tvm calc excel w audio

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Financial

Calculators andExcel

Week 2 Lecture 2



Three Ways to Solve Time

Value of Money ProlemsUse Equations

Use Financial Calculator

Use Electronic Spreadsheet



Ty!es of Prolems

Future Value

Present Value

Uneven Cash Flow StreamsTime or Funds to !ccumulate

Future Value o an !nnuit"

Present Value o an !nnuit"E!#

!morti$ation



After 1 year:FV1 = PV + Interest1 = PV + PV (r)

= PV(1 + r)= $100 (1.10)= $110.00.

After 2 years:FV

2

= PV(1 + r)2

= $100 (1.10)2

= $121.00.

After 3 years:FV

3

= PV(1 + r)3

= 100 (1.10)3

= $133.10.

In general, FVn = PV (1 + r)n

Future Value



Solve t!s e"#at!on y %l#gg!ng !n tea%%ro%r!ate val#es:

"umerical #E$uation%

Solution

= + ttFV PV(1 r)

PV = $100, r = 10&, an' t =3

$133.10)$100(1.331

$100(1.10)FV 3n

==

=



ere are var!ales. If 3 are

*non, te al#lator !ll solve forte t.

Financial Calculator

Solution

= +t

tFV PV(1 r)



INPUTS

CPT

3 10 -100 0 ? N I/YR PV PMT FV

FV =

133.10

-eres te set#% to /n' FV:

lear!ng a#toat!ally sets everyt!ng to 0, #tfor safety enter P = 0.

P FV


Solution



S!readsheet Solution

4eferene ells:

4ate = !nterest

rate, r5%er = n#erof %er!o's!nterest !s

earne'

Pt = %er!o'!%ayent

PV = %resentval#e of te



Present Value Present value is the value toda" o a uture cash

low or series o cash lows%

Discounting is the process o indin& the presentvalue o a uture cash low or series o uturecash lows' it is the reverse o compoundin&%

Example

What is the PV o ()** due in three "ears i r +)*,-



100

0 1 2 310%

PV = ?

What is the PV of &'(( due

in three years if ) * '(+,



Solve FVt = PV (1 + r )t for PV:

( ) ÷

t

t tt

FV 1PV = = FV 1+r1+r

( ) $67.13=0.6713$100=

1.101$100=PV

3

What is the PV of &'(( due

in three years if r * '(+,

!s !s te n#er!al sol#t!on to solve for PV.



INPUTS

CPT

3 10 ? 0

100N I/YR PV PMT FV

PV = -75.13


Solution

8!ter PV or FV #st e negat!ve. -erePV = 967.13. Invest $67.13 to'ay, ta*eo#t $100 after 3 years.



Time for Funds to

-ccumulate. sales &row at 2*, per"ear/how lon& 0eore sales

dou0le-

Solve or n



Solve for !FV = 1"1 # I$

2 = 1"1.20$

Time for Funds to

-ccumulate

e n#er!al sol#t!on !s soeat'!#lt.



Time for Funds to

-ccumulate 2 + )1)%2*n

Ln 2 + n ln )%2

%345) + n %)6252

7 + 5%6



INPUTS

CPT

? 20 -1 0 2

N I/YR PV PMT FV

=3.

;ra%!al

Ill#strat!on:

0 1 2 3 &

1

2

FV

3.

Ye'r


Solution



Fractional Time Periods

0 0.25 0.50 0.75

10%

- 100

1.00

FV = ?

8<a%le: $100 'e%os!te' !n a an* at8A4 = 10& for 0.67 of te year

INPUTS

CPT

0.75 10 -100 0?

FV

N I/YR PV PMT FV



Future Value of an -nnuity

Annuity: ! series o pa"ments o equalamounts at i8ed intervals or a speciiednum0er o periods%

Ordinary (deferred) Annuity: !n annuit"whose pa"ments occur at the end o eachperiod%

Annuity Due: !n annuit" whose pa"ments

occur at the 0e&innin& o each period%



PMT PMTPMT

0 1 2 3r%

PMT PMT

0 1 2 3

r%

PMT

.rdinary -nnuity Versus -nnuity /uer'!nary Ann#!ty

Ann#!ty >#e



100 100100

0 1 2 310%

110

121

FV = 331

What0s the FV of a 12year

.rdinary -nnuity of &'((at '(+,




Solution

INPUTS

CPT

3 10 0 -100 ?

FV

=331.00

N I/YR PV PMT FV



Present Value of an -nnuity

PV!n + the present value o an annuit"

with n pa"ments%

Each pa"ment is discounted/ and the sumo the discounted pa"ments is the presentvalue o the annuit"%



2&.() = PV

100 100100

0 1 2 310%

)0.)1

2.(&

75.13

What is the PV of this

.rdinary -nnuity,



"umerical Solution

+

=

= =

+

∑n

1n(1 I)

n t

t 1

191PVA P P

(1 I) I

$2?.@?7)$100(2.?@

0.10

91$100PVA

3(1.10)

1

3

==

=



Be *no te %ayents #t no l#% s# Fso enter 0 for f#t#re val#e.


