Engineering Economy 3

Engineering Economy Department of Civil Engineering ara yangan a o c n vers y

September 2011

(3 & ! 1

"evie#$$ % Simple Interest  I = P.n.i  T = P + I  =

.

% Compound Interest  '  P (1)i!n

Simple an* Compo+n* Exercises (Cont,*! 1$

-n or* or*er er to b+il b+il* * a ne# ne# #are #areh ho+se o+se faci facili lity ty.. th the reg regio iona nall *istrib+tor for /alco +ltiPosition /alves borro#e* 1$ million at 104 per year simple interest$ -f the company repai* the loan in a l+mp s+m amo+nt after 2 years. #hat #as (a! the amo+nt of the payment. an* (b! the amo+nt of interest5

2$

'#o ye year arss ag ago.6S o.6S6" 6"C7 C7.. -nc$ -nc$ inves nveste te* * 89 890. 0.00 000 0 in in a certi:cate of *eposit that pai* simple interest of ;4 per year$
3$

-f 000 is investe* at an ann+al rate of $04 compo+n*e* monthly.. #hat #ill be the final val+e of the investment monthly after 10 years5

'erminology & Symbol Example:

% =P borro#e* money to *o rapi* prototyping for a ne# r+gge*i>e* comp+ter that targets *esert oil :el* con*itions$ 'he loan is 1 million for 3 years at 84 per year compo+nt interest$ =o# m+ch money #ill =P repay at the en* of 3 years5 % 6 ne# college gra*+ate has a ?ob #ith @oeing 6erospace$ She plans to borro# 10.000 no# to help in b+ying a car$ She has arrange* to repay the entire principal pl+s 94 per year interest after 8 years$ ANY SIMILARITY?? 4

'erminology & Symbol % P  val+e or amo+nt of money at a time *esignate* as the present or time (0)$ 6lso. P is referre* to as present #orth (PA!. present val+e (P/!. net present val+e (
e* cost (CC! % F = val+e or amo+nt of money at some future time$ 6lso. B is calle* f+t+re #orth (BA! an* f+t+re val+e (B/! % A = series of consec+tive. e+al. en*ofperio* amo+nts of money$ 6lso. 6 is calle* the ann+al #orth (6A! an* e+ivalent +niform ann+al #orth (EU6A! per year. per month % n  n+mber of interest perio*s years. months. *ays %

i  interest rate or rate of ret+rn per time perio* percent per year. percent per month. percent per *ay 5

Cash Blo# % Cash o#s are ino#s an* o+to#s of money$ % Cash o#s occ+r *+ring speci:e* perio*s of time. s+ch as 1 month or 1 year % ay be estimates or observe* val+es$ % Cash o# estimates are ?+st that estimates abo+t an +ncertain f+t+re$

( Leland Blank, Anthony Tarquin, 2008)

6

Cash Blo# % Cash o#s normally taFe place at varying times #ithin an interest perio*. a simplifying en*ofperio* ass+mption is ma*e$ % 'he en*ofperio* convention means that all cash o#s are ass+me* to occ+r at the en* of an interest perio*$ .



% So. -f the *eposit tooF place on G+ly 1. 2009. an* the #ith*ra#als #ill taFe place on G+ly 1 of each s+ccee*ing year for 10 years$ ( Leland Blank, Anthony Tarquin, 2008)

7

Cash Blo# Diagram (CBD! % -t is a graphical representation of cash o#s *ra#n on a time scale$ % Cash o# *iagram time t=0 is the present. an* t=1 is the en* of time perio* 1$ Beginning of Year 1

End of Year 1

% Since the en*ofyear convention places cash o#s at the en*s of years. the H1I marFs the en* of year 1$ ( Leland Blank, Anthony Tarquin, 2008)

8

Cash Blo# Diagram (CBD! % 'he *irection of the arro#s on the cash o# *iagram is important$ %

6 vertical arro# pointing up in*icates a positive cash o# an arro# pointing do!n in*icates a negative cash o#$

% -t is not necessary to +se an eJact scale on the cash o# *iagram


9

Cash Blo# Diagram (CBD! Example:

% 6 ne# college gra*+ate has a ?ob #ith @oeing 6erospace$ She plans to borro# 10.000 no# to help in b+ying a car$ She has arrange* to repay the entire $


10

Cash Blo# Diagram (CBD! Exercise: % Each year EJJonobil eJpen*s large amo+nts of f+n*s for mechanical safety feat+res thro+gho+t its #orl*#i*e operations$ Carla "amos. a lea* engineer for eJico an* Central 6merican operations . plans eJpen*it+res of 1 million no# an* each of the neJt  years ?+s t for the im rovement of :el*bas e* ress+rerelease valves$ Constr+ct the cash o# *iagram to :n* the e+ivalent val+e of these eJpen*it+res at the en* of year . +s ing a cos t of capital estimate for safetyrelate* f+n*s of 124 per year$


