© 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.

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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 $ at the end of eight years? Yr3 $ ? Present Value Future Value Today Yr1 Yr2Yr4 Yr7 Yr5 Yr6Yr8 LO2

© 2012 McGrawHill Ryerson Ltd.Chapter 5 -2  Simply invert the FV formula to get the PV formula Yr3 $ Future Value Today Yr1 Yr2Yr4 Yr7 Yr5 Yr6Yr8 Present value = $ ( ) 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 million Present value = $1,000,000 ( ) 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/ ( ) 5 = $620,921 FV = PV x (1 + r) t = $620,921 x ( ) 5 = $1 million LO2

© 2012 McGrawHill Ryerson Ltd.Chapter 5 -6 LO2

 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.7 LO2 Chapter 5 -