FM 2016 Week 6 - Chapter 6

7/21/2019 FM 2016 Week 6 - Chapter 6

1/25

Chapter 6

The Time Value

of MoneyAnnuities andOther Topics

7/21/2019 FM 2016 Week 6 - Chapter 6

2/25

Copyright 2014 Pearson Education, Inc. All rights reserved. 62

Slide Contents

Principles Applied in !his Chapter1. Annuities

2. Perpetuities

". Co#ple$ Cash %lo& 'trea#s

7/21/2019 FM 2016 Week 6 - Chapter 6

3/25

Copyright 2014 Pearson Education, Inc. All rights reserved. 6"

6.1 ANNUT!S

7/21/2019 FM 2016 Week 6 - Chapter 6

4/25


Ordinary Annuities

An annuityis a series o( equal dollarpay#ents that are #ade at the end o(e)uidistant points in ti#e, such as #onthly,)uarterly, or annually. I( pay#ents are #adeat the end of each period, the annuity isre(erred to as ordinary annuity.

7/21/2019 FM 2016 Week 6 - Chapter 6

5/25

Copyright 2014 Pearson Education, Inc. All rights reserved. 6*

Ordinary Annuities "cont.#

+ E$a#ple o& #uch #oney &ill youaccu#ulate -y the end o( year 10 i( youdeposit ",000 each year (or the ne$t tenyears in a savings account that earns */per year

+ eter#ine the ans&er -y using the e)uation

(or co#puting the % o( an ordinary annuity.

7/21/2019 FM 2016 Week 6 - Chapter 6

6/25


The $uture Value of anOrdinary Annuity

+ %n3 % o( annuity at the end o( nth period.

+ P! 3 annuity pay#ent deposited orreceived at the end o( each period

+ i 3 interest rate per period

+ n3 nu#-er o( periods (or &hich annuity &illlast

7/21/2019 FM 2016 Week 6 - Chapter 6

7/25Copyright 2014 Pearson Education, Inc. All rights reserved. 65

The $uture Value of anOrdinary Annuity "cont.#

sing e)uation 61c,

$V3 "000 78 91:.0*;10 1< = 9.0*;>

3 ",000 7 80.6"< = 9.0*; >3 ",000 712.*?>

3 %&'(')*

7/21/2019 FM 2016 Week 6 - Chapter 6

8/25Copyright 2014 Pearson Education, Inc. All rights reserved. 6?

$i+ure 6.1 $uture Value of a $i,e-ear AnnuitySa,in+ for /radSchool

7/21/2019 FM 2016 Week 6 - Chapter 6

9/25Copyright 2014 Pearson Education, Inc. All rights reserved. 6@

Sol,in+ for the 0MT in anOrdinary Annuity

ou #ay liBe to Bno& ho& #uch you need tosave each period 9i.e. P!; in order toaccu#ulate a certain a#ount at the end o( nyears.

7/21/2019 FM 2016 Week 6 - Chapter 6

10/25


The 0resent Value of anOrdinary Annuity

"cont.#

+ P! 3 annuity pay#ent deposited orreceived

+ i 3 discount rate 9or interest rate;

+ n 3 nu#-er o( periods

7/21/2019 FM 2016 Week 6 - Chapter 6

11/25


Amortied 2oans

An amortied loan is a loan paid o(( in e)ualpay#ents conse)uently, the loan pay#entsare an annuity. E$a#plesD o#e #ortgageloans, Auto loans

7/21/2019 FM 2016 Week 6 - Chapter 6

12/25


Amortied 2oans "cont.#

E$a#ple ou plan to o-tain a 6,000 loan(ro# a (urniture dealer at 1*/ annual interestrate that you &ill pay o(( in annual pay#entsover (our years. eter#ine the annualpay#ents on this loan and co#plete thea#ortiation ta-le.

7/21/2019 FM 2016 Week 6 - Chapter 6

13/25


Amortied 2oans "cont.#

+ sing a %inancial Calculator

F 3 4

iGy 3 1*.0

P 3 6000

% 3 0

P! 3 -%3(1*1.45

7/21/2019 FM 2016 Week 6 - Chapter 6

14/25


The 2oan Amortiation Schedule

Tale 6.1 The 2oan Amortiation Schedule for a %6(***2oan at 147 to 8e 9epaid in $our ears

7/21/2019 FM 2016 Week 6 - Chapter 6

15/25

Copyright 2014 Pearson Education, Inc. All rights reserved. 61*

Amortied 2oans :ithMonthly 0ayments

any loans such as auto and ho#e loansre)uire #onthly pay#ents. !his re)uiresconverting nto nu#-er o( #onths andco#puting the #onthly interest rate.

7/21/2019 FM 2016 Week 6 - Chapter 6

16/25


Annuities ;ue

Annuity due is an annuity in &hich all thecash (lo&s occur at the beginning of each

period. %or e$a#ple, rent pay#ents onapart#ents are typically annuities due-ecause the pay#ent (or the #onthHs rentoccurs at the -eginning o( the #onth.

7/21/2019 FM 2016 Week 6 - Chapter 6

17/25


Annuities ;ue< $uture Value

Co#putation o( (uture value o( an annuity duere)uires co#pounding the cash (lo&s (or oneadditional period, -eyond an ordinary annuity.

7/21/2019 FM 2016 Week 6 - Chapter 6

18/25

Copyright 2014 Pearson Education, Inc. All rights reserved. 61?

Annuities ;ue< 0resent Value

'ince &ith annuity due, each cash (lo& isreceived one year earlier, its present value &ill-e discounted -acB (or one less period.

7/21/2019 FM 2016 Week 6 - Chapter 6

20/25


0erpetuities

A perpetuityis an annuity that continues(orever or has no #aturity. %or e$a#ple, adividend strea# on a share o( pre(erred stocB.!here are t&o -asic types o( perpetuitiesD

/ro:in+ perpetuity in &hich cash (lo&s gro&at a constant rate (ro# period to period overti#e.

2e,el perpetuity in &hich the pay#ents areconstant over ti#e.

7/21/2019 FM 2016 Week 6 - Chapter 6

21/25


Calculatin+ the 0resent Valueof a 2e,el 0erpetuity

P 3 the present value o( a level perpetuity

P! 3 the constant dollar a#ount provided -ythe perpetuity

i 3 the interest 9or discount; rate per period

7/21/2019 FM 2016 Week 6 - Chapter 6

22/25


0resent Value of a/ro:in+ 0erpetuity

In gro&ing perpetuities, the periodic cash(lo&s gro& at a constant rate each period.

7/21/2019 FM 2016 Week 6 - Chapter 6

23/25


6.& COM02!= CAS> $2O?ST9!AMS

7/21/2019 FM 2016 Week 6 - Chapter 6

24/25


Comple@ Cash $lo: Streams

!he cash (lo&s strea#s in the -usiness &orld#ay not al&ays involve one type o( cash(lo&s. !he cash (lo&s #ay have a #i$edpattern o( cash in(lo&s and out(lo&s, single

and annuity cash (lo&s. %igure 64su##aries the co#ple$ cash (lo& strea# (orarriott.

FM 2016 Week 6 - Chapter 6

Documents

Transcript of FM 2016 Week 6 - Chapter 6