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
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CAPITALIZED EQUIVALENT (CE) Present Worth / Value of an alternative where interest earned is withdrawn on a regular basis leaving the principal intact is called Capitalized Equivalent .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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