chap005 with additions with slide 9 corrected

# chap005 with additions with slide 9 corrected - Chapter 5...

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1 Chapter 5 – Discounted Cash Flow Valuation Future and Present Values of Multiple Cash Flows Valuing Level Cash Flows: Annuities and Perpetuities Comparing Rates: The Effect of Compounding Periods Loan Types, Loan Payments and Loan Amortization General Scenarios when there are “multiple cash flows”: Cash flow series with uneven cash flows: C01 ≠ C02 ≠ C03, etc. Use Cash flow techniques and find NPV Cash flow series with even cash flows : C01 = C02 = C03, etc. You have PMTs, so use basic TVM and find PV

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2 Find the Future Value of Earlier Cash Flows C01 0 1 2 3 4 5 C03 C02 C04 C05 N = I = ? CF0 Even Cash Flows are PMTs -- so use basic TVM and find FV Uneven Cash Flows: Use Cash flow techniques and find NFV NOTE: Some calculators don’t have NFV function…more later! FV or NFV
3 Find the Present Value of Future Cash Flows 0 1 2 3 4 C01 C02 C03 C04 PV or NPV I = ? N = 5 C05 (Sometimes = to PMT + FV) Even Cash Flows are PMTs -- so use basic TVM and find PV Uneven Cash Flows: Use Cash flow techniques and find NPV

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4 Multiple Cash Flows – Find NPV Two General Methods: 1. Using Ch. 4 techniques, find PV of each CF and add 2. Using Ch. 5 CF discussion, find NPV with calculator Method 1: Find the PV of each cash flow and add up Year 1 CF: 200 / (1.12) 1 = 178.57 Year 2 CF: 400 / (1.12) 2 = 318.88 Year 3 CF: 600 / (1.12) 3 = 427.07 Year 4 CF: 800 / (1.12) 4 = 508.41 Total PV = 178.57 + 318.88 + 427.07 + 508.41 = 1,432.93
5 Example 5.3 Timeline 0 1 2 3 4 200 400 600 800 178.57 318.88 427.07 508.41 1,432.93

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6 Multiple Uneven Cash Flows – NPV Method 2: Find NPV with calculator – Calculator Facts Another way to use the financial calculator for uneven cash flows is to use the cash flow keys Texas Instruments BA-II Plus Clear the cash flow keys by pressing CF and then 2nd CLR Work Press CF and enter the cash flows beginning with year 0. You have to press the “Enter” key for each cash flow Use the down arrow key to move to the next cash flow The “F” is the number of times a given cash flow occurs in consecutive years Use the NPV key to compute the present value by [ENTER]ing the interest rate for I, pressing the down arrow and then compute
7 Multiple Cash Flows –Find NPV Method 2: Find NPV with calculator

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8 Multiple Cash Flows – NPV Another Example You are considering an investment that will pay you \$1,000 in one year, \$2,000 in two years and \$3,000 in three years. If you want to earn 10% on your money, how much would you be willing to pay? Method 1: Find the PV of each cash flow and add up PV = 1,000 / (1.1) 1 = 909.09 PV = 2,000 / (1.1) 2 = 1,652.89 PV = 3,000 / (1.1) 3 = 2,253.94 PV = 909.09 + 1,652.89 + 2,253.94 = 4,815.92
9 Multiple Cash Flows – NPV Another Example Method 2: Find NPV with calculator

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Decisions, Decisions - NPV You are considering a “great” investment opportunity. Invest \$100 today, receive \$40 in one year and \$75 in two years. If you require a 15% return
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## chap005 with additions with slide 9 corrected - Chapter 5...

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