ENGINEERING ECONOMY
Engr. Aldrin Aldrin Lorrenz A. Chan
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FEU TECH ENGINEERING ECONOMY WITH ACCOUNTING
THE ANNUITY SERIES Annuity
a fixed sum of money paid or earned in regular period of time.
evaluated by using the annual worth, A, which is a series of consecutive, equal, end-of-period amounts of money
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FEU TECH ENGINEERING ECONOMY WITH ACCOUNTING
THE ANNUITY SERIES Example
For maintenance of safety features of automobiles, the lead engineer plans expenditures of 1 million dollars now and each of the next 4 years.
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FEU TECH ENGINEERING ECONOMY WITH ACCOUNTING
SINGLE AMOUNT FACTORS (P/F AND F/P) P/F and F/P are find/given notations used in the analysis of engineering economy problems.
In the equation for compound interest, F = P(1+i)n, the factor (1+i) n is called the single-payment compound amount factor (SPCAF) or, simple, the F/P factor .
To determined P, the equation becomes
=
1 ( 1 + )
= (1 + )−
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FEU TECH ENGINEERING ECONOMY WITH ACCOUNTING
SINGLE AMOUNT FACTORS (P/F AND F/P) The F/P factor, (1+i)n, when multiplied with P yields the future amount F of an initial amount P after n years at an interest rate i.
P/F factor, (1+i)-n, when multiplied with F yields the present worth P of a future amount F after n years at an interest rate i.
The The
standard notation equation follows the form: missing variable = given (find/given, i n)
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FEU TECH ENGINEERING ECONOMY WITH ACCOUNTING
UNIFORM SERIES PRESENT WORTH FACTOR (P/A) AND CAPITAL RECOVERY FACTOR (A/P) Considering each A value as a future worth F and calculating its present worth with the P/F factor:
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FEU TECH ENGINEERING ECONOMY WITH ACCOUNTING
UNIFORM SERIES PRESENT WORTH FACTOR (P/A) can be simplified as =
( 1 + ) 1 (1 +
)
, ≠ 0
The term inside the bracket is referred to as the uniform series present worth factor (USPWF) or simple the P/A factor used to calculate the
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FEU TECH ENGINEERING ECONOMY WITH ACCOUNTING
CAPITAL RECOVERY FACTOR (A/P FACTOR) If P is known and the annual worth A is sought (1 + ) = ( 1 + ) 1 The term inside the bracket is called the capital recovery factor (CRF) or A/P factor . It is used to calculate the annual worth A over n years for a given P in year 0.
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FEU TECH ENGINEERING ECONOMY WITH ACCOUNTING
P/A AND A/P FACTOR Sample Problem
How much money should you be willing to pay now for a guaranteed ₱600 per year for 9 years starting next year, at a rate of return of 16% per year? P = 600 (P/A,16%,9)
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FEU TECH ENGINEERING ECONOMY WITH ACCOUNTING
SINKING FUND FACTOR (A/F) Substituting P/F factor into =
(1 + ) ( 1 + ) 1
will turn the equation to =
1
(1 + )
( 1 + )
( 1 + ) 1
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FEU TECH ENGINEERING ECONOMY WITH ACCOUNTING
SINKING FUND FACTOR (A/F) =
( 1 + ) 1
The expression in brackets is the sinking fund factor or A/F factor. It determined the uniform annual series A that is equivalent to a given future amount F at a given i and after n periods. Note: A begins at the end of year (period) 1 and continues through the
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FEU TECH ENGINEERING ECONOMY WITH ACCOUNTING
USCAF OR F/A FACTOR For a given A, F can be calculated by ( 1 + ) 1 = The expression in brackets is the uniform series compound amount factor (USCAF) or F/A factor . Note: A begins at the end of year (period) 1 and continues through the
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FEU TECH ENGINEERING ECONOMY WITH ACCOUNTING
USCAF OR F/A FACTOR Sample Problem
The president of Ford Motor Company wants to know the equivalent future worth of a 1 thousand dollar capital investment each year for 8 years, starting 1 year from now . Ford capital earns at a rate of 14% per year. F = 1000 (F/A,14%,8)
Seatwork. Answer in piece/s of yellow paper; to be submitted today. Provide the cash flow diagram & standard notation equation for each problem, present complete solution and box the final answer.
1. How much can Cocolyn Inc. afford to spend now on renewable energy systems if the project will entitle a savings of ₱21,300 per year for the next 5 years? Interest rate is 10% per year. 2. An investment that provides you a uniform yearly dividend in 6 years amounted to a future worth of ₱55,450. If the rate of return is 12%, how much is the yearly dividend? 3. A sinking fund consists of 15 annual deposits of ₱2,000 each, with