11

Cash Blo# Diagram (CBD! Exercise: % 6 father #ants to *eposit an +nFno#n l+mps+m amo+nt into an investment opport+nity 2 years from no# that is large eno+gh to #ith*ra# 000 per year for state +niversity t+ition for 8 years starting 3 years from no#$ -f the rate of ret+rn is estimate* to be 18$84 per year. constr+ct the cash o# *ia ram$


12

Cash Blo# Diagram (CBD! Exercise: % @efore eval+ating the economic merits of a propose* investment. the KLM Corporation insists that its engineers *evelop a cash flo# *iagram of the proposal$ 6n investment of 10.000 can be ma*e that #ill pro*+ce +niform ann+al reven+e of 8.310 for 8 years an* then have a positive sa vage va +e o . a e en o year $ nn+a eJpenses # e 3.000 at the en* of each year for operating an* maintenance the pro?ect$ "#A$ A CAS% F&'$ "IA#A F'# *%E +,-EA# &IFE 'F *%E P#'.EC*


13

'ime & -nterest on Single Cash Blo# Problem % "elate* to P to F or F to P cases % Separate by < perio*s #ith interest at i% per perio* *he E uations: P to F

F to P

N

F = P (1 + i )

P = F (

1

1+ i

N

)

N

(1 + i )

1 N ( ) 1+ i

single-payment singlecompound amount factor (SPCAF)

single-payment singlepresent worth factor (SPPWF)

(Sullivan et al., 2008)

14

'ime & -nterest on Single Cash Blo# Problem % "elate* to P to F or F to P cases % Separate by < perio*s #ith interest at i% per perio* *he "ia ram:

P to F

F to P

15 ( Leland Blank, Anthony Tarquin, 2008)

'ime & -nterest on Single Cash Blo# Problem *he 1otation: 1otation:

Example:

6 ne# college gra*+ate has a ?ob #ith @oeing 6erospace$ She plans to borro# 10.000 no# to help in b+ying a car$ She has arrange* to repay the entire principal pl+s 94 per year interest after 8 years$ 16 ( Leland Blank, Anthony Tarquin, 2008)

'ime & -nterest on Single Cash Blo# Problem Interest Factor *a2le


'ime & -nterest on Single Cash Blo# Problem *he 1otation: 1otation:

Example:

6n investor has an option to p+rchase a tract of lan* that #ill be #orth 3405000 in 6 years$ -f the val+e of the lan* increases at 78 each year. ho# m+ch sho+l* the investor be #illing to pay no# for this property5 18 ( Leland Blank, Anthony Tarquin, 2008)

'ime & -nterest on Single Cash Blo# Problem Example:

% Gamie has become more conscientio+s abo+t paying off his cre*it car* bill promptly to re*+ce the amo+nt of interest pai*$ =e #as s+rprise* to learn that he pai* 00 in interest in 200N an* the amo+nts sho#n in Big+re belo# over the previo+s severa years$ - e ma e is payments to avoi interest charges. he #o+l* have these f+n*s pl+s earne* interest available in the f+t+re$ Ahat is the e+ivalent amo+nt 8 years from no# that Gamie co+l* have available ha* he not pai* the interest penalties5 Oet i  84 per year$


'ime & -nterest on Single Cash Blo# Problem Solution


Interest Factor *a2le

21

'ime & -nterest on Uniform Series Problem Example:

1$ =o# m+ch money sho+l* yo+ be #illing to pay no! for a g+arantee* 00 per year for ; years starting neJt year. at a rate of ret+rn of 14 per year5 2$ Bormasa Plastics has ma?or fabrication plants in 'eJas an* =ong ong$ 'he presi*ent #ants to Fno# the e/ui9alent future !orth of 1 million capital investments each year for 9 years. starting 1 year from no#$ Bormasa capital earns at a rate of 14 per year$


'ime & -nterest on Uniform Series Problem Diagram

=o# m+ch money sho+l* yo+ be #illing to pay no! for a g+arantee* 00 per year for ; years starting neJt year. at a rate of ret+rn of 14 per year5


'ime & -nterest on Uniform Series Problem Diagram

Bormasa Plastics has ma?or fabrication plants in 'eJas an* =ong ong$ 'he presi*ent #ants to Fno# the e/ui9alent future !orth of 1 million capital investments each year for 9 years. $ 14 per year$


'ime & -nterest on Uniform Series Problem Notation


'ime & -nterest on Uniform Series Problem Notation


'ime & -nterest on Uniform Series Problem The Interest Table (Example)


'ime & -nterest on Uniform Series Problem Solution =o# m+ch money sho+l* yo+ be #illing to pay no! for a g+arantee* 00 per year for ; years starting neJt year. at a rate of ret+rn of 14 per year5

P = 600(PA54685;) = 600(<606+) = 3>6?;0 28 ( Leland Blank, Anthony Tarquin, 2008)

