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Unformatted text preview: CE 395
Engineering Economics
Spring 2005
W. Hitchcock Cash Flow Time Value of Money Quotes "Personally, I'm always ready to learn, although I do not
always like being taught." Winston Churchill Famous People or Historical Figures "Far and away the best prize that life offers is the chance to
work hard at work worth doing" Theodore Roosevelt "Nearly all men can stand adversity, but if you want to test a
man's character, give him power" Abraham Lincoln "It is not the employer who pays wages he only handles the
money. It is the product that pays wages" Henry Ford "Never tell people how to do things. Tell them what to do
and they will surprise you with their ingenuity" George Patton Financial Concepts
Cash Flows
Benefits above the line Time Costs below the line Note: In practice it becomes very important to denote benefits or cash inflows as positive numbers and costs and cash outflows as negative numbers. Financial Concepts  Equivalence
Present Time F
Future Time P Equivalence: Time Increments To compare the value of money at different points in time we must understand the concept of equivalence If we say we are indifferent to whether I have a sum of money now (P) or the assurance of some other sum of money in the future (F), we say the sums are equivalent Financial Concepts
Interest Rate The Equivalence Link To say a present sum (P) will be equivalent to some
future sum (F) with no other information, if we fix P, the possible answers for F are infinite Therefore, the relationship between the present sum (P) and Future sum (F) must be defined mathematically with at least one defined variable Interest Rate (i) : Money paid for the use of borrowed money (principal) for a specific period of time ( expressed in % ) Financial Concepts
Single Period Interest
If a sum of money (P) is invested for a length of time (called a period) and interest is paid at i (%) per period, then the simple relationship between (P) and the future value sum of (P) plus the interest fee paid for the use of (P) yields the value for (F) : F = P(1+i) (single period) Simple Interest Total interest earned is linear relationship of the
following variables: Principal (P) Interest Rate ( i ) Number of interest periods (N) Total interest paid is found in the relationship:
Total Interest Paid = P(i)(N) Simple interest is generally used in cases where interest payments (and perhaps some return of principal) are made at the end of each period Simple interest is not normally used in typical time value of money applications. Financial Concepts
Compounded Interest
If the initial sum (P) is deposited for multiple periods at the fixed interest rate (i) and the interest earned each period is reinvested and becomes part of the borrowed sum for purposes of calculating interest payments, we say that interest is compounding and we have the relationship: F = P(1+i)n Where n = the number of periods between (P) and (F) and (F) is the sum of money withdrawn at the end of the deposit period Financial Concepts
Compounded Interest
If F = P(1+i)n then so also P = F(1+i)n Where n = the number of periods between (P) and (F) We then say that (P) is the Present Value of (F) at interest rate (i) over (n) compounding periods In practice we say (P) is the Present Value of (F) (it is assumed the audience recognizes the need for a specific (i) and number of periods (n)) Equivalent Cash Flows
Uniform Terminology i = interest rate per period (effective rate for the period) N or n = number of compounding periods P = Present equivalent value of any arbitrary cash flow(s) at a specific point in time called the present F = Future equivalent value of any arbitrary cash flow(s) at a specific point in time called the present A = Uniform (magnitude equal) end of period cash flows starting at the end of the first period continuing each period until the end of the last period in the series Uniform Series of Cash Flows (Annuities)
A A A A A A A A A A P F Uniform equivalent cash flows occur at the end of each interest period in the cash flow series. P occurs one interest period before the first A. F occurs at the same point in time as the last A. Financial Concepts Equivalence Formulas
A A A A A A A A A A Time Increments P
P=A (1+i)n 1 i (1+i)n Series Present Worth F=A (1+i)n 1 i A=F A=P F i (1+i)n (1+i)n 1 Capital Recovery i (1+i)n 1 Sinking Fund Series Compound Amount Example of Equivalence:
Multiple Loan Repayment Methods ...
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This note was uploaded on 09/26/2008 for the course CE 395 taught by Professor Hitchcock during the Summer '05 term at University of Alabama at Birmingham.
 Summer '05
 Hitchcock

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