1 Prentice Hall, 1998 Chapter 5 The Time Value of Money.

1Prentice Hall, 1998

Chapter 5Chapter 5

The Time Value of MoneyThe Time Value of Money


Learning ObjectivesLearning Objectives

Calculate present and future values of any Calculate present and future values of any set of expected future cash flowsset of expected future cash flows..

Explain how the present value and discount Explain how the present value and discount rate are inversely relatedrate are inversely related..

Calculate payments on a debt contractCalculate payments on a debt contract..

Compute the APR and APY for a contractCompute the APR and APY for a contract..

Value Value ““special financingspecial financing”” offers offers..


Definitions and AssumptionsDefinitions and Assumptions

A point in time is denoted by the letter A point in time is denoted by the letter ““tt””..

Unless otherwise stated, tUnless otherwise stated, t==0 represents 0 represents today today ((the decision pointthe decision point))..

Unless otherwise stated, cash flows occur at Unless otherwise stated, cash flows occur at the end of a time intervalthe end of a time interval..

Cash inflows are treated as positive Cash inflows are treated as positive amounts, while cash outflows are treated as amounts, while cash outflows are treated as negative amountsnegative amounts..

Compounding frequency is the same as the Compounding frequency is the same as the cash flow frequencycash flow frequency..


The Time LineThe Time Line

tt==00 tt==11 tt==22 tt==33 tt==44



t=0 t=1 t=2 t=3 t=4

TodayToday



tt==00 tt==11 tt==22 tt==33 tt==44

TodayToday End of theEnd of thethird yearthird year



tt==00 tt==11 tt==22 tt==33 tt==44

TodayToday Beginning of the Beginning of the fourth yearfourth year

End of theEnd of thethird yearthird year


Future Value FormulaFuture Value Formula

Let PVLet PV= = Present ValuePresent Value

FVFVnn= = Future Value at time nFuture Value at time n

rr= = interest rate interest rate ((or discount rateor discount rate) ) per periodper period..

)nr,PV(FVF)1(PVnFV nr


r = 0%

r = 10%

Future Value FactorFuture Value Factor

0.000.00

2.002.00

4.004.00

6.006.00

8.008.00

10.0010.00

00 55 1010 1515TimeTime

FV

Fac

tor

FV

Fac

tor

r = 5%

r = 15%


Present Value FormulaPresent Value Formula

Let PVLet PV= = Present ValuePresent Value

FVFVnn= = Future Value at time nFuture Value at time n

rr= = interest rate interest rate ((or discount rateor discount rate) ) per periodper period..

)nr,(PVFnFV)(1

1nFVPV

nr


Present Value FactorsPresent Value Factors

0.000.00

0.200.20

0.400.40

0.600.60

0.800.80

1.001.00

00 55 1010 1515TimeTime

PV

Fac

tor

r = 5%

r = 10%

r = 0%

r = 15%


Solving for an Unknown Interest Rate Solving for an Unknown Interest Rate ((CDCD))

The First Commerce Bank offers a Certificate of The First Commerce Bank offers a Certificate of Deposit Deposit ((CDCD) ) that pays you $5,000 in four that pays you $5,000 in four yearsyears. . The CD can be purchased today for The CD can be purchased today for $3,477.87$3,477.87. . Assuming you hold the CD to Assuming you hold the CD to maturity, what annual interest rate is the bank maturity, what annual interest rate is the bank

paying on this CDpaying on this CD??



PV PV = = $3,477.87; FV$3,477.87; FV44 = $5,000 = $5,000; n ; n = = 4 years4 years..

SinceSince FVFV PVPV rr((nnnn ))11

1PV

FV1

nnr



PV PV = = $3,477.87; FV$3,477.87; FV44 = $5,000 = $5,000; n ; n = = 4 years4 years..

SinceSince FVFV PVPV rr((nnnn ))11

%5.9095.0187.477,3$

000,5$ 4

1

or

1PV

FV1

nnr


AnnuitiesAnnuities

An annuity is a series of identical cash flows An annuity is a series of identical cash flows that are expected to occur each period for a that are expected to occur each period for a specified number of periodsspecified number of periods..

Thus, CFThus, CF11 = = CFCF22 = = CFCF33 = = CfCf44 = ... = = ... = CFCF

Examples of annuitiesExamples of annuities::Installment loans Installment loans ((car loans, mortgagescar loans, mortgages))..

