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© 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
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© 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
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© 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
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© 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
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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
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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 -