02_Time_Value_of_Money-Day_7

02_Time_Value_of_Money-Day_7 - Time Value of Money Day 7:...

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Time Value of Money Day 7: Complex Annuities Thomas Hogan FNAN 301 February 17, 2011
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Agenda Combining multiple annuities Combining annuities, perpetuities, and other cash flows
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PMTs of Multiple Annuities each security as an annuity or annuity due. Then solve in 2 steps as we did with regular annuities. Step 1: Solve for the value of the annuity for which you have all info (FV of first or PV of second). Step 2: Set the FV of the first = PV of the second, and solve for the missing PMT. Solving for the PMT of multiple annuities may require some combination of regular annuities and annuities due. First, draw a timeline and identify
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Ex. 1: Multiple Annuities, Q.1 Jesica will save $1,000 at the end of each month for the next 3 months. Her savings account pays 1.5% per month. She plans to withdraw equal payments for travel at the start of the 2 following months with her first withdrawal 3 months from today. What is the amount of each withdrawal? When are the CFs? What types of securities are involved? How do you value them?
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Ex. 2 Solution Draw a timeline. The first security is a regular annuity, and the second is an annuity due. Step 1: Find the FV of her savings at time 3. Solve for FV. FV = $3,045.225 Step 2: Find the amount of payments in times 4 and 5. Solve for PMT. PMT = $1,533.95 N I PV PMT FV Mode 2 1.5% -3,045 ? 0 BEGIN N I PV PMT FV Mode 3 1.5% 0 -1,000 ? END
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Timelines for Each Step Step 1: Solve for the FV of the first annuity at time t = 3. Step 2: Set the FV of the first = PV of the second, and solve for the missing PMT.
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Note on Multiple Annuities If the last payment of the first annuity and the first payment of the second annuity occur in the same time period, then the first payment must be an annuity and the second must be an annuity due (as in the previous example). If the last payment of the first annuity and the
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02_Time_Value_of_Money-Day_7 - Time Value of Money Day 7:...

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