Engineering Orientation

Engineering Economics

Engineering Economics

Value and Interest Cost of Money Simple and Compound Interest Cash Flow Diagrams Cash Flow Patterns Equivalence of Cash Flow Patterns

Value and Interest

Money, Amount vs. Value First Cost is what you pay for an item

when you buy it

http://en.wikipedia.org/wiki/Time_value_of_money

The time value of money is the value of money with a given amount of interest earned or inflation accrued over a given amount of time.

The ultimate principle suggests that a certain amount of money today has different buying power than the same amount of money in the future.

$100 of today's money invested for one year and earning 5% interest will be worth $105 after one year.

Interest / Interest Rate

The difference between the anticipated amount in the future and its current value is called interest.

At an annual interest rate of 10% what is the value now of the expectation of receiving $1 in one year?

Cost of Money

Interest that could be earned if the amount invested in a business or security was instead invested in government bonds or in time deposit.

Cost of Money

Buy a car for $20,000 of your own cash vs. US bonds returning 5%/yr ($1,000 forever)

In effect you are paying $1,000 for ever

Simple and Compound Interest

You have a business project costing $100,000

• You get a loan for 7.5% yearly for 5 years at simple interest payable at the end of the loan

•The loan costs $7,500 for each of five years for a total interest of $37,500

Total cost over 5 years = $137,500

Simple and Compound Interest

In the previous example, are you borrowing?• $7,500 for four years,

• $7,500 for three years,

• $7,500 for two years,

• $7,500 for one year

Formulae

P or PV Principal is the amount borrowed N # of pay periods i Interest rate per period F or FV, Future worth, value in the future of

what you have to payback Formulae:

• Simple interest = P(1 + Ni) ( = $137,500)

• Compound interest = P(1 + i)N ( = $143,563)

Pay periods

Calculate FV Assume your loan is compounded

quarterly, monthly or daily instead of yearly.

Student loan of $25,000 at 8% for • Annually for two years,

• Quarterly for two years and

• Daily for two years

Pay periods

PV 25,000.00 PV 25,000.00 PV 25,000.00 i 8% i/n 2% i/n 0.0219%n*N 2 n*N 8 n*N 730FV (29,160.00) FV (29,291.48) FV (29,337.26)

Yearly n=1 Quarterly n=4 Dayly n=365

nNnrPVFV )/1(

Continuous Interest Rate

Compute the effective annual interest rate ie equivalent to 8% nominal annual interest compounded continuously.

Calculate the FV

In the limitiNPVeFV

NnnN niPVniPVFV /1)/1(

Compare

29,337.77 rNPVeFV

PV 25,000.00 PV 25,000.00 PV 25,000.00 i 8% i/n 2% i/n 0.0219%n*N 2 n*N 8 n*N 730FV (29,160.00) FV (29,291.48) FV (29,337.26)

Yearly n=1 Quarterly n=4 Dayly n=365

Example

What amount must be paid in two years to settle a current debt of $1,000 if the interest rate is 6% Annually?

PV = 1,000 i = .06 N = 2 n = 1 nNnrPVFV )/1(

Cash Flow Diagrams

Cash Flow Patterns

Example A new widget twister, with a life of six years, would save $2,000

in production costs each year. Using a 12% interest rate, determine the highest price that could be justified for the machine. Although the savings occur continuously throughout each year, follow the usual practice of lumping all amounts at the ends of years.

Example A new widget twister, with a life of six years, would save $2,000

in production costs each year. Using a 12% interest rate, determine the highest price that could be justified for the machine. Although the savings occur continuously throughout each year, follow the usual practice of lumping all amounts at the ends of years.

PV -8,222.81FVA 2,000.00n 6.00i 12.00

Example

How soon does money double if it is invested at 8% interest?

Example

Compute the annual equivalent maintenance costs over a 5-year life of a laser printer that is warranted for two years and has estimated maintenance costs of $100 annually. Use i = 10%.

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Return on Investment

ROI = The ratio of annual return to the cost of the investment

If an investment of $500,000 produces an income of $40,000 per year, its ROI = $40,000/$500,000 = 0.08 = 8%.

Many successful large companies operate with ROI’s of 15% or more

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Return on Investment

Company ROI, annual %DOW Chemical 10.5Exxon Mobil 22.4DuPont 18.5PPG Industries 20.2Air Products 11.0Eastman Chemical 10.9W.R. Grace 9.8

Cost of losing one semester

Two students, Frank and Mary start they Engineering Studies on the same date and they make the commitment of retiring thirty years after their forecasted graduation date (the date they would graduate if no delays are introduced). This date will not change if any delays make any of them graduate later.

