Estimating Life Expectancies of Highway Assets, Volume 2: Final Report (2012)

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226 A p p e n d i x d Interest Formulae for LCCA

interest Formulae for LCCA 227 Description Cash Flow Diagram Computational Note: N represents the analysis period Formul a Factor Computatio n 1 Finding the future compounded amount (F) at the end of a specified analysis period, given the initial amount (P) and interest rate . P F? 0 1 N F = P * SPCAF T he Single Payment Compound Amount Factor, SPCAF (i%, N) may be read off from standard economic analysis tables, or may be computed as shown. N i SP CA F ) 1 ( + = i N e SP CA F * = Finding the initial amount (P) that w ould yield a given future amount (F) at the end of a specifie d analysis period, given the interest rate . P? F 0 1 N P = F * SPPW F T he Single Payment Present Worth Factor, SPPWF (i%, N) may be read off from standard economic analysis tables, or may be computed as shown. N i SP PW F ) 1 ( 1 + = i N e SP PW F * 1 = A? F 0 1 2 N A = F * SFDF T he Sinking Fund D eposit Factor, SFDF (i%, N) may be read o ff standard econom ic analysis tables, or may be computed as shown. (1 ) 1 N i SFDF i = + − * 1 1 i N i e SFDF e − = − Finding the future compounded amount (F) at the end of a specified analysis period due to annual payments (A), given the interest rate . A F? 0 1 2 N F = A * USCA F T he Uniform Series Compounded Amount Factor, USCAF (i%, N) may be read off from standard economic analysis t ables, or may be computed as shown. i i US CA F N 1 ) 1 ( − + = 1 1 * − − = i i N e e US CA F Finding the initial amount (P) that is equivalent to a series of uniform annual payments (A), given the interest rate and a specified analysis period. P? A 0 1 2 N P = A * USPW F T he Uniform Series Present Worth Factor, U SPWF (i%, N) may be read off from standard economic analysis tables, or may be computed as show n. N N i i i US PW F ) 1 ( * ) 1 1 ( + − + = 1 1 * − − = − i i N e e US PW F Finding the amount of uniform yearly payments (A) that would completely recover an initial amount (P) at the end of a specified analysis period, given the interest rate. P A? 0 1 2 N A = P * USCRF T he Uniform Series capital Recovery Factor, USCRF (i%, N) may be read off from standard economic analysis t ables, or may be computed as shown. 1 ) 1 ( ) 1 ( * − + + = N N i i i US CR F i N i e e US CR F * 1 1 − − − = Note: 1) In column 4, upper and lower formulae are for discrete and continuous compounding, respectively. 2) For fixed discrete compounding yearly, i = nominal interest rate and N represents years. 3) When there is more than one compounding period per year, the formulae and tables can be used as long as there is a cash flow at the end of each interest period. i represents the interest rate per period and N is the number of periods. 4) When the compounding is more frequent than a year, but the cash flows are annual, the formulae can be used with N as number of years and i as the effective annual interest rate. Finding the uniform yearly amount (A) that would yield a given future amount (F) at the end of a specified analysis period, given the interest rate. Table D-1. Interest formulae for LCCA (Sinha & Labi, 2007).