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**Unformatted text preview: **Click to edit Master subtitle style Introduction to Valuation: The Time Value of Money 1 5 2 ◦ Assume interest rates are 4.3884%. ◦ You have just won a lottery and must choose between the following two options:  Receive a cheque for $150,000 today.  Receive $10,000 a year for the next 25 years. KEY QUESTIONS FOR YOU: Which option gives you the biggest “winnings” How should you tackle this kind of problem? 1. Be able to compute the future value of an investment made today 2. Be able to compute the present value of cash to be received at some future date 3. Be able to compute the return on an investment 4. Be able to compute the number of periods that equates a present value and a future value given an interest rate 5. Be able to use a financial calculator and/or a spreadsheet to solve time value of money problems 3 Key Concepts and Skills 4 Consider the time line below: PV is the Present Value, that is, the value today . FV is the Future Value, or the value at a future date. The number of time periods between the Present Value and the Future Value is represented by “t”. The rate of interest is called “r”. All time value questions involve the four values above: PV, FV, r, and t. Given three of them, it is always possible to calculate Time Value Terminology 1 2 3 t P V FV … ….. Present Value – earlier money on a time line Future Value – later money on a time line Interest rate – “exchange rate” between earlier money and later money ◦ Discount rate ◦ Cost of capital ◦ Opportunity cost of capital ◦ Required return 5 Basic Definitions Suppose you invest $1,000 for one year at 5% per year. What is the future value in one year? ◦ Interest = 1,000(.05) = 50 ◦ Value in one year = principal + interest = 1,000 + 50 = 1,050 ◦ Future Value (FV) = 1,000(1 + .05) = 1,050 Suppose you leave the money in for another year. How much will you have two years from now? ◦ FV = 1,000(1.05)(1.05) = 1,000(1.05)2 = 1,102.50 6 1. Future Values Simple interest Compound interest Consider the previous example ◦ FV with simple interest = 1,000 + 50 + 50 = 1,100 ◦ FV with compound interest = 1,102.50 ◦ The extra 2.50 comes from the interest of .05(50) = 2.50 earned on the first interest payment 7 Effects of Compounding 8 Future Value of $100 at 10 Beginning Simple Compound Total Total Year Amount Interest Interest Interest Amount 1 $100.00 $10.00 $ 0.00 $10.00 $110.00 2 110.00 10.00 1.00 11.00 121.00 3 121.00 10.00 2.10 12.10 133.10 4 133.10 10.00 3.31 13.31 146.41 5 146.41 10.00 4.64 14.64 161.05 Totals $50.00 $ 11.05 $ 61.05...

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