Solution

INPUTS

*UTPUT

3 10 ? 100 0

-2&.()

N I/YR PV PMT FV



100 100

0 1 2 310%

100

Find the FV and PV if the

-nnuity 4ere an -nnuity/ue5



"umerical Solution

+

=

= = × + +

∑t

1t91(1 r)

n tt 0

191PVA P P (1 r)

(1 r) r

[ ]

$263.773)$100(2.637

1.10(2.?@?7)$100

(1.10)

0.10

91$100PVA

3(1.10)

1

3

==

×=

×

=



S!t fro C8n'D to CE;5D 9 2n' ten E;5 (Pt) en2n' S8. Ee s#re to ange !t a* to 85> to ret#rn to r'!naryAnn#!t!es.

en enter var!ales to /n' PVA3 = $263.77

o /n' FV, enter PV = 0 an' %ress FV to/n'

FV = [email protected].

Financial CalculatorSolution

INPUTS

CPT

3 10 ? 100 0

-273.55

N I/YR PV PMT FV



250 250

0 1 2 3r = ?

- &(.0

&

250 250

o# %ay $?@.?0 for an !nvestent tat%ro!ses to %ay yo# $270 %er year for te

ne<t fo#r years, !t %ayents a'e at teen' of ea year. Bat !nterest rate !llyo# earn on t!s !nvestentG

Solving for )nterest 6ates

4ith -nnuities



Hse tr!al9an'9error y s#st!t#t!ng '!erentval#es of r !nto te follo!ng e"#at!on #nt!l

te r!gt s!'e e"#als $?@.?0.

"umerical Solution

+

=

1

(1 r)19

$?@.?0 $270 r




Solution

INPUTS

CPT

& ? -&(.0 250

0

7.0

N I/YR PV PMT FV



+100 "1 # r $3 = +125.)7.

What interest rate 4ould cause&'(( to gro4 to &'7859: in 1

years,

INPUTS

*UTPUT

N I/YR PV PMT FV

3 ? -100 0

125.)7

%



EFF vs -P6 To clear 2nd #eset+

.C97V :ispla" will 0e 79;

)2 E7TE#

:ispla" will 0e C<=

)2 E7TE#

:ispla" will 0e EFF

CPT :ispla" will 0e )2%36

Choose F> 1conversion

7+)2 i,+)2

E + )2%36,

!P#+)2,



-morti;ed <oans !morti$ed Loan? ! loan that is repaid in equal pa"ments

over its lie%

!morti$ation ta0les are widel" used or home mort&a&es/auto loans/ retirement plans/ and so orth to determine howmuch o each pa"ment represents principal repa"ment andhow much represents interest% The" are ver" important/ especiall" to homeowners@

Financial calculators 1and spreadsheets are &reat orsettin& up amorti$ation ta0les%



PMT PMTPMT

0 1 2 310%

-1000

Ste! '3 /etermine there$uired !ayments

( )

3

11

1 .1$1000.1

Pmt

−

+ = ×

$402.11 Pmt =



PMT PMTPMT

0 1 2 310%

-1000

INPUTS

*UTPUT

3 10 -1000 ?

0

&02.11

N I/YR PV PMT FV

Ste! '3 /etermine the

re$uired !ayments



Ste! 73 Find interest

charge for >ear 'I5t = Eeg!nn!ng alanet (I)

I51 = 1,000(0.10) = $100.00



4e%ayent = P 9 I5

= $02.11 9 $100.00= $302.11.

Ste! 13 Find re!ayment

of !rinci!al in >ear '



8n'!ng al. = Eeg!nn!ng al. 9

4e%ayent= $1,000 9 $302.11 =

$@6.?.

4e%eat tese ste%s for te rea!n'erof te %ayents (ears 2 an' 3 !n t!sase)to o%lete te aort!Jat!on tale.

Ste! ?3 Find ending

alance after >ear '



Calculator 7ot worth the trou0le



Interest 'el!nes, ! as ta< !%l!at!ons.

<oan -morti;ation Tale

'( Percent )nterest 6ate YR Beg Bal PMT INT Prin PMT End Bal

1 $1000.00 $402.11 $100.00 $302.11 $697.89

2 697.89 402.11 69.79 332.32 365.57

3 365.57 402.11 36.56 365.55 0.02

Toal 1!206.33 206.35 999.98 "

K 4o#n'!ng '!erene



Uneven Cash Flo4 Streams ! series o cash lows in which the amount varies

rom one period to the ne8t?

Pa"ment 1P;T desi&nates constant cash lowsAthat is/ an annuit" stream%

Cash low 1CF desi&nates cash lows in&eneral/ 0oth constant cash lows and unevencash lows%



0

100

1

300

2

300

310%

-50

&

)0.)1

2&7.)3

225.3)

-3&.15

530.0 = PV

What is the PV of this

Uneven Cash Flo4Stream,



"umerical Solution

t

= + + +

+ + + 1 21 2 t

1 1 1PV F F ... F

(1 r) (1 r) (1 r)

−+

+

+

=

321 (1.10)

170)(

(1.10)

1300

(1.10)

1300

(1.10)

1100PV

$730.0

01)$70)(0.@?3(31)$300(0.6717)$300(0.?2@0)$100(0.0

=

−+++=

Fi i l C l l



Financial CalculatorSolution CL# TV; B 0ut this doesnt clear ever"thin&

7eed to #ESET to clear ever"thin& CF

C** + *

C*) + )** Enter F*)+) C*2 + 5** Enter F*2+) C*5 + 5** Enter F*5+) C*D + >* Enter B F*D+)

CPT 7PV . + )* Enter

7PV CPT 7PV + >5*%*6



Three Ways to Solve Time

Value of Money ProlemsUse Equations

Use Financial Calculator

Use Electronic Spreadsheet

tvm calc excel w audio

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