Ch2-Lecture_Notes

# Ch2-Lecture_Notes - ENGINEERING ECONOMY Sixth Edition Blank...

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Chapter 2 Factors: How Time and Interest Affect Money ENGINEERING ECONOMY Sixth Edition Blank and Tarquin

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Learning Objectives 05/13/09 2 1. F/P and P/F Factors  (Single Payment Factors) 2. P/A and A/P Factors  (Uniform Series Present Worth Factor  and Capital Recovery Factor) 3. F/A and A/F Factors  (Sinking Fund Factor and Uniform- Series Compound Amount Factor) 4. Interpolate Factor Values 5. P/G and A/G Factors  (Arithmetic Gradient Factors) 6. Geometric Gradient 7. Calculate i  (unknown interest rate) 8. Calculate “n”  (number of years)
Single Payment Factors (F/P and P/F) Objective: Derive factors to determine the present or future worth of a cash flow Cash Flow Diagram – basic format    0                 1                 2               3                                                    n-1              n  i% / period

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Basic Derivation: F/P factor 05/13/09 4 F n  = P 0 (1+i)     (F/P, i%, n) factor:  Excel: =FV(i%, n, ,P)   P 0  = F n 1/(1+i) n   (P/F, i%, n) factor:  Excel: =PV(i%, n, , F)
Derivation: F/P factor Find F given P 05/13/09 5

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Present Worth Factor from F/P N n 05/13/09 6
P/F factor – discounting back in time Discounting back from the future 05/13/09 7 P F n N ………… . P/F factor brings a single future  sum back to a specific point in  time.

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Example- F/P Analysis Example: P= \$1,000;n=3;i=10% What is the future value, F? 05/13/09 8  0         1             2             3 P=\$1,000 F = ?? i=10%/year F 3  = \$1,000 [F/P,10%,3] = \$1,000[1.10] 3      = \$1,000[ 1.3310 ] = \$1,331.00
Example – P/F Analysis Assume F = \$100,000, 9 years from now. What is the present worth of this amount now if i =15%? 05/13/09 9   0         1            2           3                                       8            9 ………… F 9  = \$100,000 P= ??  i = 15%/yr P 0  = \$100,000(P/F, 15%,9) = \$100,000(1/(1.15) 9 )     = \$100,000( 0.2843 ) = \$28,426  at time t = 0

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05/13/09 10 Uniform Series Present Worth and Capital Recovery Factors
Uniform Series Present Worth This expression will convert an annuity cash flow to an equivalent present worth amount one period to the left of the first annuity cash flow. (1 ) 1 0 (1 ) n n i P A for i i i + - = + / %, P A i n factor 05/13/09 11

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Capital Recovery Factor (CRF) = A/P factor Given the P/A factor (1 ) 1 0 (1 ) n n i P A for i i i + - = + (1 ) (1 ) 1 n n i i A P i + = + - 05/13/09 12 Solve for A in terms of P Yielding…. A/P, i%, n
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## This note was uploaded on 04/07/2008 for the course MSE 304 taught by Professor Reiner during the Spring '08 term at CSU Northridge.

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Ch2-Lecture_Notes - ENGINEERING ECONOMY Sixth Edition Blank...

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