BCOR 2200 Chapter 5

# BCOR 2200 Chapter 5 - Chapter 5 Discounted Cash Flow...

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1 Chapter 5 Discounted Cash Flow Valuation (Valuing Multiple CFs)

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2 Chapter Outline FV and PV of Multiple Cash Flows Valuing Annuities and Perpetuities Comparing Rates of Different Compounding Periods Loan Types and Loan Amortization
3 5.1 Multiple CF’s When you have multiple CF’s, Take the PV or FV of each individual CF, then ADD them together: FV Examples: \$100 at t = 0 and t = 1. Calc value at t = 2. The first \$100 increases twice. The second \$100 increases once. [\$100(1.08) + \$100](1.08) = \$224.64 \$100(1.08) 2 + \$100(1.08) = \$224.64

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4 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, 2 and 3) How much will you have at time 3 and at time 4 at 8%? Method 1: Calculate the FV of the pervious period’s total and add the CF from the current period: Make sure you can do this with your Calculator 4 0 1 2 \$7,000 \$4,000 \$4,000 3 \$4,000 \$7,560 \$11,560 \$12,485 \$16,485 \$17,804 \$21,804 \$23,548 \$23,548
5 Same Problem, Different Method: 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, 2 and 3) How much will you have at time 3 and at time 4 at 8%? Calculate the FV of each cash flow and then sum the FV’s: Make sure you can do this with your Calculator \$23,548 \$7,560 \$4,000 \$4,000 \$21,804 \$4,000 \$4,320 \$4,666 \$4,320 \$4,666 \$5,039 \$4,320 4 \$7,000 \$8,165 \$8,818 \$9,523 0 1 2 3

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6 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
7 New Example: \$2,000 at the end of each year for 5 years @ 10%

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8 PV of Multiple Cash Flows: 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) = \$2,600.79 0 \$1,683.36 \$2,600.79 \$917.43 2 \$1,000 1 \$2,000
9 Do it the opposite way: Invest \$2,601 at 9%. Show that if you withdraw \$1,000 at t = 1 you will have \$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) = \$2,000 (at t = 2)

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10 PV of \$1,000 per for 5 years @ 6%:
11 5.2 PV and FV of Annuities Definition of an Annuity (Economic Definition): 1. All CF’s are the same 2. CF’s occur at regular intervals (Annually, Semi-annually, Quarterly, Monthly…) 3. All CF’s are discounted at the same rate Definition of an Annuity (Financial Product): 1. Pay an insurance company or a bank a lump sum today 2. Receive CF’s at regular intervals for a fixed period or until you die 3. Sometimes you pay now (or make regular payments starting now) and then receive payments when you retire at 65 Both are Annuities. Same pattern for: Loans (you pay) Purchased Annuities (you are paid)

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12 Formula for PV of an Annuity
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## This note was uploaded on 03/17/2009 for the course BCOR 2200 taught by Professor Tomnelson during the Fall '08 term at Colorado.

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BCOR 2200 Chapter 5 - Chapter 5 Discounted Cash Flow...

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