Slide 1 ___________________________________ 8.4 T ime value of - - PDF document

Slide 1

8.4 T ime value of money

2005 K D Ha the wa y-Dia l

Money has time value

• Most people ar

e willing to ac cept

• less today than they would if
• they wer

e paid the same amount in the futur e

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Calculating Present value fac tor s – Pr esent value of a lump sum

• 1. F

inanc ial c alc ulator

• 2. PV tables (see appendix in
• nline Wiley text)
• 3. PV factor

equations – per sonal favor ite

PV factor for lump sum = 1 ( 1 + i )N Where “i” equals interest rate and “N” equals periods

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Pr esent Value and F utur e Value

• Pr

esent value of $1

• T

he value today of $1 to be r eceived or paid at some futur e date, given a spec ified inter est r ate

Present Value $90.91 One year @ 10% Future Value $100

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Slide 4

Pr esent Value and F utur e Value

F utur e value……….…….……$10,000 PV fac tor

• f $1

wher e n=4 wher e i=10%.....................X 0.6830 PV of payment $ 6,830

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Pr esent Value and F utur e Value

Pr esent Value in Savings…….$ 6.830 F V fac tor

• f a $1

wher e n=4 wher e i=10%......................x1.4641 F utur e Value………………......$10,000

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Calculating pr esent value of a lump sum Computing PV of a single Sum

• 1. $15,000 due in 5 year

s at 8% c ompounded annually

• 2. $25,000 due in 8 ½ year

s at 10% c ompounded semi- annually

• 3. $9,500 due in 4 year

s at 12% c ompounded quar ter ly

• 4. $20,000 due in 20 year

s at 8% c ompounded semi-annually

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Slide 7

Calculating futur e value of a lump sum

Computing the F V of a single sum

• 1. $10,209 invested to ear

n inter est 8% c ompounded annually for 5 year s

• 2. $10,907 invested to ear

n inter est 10% c ompounded semi-annually 8 ½ year s

• 3. $5,920 invested to ear

n inter est 12% c ompounded quar ter ly for 4 year s

• 4. $4,166 invested to ear

n inter est 8% c ompounded semi-annually for 20 yr s

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Calc ulating Pr esent value fac tor s – Pr esent value of an annuity

PV factor for an annuity or a str eam of equal c ash flows

PV factor for an annuity = 1 ( 1 + i )N Where “i” equals interest rate and “N” equals periods 1 -

i

This part of the expression is essentially the present value factor of a lump sum

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Pr esent Value of an Annuity

Amount of the annual payment.....................................$10,000 PV fac tor

• f an annuity

wher e n= 10 payments wher e i = 12% X5.6502 Pr esent Value $56,502

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Slide 10

Calc ulating pr esent value of an annuity What is the pr esent value (r

• unded to the near

est dollar ) of an annuity of $8,000 per year for five year s if the inter est r ate is:

• 1. 8% compounded annually
• 2. 10% c ompounded annually

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Calc ulating pr esent value of an annuity Answer :

• 1. 8% compounded annually
• 2. 10% c ompounded annually

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