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Unformatted text preview: Slide #1 ECE 4001 L15 T. Michaels 2008 Lecture 15 Engineering Economics: Applications and Examples Slide #2 ECE 4001 L15 T. Michaels 2008 F/P P/F A/F F/A A/P P/A Gradient Factors Slide #3 ECE 4001 L15 T. Michaels 2008 All Factors Obey Rules of Algebra ( / ) A P A P = 1 ( / ) ( / ) F P P F = 1 1 P = (P/F ) F 1 1 F = (F/P) (P/F ) F ETC... Slide #4 ECE 4001 L15 T. Michaels 2008 Cash Flow Diagrams Slide #5 ECE 4001 L15 T. Michaels 2008 Arithmetic Gradient Series Payment End of Year $0 1 $1000 2 $2000 3 $3000 4 $4000 5 Compute present value for above payments for an interest rate of 4% (note payment total is $10,000 and G is the payment made at the end of year 2) Slide #6 ECE 4001 L15 T. Michaels 2008 Present Value of Arithmetic Gradient Series (assume interest rate of 4%, G = $1000, 4 payments with n = 5) ( / , %, ) ( / ,4%,5) 1000 P P G i n G P G = = Slide #7 ECE 4001 L15 T. Michaels 2008 Present Value of Arithmetic Gradient Series (assume interest rate of 4%, G = $1000, 5 yrs of payments) 5 2 5 ( / , %, ) ( / ,4%,5) 1000 [(1.04) (0.04) 5 1] 1000 8,554.67 (0.04) (1.04) P P G i n G P G P = =   = = Note payment total = $10,000 Slide #8 ECE 4001 L15 T. Michaels 2008 Arithmetic Gradient Series Plus Annualized Series Payment End of Year $1000 $1000 $0 1 $1500 $1000 $500 2 $2000 $1000 $1000 3 $2500 $1000 $1500 4 $3000 $1000 $2000 5 = + = + = + = + = + A=$1000, G=500 Compute present value for above payments for a interest rate of 4% (total of payments = $10,000) Slide #9 ECE 4001 L15 T. Michaels 2008 Present Value of Arithmetic Gradient Plus Annualized Series (assume interest rate of 4%, A = $1000, G = $500, 5 yrs of payments) 5 5 5 2 5 ( / ) ( / ) ( / ) ( / ,4%,5) 1000 (1.04) 1 ( / ) 1000 4,451.82 0.04 (1.04) ( / ) ( / ,4%,5) 500 (1.04) 0.2 1 ( / ) 500 4,277.34 (0.04) (1.04) ( / ) ( / ) 8,729.16 P P A A P G G P A A P A P A A P G G P G P G G P P A A P G G = + =  = = =  = = = + = Slide #10 ECE 4001 L15 T. Michaels 2008 Present Value of Arithmetic Gradient Plus Annualized Series (assume interest rate of 4%, A = $1000, G = $500, 5 yrs of payments) 5 5 5 2 5 ( / ) ( / ) ( / ) ( / ,4%,5) 1000 (1.04) 1 ( / ) 1000 4,451.82 0.04 (1.04) ( / ) ( / ,4%,5) 500 (1.04) 0.2 1 ( / ) 500...
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 Spring '09
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