ch02-TimeValueOfMoney.ppt

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Engineering Economics

Chapter 2

Time Value of Money

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Engineering Economics, Fifth Edition

Outline

2.1 Introduction

2.2 Interest and Interest Rates

2.3 Compound and Simple Interest

2.4 Eecti!e and "ominal Interest Rates2.# Continuous Compounding

2.$ Cash %lo& 'iagrams

2.( E)ui!alence

2.(.1 *athematical E)ui!alence

2.(.2 'ecisional E)ui!alence

2.(.3 *ar+et E)ui!alence



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, Engineering decisions re)uently in!ol!e tradeosamong costs and -eneits occurring at dierent times /ypically in!est in proect today to gain -eneits in uture

, Chapter 2 discusses economic methods used tocompare -eneits and costs occurring at dierent times

, /he +ey to ma+ing these comparisons is the use ointerest rates.

2.1 ntroduction

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, Interest I is compensation or gi!ing up use o money dierence -et&een the amount loaned and the amount repaid.

, n amount o money today P can -e related to a utureamount F -y the interest amount I or interest ratei5

, Right to Pat -eginning time period e6changes

or right to Fat end &here F = P1+i, iinterest rate, Ppresent "orthoF, Ffuture "orthoP, -ase periodinterest period

2.2 nterest and nterest #ates

F = P + I = P + Pi = P$1+ i%

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Figure 2.1 'resent and Future (orth

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2.2 nterest and nterest #ates $cont*d%

, /he dimension o an interest rate is dollars7dollars7time.

, i.e. i 81 is lent at a 9: interest rate then 80.097year&ould -e paid in interest per time period

, period o!er &hich interest calculated is interest period.

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C;P 2.1 Interest PeriodsC;P 2.1 Interest Periods

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2.! Compound and imple nterest

, I amount Pis lent or one interest period at theinterest rate i the amount that must -e repaid atthe end o the period is F = P1+ i.

, I num-er o periods is greater than one interestusually compoundedat the end o each periodinterest is added to principal that there &as at the-eginning o that period.

, /he interest accumulated is5F = P$1+ i%

N


IC= F P = P$1 + i%N P

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Tale 2.1 Compound nterest Computations

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'ractice 'rolem, E0ample 2.!

, ?ith i@ 10: per year ho& much is o&ed ona loan o 8100 at the end o 3 yearsA

, ?hat is the compound interest amountA

F = P1+ iN = 1001 B 0.103 = 8133.10

IC= F P = 8133.10 8100.00 @ 8 33.10

/he amount o&ed is 8133.10 /he interest o&edis 833.10 See /a-le 2.2 on p 24

?hat is the amount o&ed at each year endA

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imple nterest interest &ithout compoundinginterest is not added to principal at end o eachperiod

, Compound and simple interest amounts e)ual i N@ 1.

,s

Nincreases dierence -et&een accumulated interestamounts or the t&o methods increases e6ponentially.

, /he con!entional approach or computing interest is thecompound interestmethod. Simple interest rarely used.

2.! Compound and imple nterest $cont*d%

IS= P i N



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Figure 2.2 Compound and imple

nterest at 2&3 'er 4ear for 2 4ears



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2.& Effecti5e and 6ominal nterest #ates

, Interest rates stated or some period li+e a year.

, Computation -ased on shorter compounding su-periods

, In this section &e consider the relation -et&een5

/he nominal interest ratestated or the ull period. /he effecti5e interest ratethat results rom the

compounding -ased on the su-periods.

, >nless other&ise noted rates are nominal annual rates

, Suppose5 r is nominal rate stated or a period 1 yearconsisting o me)ual compounding periods su-=periods

, If is@ r7mD thenF = P1+ iSm= P1+ ie



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, Effecti5e interest rate,, ie gi!es same uture amount F,

o!er the ull period as &hen su-period interest rate iS is

compounded o!er msu-periods.F = P$1+ iS%m= P$1+ ie%

, E78M'9E 2.+ p2( Carde6 Credit Card Co. charges anominal 24 percent interest on o!erdue accountscompounded daily. (hat is the effecti5e interest rate:

ince F = P$1+ iS%m= P$1+ ie%, ie= $1+ iS%m 1

"here is; r, The effecti5e interest rate is 2.13

2.& Effecti5e and 6ominal nterest $cont*d%

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, Suppose that the nominal interest rate is 12: andinterest is compounded semi-annually.

, ?e compute the eecti!e interest rate as ollo&s5&here r@ 0.12 m@ 2

is; r


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, /he eecti!e interest rate under continuouscompounding is5

2.) Continuous Compounding $cont*d%

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Figure 2.! ?ro"th in Value at @1 at !3nterest for Various Compounding 'eriods

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, "o& &e may compute the eecti!e interestrate or a nominal interest rate o 12: undercontinuous compounding5

ie; er

1 ; e.12

1 ; .12) ; 12.)3, lthough continuous compounding ma+es

sense in some circumstances i.e large cashlo&s it is not oten used

, 'iscrete compounding is the norm.

2.) Continuous Compounding $cont*d%



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2.+ Cash Flo" >iagrams

, Cash lo& diagram is a graphical summary o thetiming and magnitude o a set o cash lo&s

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ssumptions5ssumptions5

Cash lo&s occur at theCash lo&s occur at the ends o periods.ends o periods.End o time period 1 @ -eginning o time period 2 etc.End o time period 1 @ -eginning o time period 2 etc./ime 0 @ no&F/ime 0 @ no&F

Fig 2.) Aeginning and Ending of 'eriods

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E i i E i Fifth Editi


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2. EBui5alence

, Engineering Economics utilises time !alue o moneyFto compare certain !alues at dierent points in time.

, /hree concepts o e)ui!alence are distinguished

underlying comparisons o costs7-eneits at dierenttimes5

1.*athematical E)ui!alence

2.'ecisional E)ui!alence

3.*ar+et E)ui!alence




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2. EBui5alence $cont*d%

, Mathematical EBui5alence5 'ecision=ma+ers e6changeP dollars no& or Fdollars Nperiods rom no& rate i andthe mathematical relationship5 F = P1+ iN

, >ecisional EBui5alence5'ecision=ma+er is indierent as

toP

dollars no& orF

dollarsN

periods rom no&. ?e inferdecision=ma+erGs implied interest rate

, Maret EBui5alence5'ecision=ma+ers e6changedierent cash lo&s in a mar+et at Hero cost.

In a inancial mar+et indi!iduals7companies arelending and -orro&ing money.

i.e. -uying a car and o&ing 81# 000 a lender pro!idesthe 81# 000 no& or 8#007month o!er 3$months.




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2. EBui5alence $cont*d%

, %or the remainder o this te6t &e assume5

1. mar+et e)ui!alence holds

2. decisional e)ui!alence can -e e6pressed in

monetary terms

, I these t&o assumptions are reasona-ly !alidthen mathematical e)ui!alence can -e usedas an accurate model o ho& costs and-eneits relate to one another o!er time.




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ummary

, "otion o Interest and Interest Rates

, Compound and Simple Interest

,Eecti!e and "ominal Interest, Continuous Compounding

, Cash %lo& 'iagrams

, E)ui!alence

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ch02-TimeValueOfMoney.ppt

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