Upload
jera-garcia
View
216
Download
0
Embed Size (px)
Citation preview
8/7/2019 36636052-Engineering-Economy
1/35
1
Engineering Economics
November 3, 2004
8/7/2019 36636052-Engineering-Economy
2/35
2
Engineering Economy
It deals with the concepts and techniquesof analysis useful in evaluating the worthof systems, products, and services in
relation to their costs
8/7/2019 36636052-Engineering-Economy
3/35
3
Engineering Economy
It is used to answer many differentquestions Which engineering projects are worthwhile?
Has the mining or petroleum engineer shown that
the mineral or oil deposits is worth developing? Which engineering projects should have ahigher priority?
Has the industrial engineer shown which factoryimprovement projects should be funded with the
available dollars?
How should the engineering project bedesigned?
Has civil or mechanical engineer chosen the best
thickness for insulation?
8/7/2019 36636052-Engineering-Economy
4/35
4
Basic Concepts
Cash flow
Interest Rate and Time value of money
Equivalence technique
8/7/2019 36636052-Engineering-Economy
5/35
5
Cash Flow Engineering projects generally have economic
consequences that occur over an extendedperiod of time
For example, if an expensive piece of machinery isinstalled in a plant were brought on credit, the simpleprocess of paying for it may take several years
The resulting favorable consequences may last aslong as the equipment performs its useful function
Each project is described as cash receipts ordisbursements (expenses) at different points intime
8/7/2019 36636052-Engineering-Economy
6/35
6
Categories of Cash Flows The expenses and receipts due to
engineering projects usually fall into one ofthe following categories: First cost: expense to build or to buy and install
Operations and maintenance (O&M): annual
expense, such as electricity, labor, and minorrepairs
Salvage value: receipt at project termination forsale or transfer of the equipment (can be asalvage cost)
Revenues: annual receipts due to sale of productsor services
Overhaul: major capital expenditure that occursduring the assets life
8/7/2019 36636052-Engineering-Economy
7/35
7
Cash Flow diagrams
The costs and benefits of engineeringprojects over time are summarized on a cashflow diagram (CFD). Specifically, CFDillustrates the size, sign, and timing ofindividual cash flows, and forms the basis forengineering economic analysis
A CFD is created by first drawing asegmented time-based horizontal line,divided into appropriate time unit. Each time
when there is a cash flow, a vertical arrow isadded pointing down for costs and up forrevenues or benefits. The cost flows aredrawn to relative scale
8/7/2019 36636052-Engineering-Economy
8/35
8
Drawing a Cash Flow Diagram
In a cash flow diagram (CFD) the end of period t isthe same as the beginning of period (t+1)
Beginning of period cash flows are: rent, lease, andinsurance payments
End-of-period cash flows are: O&M, salvages,
revenues, overhauls The choice of time 0 is arbitrary. It can be when a
project is analyzed, when funding is approved, orwhen construction begins
One persons cash outflow (represented as a
negative value) is another persons inflow(represented as a positive value) It is better to show two or more cash flows occurring
in the same year individually so that there is a clearconnection from the problem statement to each cashflow in the diagram
8/7/2019 36636052-Engineering-Economy
9/35
9
An Example of Cash Flow Diagram A man borrowed $1,000 from a bank at 8%
interest. Two end-of-year payments: at theend of the first year, he will repay half of the$1000 principal plus the interest that is due.
At the end of the second year, he will repay
the remaining half plus the interest for thesecond year.
Cash flow for this problem is:
End of year Cash flow
0 +$1000
1 -$580 (-$500 - $80)
2 -$540 (-$500 - $40)
8/7/2019 36636052-Engineering-Economy
10/35
10
Cash Flow Diagram
$1,000
0
1 2
$580 $540
8/7/2019 36636052-Engineering-Economy
11/35
11
Time Value of Money
Money has value Money can be leased or rented
The payment is called interest
If you put $100 in a bank at 9% interest for one timeperiod you will receive back your original $100 plus$9
Original amount to be returned = $100
Interest to be returned = $100 x .09 = $9
8/7/2019 36636052-Engineering-Economy
12/35
12
Compound Interest
Interest that is computed on the originalunpaid debt and the unpaid interest
Compound interest is most commonlyused in practice
Total interest earned = In = P (1+i)n - P
Where,
P present sum of money
i interest rate n number of periods (years)
I2 = $100 x (1+.09)2 - $100 = $18.81
8/7/2019 36636052-Engineering-Economy
13/35
13
Future Value of a Loan With
Compound Interest Amount of money due at the end of a loan
F = P(1+i)1(1+i)2..(1+i)n or F = P (1 + i)n
Where, F = future value and P = present value Referring to slide #10, i = 9%, P = $100 and say
n= 2. Determine the value of F.