'ime & -nterest on Uniform Series Problem Diagram Bormasa Plastics has ma?or fabrication plants in 'eJas an* =ong ong$ 'he presi*ent #ants to Fno# the e/ui9alent future !orth of 1 million capital investments each year for 9 years. starting 1 year from no#$ Bormasa capital earns at a rate of 14 per year$

F = 4000( FA54<857) = 4000(4??7) = 34?5?70 29 ( Leland Blank, Anthony Tarquin, 2008)

Summary on Sinle @ niform Series Pro2lem


Sinle and niform Cash Flo! Pro2lem Exercises 1$ @ecFton Steel Pro*+cts. a company that speciali>es in cranFshaft har*ening. is investigating #hether it sho+l* +p*ate certain e+ipment no# or #ait an* *o it later$ -f the cost no# is 190.000. #hat #o+l* the e+ivalent amo+nt be 3 years from no# at an 2$ 6n engineer receive* a bon+s of 12.000 that he #ill invest no#$ =e #ants to calc+late the e+ivalent val+e after 2 years. #hen he plans to +se all the res+lting money as the *o#n payment on an islan* vacation home$ 6ss+me a rate of ret+rn of 94 per year for each of the 2 years$ Bin* the amo+nt he can pay *o#n5Q


'ime & -nterest on Single Cash Blo# Problem Exercises 3$ S+ppose yo+ are offere* the alternative of receiving either 3.000 at the en* of five years or P *ollar to*ay$ 'here is no +estions that the 3.000 #ill be pai* in f+ll (i$e$. no risF!$ @eca+se yo+ have no c+rrent nee* for the money. yo+ #o+l* *eposit the P *ollars in an $ in*ifferent to yo+r choice bet#een P *ollar to*ay an* the promise of 3.000 at the en* of five years5 $ Lo+ have ?+st p+rchase* 100 shares of RE company stocF at 30 per share$ Lo+ #ill sell the stocF #hen its marFet price *o+bles$ -f yo+ eJpect the stocF price to increase 124 per year. ho# long *o yo+ to #ait before selling the stocF5 32 ( Leland Blank, Anthony Tarquin, 2008)

'ime & -nterest on Single Cash Blo# Problem Exercises 8$ S+ppose yo+ b+y a share of stocF for 10 an* sell it for 20 yo+r profit it th+s 10$ -f that happen #ithin a year. yo+r rate of ret+rn is an impressive 1004$ -f it taFe five years. #hat #o+l* be the rate of ret+rn on yo+r investment5 $ 10 million. Lo+ save money in the banF 10 months ago$ 'o*ay yo+ receive* 11.8 million$ =o# m+ch interest yo+ earne*5


'ime & -nterest on Single Cash Blo# Problem Exercises


'ime & -nterest on Uniform Series Problem Exercises N$

Ailson 'echnology. a gro#ing machine shop. #hishes to set asi*e money no# to invest over the neJt fo+r years in a+tomating its c+stomer service *epartment$ 'he company can earn 104 on a l+mp s+m *eposite* no#. an* its #ishes to #ith*ra# the money in the follo#ing increments

•

Lear 1 28.000 to p+rchase a comp+ter an* *atabase an* soft#are *esigne* for c+stomer service +se

•

Lear 2 3.000 to p+rchase a**itional har*#are to accommo*ate anticipate* gro#th in +se of the systems

•

Lear 3
•

Lear  8.000 to p+rchase soft#are +pgra*es

=o# m+ch money m+st be *eposite* no# in or*er to cover the anticipate* payment over the neJt fo+r years5

35


'ime & -nterest on Uniform Series Problem Exercises 9$

Lo+ #ant to renovate yo+r apartment after 9 years from no#$ 'he cost at least 100.000 #ill be nee*e*$ =o# m+ch *o yo+ nee* to save each year in or*er to have necessary f+n*s if the c+rrent rate of interest is N45 (ass+me that en*ofyear payments are ma*e!

;$

Lo+r borro#e* 21 01$92 to finance the e*+cational eJ enses for o+r senior year of college$ 'he loan #ill be pai* off over five years$ 'he loan carries an interest rate of 4 per year an* is to be repai* in e+al ann+al installments over the neJt five years$ 6ss+me that the money #as borro#e* at the beginning of yo+r senior year an* that the first installment #ill be *+e a year later$ Comp+te the amo+nt of the ann+al installments$

10$ S+ppose problem in n+mber ; that yo+ #ante* to negotiate #ith the banF to *efer the first loan installment +ntil the en* of year t#o (b+t still *esire to maFe five e+al installment at 4 interest!$ -f the banF #ishe* to earn the same profit as problem n+mber ;. #hat sho+l* the ann+al installment5 36 ( Leland Blank, Anthony Tarquin, 2008)

Engineering Economy 3

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