Part 4 Ch 03

# Part 4 Ch 03 - CHAPTER 3 INTEGRATIVE PROBLEM 3-33 ASSUME...

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CHAPTER 3 INTEGRATIVE PROBLEM ANSWER : Discuss basic time value concepts, terminology, and solution methods. A cash flow time line is a graphical representation that is used to show the timing of cash flows. The tick marks represent end of periods (often years), so time 0 is today; time 1 is the end of the first year, or 1 year from today; and so on. LUMP-SUM AMOUNT—a single flow; for example, a \$100 inflow in Year 2: 0 1 2 3 Year 100 Cash flow ANNUITY—a series of equal cash flows occurring over equal intervals: 0 1 2 3 Year 100 100 100 Cash flow UNEVEN CASH FLOW STREAM—an irregular series of cash flows that do not constitute an annuity: 0 1 2 3 Year -50 100 75 50 Cash flow CF = -50 represents a cash outflow rather than a receipt or inflow. 44 3-33 ASSUME THAT YOU ARE NEARING GRADUATION AND THAT YOU HAVE APPLIED FOR A JOB WITH A LOCAL BANK. AS PART OF THE BANK'S EVALUATION PROCESS, YOU HAVE BEEN ASKED TO TAKE AN EXAMINATION THAT COVERS SEVERAL FINANCIAL ANALYSIS TECHNIQUES. THE FIRST SECTION OF THE TEST ADDRESSES TIME VALUE OF MONEY ANALYSIS. SEE HOW YOU WOULD DO BY ANSWERING THE FOLLOWING QUESTIONS: A. DRAW CASH FLOW TIME LINES FOR (1) A \$100 LUMP SUM CASH FLOW AT THE END OF YEAR 2, (2) AN ORDINARY ANNUITY OF \$100 PER YEAR FOR THREE YEARS, AND (3) AN UNEVEN CASH FLOW STREAM OF -\$50, \$100, \$75, AND \$50 AT THE END OF YEARS 0 THROUGH 3. k% k% k%

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B. (1) WHAT IS THE FUTURE VALUE OF AN INITIAL \$100 AFTER THREE YEARS IF IT IS INVESTED IN AN ACCOUNT PAYING 10 PERCENT ANNUAL INTEREST? ANSWER : Show dollars corresponding to question mark, calculated as follows: 0 1 2 3 100 FV = ? After 1 year: FV 1 = PV + INT 1 = PV + PV(k) = PV(1 + k) = \$100(1.10) = \$110.00. Similarly: FV 2 = FV 1 + INT 2 = FV 1 + FV 1 (k) = FV 1 (1 + k) = \$110(1.10) = \$121.00 = PV(1 + k)(1 + k) = PV(1 + k) 2 . FV 3 = FV 2 + INT 3 = FV 2 + FV 2 (k) = FV 2 (1 + k) = \$121(1.10) = \$133.10 = PV(1 + k) 2 (1 + k) = PV(1 + k) 3 In general, we see that: FV n = PV(1 + i) n , so FV 3 = \$100(1.10) 3 = \$100(1.3310) = \$133.10. Note that this equation has four variables: FV n , PV, k, and n. Here we know all except FV n , so we solve for FV n . However, often, we will solve for one of the other three variables. By far, the easiest way to work all time value problems is with a financial calculator. Just plug in any three of the four values and find the fourth. Finding future values (moving to the right along the time line) is called compounding . Note we generally find FV using one of these methods: (1) Numerical approach use a regular calculator: FV 3 = \$100(1.10) 3 = \$133.10. (2) Financial calculator: This is especially efficient for more complex problems, including exam problems. Input the following values: N = 3, I = 10, PV = -100, and PMT = 0; compute FV = \$133.10. (3) Spreadsheet: Set up your spreadsheet and use the FV financial function similar to the following: 45 10%
Step 1: Set up the spreadsheet: Step 2: Select FV in the financial function category: Step 3: Input the cell locations of the data: Step 4: Press OK to display the solution: B. (2) WHAT IS THE PRESENT VALUE OF \$100 TO BE RECEIVED IN 3 YEARS IF THE APPROPRIATE INTEREST RATE IS 10 PERCENT?

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ANSWER : Finding present values, or discounting (moving to the left along the time line), is the reverse of compounding, and the basic present value equation is the reciprocal of the compounding
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