Coupon payment on corporate bondsCoupon payment on corporate bonds..Rent payment on your apartmentRent payment on your apartment..


Types of AnnuitiesTypes of Annuities

Ordinary AnnuityOrdinary Annuity::An annuity with An annuity with endend--ofof--PeriodPeriod cash flows, cash flows,

beginning one period from todaybeginning one period from today..

Annuity DueAnnuity Due::An annuity with An annuity with beginningbeginning--ofof--periodperiod cash flows cash flows..

Deferred AnnuityDeferred Annuity::An annuity that begins more than one period An annuity that begins more than one period

from todayfrom today..


Future Value of an AnnuityFuture Value of an Annuity

FVAFVAnn = = CFCF((1+r1+r))00 + + CFCF((1+r1+r))11 + . . . + + . . . + CFCF((1+r1+r))n-1n-1



FVAFVAnn = = CFCF[[summation {from 0 to n-1} of summation {from 0 to n-1} of ((1+r1+r))t t ]]

FVAFVAnn = = CFCF((1+r1+r))00 + + CFCF((1+r1+r))11 + . . . + + . . . + CFCF((1+r1+r))n-1n-1

= =CFCF[([(1+r1+r))00 + (1+ + (1+rr))11 + . . . + (1+ + . . . + (1+rr))n-1n-1 ] ]



r

r n

n

1)1(CFFVA


Future Value of Your SavingsFuture Value of Your Savings

Suppose you save $1,500 per year for 15 Suppose you save $1,500 per year for 15 years, beginning one year from todayyears, beginning one year from today. . The The savings bank pays you 8% interest per yearsavings bank pays you 8% interest per year..

How much will you have at the end of 15 yearsHow much will you have at the end of 15 years??


Future Value of Your SavingsFuture Value of Your Savings

4040 728728 1717 $$ ,, ..

r

r n 1)1(CFFVA 15

1521.27500,1$1)08.1(

500,1$15

r


Present Value of an AnnuityPresent Value of an Annuity

nnn r )1(

1FVAPVA



nnn r )1(

1FVAPVA

n

n

rr

r

)1(

11)1(CF



n

n

rr

r

)1(

1)1(CF

nnn r )1(

1FVAPVA

n

n

rr

r

)1(

11)1(CF


Present Value of Your Bank LoanPresent Value of Your Bank Loan

Cindy agrees to repay a loan in 24 monthly Cindy agrees to repay a loan in 24 monthly installments of $250 eachinstallments of $250 each. . If the interest rate on If the interest rate on the loan is 0.75% per month, what is the the loan is 0.75% per month, what is the

present value of the loan paymentspresent value of the loan payments??


Present Value of Your Bank LoanPresent Value of Your Bank Loan

472472 2828 $5$5,, ..

n

n

rr

r

)1(

1)1(CFPVA 24

8891.21250$)075.1(075.0

1)075.1(250$

24

24


Payments of an Annuity Payments of an Annuity ((Given FVAGiven FVAnn))

r

r n

n

1)1(CFFVA Since

1)1(

FVACFnn r

r


Saving for RetirementSaving for Retirement

You wish to retire 25 years from today with You wish to retire 25 years from today with $2,000,000 in the bank$2,000,000 in the bank. . If the bank pays 10% If the bank pays 10% interest per year, how much should you save interest per year, how much should you save

each year to reach your goaleach year to reach your goal??


Saving for RetirementSaving for Retirement

336336 1414$20$20,, ..

1)1(

FVACFnn r

r

]0101681.0[000,000,2$1)10.1(

10.0000,000,2$

25


Payments of an Annuity Payments of an Annuity ((Given PVAGiven PVAnn))

n

n

n rr

r

)1(

1)1(CFPVA Since

11

1PVACF

n

n

n r)(

r)r(


Installment Payments on a LoanInstallment Payments on a Loan

Rob borrows $10,000 to be repaid in four equal Rob borrows $10,000 to be repaid in four equal annual installments, beginning one year from annual installments, beginning one year from todaytoday. . What is RobWhat is Rob’’s annual payment on this s annual payment on this loan if the bank charges him 14% interest per loan if the bank charges him 14% interest per

yearyear??


Installment Payments on a LoanInstallment Payments on a Loan

432432 0505$3$3,, ..

1)1(

)1(PVACF

n

n

n r

rr

]343205.0[000,10$1)14.1(

)14.1(14.0000,10$

4

4


Loan Amortization ScheduleLoan Amortization Schedule

It shows how a loan is paid off over timeIt shows how a loan is paid off over time..

