© 2012 McGrawHill Ryerson Ltd. Chapter 5 -1

Let’s turn things around… How much do you need to invest today into an account

paying compound interest at the rate of 5% per year, in order to receive $1477.45 at the end of eight years?

Yr3

$1477.45

?

Present Value

FutureValue

Today Yr1 Yr2 Yr4 Yr7Yr5 Yr6 Yr8

LO2

© 2012 McGrawHill Ryerson Ltd. Chapter 5 -2

Simply invert the FV formula to get the PV formula

Yr3

$1477.45

FutureValue

Today Yr1 Yr2 Yr4 Yr7Yr5 Yr6 Yr8

Present value = $1477.45

(1+ 0.05)8 = $1,000

LO2

© 2012 McGrawHill Ryerson Ltd. Chapter 5 -3

In general, we can write the PV formula as

PV = FV after t periods(1 + r)t

LO2

© 2012 McGrawHill Ryerson Ltd. Chapter 5 -4

Example:You have been offered $1 million five years from now. If the interest rates is expected to be 10% per year, how much is this prize worth to you in today’s dollars?

Today Year 5

$1 millionPresent value = $1,000,000

(1+ 0.10)5

= $620,921

LO2

© 2012 McGrawHill Ryerson Ltd. Chapter 5 -5

The PV and the FV are very much related to each other

PV = FV x 1/(1 + r)t

= $1 million x 1/ (1 + 0.10)5

= $620,921

FV = PV x (1 + r)t

= $620,921 x (1 + 0.10)5

= $1 million

LO2

© 2012 McGrawHill Ryerson Ltd. Chapter 5 -6LO2

Can be found the same way

◦ Use your financial calculator◦ Use the tables – look up the discount factor◦ Rearrange the expression

© 2012 McGrawHill Ryerson Ltd. 7LO2

Chapter 5 -