Calculate the difference in their earnings if for some reasons Frank is required to graduate one semester later than what was intended.

The Model

Assumptions:• We have a constant inflation

• You have a yearly Salary Increase greater than what you loose because of inflation

• Salary increases and inflation are constant

• They work for the same company their entire carrier

One year window

Starting Salary 4000 Year Beginning Year 1 Beginning Year n Jan Feb Mar Apr MaySalary Inc. % 5 1 ($15,867.55) ($15,867.55) 4,000.00 4,000.00 4,000.00 4,000.00 0.00Inflation % 4Registration 2,000.00Loss 17,867.55

Four year window

Starting Salary 4000 Year Beginning Year 1 Beginning Year n Salary Jan Feb Mar Apr MaySalary Inc. % 5 1 (15,867.55) (15,867.55) 4,000.00 4,000.00 4,000.00 4,000.00 4,000.00 0.00Inflation % 4 2 (762.86) (793.38) 4,200.00 200.00 200.00 200.00 200.00 0.00Registration 2,000.00 3 (770.20) (833.05) 4,410.00 210.00 210.00 210.00 210.00 0.00Loss 20,178.22 4 (777.60) (874.70) 4,630.50 220.50 220.50 220.50 220.50 0.00

Thirty year windowStarting Salary 4000 Year Beginning Year 1 Beginning Year n Salary Jan Feb Mar Apr MaySalary Inc. % 5 1 (15,867.55) (15,867.55) 4,000.00 4,000.00 4,000.00 4,000.00 4,000.00 0.00Inflation % 4 2 (762.86) (793.38) 4,200.00 200.00 200.00 200.00 200.00 0.00Registration 2,000.00 3 (770.20) (833.05) 4,410.00 210.00 210.00 210.00 210.00 0.00Loss 43,243.31 4 (777.60) (874.70) 4,630.50 220.50 220.50 220.50 220.50 0.00

5 (785.08) (918.43) 4,862.03 231.53 231.53 231.53 231.53 0.006 (792.63) (964.36) 5,105.13 243.10 243.10 243.10 243.10 0.007 (800.25) (1,012.57) 5,360.38 255.26 255.26 255.26 255.26 0.008 (807.95) (1,063.20) 5,628.40 268.02 268.02 268.02 268.02 0.009 (815.71) (1,116.36) 5,909.82 281.42 281.42 281.42 281.42 0.0010 (823.56) (1,172.18) 6,205.31 295.49 295.49 295.49 295.49 0.0011 (831.48) (1,230.79) 6,515.58 310.27 310.27 310.27 310.27 0.0012 (839.47) (1,292.33) 6,841.36 325.78 325.78 325.78 325.78 0.0013 (847.54) (1,356.94) 7,183.43 342.07 342.07 342.07 342.07 0.0014 (855.69) (1,424.79) 7,542.60 359.17 359.17 359.17 359.17 0.0015 (863.92) (1,496.03) 7,919.73 377.13 377.13 377.13 377.13 0.0016 (872.23) (1,570.83) 8,315.71 395.99 395.99 395.99 395.99 0.0017 (880.61) (1,649.37) 8,731.50 415.79 415.79 415.79 415.79 0.0018 (889.08) (1,731.84) 9,168.07 436.57 436.57 436.57 436.57 0.0019 (897.63) (1,818.44) 9,626.48 458.40 458.40 458.40 458.40 0.0020 (906.26) (1,909.36) 10,107.80 481.32 481.32 481.32 481.32 0.0021 (914.98) (2,004.83) 10,613.19 505.39 505.39 505.39 505.39 0.0022 (923.77) (2,105.07) 11,143.85 530.66 530.66 530.66 530.66 0.0023 (932.66) (2,210.32) 11,701.04 557.19 557.19 557.19 557.19 0.0024 (941.62) (2,320.84) 12,286.10 585.05 585.05 585.05 585.05 0.0025 (950.68) (2,436.88) 12,900.40 614.30 614.30 614.30 614.30 0.00

Engineering Economics

Value and Interest Cost of Money Simple and Compound Interest Cash Flow Diagrams Cash Flow Patterns Equivalence of Cash Flow Patterns