It breaks down each payment into the It breaks down each payment into the interest component and the principal interest component and the principal componentcomponent..

LetLet’’s illustrate this using Robs illustrate this using Rob’’s 4-year s 4-year $10,000 loan which calls for annual $10,000 loan which calls for annual payments of $3,432.05payments of $3,432.05. . Recall that the Recall that the interest rate on this loan is 14% per yearinterest rate on this loan is 14% per year..



PeriodPeriod:: 11 22 33 44

Principal @ StartPrincipal @ Start

of Periodof Period

Interest for PeriodInterest for Period

BalanceBalance

PaymentPayment

Principal RepaidPrincipal Repaid

Principal @ EndPrincipal @ End

of Periodof Period

$10000.00$10000.00

$1,400.00$1,400.00

$11,400.00$11,400.00

$3,432.05$3,432.05

$2,032.05$2,032.05

$7,967.95$7,967.95




of Periodof Period


BalanceBalance

PaymentPayment



of Periodof Period

$10000.00$10000.00

$1,400.00$1,400.00

$11,400.00$11,400.00

$3,432.05$3,432.05

$2,032.05$2,032.05

$7,967.95$7,967.95

$7,967.95$7,967.95

$1,115,51$1,115,51

$9,083.47$9,083.47

$3,432.05$3,432.05

$2,316.53$2,316.53

$5,651.42$5,651.42





of Periodof Period


BalanceBalance

PaymentPayment



of Periodof Period

$10000.00$10000.00

$1,400.00$1,400.00

$11,400.00$11,400.00

$3,432.05$3,432.05

$2,032.05$2,032.05

$7,967.95$7,967.95

$7,967.95$7,967.95

$1,115,51$1,115,51

$9,083.47$9,083.47

$3,432.05$3,432.05

$2,316.53$2,316.53

$5,651.42$5,651.42

$5,651.42$5,651.42

$791.20$791.20

$6,442.62$6,442.62

$3,432.05$3,432.05

$2,640.85$2,640.85

$3,010.57$3,010.57





of Periodof Period


BalanceBalance

PaymentPayment



of Periodof Period

$10000.00$10000.00

$1,400.00$1,400.00

$11,400.00$11,400.00

$3,432.05$3,432.05

$2,032.05$2,032.05

$7,967.95$7,967.95

$7,967.95$7,967.95

$1,115,51$1,115,51

$9,083.47$9,083.47

$3,432.05$3,432.05

$2,316.53$2,316.53

$5,651.42$5,651.42

$5,651.42$5,651.42

$791.20$791.20

$6,442.62$6,442.62

$3,432.05$3,432.05

$2,640.85$2,640.85

$3,010.57$3,010.57

$3,010.57$3,010.57

$421.48$421.48

$3,432.05$3,432.05

$3,432.05$3,432.05

$3,010.57$3,010.57

$0.00$0.00



Deferred AnnuityDeferred Annuity

The first cash flow in a deferred annuity is The first cash flow in a deferred annuity is expected to occur later than texpected to occur later than t==11..

The PV of the deferred annuity can be The PV of the deferred annuity can be computed as the difference in the PVs of two computed as the difference in the PVs of two annuitiesannuities..



An annuityAn annuity’’s first cash flow is expected to occur s first cash flow is expected to occur 3 years from today3 years from today. . There are 4 cash flows in There are 4 cash flows in this annuity, with each cash flow being $50this annuity, with each cash flow being $500. 0. At At an interest rate of 10% per year, find the an interest rate of 10% per year, find the annuityannuity’’s present values present value..



00 11 22 33 44 55 66

$500$500 $500$500 $500$500 $500$500



00 11 22 33 44 55 66

$500$500 $500$500 $500$500 $500$500

00 11 22 33 44 55 66

$500$500 $500$500 $500$500 $500$500 $500$500 $500$500

00 11 22 33 44 55 66

$500$500 $500$500

equalsequals

minusminus



PV of the deferred annuityPV of the deferred annuity = =

PV of 6 year ordinary annuityPV of 6 year ordinary annuity --

PV of 2 year ordinary annuityPV of 2 year ordinary annuity..



$2$2,, .. $867$867..

$1$1,, ..

