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**Unformatted text preview: **Click to edit Master title style 12/29/11 1 12/29/11 Chapter 5 Introduction to Valuation: The Time Value of Money Calculators Click to edit Master title style 12/29/11 2 12/29/11 Key Concepts and Skills 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 Be able to compute the number of periods that equates a present value and a future value given an interest rate Be able to use a financial calculator and a spreadsheet to solve time value of money problems Click to edit Master title style 12/29/11 3 12/29/11 Basic Definitions Present Value the current value of future cash flows discounted at the appropriate discount rate. Earlier money on a time line Future Value the amount an investment is worth after one or more periods. 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 rate of return Click to edit Master title style 12/29/11 4 12/29/11 Future Values Simple Interest 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 Click to edit Master title style 12/29/11 5 12/29/11 Future Values: General Formula FV = PV x (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 Click to edit Master title style 12/29/11 6 12/29/11 Compounding Compounding = The ability of an asset to generate earnings, which are then reinvested in order to generate their own earnings. In other words, compounding refers to generating earnings from previous earnings. Also known as "compound interest". Compound interest means that interest paid on a loan or investment is periodically added to the principal. The result is that interest is earned on interest as well as principal. Click to edit Master title style 12/29/11 7 12/29/11 Effects of Compounding 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 Click to edit Master title style 12/29/11 8 12/29/11 Calculator Keys Texas Instruments BA-II Plus FV = future value PV = present value I/Y = period interest rate P/Y must equal 1 for the I/Y to be the period rate Interest is entered as a percent, not a decimal N = number of periods Remember to clear the registers (CLR TVM) after each problem Other calculators are similar in format Click to edit Master title style...

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