P negative as we are spending the money to get the machine and SV positive as

# P negative as we are spending the money to get the

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P (negative) as we are spending the money to get the machine, and +SV (positive) as this is what we are selling the machine for at the end of year ‘n’. Applying EUAS here, we get, EUAS = PW x (A/P,i%,n) EUAC = - EUAS = - [(-P + SV(P/F,i%,n)] x (A/P,i%,n) = [P SV(P/F,i%,n)]x(A/P,i%,n) EUAC = (P-SV)(A/P,i,%,n) + i*SV 10 IE 492 Engineering Economics

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CAPITAL RECOVERY (CRF) Also , in other words, Capital Recovery factor converts a present value into cash flows of equal annual payments over a specific time, at a specific discount rate (interest). From chapter 2, we know the Capital Recovery Factor formula: A/P = i(1+i) n / [(1+i) n 1] Therefore, A = P x (A/P,i%,n) = P x CRF CRF is basically amount of uniform payments received for n period such that total present value of these payments is equivalent to payment of one dollar at present, at interest rate ‘i‘. 11 IE 492 Engineering Economics
CAPITALIZED EQUIVALENT (CE) Present Worth / Value of an alternative where interest earned is withdrawn on a regular basis leaving the principal intact is called Capitalized Equivalent . As an example, Capitalized Equivalent is the PW of an alternative that lasts forever i.e. bridges, roadways, as well as permanent endowments. CE = P = A x (P/A,i%,n) where n = A = i x P CE = A / i Example: What is the difference between an investment of \$10,000 per year for 100 years, and \$10,000 per year in perpetuity at interest rate of 10% per year. PW = 10,000 x (P/A,10%,100) = 10,000 x (.10001)-1 = 10,000 x 9.9990 = \$99,990.00 CE = PW/i = 10,000 / .01 CE = \$100,000 Difference = \$100,000 - \$99,990.00 = \$10 12 IE 492 Engineering Economics
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