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Chapter 4 introduction to valuation: The time value of money. After completing this unit, you should be able to compute the future value of an investment made today, be able to compute the present value of cash to be received at some future date, be able to compute the return on an investment. | 4- McGraw-Hill/Irwin Copyright © 2011 by the McGraw-Hill Companies, Inc. All rights reserved. 4- Key Concepts and Skills Be able to compute: The future value of an investment made today The present value of cash to be received at some future date The return on an investment The number of periods that equates a present value and a future value given an interest rate Be able to solve time value of money problems using: Formulas A financial calculator A spreadsheet 4. 4- Chapter Outline 4.1 Future Value and Compounding 4.2 Present Value and Discounting 4.3 More on Present and Future Values Solving for: Implied interest rate Number of periods 4. 4- Basic Definitions Present Value (PV) The current value of future cash flows discounted at the appropriate discount rate Value at t=0 on a time line Future Value (FV) The amount an investment is worth after one or more periods. “Later” money on a time line 4. 4- Basic Definitions Interest rate (r) Discount rate . | 4- McGraw-Hill/Irwin Copyright © 2011 by the McGraw-Hill Companies, Inc. All rights reserved. 4- Key Concepts and Skills Be able to compute: The future value of an investment made today The present value of cash to be received at some future date The return on an investment The number of periods that equates a present value and a future value given an interest rate Be able to solve time value of money problems using: Formulas A financial calculator A spreadsheet 4. 4- Chapter Outline 4.1 Future Value and Compounding 4.2 Present Value and Discounting 4.3 More on Present and Future Values Solving for: Implied interest rate Number of periods 4. 4- Basic Definitions Present Value (PV) The current value of future cash flows discounted at the appropriate discount rate Value at t=0 on a time line Future Value (FV) The amount an investment is worth after one or more periods. “Later” money on a time line 4. 4- Basic Definitions Interest rate (r) Discount rate Cost of capital Opportunity cost of capital Required return Terminology depends on usage 4. 4- Time Line of Cash Flows CF3 CF0 CF1 CF2 0 1 2 3 r% Tick marks at ends of periods Time 0 is today; Time 1 is the end of Period 1 +CF = Cash INFLOW -CF = Cash OUTFLOW PMT = Constant CF 4. 4- Time Line for a $100 Lump Sum due at the End of Year 2. 100 0 1 2 Year r% 4. 4- Future Values: General Formula FV = PV(1 + r)t FV = future value PV = present value r = period interest rate, expressed as a decimal t = number of periods Future value interest factor = (1 + r)t Note: “yx” key on your calculator 4. 4- Future Values – Example 1 Suppose you invest $100 for one year at 10% per year. What is the future value in one year? Interest = 100(.10) = 10 Value in one year = Principal + interest = 100 + 10 = 110 Future Value (FV) = 100(1 + .10) = 110 4. 4- Future Values – Example 1 Suppose you leave the money in for another year. How much will you have two years from now?
