Engineering Economic Analysis Evaluates the monetary aspects of the
products, projects, and processes that engineers design
Aids in the decision making process when alternatives are compared
Especially useful when resources are limited Replace vs. keep Build vs. buy
Time Value of Money $1 today is more valuable than $1 a year
later
Engineering economy adjusts for the time value of money to balance current and future revenues and cost
0 5 10Years
Capital vs. Interest Capital
Invested money and resources Whoever owns it should expect a
return from whoever uses it Bank lends you money
Buy a car Go to college
Firm invests in a project Buy equipment Buy “knowledge”
Capital vs. Interest Interest
Return on capital Typically expressed as an interest
rate for a year
Interest rates are needed to evaluate engineering projects!!
Interest rate =Interest $ amount
Capital $ amount
“Interest”-ing Example
The engineering group of Baker Designs must decide whether to spend $90K (K for thousands) on a new project. This project will cost $5K per year for operations, and it will increase revenues by $20K annually. Both the costs and the revenues will continue for 10 years. Should the project be done? Eschenbach, T.G., Engineering Economy: Applying Theory to Practice, Irwin, 1995, p.22
Types of Interest Nomenclature
P = Initial deposit (or principal) N = Number of years i = Interest rate per year F = Future value after N years
Types of Interest Simple Interest
The interest calculated for N periods is based on the initial depositF0 = PF1 = P + P*i = P*(1 + i)F2 = P + P*i + P*i = P* (1 + i + i) = P* (1 + 2i)……Fn = P + P*i + P*i + … = P* (1 + i + i + …) = P* (1 + Ni)
Types of Interest Compound Interest
Interest type used in engineering economic evaluations
Interest is computed on the current balance that has not yet been paid
Includes accrued interestF0 = PF1 = P + P*i = P *(1 + i)F2 = P1 + P1 * i = P1 *(1+i) = P *(1+i) *(1+i) = P *(1+i)2
……Fn = Pn-1 + Pn-1 * i = Pn-1 *(1+i) = P *(1+i)n-1 *(1+i) = P *(1+i)n
Simple vs. Compound Interest
If $100 is deposited in a savings account, how much is in the account at the end of each year for 20 years, if interest is deposited in the account and no withdrawals are made? Assume a 5% interest per year.
Year F (Simple) F (Compound) Year F (Simple) F (Compound)0 100 100.00 11 155 171.031 105 105.00 12 160 179.592 110 110.25 13 165 188.563 115 115.76 14 170 197.994 120 121.55 15 175 207.895 125 127.63 16 180 218.296 130 134.01 17 185 229.207 135 140.71 18 190 240.668 140 147.75 19 195 252.709 145 155.13 20 200 265.3310 150 162.89
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End of year
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Simple vs. Compound Interest
Compound
Simple
In Class Problem #1If $500 is deposited in a savings account, would a 5% simple interest rate be better than a 3% compound interest rate if you were planning to keep the money for 3 years? For 35 years? Assume that all earned interest is deposited in the account and no withdrawals are made.
Example #1
Sam Bostro borrows $4000 from his parents for his final year of college. He agrees to repay it 3 years later in one payment to which a 7% compound interest rate will be applied.
a) How much does he repay?
F = (4000)(1 + 0.07)3 = $4,900.17
b) How much of this is interest and how much is principal?
F = P + I P = $4,000; I = $900.17
Example #2
Susan Cardinal deposited $500 in her savings account and six years later the account has $600 in it. What compound rate of interest has Susan earned on her capital?
F = P(1+i)n i = [F/P]1/n – 1i = [600/500] 1/6 – 1 = .031i = 3.1%
In Class Problem #2Your friend is willing to loan you $1500 to buy a new computer, but you must agree to pay him back $2500 when you graduate in 4 years? What is the compound interest rate you will be paying your friend?
Cash Flow Diagrams Pictorial description of when and
how much money is spent or received
Summarizes the economic aspects of an engineering project
0 1 2 3 4 5
Cash Flow Categories First Cost
Expense to build or to buy and install Operation and maintenance (O&M)
Annual expenses (electricity, labor, minor repairs, etc.)
Salvage value Receipt at project termination for sale or
transfer of equipment There can also be a salvage COST
Cash Flow Categories Revenues
Annual receipts due to sale of products or services
Overhauls Major capital expenditures that occurs part
way through the life of the asset Prepaid expenses
Annual expenses that must be paid in advance (e.g., leases, insurance)
ExamplesErnie’s Earthmoving is considering the purchase of a piece of heavy equipment. What is the cash flow diagram if the following cash flows are anticipated?First cost $120KO&M cost $30k per yearOverhaul cost $35K in year 3Salvage value $40K after 5 yearsHow would the cash flow diagram change if Ernie decides to lease the equipment (at $25K per year) instead of purchasing it?
a)
b)
Solution
0 1 2 3 4 5
0 1 2 3 4 5
a)
b)
120K
30K 30K30K +35K
30K 30K
40K
25K25 +30K
25 +30K 25K +
30K +35K
25K +30K
30K
Frequency of Compounding Interest rates are typically
specified on an annual basis However, interest is often
compounded more often Semiannually Quarterly Monthly Daily
Frequency of Compounding How does that change our formula?
m = # of compounding periods per year n = # of compounding periods
n = m x N Quarterly?
Monthly?
m = 4n = 4N F = P(1+i/m)m*N = P(1+i/4)4N
m=12n = 12N F = P(1+i/12)12N
ExampleSuppose you borrow $3000 at the beginning of your senior year to meet college expenses. If you make no payments for 10 years and then repay the entire amount of the loan, including accumulated interest, how much money will you owe? Assume interest is 6% per year, compoundeda) Annually m=1 P=3,000b) Quarterly m=4 N=10 yearsc) Monthly m=12 i=6% per yeard) Daily m=365How significant is the frequency of compounding?
SolutionFA = P(1+i/1)1N = 3000(1+0.06/1)10 = $5,372.54
FQ = P(1+i/4)4N = 3000(1+0.06/4)40 = $5,442.05
FM = P(1+i/12)12N = 3000(1+0.06/12)120 = $5,458.19
FD = P(1+i/365)1N = 3000(1+0.06/365)3650 = $5,466.08
SolutionCollege Loan Payment Options
$3,000.00
$3,000.00
$3,000.00
$3,000.00
$2,372.54
$2,442.06
$2,458.19
$2,466.09
$0 $1,000 $2,000 $3,000 $4,000 $5,000 $6,000
Annually
Quarterly
Monthly
Daily
Freq
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Com
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Amount owed
Principal
Interest