177177 6363 7777

309309 8686

2

2

6

6

deferred )10.1(10.0

1)10.1(500$

)10.1(10.0

1)10.1(500$PVA


PerpetuityPerpetuity

A perpetuity is an annuity with an infinite A perpetuity is an annuity with an infinite number of cash flowsnumber of cash flows..

The present value of cash flows occurring in The present value of cash flows occurring in the distant future is very close to zerothe distant future is very close to zero..

At 10% interest, the PV of $100 cash flow At 10% interest, the PV of $100 cash flow occurring 50 years from today is $0.85occurring 50 years from today is $0.85!!

The PV of $100 cash flow occurring 100 years The PV of $100 cash flow occurring 100 years from today is less than one pennyfrom today is less than one penny!!


Present Value of a PerpetuityPresent Value of a Perpetuity

n

n

rr

r

)1(

1)1(CFPVA n



nn

n

n

n

rrrr

r

rr

r

)1(

1CF

)1(

)1(CF

)1(

1)1(CFPVA n



nn

n

n

n

rrrr

r

rr

r

)1(

1CF

)1(

)1(CF

)1(

1)1(CFPVA n

nrrr )1(

CFCF



As n goes to infinity, 1/(1+r)n goes to 0

and PVAperpetuity = CF/r

nn

n

n

n

rrrr

r

rr

r

)1(

1CF

)1(

)1(CF

)1(

1)1(CFPVA n

nrrr )1(

CFCF



What is the present value of a perpetuity of $270 per What is the present value of a perpetuity of $270 per year if the interest rate is 12% per yearyear if the interest rate is 12% per year??

PVPVCFCF

rrperpetuityperpetuity $270$270

..$2$2,,

00 1212250250


Multiple Cash FlowsMultiple Cash Flows

PV of multiple cash flows PV of multiple cash flows = = the sum of the the sum of the present values of the individual cash flowspresent values of the individual cash flows..

FV of multiple cash flows FV of multiple cash flows at a common point at a common point in time in time = = the sum of the future values of the the sum of the future values of the individual cash flows individual cash flows at that point in timeat that point in time..


Multiple Cash Flow ExampleMultiple Cash Flow Example

Consider the following cash flowsConsider the following cash flows::

TimeTimeNotationNotationCash FlowCash Flow

00CF0CF0- $ 2,000- $ 2,000

11CF1CF1+ $ 1,000+ $ 1,000

22CF2CF2+ $ 1,500+ $ 1,500

33CF3CF3+ $ 2,000+ $ 2,000

The interest rate The interest rate ((rr) ) is 10% per periodis 10% per period..


Time Line of Multiple Cash FlowsTime Line of Multiple Cash Flows

tt==00 tt==11 tt==22 tt==33

$- $-2,0002,000 $+ $+1,0001,000 $+ $+1,5001,500 $+ $+2,0002,000


PV of Multiple Cash FlowsPV of Multiple Cash Flows

PVPV

$2$2,,

..

$1$1,,

..

$1$1,,

..

$2$2,,

..

$2$2,, $909$909.. $1$1,, .. $1$1,, ..

$1$1,, ..

000000

))11 1010((

000000

))11 1010((

500500

))11 1010((

000000

))11 1010((

000000 0909 239239 6767 502502 6363

6516513939

00 11 22 33


FV FV ((at tat t==33) ) of Multiple Cash Flowsof Multiple Cash Flows

662662 210210 000000

198198 0000

$2$2,, $1$1,, $1650$1650 $2$2,,

$2$2,, ..

103 )10.1(000,1$)10.1(000,2$FV

32 )10.1(000,2$)10.1(500,1$



AlternativAlternativelyely

FVFV PVPV rr((

,,

$1$1,, .. .. $2$2,, ..

3333

33

))11

6516513939 ))11 1010(( 198198 0000



FVFV2222 11

0011

000000 ))11 1010(( 000000 ) ) 11 1010((

500500 ))11 1010((000000

))11 1010((

420420 0000 100100 0000 500500 818818 1818

998998 1818

$2$2,, .. $1$1,, ..

$1$1,, ..$2$2,,

..

$2$2,, .. $1$1,, .. $1$1,, $1$1,, ..

$1$1,, ..



AlternativAlternativelyely

oror

FVFVFVFV

rr((

,,

$2$2,, ..

..$1$1,, ..22

3311 11))11

198198 0000

))11 1010((998998 1818

18.998,1$)10.1(39.651,1$)1(PVFV 222 r


More Frequent CompoundingMore Frequent Compounding

Interest may be compounded more than Interest may be compounded more than once per yearonce per year..

