FE Reference 8-2.1104web - University of Idaho

1 114 engineering ECONOMICSENGINEERING ECONOMICSF actor Name ConvertsSymbolFormulaSingle Payment Compound Amount toF given P (F/P,i%,n) (1 + i)nSingle Payment Present Worth toP given F (P/F,i%,n) (1 + i) nUniform Series Sinking Fund toA given F (A/F,i%,n)()11 +niiCapital Recovery to A given P (A/P,i%,n)()()111 ++nniiiUniform Series Compound Amount toF given A (F/A,i%,n)()iin11 +Uniform Series Present Worth toP given A (P/A, i%,n)()()nniii+ +111 Uniform GradientPresent Worth toP given G (P/G,i%,n)()()()nnniiniii+ + +11112 Uniform Gradient Future Worth toF given G (F/G,i%,n)()iniin +211 Uniform GradientUniform Series toA given G (A/G,i%,n)()111 + niniNOMENCLATURE AND DEFINITIONSA.

2 Uniform amount per interest periodB .. BV .. Book valueC .. Combined interest rate per interest periodDj .. Depreciation in year jF ..Future worth, value, or amountf .. G .. Uniform gradient amount per interest periodi .. Interest rate per interest periodie .. Annual effective interest ratem .. Number of compounding periods per Number of compounding periods; or the expected life of an assetP ..Present worth, value, or amountr ..Nominal annual interest rateSn .. Expected salvage value in year nSubscriptsj .. at time at time n ..F/G = (F/A n)/i = (F/A) (A/G)NON-ANNUAL COMPOUNDINGimr11em=+ -blBREAK-EVEN ANALYSISBy altering the value of any one of the variables in a situation, value for that variable that makes the two alternatives equally economical. This value is the break-even analysis is used to describe the percentage of capacity of operation for a manufacturing plant at which income will just cover expenses.

3 F, and then they are shifted over the time scale using the interest rate per interest period i. Use a combined interest rate per interest period d for computing present worth values P and Net formula for d is d = i + f + (i f)115 engineering ECONOMICSDEPRECIATIONS traight LineDnCSjn=-Accelerated Cost Recovery System (ACRS)Dj = (factor) C !"Sum of the Years DigitsDjnjCS1jjnn1=+--=_i!BOOK VALUEBV = initial cost DjTAXATION# $ $ " Taxable income is total income less depreciation and ordinary expenses. Expenses do not include capital items, which should be COSTSC apitalized costs are present worth values using an assumed perpetual period of Costs = PiA=BONDSBond Value equals the present worth of the payments the purchaser (or holder of the bond) receives during the life of the bond at some interest rate Yield equals the computed interest rate of the bond value when compared with the bond minimum acceptable rate-of-return (MARR) is that interest rate that one is willing to accept, or the rate one desires to earn on investments.

4 The rate-of-return on an ANALYSIS# % B of a project should exceed the estimated costs C 0, or B/C 1 MODIFIED ACRS FACTORS Recovery Period (Years)35710 YearRecovery Rate (Percent)1 2 3 4 7 8

5 9 10 116 engineering ECONOMICSF actor Table - i = 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 30 40 50 60 100

6 1, 1, 3.

7

8 Table - i = 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

9 18 19 20 21 22 23 24 25 30 40 50 60 100

10 1, 2.