# เศรษฐศาสตร์วิศวกรรม Part i

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1 .. ?

1 ? 1

1 10 (Interest) (Credit risk or Price of credit) (Opportunity cost)

() ? (Interest)

.. 2550 1 10 .. 2560 1 1,000 ( 1 ) 10 ......1,000 10 10 100 Equivalence value? (Interest)?

1 .. ? 1 . 100

... PROJECT 10 ENGINEERING ECONOMY ... () = S D C A I (p-d-c-a)Management : Q, C, D, S, M, P, E, E = TQ

Kaizen E C R SELIMINATECOMBINEREARRANGESIMPLIFY : : : : VALUE ENGINEERING

Value Engineering

(Time value of money) 100 .. (equivalent) 100 + X 1 100 + Y 2

Cash Flow Analysis

Loan() / Debt ()Interest ()Compound interest ()Interest rate (i) ()Number of interest periods (n) ( )Present value (P or PV) = Future value (F or FV) = Uniform series (A = Annuity) = Uniform gradient (G) = (SIMPLE INTEREST) I = P n iI = , P = , n = , i = P = 100, n = 2 , i = 6 %

I = 100 2 0.06 = 12 (COMPOUND INTEREST)

() ( )

(COMPOUND INTEREST) (Fn-1)(Fn)1PiPP(1+i)2P(1+i)iP(1+i)P(1+i)2....nP(1+i)n-1iP(1+i)n-1P(1+i)nFn = P (1+i)n(1+i)n factor F P (F/P,i%,n) Single payment compound amount (SPCAF) P F ; P = F (P/F, i , n) F P ; F = P (F/P, i , n) P A ; P = A (P/A , i , n) A P ; A = P (A/P , i , n) A F ; A = F (A/F, i , n) F A ; F = A (F/A, i , n) P G ; P = G (P/G, i, n) A G ; A = G (A/G, i, n) (Notation)

(Compound Interest Table)

CASH FLOW DIAGRAM012345678-+ inSingle cash flowEqual (uniform) payment seriesLinear gradient seriesGeometric gradient seriesIrregular payment series

CASH FLOW DIAGRAM Cash Flow Diagram 1,000 1 2530 6% 1 2540 1P = 1,000 , i = 6%, n =10 F F = P(F/P,6%,10) = 1,000(1.7908) = 1,791

840 1 2530 6% 10 2P = 840 , i = 6%, n = 10 AA = P(A/P,6%,10) = 840 (0.13587) = 114.1

A = ? 2,000 1,500 2 1,000 4 8% 10 3P0 = 2,000, i = 8%, n = 10 P2 = 1,500, i = 8%, n = 8 P4 = 1,000, i = 8%, n = 6 F

F= P0(F/P,8%,10) + P2(F/P,8%,8) + P4(F/P,8%,6) = 2,000(2.1589) + 1,500(1.8569) + 1,000(1.5869) = 4,318 + 2,776 + 1,587 = 8,681 4 80 100 5 P = 80, F = 100, n = 5 i

(F/P,i%,5) = F/P = 100/80 = 1.25

Trial & Errori = 4.5%, F/P = 1.2462i = 5.0%, F/P = 1.2763i = 4.5 + 0.5[(1.25-1.2467)/(1.2763-1.2462)] = 4.56%

5 2,000 2,400 2,100 300 6 8% 6 A P

5P = 2000, i = 8%,n = 6A = 2400, i = 8%,n = 6G = -300, i = 6%,n = 6A= P(A/P,8%,6) + A - G(A/G,8%,6) = 2000(0.21632) + 2400 - 300(2.276) = 2150P = 2000 + 2400(P/A,8%,6) - 300(P/G,8%,6) = 2000 + 2400(4.632) - 300(10.523) = 9938

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