This topic explains the various concepts used to calculate future values or present values of a series of cash flows that result from engineering decisions to buy new equipment or replace old equipments.

## Introduction

^{n}represents the future value of money.

^{-n}represents the present value of money received after n years.

## Single Payment Cashflow

^{n}

^{-n}

## Uniform Periodic Payments

**Compounding of uniform series of cash payments**

^{n}- 1]/i

** **

**Discounting of uniform series of cash payments**

P = R [(1+i)^{n} - 1]/[i 1+i)^{n} ]

Where

P = Present Value

R = Uniform series of periodic payments

i = interest rate

n = number of periods of payments

These time value formulas are expressed in factors

A = P*Single payment future worth factor =P*Spfwf

P = A* Single payment present worth factor = A*Sppwf

S = R* Uniform series future worth factor = R*Usfwf

P = R*Unform series present worth factor = R*Uspwf

## Two More Factors

**Sinking Fund Deposit Factor**

Sfdf = 1/Usfwf

Sinking fund is fund accumulated with periodic payments for incurring a lumpsum expenditure at the end of a long period. Sfdf gives the amount to be deposited at the end of each period for n period to accumulate one dollar at the end n periods.

**Capital Recovery Factor**

Crf = 1/Uspwf

Capital recovery factor gives the uniform payment to be received by you at the end period of n years to get recover back the investment you made today.

The factor tables are available and factors depend on interest rate i and term n.

**Factors for a required rate of return of 10% and 5 years term.**

Spfwf - 1.6105

Sppwf - .62092

Usfwf - 6.1051

Uspwf - 3.7908

Sfdf - 0.16380

Crf - 0.26380

## References

**Engineering Economics, 4th Edition, James L. Riggs, David D. Bedworth, and Sabah U. Randhawa, McGraw Hill, New York, 1996**

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