ENG 209 Engineering Economy Lecture 5, Section 3.3 (Continue)

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1 ENG 29 Egieerig Ecoomy Lecture 5, Sectio 3.3 (Cotiue) Equal-aymet-Series Sikig-Fud Factor, (F/, i, ) Give: Fid: i = the aual iterest rate. = the umber of iterest periods. F = the future amout. = paymet per period 2 i = F = F( / F, i, ) ( + i) i F ENG 29 Egieerig Ecoomy

2 Example : What amout of equal aual deposits i 6 years at % compouded aually that will be accumulated to KD,? KD, i=% 2 6 ENG 29 Egieerig Ecoomy

3 Example 2: What series of equal paymets is ecessary to repay the KD 5, i 6 years at 5% compouded aually with aual paymets? KD 5, i=5% 2 6 ENG 29 Egieerig Ecoomy 2

4 Equal-aymet-Series Capital-Recovery Factor, (/, i, ) Give: i = aual iterest rate. = umber of aual iterest periods. = preset priciple amout. Fid: = sigle paymet i a series of equal paymet i = F ( + i) ( + i) ( + i ) = i 2 i i( + i) ( + i) = ENG 29 Egieerig Ecoomy 3

5 Example 3: What series of equal paymets is ecessary to repay the KD 5, i 6 years at 5% compouded aually with aual paymets? KD 5, i=5% 2 6 ENG 29 Egieerig Ecoomy 4

6 Equal-aymet-Series reset-worth Factor, (/, i, ) Give: Fid: i = aual iterest rate. = umber of aual iterest periods. = sigle paymet i a series of equal paymet = preset priciple amout 2 i = ( /, i, ) = ( ) + i i( + i) ENG 29 Egieerig Ecoomy 5

7 Example 4: What is the preset worth of a series of eight equal paymets of KD 2 at a iterest rate of 5% compouded aually? ENG 29 Egieerig Ecoomy 6

8 Uiform-Gradiet-Series Factor, (/G, i, ) Ofte periodic paymets do ot occur i equal amouts, ad may icrease or decrease by costat amouts (e.g. KD, KD 2, KD 4, KD 6... KD 2). The gradiet (G) is a value i the cash flow that starts with at the ed of year, G at the ed of year 2, 2G at the ed of year 3, ad so o to (-)G at the ed of year. = G( / G, i, ) G 2 = G i 2 G 3 ( + i) (-2) G - (-) G ENG 29 Egieerig Ecoomy 7

9 Uiform-Gradiet-Series Factor, (/G, i, ) Give: i = aual iterest rate. = umber of aual iterest periods. G = aual charge or gradiet. 2 G G (-2) G (-) G Fid: = sigle paymet = G( / G, i, ) = G i ( + i) ENG 29 Egieerig Ecoomy 8

10 Example 4: O a piece of equipmet, it is estimated that the service expese will be as follows: Year Maiteace KD 2 KD 5 3 KD 4 KD 5 5 KD 2 i=5% What is the equivalet uiform aual maiteace cost for the machiery if the iterest rate is 5%? ENG 29 Egieerig Ecoomy 9

11 Example 5: How much do you have to deposit ow i a savigs accout that ears a 2% aual iterest, if you wat to withdraw the aual series as show i the figure? KD, KD,25 KD,5 KD,75 KD 2, =? ENG 29 Egieerig Ecoomy

12 Example 5: How much do you have to deposit ow i a savigs accout that ears a 2% aual iterest, if you wat to withdraw the aual series as show i the figure? KD, KD,25 KD,5 KD,75 KD 2, =? ENG 29 Egieerig Ecoomy

13 Geometric-Gradiet-Series Factor (/, gꞌ, ) F (+g) - F F (+g) F (+g) 2 F (+g) May egieerig ecoomic problems, particularly those relatig to costructio costs, ivolve cash flows that icrease or decrease over time, ot by a costat amout, but rather by a costat percetage (geometric), called compoud growth. ENG 29 Egieerig Ecoomy 2

14 Geometric-Gradiet-Series Factor (/, gꞌ, ) Give: g = paymet percetage chage. = umber of aual iterest periods. F = first paymet. Calculate: Fid: gꞌ = growth-free rate. = preset priciple amout. F F (+g) 2 F (+g) 2 F (+g) F (+g) - ENG 29 Egieerig Ecoomy 3

15 Geometric-Gradiet-Series Factor (/, gꞌ, ) F (+g) - g = + i + g F F (+g) 2 F (+g) 2 F (+g) F = ( /, g, + g ) F + g ( ) + g g ( + g ) = ENG 29 Egieerig Ecoomy 4

16 Example 5: Use the followig cash flow diagram to calculate the preset worth, where g = 25%, i=3%. F = = 2 ENG 29 Egieerig Ecoomy 5

17 Iterest Formula Summary Fid Give Formula Cash Flow F F = (F/, i, ) F = F (/F, i, ) F F = (F/, i, ) F = F (/F, i, ) = (/, i, ) = (/, i, ) iii F F G F (+g) 2 G (-2) G F (+g) 2 F (+g)-2 - (-) G F (+g) - G = G (/G, i, ) F = F / (+g) (/, gꞌ, ) ENG 29 Egieerig Ecoomy 6

18 Iterest-Factor Extreme Values Iterest Formula = ; i kow i = ; kow (F/, i, ) (/F, i, ) (F/, i, ) (/F, i, ) / (/, i, ) /i (/, i, ) i / ENG 29 Egieerig Ecoomy 7

ENG 209 Engineering Economy Lecture 9, Sections

ENG 209 Engineering Economy Lecture 9, Sections ENG 29 Egieerig Ecoomy Lecture 9, Sectios 6.1 6.8 6.1) Preset Worth (PW) 6.2) Aual Equivalet (AE) 6.3) Future Worth (FW) 6.4) Iteral Rate of Retur (IRR) 6.5) Payback Period (PP) 6.6) Capitalized Equivalet