hogan fin3331 ch5 part4

8/9/2019 Hogan FIN3331 Ch5 Part4

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Time Value of MoneyPart 4: Annuities


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Agenda

What is an annuity?Annuity calculations

More complicated examples

Present value of a future annuityMultiple annuities


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What is an Annuity?

An annuity is a series of equal, periodicpayments which recur for a finite number ofperiods

!i"e a fixed perpetuity, annuity payments mustbe equal in amount and occur at re#ularintervals

$nli"e a perpetuity, only a limited number of

payments occur %rather than payments #oin#on forever&

Payments must be constant, not #rowin#


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Calculations with Annuities

'he present value of an annuity can becalculated with a formula or in your calculator

'he annuity formula is:

PV = C [{1 1!"1#$%t& ! $'

(owever, we will not use the formula in this class

All annuity calculations can be done in thecalculator


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(ol)ing in the Calculato$

We can )olve for the P* or +* of an annuity ustas we did for a sin#le -+, but now we use PM' P* . -ash flow at be#innin# of investment period

PM' . Periodic payment

+* . -ash flow at the end of investment period / . /umber of payments

0 . 0nterest rate %per period&

1/2 Mode . Payments occur at the end of the period 0n 1/2 Mode, the calculator solves for P* as of

time t . 3 and the first payment at time t .


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Pe$iodic *nte$est +ates

5 +or periods less than year, we use the6periodic rate7 for any calculations

5 All rates are annual unless told otherwise

5+or any period other than years, you mustconvert the annual rate into a periodic rate

5 2ivide the rate by the number of periods per year

5 1x: 'he interest rate is 89, but payments are

made monthly What is the monthly rate?

r . 89 per year ; < . =9 per month


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,-. 1/ PV of an Annuity

What is the present value of the cash flowsassociated with leasin# a car for 4 years withannual payments of >=,333 that start in a year

if the opportunity cost of capital is

percent?

)olve for P* P* . >@,


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,-. 0/ V of an Annuity

'he Bi# !ottery ust paid off >3 million to bepaid out in 3 equal annual installments, withthe first payment in year 0f the discountrate is =9, then how much money would the

winner have in 3 years if payments areplaced in a trust and reinvested?

)olve for +* +* . >,48,84@=3

N I PV PMT FV Mode

30 5% 0 -1M ? END


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,-. 2 Annuity Payments

0f you borrow > CD@D8D

N I PV PMT FV Mode

512 0.6% 20,000 ? 0 END


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,-. 3/ Time Pe$iods of an Annuity

0f you borrow >33, how manyloan payments will you ma"e if your first paymentis due in a month and all payments are equal?

)olve for / / . 8=D


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,-. 4/ *nte$est +ate of an Annuity

0f you borrow >@=, then what is themonthly interest rate associated with your loan ifyour first payment is due in one month and all

payments are equal?

)olve for 0 0 . 3D4=@


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PV of a utu$e Annuity

0f an annuity does notbe#in until sometime inthe future, but we wantto "now its value today,we can solve for the P*usin# a


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Timelines 5 PV of a utu$e Annuity

)tep : +ind the P*tin the period beforepayment be#ins

)tep


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,-. 6/ PV of a utu$e AnnuityPhillip bou#ht a security that will ma"e equal

payments of >833 in exactly < years, years, and 4years (is expected return is 49 (ow much didPhillip pay for this security?

)tep : +ind the P* of the payments at time

)olve for P* P* . >C,8=@3=


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PMTs of Multi7le Annuities

)ome activities %such assavin# for retirement&involve multiple annuitiesEiven information about

annuity, we can solve forthe PM' of the other

)tep : )olve for the value of the annuity forwhich you have all info %+* of first or P* ofsecond&

)tep


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Timelines/ ind PMT of 0ndAnnuity

)tep : +ind the +*tofthe first annuity in thefinal period t

)tep


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,-. 8/ PMT of 0ndAnnuity Fesica will save >,333 at the end of each month for

the next months at =9 'hen she plans to withdraw< equal payment for travel at the end of the followin#months What is the amount of each withdrawal?

)tep : +ind the +* of her savin#s at time

)olve for +* +* . >,34=


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Timelines/ ind PMT of 1stAnnuity

)tep : +ind the P*tofthe second annuity inthe period t before thefirst payment

)tep


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,-. 9/ PMT of 1stAnnuity Facob has saved equal endCofCmonth payments for the last

months (e will withdraw equal payments at the end of thenext ,


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:ectu$e P$o;lems

What is the present value of an investment that pays

you >,333 a month with the first payment in monthand the last payment in months if the discount rate is9 per month?

0f you borrow >4


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hogan fin3331 ch5 part4

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