The The Annual Percentage Rate Annual Percentage Rate ((APRAPR) ) is the is the periodic rate times the number of periods per periodic rate times the number of periods per yearyear..

The The Annual Percentage Yield Annual Percentage Yield ((APYAPY) ) is the is the ““truetrue”” annually compounded interest rate annually compounded interest rate..


APR and APY for an Installment LoanAPR and APY for an Installment Loan

Suppose you borrow $5,000 from the bank and Suppose you borrow $5,000 from the bank and promise to repay the loan in 12 equal monthly promise to repay the loan in 12 equal monthly installments of $437.25 each, with the first installments of $437.25 each, with the first payment to be made one month from todaypayment to be made one month from today..

What is the APRWhat is the APR??

What is the APYWhat is the APY??



Solving this for r, we get r Solving this for r, we get r = = 0.75%0.75% per monthper month

APR APR = = 0.75 x 120.75 x 12 = = 9% per year9% per year

12

12

)1(

1)1(25.437$000,5$

rr

r



To calculate the APY, compound the periodic To calculate the APY, compound the periodic rate for the number of periods in one yearrate for the number of periods in one year

in this case, 12 months to make one yearin this case, 12 months to make one year::

oror 00 09380938 99 38%38%.. ..

112

09.011

APR1APY

12

m

m


Effect of Compounding Frequency on Effect of Compounding Frequency on Future ValueFuture Value

Find the future value at the end of one year if Find the future value at the end of one year if the present value is $20,000 and the APR is the present value is $20,000 and the APR is 16%16%. . Use the following compounding Use the following compounding frequenciesfrequencies::

Annual Compounding

Semiannual Compounding

Quarterly Compounding

Monthly Compounding

Daily Compounding

Continuous Compounding


Annual CompoundingAnnual Compounding

Since m Since m = = 1, the periodic rate is 16%1, the periodic rate is 16%..

FVFV1111000000 ))11 1616(( 200200 0000 $20$20,, .. $23$23,, ..

APY APY = = APR APR = = 16%16%


Semi Semi - - Annual CompoundingAnnual Compounding


APR APR = = 2 x 82 x 8 = = 16%16%

FVFV22 = 20,000(1.08) = 20,000(1.08)22 = $23,328.00 = $23,328.00

%640.1616640.012

16.01APY

2


Quarterly CompoundingQuarterly Compounding


APR APR = = 4 x 44 x 4 = = 16%16%

FV44000 )1 04( 397 17 $20, . $23, .

%986.1616986.014

16.01APY

4


Effect of Compounding Frequency on Effect of Compounding Frequency on Future ValueFuture Value

CompoundingCompounding mm FVFV APYAPY

AnnualAnnual

SemiSemi--AnnualAnnual

QuarterlyQuarterly

MonthlyMonthly

DailyDaily

11

22

44

1212

365365

$23,200.00$23,200.00

$23,328.00$23,328.00

$23,397.17$23,397.17

$23,445.42$23,445.42

$23,469.39$23,469.39

16.000%16.000%

16.640%16.640%

16.986%16.986%

17.227%17.227%

17.347%17.347%

APR APR = = 16%16%


Continuous CompoundingContinuous Compounding

With continuous compounding, m becomes With continuous compounding, m becomes very largevery large..

As m approaches infinity, As m approaches infinity, APY APY = = eeAPRAPR - 1 - 1, , where e where e = = 2.718282.71828..

So APY So APY = (= (2.718282.71828))0.160.16 - 1 = 0.17351 - 1 = 0.17351 or or 17.351%17.351%..

FV FV = = $20,000$20,000 ( (1.173511.17351))11 = $23,469.39 = $23,469.39


Partial Time PeriodsPartial Time Periods

What is the future value 3.5 years from today of What is the future value 3.5 years from today of $5,000 at an APR of 12%$5,000 at an APR of 12%??


Partial Time PeriodsPartial Time Periods

What is the future value 3.5 years from today of What is the future value 3.5 years from today of $5,000 at an APR of 12%$5,000 at an APR of 12%??

FVFV PVPV rr((33 5533 55 33 55))11 000000 ))11 1212((

434434 1818

.... ..$5$5,, ..

$7$7,, ..


Valuing Special Financing OffersValuing Special Financing Offers

Miller Motors is offering the following Miller Motors is offering the following alternatives on a Dodge Intrepid, which has a alternatives on a Dodge Intrepid, which has a stated price of $24,000stated price of $24,000..

