Chapter 4 - 1 Chapter4 Time Value of Money Part 2...

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Principles of Finance – FIN 3100 Chapter 4  – Time Value of Money – Part 2 1 Patty Robertson May not be 
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A Quick Trip Down Memory Lane FV = PV(1 +  r ) t PV = FV / (1 +  r ) t 2
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Agenda Determine how the concepts learned to value  single cash flows  can be used to value  multiple cash flows. Learn how to calculate loan payments and to  find the interest rate on a loan. Understand how loans are amortized. 3
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Abbreviations 4
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More Abbreviations 5
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Multiple Cash Flows In the previous chapter, we laid the groundwork for  discounted  cash flow valuation  with single cash flows. Now, we learn how to deal with multiple cash flows, which is  more realistic in making financial decisions. Usually a large cash outflow is followed by an stream of future  cash inflows.  From this point forward, we will assume compound  interest in all our work. 6
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Timelines Visualizing what is happening is helpful in  setting up the problem. Draw at  timeline  for the following scenarios: Deposit $1,000 per year into your savings account  for four years, starting now, to save for a house. Receive lottery winnings of $10,000 a year for five  years starting one year from now. Invest $1,000 toward retirement today and invest  7
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Time Lines Deposit $1,000 per year into your savings account for four  years, starting now , to save for a house. 8 0 1 2 3 4 $1,000 $1,000 $1,000 $1,000
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Time Lines Receive lottery winnings of $10,000 a year for five years  starting one year from now . 9 0 1 2 3 4 $10,000 $10,000 $10,000 $10,000 $10,000 5
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Time Lines Invest $1,000 toward retirement today  and invest twice that  amount at the same time every year for five years. 10 0 1 2 3 4 $1,000 $2,000 $2,000 $2,000 $2,000 $2,000 5
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Time Lines Pay your $500 car payment monthly for one year. Is this right?? 11 0 1 2 3 4 5 6 7 8 9 10 11 12 $500 $500 $500 $500 $500 $500 $500 $500 $500 $500 $500 $500
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Multiple Cash Flows - FV Let’s solve the first one…you deposit $1,000 per  year into your savings account for four years,  starting now, to save for a house.  How much  money will you have at the end of four years? What are we missing?? 12
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Multiple Cash Flows - FV 13 r  = .08 0 1 2 3 4 $1,000 $1,000 $1,000 $1,000 Why can’t we just add the four amounts and  grow them at 8% like we did before? We already know that we can calculate  equivalent values for single cash flows in the  future. ??
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Multiple Cash Flows - FV 14 r = .08 $1,000 $1,000 $1,000 $1,259.71 $1,080.00 $1,166.40 $4,866.60 (rounding) 0 1 2 3 4 $1,000 $1,360.49 $1,000(1.08)4 $1,000(1.08)3 $1,000(1.08)2 $1,000(1.08)1 ?? FV t  = PV(1 +  r ) t Calculate the FV of each  cash flow and add them.
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Multiple Cash Flows - FV Let’s do it again but, this time, instead of making the  first deposit now , you wait  one year  to make your  initial deposit and then save annually for three more  years thereafter.  How much money will you have at 
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