BCOR 2200 Chapter 5 with CQ - Chapter 5 Discounted Cash...

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1 Chapter 5 Discounted Cash Flow Valuation: Valuing Multiple CFs
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2 Chapter Outline 1.FV and PV of Multiple Cash Flows Using the calculator 2.Valuing Annuities and Perpetuities 3.Comparing Rates of Different Compounding Periods Comparing “apples to apples” given the different ways rates are quoted (annual, semi-annual, monthly…) 4.Loan Types and Loan Amortization Definitions of different finance contracts
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3 5.1 Multiple CF’s To find the FV of multiple CF’s: Calculate the FV of each individual CF Then ADD the individual CFs FVs together: Example: Receive $100 at t = 0 and t = 1. Calc value the Future Value at t = 2. The first $100 increases twice. The second $100 increases once. $100(1.08) 2 + $100(1.08) = $224.64
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4 5.1 Multiple CF’s Figure 5.1:
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5 Example 5.1 Page 117 You currently have $7,000 in an account (at t = 0) You will deposit $4,000 at the end of each of the next 3 years (at t = 1, t = 2 and t = 3) How much will you have at time 3 at 8%? $7,000 at t = 0 with 3 years of interest $7,000(1.08) 3 = $8,818 $4,000 at t = 1 with 2 years of interest $4,000(1.08) 2 = $4,666 $4,000 at t = 2 with 1 year of interest $4,000(1.08) 1 = $4,320 $4,000 at t = 3 $4,000 = $4,000
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6 Example continued Same Example, but now… How much will you have at time 4 at 8%? $7,000 at t = 0 with 4 years of interest $7,000(1.08) 4 = $9,523 $4,000 at t = 1 with 3 years of interest $4,000(1.08) 3 = $5,039 $4,000 at t = 2 with 2 years of interest $4,000(1.08) 2 = $4,666 $4,000 at t = 3 with 1 year of interest $4,000(1.08) 1 = $4,320
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7 Calculations: FV at t = 3: $7,000(1.08) 3 = $8,818 $4,000(1.08) 2 = $4,666 $4,000(1.08) 1 = $4,320 $4,000(1.08) 0 = $4,000 $21,804 FV at t = 4: $7,000(1.08) 4 = $9,523 $4,000(1.08) 3 = $5,039 $4,000(1.08) 2 = $4,666 $4,000(1.08) 1 = $4,320 $23,548
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Clicker Question: You currently have $600 in an account You will deposit $1,000 at time 1and at time 2. How much will you have at time 2 if your account earns 10%? A. $1,600 B. $2,600 C. $2,826 D. $3,600 E. $3,826 8
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Clicker Answer: The $600 in the account now (at time 0) will earn 10% for 2 years 9
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10 Another FV Example: $2,000 at the end of each year for 5 years Calculate FV at time 5 at 10%
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11 Now Calculate the PV of Multiple CFs: You need $1,000 at t = 1 and $2,000 at t = 2 How much do you need to invest today if you earn 9%? Or what is the PV of these cash flows at 9%? $1,000/(1.09) + $2,000/(1.09) 2 = $2,600.79 0 $1,683.36 $2,600.79 $917.43 2 $1,000 1 $2,000
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12 Think about the PV this way: Invest $2,601 at 9%. Show that you can withdraw $1,000 at t = 1 and $2,000 at t = 2: $2,600.79(1.09) = $2,834.86 (at t = 1) $2,834.86 - $1,000 = $1,834.86 (withdraw $1,000 at t = 1) $1,834.86(1.09) 2 = $2,000 (at t = 2) So if you invest $2,601 at 9%, you can withdraw $1,000 at time 1 and $2,000 at time 2
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Clicker Question: How much would you have to invest now to be able to withdraw $500 in one year and $800 in two years if your investment earned 10%?. A. $1,000 B. $1,116 C. $1,200 D. $1,226 E. $1,300 13
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Clicker Answer: In order to withdraw $500 in one year and then $800 in two years, you must invest the sum of the PV of these withdrawals. PV of $500 in one year = $500/(1.1) = $455 PV of $800 in two years = $800/(1.1) 2 = $661 Sum = $455 + $661 = $1,116 The answer is B 14
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15 5.2 Annuities The word Annuity has two definitions Economic Definition : 1. All CFs are the same 2. CFs occur at regular intervals (Annually, Semi-annually, Quarterly, Monthly…) 3. All CFs are discounted at the same rate The Financial Product : 1. Pay an insurance company or a bank a lump sum today 2. Receive CFs at regular intervals for a fixed period or until you die 3.
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