$1500$1500 ““cash back,cash back,”” or or

““SpecialSpecial”” 36- 36-month 3.5% APR financingmonth 3.5% APR financing??

If you can borrow from M&T Bank at 9% APR, If you can borrow from M&T Bank at 9% APR, which alternative is betterwhich alternative is better??



The general procedure is to measure the opportunity cost of the special financing, and compare this cost to the net “cash-back” price.



First, compute the monthly payments for the First, compute the monthly payments for the special financing planspecial financing plan. . 3.50% APR implies a 3.50% APR implies a monthly rate of 3.50%monthly rate of 3.50%//12, or12, or

0.292%0.292% per monthper month..



First, compute the monthly payments for the First, compute the monthly payments for the special financing planspecial financing plan. . 3.50% APR implies a 3.50% APR implies a monthly rate of 3.50%monthly rate of 3.50%//12, or12, or


$703$703..2525PMTPMT perper monthmonth

36

36

)00292.1(00292.0

1)00292.1(PMT000,24$



NoteNote: : The monthly payments are The monthly payments are ““real,real,”” even even though the 3.5% APR is not though the 3.5% APR is not ““realreal..””

Next, find the present value of these payments at the Next, find the present value of these payments at the bank’bank’s lending rates lending rate. . The 9% APR bank loan The 9% APR bank loan implies a monthly interest rate is 9%implies a monthly interest rate is 9%//12, or12, or




Next, find the present value of these payments at Next, find the present value of these payments at the bankthe bank’’s lending rates lending rate. . The 9% APR bank loan The 9% APR bank loan implies a monthly interest rate is 9%implies a monthly interest rate is 9%//12, or12, or


The present value isThe present value is::

96.114,22$)0075.1(0075.0

1)0075.1(25.703$PVA

36

36



Next, find the present value of these payments at Next, find the present value of these payments at the bankthe bank’’s lending rates lending rate. . The 9% APR bank loan The 9% APR bank loan implies a monthly interest rate is 9%implies a monthly interest rate is 9%//12, or12, or


The present value isThe present value is::

This is a This is a ““realreal”” price for buying the car price for buying the car..

96.114,22$)0075.1(0075.0

1)0075.1(25.703$PVA

36

36



Finally, compare this present value of Finally, compare this present value of $22,114.96 to the net price under the cash$22,114.96 to the net price under the cash--back back planplan::

Price net of $1,500 cash backPrice net of $1,500 cash back

= =$24,000$24,000 - - $1,500$1,500 = = $22,500$22,500

This is also a This is also a ““realreal”” price for buying the car price for buying the car..

Which price would you preferWhich price would you prefer??



The The ““special financingspecial financing”” at $22,114.96, or at $22,114.96, or

The The ““cash backcash back”” price at $22,500 price at $22,500??

The difference of $385.04 between the two The difference of $385.04 between the two amounts is the amounts is the Net Present Value Net Present Value ((NPVNPV) ) of the of the special financing planspecial financing plan..



Another way to look at this problem is to find the Another way to look at this problem is to find the monthly payments if you borrow the monthly payments if you borrow the ““cash cash backback”” price price (($22,500$22,500) ) from the bank at 9% from the bank at 9% APRAPR..



Another way to look at this problem is to find the Another way to look at this problem is to find the monthly payments if you borrow the monthly payments if you borrow the ‘‘cashcash--backback’’ price price (($22,500$22,500) ) from the bank at an APR of 9%from the bank at an APR of 9%..

These payments areThese payments are::

$715.49PMT per month

36

36

)0075.1(0075.0

1)0075.1(PMT500,22$



The monthly payments under the cash back The monthly payments under the cash back plan would be $715.49plan would be $715.49..

Under the special financing plan, the Under the special financing plan, the monthly payments are $703.25monthly payments are $703.25..

Thus, you save $12.24 per month Thus, you save $12.24 per month ((for 36 for 36 monthsmonths) ) under the special financing planunder the special financing plan..

The PV of these savings at the bankThe PV of these savings at the bank’’s rate s rate of 0.75% per month is exactly the NPV of of 0.75% per month is exactly the NPV of the special financing plan the special financing plan ( = ( = $385.04$385.04))

1 Prentice Hall, 1998 Chapter 5 The Time Value of Money.

Documents

Transcript of 1 Prentice Hall, 1998 Chapter 5 The Time Value of Money.