Present Value
•What a future sum of money is worth today,
given a particular interest (or discount) rate.
( )
=n
0
n
FV
PV
1+i
FV = future value
PV = present value
i = interest (or discount) rate
n = number of periods
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Present Value and Annuities: Calculating the Worth of Future Cash Flows, Slides of Fundamentals of E-Commerce
The concept of present value, which is the worth of a future sum of money today, given a particular interest rate. It also covers annuities, the payment or receipt of equal cash flows per period for a specified number of periods, and their future value. Examples and formulas for calculating present value and annuity values.
Typology: Slides
2012/2013
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Present Value
•^ What a future sum of money is worth today,given a particular interest (or discount) rate.
FVn = PV 0 n 1+i ( ) FV = future valuePV = present valuei = interest (or discount) raten = number of periods
Present Value
Example:^
You will receive $1,000 in three years.
If the discount rate is 6%, what is the presentvalue?^ (^
)^ (^
=^ =^
= + 3 0 n^
3 FV^ $1,000 PV
$839. 1+i^1
6%^
6%^
6%
Present Value
Example: What is the present value of $1,000to be received in three years, given a discountrate of 6%?^0
PV^ = FV (FVIF^ )^3 6%,3^ =$1,000(0.840) =$840.
Table 4.2 Excerpt: PVIFs for $1^ End of Period (n)
5%^
6%^ 8%
0.907^ 0.
0.864^ 0.
0.823^ 0.
A Note of Caution
•^ Note that the algebraic solution to thepresent value problem gave an answer of839.62 •^ The table method gave an answer of $840.^ Caution:Tables provide approximate answers only.If more accuracy is required, use algebra!
Annuities
•^ Ordinary annuity: cash flows occur at theend of each period^ Example: 3-year, $100 ordinary annuity
$^
$^
Annuities
•^ Annuity Due: cash flows occur at thebeginning of each period^ Example: 3-year, $100 annuity due^ $^
$^
Annuities: Future Value ● Future value of an annuity - sum of the futurevalues of all individual cash flows. $100^ $
(^3) FVFVFV FV of Annuity Docsity.com