F = $100 (1 + .09)2 = $118.81
8/7/2019 36636052-Engineering-Economy
14/35
14
Notation for
Calculating a Future Value Formula:
F=P(1+i)n is the
single payment compound amount factor.
Functional notation:
F=P(F/P,i,n) F=5000(F/P,6%,10)
F =P(F/P) which is dimensionallycorrect.
8/7/2019 36636052-Engineering-Economy
15/35
15
Notation for
Calculating a Present Value P=F(1/(1+i))n=F(1+i)-n is the
single payment present worth factor.
Functional notation:P=F(P/F,i,n) P=5000(P/F,6%,10)
Interpretation of (P/F, i, n): a present sum P,
given a future sum, F, n interest periodshence at an interest rate i per interestperiod
8/7/2019 36636052-Engineering-Economy
16/35
16
Spreadsheet Function
P = PV(i,N,A,F,Type)
F = FV(i,N,A,P,Type)
i = RATE(N,A,P,F,Type,guess)
Where, i = interest rate, N = number of interestperiods, A = uniform amount, P = present sumof money, F = future sum of money, Type = 0means end-of-period cash payments, Type =
1 means beginning-of-period payments,guess is a guess value of the interest rate
8/7/2019 36636052-Engineering-Economy
17/35
17
Equivalence Relative attractiveness of different
alternatives can be judged by using thetechnique of equivalence
We use comparable equivalent values of
alternatives to judge the relativeattractiveness of the given alternatives
Equivalence is dependent on interest rate
Compound Interest formulas can beused to facilitate equivalencecomputations
8/7/2019 36636052-Engineering-Economy
18/35
18
Technique of Equivalence
Determine a single equivalent value at apoint in time for plan 1.
Determine a single equivalent value at apoint in time for plan 2.
Both at the same interest rate and at the same time point.
Judge the relative attractiveness of thetwo alternatives from the comparable
equivalent values.
8/7/2019 36636052-Engineering-Economy
19/35
19
Engineering Economic AnalysisCalculation
Generally involves compound interestformulas (factors)
Compound interest formulas (factors) can
be evaluated by using one of the threemethods
Interest factor tables
Calculator
Spreadsheet
8/7/2019 36636052-Engineering-Economy
20/35
20
Given the choice of these two planswhich would you choose?
Year Plan 1 Plan 2
0 $5,000
1 $1,000
2 $1,000
3 $1,000
4 $1,000
5 $1,000Total $5,000 $5,000
To make a choice the cash flows must be altered
so a comparison may be made.
8/7/2019 36636052-Engineering-Economy
21/35
21
Resolving Cash Flows to Equivalent PresentValues
P = $1,000(PA,10%,5)
P = $1,000(3.791) =$3,791
P = $5,000
Alternative 2 is better
than alternative 1 sincealternative 2 has agreater present value
8/7/2019 36636052-Engineering-Economy
22/35
22
An Example of Future Value
Example: If $500 were deposited in a
bank savings account, how much wouldbe in the account three years hence ifthe bank paid 6% interest compounded
annually? Given P = 500, i = 6%, n = 3, use F =
FV(6%,3,,500,0) = -595.91
Note that the spreadsheet gives anegative number to find equivalent of P.If we find P using F = -$595.91, we getP = 500.
8/7/2019 36636052-Engineering-Economy
23/35
23
An Example of Present Value
Example 3-5: If you wished to have
$800 in a savings account at the end offour years, and 5% interest we paidannually, how much should you put into
the savings account? n = 4, F = $800, i = 5%, P = ?
