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**Unformatted text preview: **1 Chapter 4 Time Value of Money 1: Analyzing Single Cash Flows 2 Chapter 4 Learning Goals LG1: Create a cash flow time line LG2: Compute the future value of money LG3: Use the power of compounding to increase wealth LG4: Calculate the present value of a payment made in the future LG5: Move cash flows from one year to another LG6: Apply the Rule of 72 LG7: Compute the rate of return LG8: Calculate the number of years needed to grow an investment to a specific amount of money 3 Introduction The ability to work problems using the principles of the Time Value of Money will be one of them most important skills you will learn Financial managers Any kind of manager in businesses of all sizes Personal life 4 The basic idea behind the time value of money is that $1 today is worth more than $1 promised next year Factors to consider: Size of the cash flows Time between the cash flows Rate of return Opportunity cost Interest rate Required rate of return Discount rate 5 Organizing Cash Flows A helpful tool for analysis of cash flows is the time line, which shows the magnitude of cash flows at different points in time Cash we receive is called an inflow and is represented by a positive number Cash that leaves us is called an outflow and is represented by a negative number Cash flow- 100 105 5% Period 1 2 6 Single-period Future Value You invest $100 today in an account earning 5% per year. Compute the future value in one year. Value in one year = Todays cash flow + Interest earned = $100 + ($100 x 0.05) = $100 x (1 + 0.05) = $105 In general: FV = PV x (1 + i) N 7 Compounding and Future Value In the example above, suppose you leave the money invested for two years. What is the future value? Value in 2 years = $100 x (1 + 0.05) 2 = $110.25 The total interest of $10.25 represents $10 earned on the original $100 investment plus $0.25 earned on the $5 first years interest This represents compounding, i.e. earning interest on interest Financial Calculators N I PV PMT FV Financial calculators generally have TVM keys similar to the following: N = number of interest periods N = number of interest periods I = interest per period N = number of interest periods I = interest per period PV = present value N = number of interest periods I = interest per period PV = present value PMT= payment (annuity) N = number of interest periods I = interest per period PV = present value PMT= payment (annuity) FV = future value Reset P/Yr = 1 9 Financial Calculator Solution INPUT 2 5 -100 N I/YR PV PMT FV OUTPUT 110.25 10...

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