2a - Engineering Economics - Engineering Economics CE 332...

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  CE 332  Page 1 Engineering Economics
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   CE 332 Page 2 Decision Making We make decisions for many reasons,  but usually one of the biggest factors is: How do we decide the best option? $
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   CE 332 Page 3 Considerations When to buy or sell?  Repair or rebuild? Market conditions (interest rates-loans) Rate of return on investment (interest rate- savings) Source of financing Pay-back period Product risks Project risks
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   CE 332 Page 4 Time Value of Money Time value of money  refers to the  change in the value of money over time Interest rate Time Investment or Loan
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   CE 332 Page 5 Cash Terminology P 0 = value of the money at the present P t = value of the money at end of time “t” n = number of interest periods i = interest rate per period F = future value of a present sum of money A = Annuity, a series of consecutive, equal,  end-of-period amounts of money G = gradient, uniform increase each year
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   CE 332 Page 6 Cash Flow Diagrams  Graphical depiction of cash into and out  of an account P = P 0 = initial purchase 0 1 2 3 4 A 1 =annual income F=salvage A 2 =annual cost of operation Income Expense End of year accrual F= future income F= future cost + - Monthly?
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   CE 332 Page 7 Time Value of Money (example) Suppose you deposit $1,000,000 in the bank  at an annual interest rate,  i , of 8% P 0 = $1,000,000 F 1 = P 0 (1+ i ) F 2 = F 1 (1+ i ) 0 1 2 3 4 $1,080,000 $1,166,400 $1,360,500 F 3 = F 2 (1+ i ) F 4 = F 3 (1+ i ) F 4 = F 3 (1+ i )= F 2 (1+i)(1+i)=F 1 (1+i)(1+i)(1+i)=P 0 (1+i)(1+i)(1+i)(1+i)=P 0 (1+i) 4 In general, F n = P 0 (1+i) n
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   CE 332 Page 8 Compound Interest Compound interest includes interest on the  interest earned in pervious periods The  nominal  interest rate  per year is the  period interest rate times the number of  periods per year The annual interest rate when considering the  time value of money for rates quoted for a  period (say one month) is called the  effective  interest rate
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   CE 332 Page 9 Compound Interest (cont.) Visa Card statement lists interest as 2%  per month Nominal Interest Rate =               2%/mo x 12 mo = 24%  Effective Interest Rate = i eff  = (1+i) n  = (1.02) 12  =  0.268 = 26.8%
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   CE 332 Page 10 Compound Interest (cont.) i = (1 + ) - 1 r t t where i = effective interest rate per period (year) r = nominal interest rate per period (year) t = number of compounding periods (per year)
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   CE 332 Page 11 Effective Interest Rate Example A bank quotes the interest on a credit  card balance as 1.5% per month or a  nominal annual interest of 18%.  What  is the effective interest? Thus, the effective annual interest rate  is 19.6% i = (1 + ) - 1 = (1+.015) 12 –1 = 0.196 0.18 12 12
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   CE 332 Page 12 Equivalence Different sums of money at different times can be  equal in economic value For example, at  i  = 8%, $1,000,000 today is  equivalent to $1,360,500 at the end of 4 years P 0 = $1,000,000 P 1 = P 0 (1+ i ) P 2
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This note was uploaded on 04/11/2008 for the course C E 341 taught by Professor Scanlon,andrew during the Spring '07 term at Pennsylvania State University, University Park.

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2a - Engineering Economics - Engineering Economics CE 332...

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