P = PV(5%,4,,800,0) = -$658.16
You should use P = $658.16
8/7/2019 36636052-Engineering-Economy
24/35
24
Economic Analysis Methods
Three commonly used economic analysismethods are
Present Worth Analysis
Annual Worth Analysis Rate of Return Analysis
8/7/2019 36636052-Engineering-Economy
25/35
25
Present Worth Analysis
Steps to do present worth analysis for asingle alternative (investment)
Select a desired value of the return oninvestment (i)
Using the compound interest formulas bringall benefits and costs to present worth
Select the alternative if its net present worth(Present worth of benefits Present worth of
costs) 0
8/7/2019 36636052-Engineering-Economy
26/35
26
Present Worth Analysis
Steps to do present worth analysis forselecting a single alternative (investment)from among multiple alternatives
Step 1: Select a desired value of the return on
investment (i) Step 2: Using the compound interest formulas
bring all benefits and costs to present worthfor each alternative
Step 3: Select the alternative with the largestnet present worth (Present worth of benefits Present worth of costs)
8/7/2019 36636052-Engineering-Economy
27/35
27
Present Worth Analysis
A construction enterprise is investigating the
purchase of a new dump truck. Interest rate is9%. The cash flow for the dump truck are asfollows:
First cost = $50,000, annual operating cost =$2000, annual income = $9,000, salvage valueis $10,000, life = 10 years. Is this investmentworth undertaking?
P = $50,000, A = annual net income = $
9,000 -$2,000 = $7,000, S = 10,000, n = 10.
Evaluate net present worth = present worth ofbenefits present worth of costs
8/7/2019 36636052-Engineering-Economy
28/35
28
Present Worth Analysis
Present worth of benefits = $9,000(PA,9%,10) =$9,000(6.418) = $57,762
Present worth of costs = $50,000 +$2,000(PA,9%,10) - $10,000(P`F,9%,10)=
$50,000 + $2,000(
6..41
8) - $10,000(.4224) =$58,612
Net present worth = $57,762 - $58,612 < 0 donot invest
What should be the minimum annual benefit formaking it a worthy of investment at 9% rate ofreturn?
8/7/2019 36636052-Engineering-Economy
29/35
29
Present Worth Analysis
Present worth of benefits = A(PA,9%,10)= A(6.418)
Present worth of costs = $50,000 +$2,000(PA,9%,10) - $10,000(P`F,9%,10)=
$50,000 + $2,000(6..418) - $10,000(.4224)= $58,612
A(6.418) = $58,612 A = $58,612/6.418
= $9,312.44
8/7/2019 36636052-Engineering-Economy
30/35
30
Cost and Benefit Estimates
Present and future benefits (income) andcosts need to be estimated to determinethe attractiveness (worthiness) of a newproduct investment alternative
8/7/2019 36636052-Engineering-Economy
31/35
31
Annual costs and Income for a Product
Annual product total cost is the sum ofannual material, labor, and overhead(salaries, taxes, marketing expenses,office costs, and related costs), annual
operating costs (power, maintenance,repairs, space costs, and relatedexpenses), and annual first cost minus theannual salvage value.
Annual income generated through thesales of a product = number of units soldannuallyxunit price
8/7/2019 36636052-Engineering-Economy
32/35
32
Rate of Return Analysis
Single alternative case
In this method all revenues and costs ofthe alternative are reduced to a singlepercentage number
This percentage number can be comparedto other investment returns and interestrates inside and outside the organization
8/7/2019 36636052-Engineering-Economy
33/35
33
Rate of Return Analysis
Steps to determine rate of return for a
single stand-alone investment Step 1: Take the dollar amounts to the same
point in time using the compound interest
formulas Step 2: Equate the sum of the revenues to the
sum of the costs at that point in time andsolve for i
8/7/2019 36636052-Engineering-Economy
34/35
34
Rate of Return Analysis
An initial investment of $500 is being
considered. The revenues from thisinvestment are $300 at the end of the firstyear, $300 at the end of the second, and
$200 at the end of the third. If the desiredreturn on investment is 15%, is the projectacceptable?
In this example we will take benefits andcosts to the present time and their presentvalues are then equated
8/7/2019 36636052-Engineering-Economy
35/35
35
Rate of Return Analysis
$500 = $300(P`F, i, n=1) + 300(P`F, i, n=2) +
$200(P`F, i, n=3) Now solve for i using trial and error method
Try 10%: $500 = ? $272 + $247 + $156 = $669(not equal)
Try 20%: $500 = ? $250 + $208 + $116 = $574(not equal)
Try 30%: $500 = ? $231 + $178 + $91 = $500(equal) i = 30%
The desired return on investment is 15%, theproject returns 30%, so it should beimplemented