis



Tax Consideration

Problem Solving


$400$300

$500

$600

$700


Uniform Gradient

Uniform Gradient



Cash Flow Analysis



Tax Consideration

Problem Solving


$300

$100

$200

$300

$400 $400 $400 $400

P = $300A = $400G = $100


Uniform Gradient

Uniform Gradient



Cash Flow Analysis



Tax Consideration

Problem Solving


G = $100

1. Consider determining f(2.5). Since 2.5 is midway between 2 and 3, it is reasonable to take f(2.5) midway between f(2) = 0.9093 and f(3) = 0.1411, which yields 0.5252.

2. Generally, linear interpolation takes two data points, say (xa,ya) and (xb,yb), and the interpolant is given by:


Linear InterpolationEquivalence & Conventions Interest Discount


Cash Flow Analysis



Tax Consideration

Problem Solving

economic analysis

Documents

uniform series

present value

lead project engineer

numerical value

bakr alhajri engineering

symbolsa annual

economic analysis

certified cost engineer