02_Time_Value_of_Money-Day_5-2011.02.10v2

02_Time_Value_of_Money-Day_5-2011.02.10v2 - Time Value of...

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Time Value of Money Thomas Hogan FNAN 301 February 10, 2011
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Agenda Future perpetuity Present value Payment Future annuity Present value Payment
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PV of Future Cash Flows We already know how to find the total present value of multiple unique cash flows. All we do is find the PV of each, and add all the PVs together. Today we will discuss a few special cases where we find the PV of multiple future cash flows of the same amount (an annuity) or cash flows that go on forever (a perpetuity). For each of these, we find out what the present value will be at some future time t (PV t ), then find out what that PV t is worth today.
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Ex. 1: PV of Multiple CFs Beth's work contract pays her $40,000 in 1 year and $60,000 in 2 years. What are these payments worth today if the interest rate is 6%? Draw a timeline: Find the PV of each CF: PV(C 1 )= C 1 / (1+r) t = 40,000 / (1+0.06) 1 = 37,735.85 PV(C 2 )= C 2 / (1+r) t = 60,000 / (1+0.06) 2 = 53,399.79 Add them together: PV total = PV(C 1 ) + PV(C 2 ) = $91,135.64
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We looked at the PV and future payments of a perpetuity that starts paying next period, but how can we find the PV when payment begins several years from now? If we can find the perpetuity's value at some time in the future, then we can find its value today using the compound interest formula. Or, if given the investment value today, we can
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This note was uploaded on 02/16/2011 for the course FINANCE 301 taught by Professor Murray during the Spring '09 term at George Mason.

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02_Time_Value_of_Money-Day_5-2011.02.10v2 - Time Value of...

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