Weekly_2 - and all costs to the end of the year the only...

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ChE 3171, Spring 2010, Week 2 Fixed annuities : To pay of a principal P 0 : A = P 0 (1 + i ) n n - 1 k =0 (1 + i ) k To build up a fund P n = A n - 1 s k =0 (1 + i ) k Summation formulas : n - 1 s k =0 (1 + i ) k = (1 + i ) n - 1 i , n s k =1 1 (1 + i ) k = (1 + i ) n - 1 (1 + i ) n i When substituted into the equations above, these give P 0 = A (1 + i ) n - 1 ( i + 1) n i = A 1 - (1 + i ) - n i P n = A (1 + i ) n - 1 i where i is the compound interest earned per period. Uniform gradient annuity : A n = A 0 + ( n - 1) G Present value analysis : Present value of a Fxed annuity with n periods PV n = A n s k =1 1 (1 + i ) k = A (1 + i ) n - 1 (1 + i ) n i where i is the time value of money. Present value of uniform gradient annuity PV n = A 0 (1 + i ) n - 1 (1 + i ) n i + G b (1 + i ) n - 1 (1 + i ) n i 2 - n (1 + i ) n i B where i is the time value of money. Project cash ±ow tables and diagrams. Present value of a project is done by referring all proFt
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Unformatted text preview: and all costs to the end of the year, the only exception being the sunk cost , the initial expenses needed to start the project. Sunk cost is referred to year zero. PV = n s k =0 ProFt k-Cost k (1 + i ) k Three types of present value analysis considered: Yes/no a speciFed project, choosing between alternative projects, picking investment options from a list of projects. Rate of return (ROR) : The value of the time value of money at which the present value of a project equals zero. 1...
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