FM 2016 Week 5 - Chapter 5

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Chapter 5

The Time Value

of Money—The Basics

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Slide Contents

! Principles Applied in this Chapter" 5.1 #sing $i%elines to &isuali'e Cash (lo)s

" 5.2 Co%pounding and (uture &alue

" 5.* +iscounting and Present &alue

" 5.4 a-ing Interest ates Co%para/le

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5.1 USIN TIM!"IN!S T#

VISU$"I%! C$S&'"#(S

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Usin) Timelines to Visuali*eCashflo+s

! A timeline identiies the ti%ing and a%ounto a strea% o pay%ents " /oth cashreceived and cash spent along )ith theinterest rate earned.

! A ti%eline is typically epressed in years,/ut it could also /e epressed as %onths,

days or any other unit o ti%e.

7/25/2019 FM 2016 Week 5 - Chapter 5



Time "ine !,ample

i103

ears

Cash lo) 100 *0 20 10 50

$he 4year ti%eline illustrates the ollo)ing6

" $he interest rate is 103.

" A cash outlo) o 100 occurs at the /eginning o the irst year 7atti%e 08, ollo)ed /y cash inlo)s o *0 and 20 in years 1 and 2,a cash outlo) o 10 in year * and cash inlo) o 50 in year 4.

0 1 2 * 4

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5.- C#M#UN/IN $N/

'UTU0! V$"U!

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Compoundin) and 'uture Value

$i%e value o %oney calculations involvePresent value 7)hat a cash lo) )ould /e)orth to you today8 and Future value 7)hata cash lo) )ill /e )orth in the uture8.

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Compound Interest and Time

Ea%ple6 <uppose that you deposited 500in your savings account that earns 53annual interest. =o) %uch )ill you have inyour account ater t)o years> Ater iveyears>

!(&2 P&71?i8n 50071.0582 551.-5

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Compound Interest and Time

2!$0 V orBe)innin) Value

Interest !arned 354 'V or!ndin)Value

1 566.66 5667.65 8 -5 5-5

- 5-5.66 5-57.65 8 -9.-5 551.-5

: 551.-5 551.-57.65 8-;.59 5;<.<1

= 5;<.<1 5;<.<17.658-<.>= 96;.;5

5 96;.;5 96;.;57.658:6.:> 9:<.1=

Using Equation 5-1a: FV = PV(1+i)n

= 500(1.05)5

= $638.14

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'i)ure 5.1 'uture Value and Compound InterestIllustrated3anel $ Calculatin) Compound Interest

7/25/2019 FM 2016 Week 5 - Chapter 5


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'i)ure 5.1 'uture Value andCompound Interest Illustrated 3cont.3anel C The o+er of the 0ate ofInterest

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$pplyin) Compoundin) toThin)s #ther Than Money

Ea%ple A +&+ rental ir% is currently renting;,000 +&+s per year. =o) %any +&+s )ill their% /e renting in 10 years i the de%and or+&+ rentals is epected to increase /y :3 peryear>

!#sing Euation 51a,

" (& ;00071.0:810 15?;:;.-1 /V/s

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Compound Interest +ithShorter Compoundin) eriods

Ban-s reuently oer savings account thatco%pound interest every day, %onth, oruarter.

ore reuent co%pounding )ill generatehigher interest inco%e and lead to higheruture values.

@l - h l f 166 C d d

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Ta@le 5A- The Value of 166 Compoundedat Various NonA$nnual eriods and Various0ates

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5.: /ISC#UNTIN $N/0!S!NT V$"U!

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The ey uestion

! hat is value today o cash lo) to /ereceived in the uture>

! $he ans)er to this uestion reuiresco%puting the present Dalue 3V i.e. thevalue today o a uture cash lo), and theprocess o discountin), deter%ining the

present value o an epected uture cashlo).

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The Mechanics of /iscountin)'uture Cash 'lo+s

! $he ter% in the /rac-et is -no)n as thePresent &alue Interest (actor 7P&I(8.

! P& (&n D P&I(

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T+o $dditional Types of/iscountin) ro@lems

<olving or6 718 u%/er o PeriodsF and728 ate o Interest

7186 =o) long )ill it ta-e to accu%ulate aspeciic a%ount in the uture>

! It is easier to solve or GnH using the inancial calculatoror Ecel rather than %athe%atical or%ula. 7<eechec-point 5.58

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The 0ule of ;-

! It deter%ine the nu%/er o years it )ill ta-eto dou/le the value o your invest%ent.

:2interest rate

(or ea%ple, i you are a/le to generate an annualreturn o @3, it )ill ta-e ; years 7:2@8 to dou/le

the value o invest%ent.

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SolDin) for the 0ate ofInterest

7286 hat rate o interest )ill allo) yourinvest%ent to gro) to a desired uture value>

e can deter%ine the rate o interest using%athe%atical euation.

#sing a athe%atical (or%ula

I 7(&P&81n 1

710000005000081*0 1 72080.0*** 1

1.1050 1

.1656 or 16.564

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5.= M$IN INT!0!ST 0$T!SC#M$0$B"!

l

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$nnual ercenta)e 0ate3$0

$he annual percenta)e rate 7AP8 indicatesthe interest rate paid or earned in one year)ithout co%pounding. AP is also -no)n asthe nominal or Euoted 3stated interest

rate.

C l l i h

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Calculatin) the Interest 0ateand ConDertin) it to an !$0

e cannot co%pare t)o loans /ased on AP ithey do not have the sa%e co%poundingperiod.

$o %a-e the% co%para/le, )e calculate theireuivalent rate using an annual co%poundingperiod. e do this /y calculating theeffectiDe annual rate 3!$0

FM 2016 Week 5 - Chapter 5

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