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169。 2022 The McGrawHill Companies, Inc. All rights reserved. 公司理財(cái)?shù)诹?(B) 169。 2022 The McGrawHill Companies, Inc. All rights reserved. Discounted Cash Flow Valuation (Formulas) Chapter Six McGrawHill/Irwin 169。 2022 The McGrawHill Companies, Inc. All rights reserved. Key Concepts and Skills ? Be able to pute the future value of multiple cash flows ? Be able to pute the present value of multiple cash flows ? Be able to pute loan payments ? Be able to find the interest rate on a loan ? Understand how loans are amortized or paid off ? Understand how interest rates are quoted McGrawHill/Irwin 169。 2022 The McGrawHill Companies, Inc. All rights reserved. Chapter Outline ? Future and Present Values of Multiple Cash Flows ? Valuing Level Cash Flows: Annuities and Perpetuities ? Comparing Rates: The Effect of Compounding Periods ? Loan Types and Loan Amortization McGrawHill/Irwin 169。 2022 The McGrawHill Companies, Inc. All rights reserved. Multiple Cash Flows –Future Value Example ? Find the value at year 3 of each cash flow and add them together. – Today (year 0): FV = 7000()3 = 8, – Year 1: FV = 4,000()2 = 4, – Year 2: FV = 4,000() = 4,320 – Year 3: value = 4,000 – Total value in 3 years = + + 4320 + 4000 = 21, ? Value at year 4 = 21,() = 23, McGrawHill/Irwin 169。 2022 The McGrawHill Companies, Inc. All rights reserved. Multiple Cash Flows – FV Example 2 ? Suppose you invest $500 in a mutual fund today and $600 in one year. If the fund pays 9% annually, how much will you have in two years? – FV = 500()2 + 600() = McGrawHill/Irwin 169。 2022 The McGrawHill Companies, Inc. All rights reserved. Multiple Cash Flows – Example 2 Continued ? How much will you have in 5 years if you make no further deposits? ? First way: – FV = 500()5 + 600()4 = ? Second way – use value at year 2: – FV = ()3 = McGrawHill/Irwin 169。 2022 The McGrawHill Companies, Inc. All rights reserved. Multiple Cash Flows – FV Example 3 ? Suppose you plan to deposit $100 into an account in one year and $300 into the account in three years. How much will be in the account in five years if the interest rate is 8%? – FV = 100()4 + 300()2 = + = McGrawHill/Irwin 169。 2022 The McGrawHill Companies, Inc. All rights reserved. Multiple Cash Flows – Present Value Example ? Find the PV of each cash flows and add them – Year 1 CF: 200 / ()1 = – Year 2 CF: 400 / ()2 = – Year 3 CF: 600 / ()3 = – Year 4 CF: 800 / ()4 = – Total PV = + + + = McGrawHill/Irwin 169。 2022 The McGrawHill Companies, Inc. All rights reserved. Example Timeline 0 1 2 3 4 200 400 600 800 McGrawHill/Irwin 169。 2022 The McGrawHill Companies, Inc. All rights reserved. Multiple Cash Flows Using a Spreadsheet ? You can use the PV or FV functions in Excel to find the present value or future value of a set of cash flows ? Setting the data up is half the battle – if it is set up properly, then you can just copy the formulas ? Click on the Excel icon for an example McGrawHill/Irwin 169。 2022 The McGrawHill Companies, Inc. All rights reserved. Multiple Cash Flows – PV Another Example ? You are considering an investment that will pay you $1000 in one year, $2022 in two years and $3000 in three years. If you want to earn 10% on your money, how much would you be willing to pay? – PV = 1000 / ()1 = – PV = 2022 / ()2 = – PV = 3000 / ()3 = – PV = + + = McGrawHill/Irwin 169。 2022 The McGrawHill Companies, Inc. All rights reserved. Multiple Uneven Cash Flows – Using the Calculator ? Another way to use the financial calculator for uneven cash flows is to use the cash flow keys – Texas Instruments BAII Plus ? Press CF an