Ch2 (part1)econ factors_rev2
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This document discusses various time value of money factors used to solve problems involving interest rates over time. It covers: 1) Single payment factors (F/P and P/F) which determine the future or present value of a single payment. 2) Uniform series factors (P/A and A/P) which determine the present or equivalent annual value of a uniform series of payments. 3) Sinking fund factors (A/F and F/A) which determine the annual payment or future value for accumulating to a target amount. 4) Arithmetic gradient factors (P/G and G/P) which handle cash flows that increase or decrease by a constant amount each period.
Ch2 (part1)econ factors_rev2
- 1. 1 Factors: HowTime and MoneyFactors: HowTime and Money Affect Interest (CH2)Affect Interest (CH2)
- 2. 2 ObjectivesObjectives To understand and use factors to account for TMV. ◦ Single payment compound amount (F/P) ◦ Uniform Series Present Worth (P/A) ◦ Uniform Series Sinking Fund (A/F) ◦ Interpolation in interest tables ◦ Arithmetic Gradient Factors (P/G , A/G) ◦ Geometric Gradient Factors
- 3. 3 Single Payment factors (F/P & P/F)Single Payment factors (F/P & P/F) F/P : Determines the amount of money F accumulated after n periods from a single present worth P with interest compounded one time per period Only for one payment Can you define P/F factor? n iPF )1(/ += n iFP − += )1(/
- 4. 4 Solving Factor ProblemsSolving Factor Problems Factor problems can be solved in several ways ◦ a) Using Equations ◦ Using equations: F = P(1+i)n = 12,000(1+8%)24 = $76, 094.17
- 5. 5 Solving Factor ProblemsSolving Factor Problems b) Using tables: F=P(F/P,i,n)=12,000(F/P,8%,24)=12,000 x (6.3412)=$76,094.40 c) Using Excel ◦ (F/P,i, n) FV(i%, n,P) ◦ (P/F,i,n) PV(i%, n,P)
- 6. 6 Uniform Series Present Worth (P/A) &Uniform Series Present Worth (P/A) & Capital Recovery (A/P) FactorsCapital Recovery (A/P) Factors P/A is calculated as ◦ Uniform Series Present Worth Factor Derive A/P equation ◦ Capital Recovery Factor How P/A is related to P/F? 0 )1( 1)1( ≠ + −+ = i ii i AP n n
- 7. 7 P/A Problem How much you should be willing to pay for a project that brings $600 for the next 9 years starting next year, the rate of return is 16% per year. P =600(P/A,16%,9) = 600(4,606.5)= 2763.90
- 8. 8 Sinking Fund Factor & Uniform –Series Compound Amount Factor (A/F & F/A) Sinking Fund Factor (A/F) determines the uniform annual series that is equivalent to a given future worth F. Uniform Series Compound Amount Factor (F/A) gives the future worth of a uniform series. −+ = 1)1( n i i FA −+ = i i AF n 1)1(
- 9. 9 F/A Problem Plant x wants to know the equivalent future worth of a $1 million capital investment each year for 8 yrs, starting 1 yr from now. Capital earns at a rate of 14% per yr. In $1000 units, F=1000(F/A,14%,8) = $13,232.80
- 10. 10 Linear Interpolation & Interest Tables For unlisted values in the tables we can use Factors equations Linear interpolation % 7 0.14238 7.3 x 8 0.14903
- 11. 11 Arithmetic Gradient Factors (P/G and G/P) Arithmetic gradient is a cash flow series that increases or decreases by a constant amount. Different from previous factors Gradient: constant arithmetic change in the receipts or disbursements from one time period to the next, G can be positive or negative
- 12. 12 Arithmetic Gradient Factors (P/G and G/P) Cash Flow in yr n (CFn) = base amount+(n-1)G The relation to convert an arithmetic gradient G (not including base amount) for n years into a present worth at yr 0 The equivalent uniform annual series (A value) for an arithmetic gradient G + − + −+ = nn n i n ii i i G P )1()1( 1)1( −+ −= 1)1( 1 n i n i GA
- 13. 13 Arithmetic Gradient Factors F/G factor (future worth for arithmetic gradient) is calculated as Base amount (A) and gradient (G) are considered separately Total present worth ◦ Increasing PT=PA + PG ◦ Decreasing PT=PA - PG Equivalent total annual series ◦ Increasing AT=AA + AG ◦ Decreasing AT=AA - AG − −+ = n i i i GF n 1)1(1
- 14. 14 Arithmetic Gradient Problem Gradient problems are solved for 1) base & 2) G, then add two amounts.
- 15. 15 Arithmetic Gradient Problem Total present worth = PA+PG = 500(P/A,5%,10) +100(P/G,5%,10) Total annual series = AA+AG = 500 +100(A/G,5%,10)