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Answers to MINI CASE, Chapter 2

# Answers to MINI CASE, Chapter 2 - MINI CASE Assume that you...

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MINI CASE 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 which covers several financial analysis techniques. The first section of the test addresses discounted cash flow analysis. See how you would do by answering the following questions. a. Draw time lines for (a) a \$100 lump sum cash flow at the end of year 2, (b) an ordinary annuity of \$100 per year for 3 years, and (c) an uneven cash flow stream of -\$50, \$100, \$75, and \$50 at the end of years 0 through 3. Answer: (Begin by discussing basic discounted cash flow concepts, terminology, and solution methods.) A time line is a graphical representation which 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. 0 1 2 year | | | lump sum 100 cash flow 0 1 2 3 | | | | annuity 100 100 100 0 1 2 3 | | | | uneven cash flow stream -50 100 75 50 A lump sum is a single flow; for example, a \$100 inflow in year 2, as shown in the top time line. An annuity is a series of equal cash flows occurring over equal intervals, as illustrated in the middle time line. An uneven cash flow stream is an irregular series of cash flows which do not constitute an annuity, as in the lower time line. -50 represents a cash outflow rather than a receipt or inflow. i% i% i%

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b. 1. What is the future value of an initial \$100 after 3 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 + i 1 = PV + PV(i) = PV(1 + i) = \$100(1.10) = \$110.00. Similarly: FV 2 = FV 1 + i 2 = FV 1 + FV 1 (i) = FV 1 (1 + i) = \$110(1.10) = \$121.00 = PV(1 + i)(1 + i) = PV(1 + i) 2 . FV 3 = FV 2 + i 3 = FV 2 + FV 2 (i) = FV 2 (1 + i) = \$121(1.10)=\$133.10=PV (1 + i) 2 (1 + i)=PV(1 + i) 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 4 variables: FV n , PV, i, and n. Here we know all except FV n , so we solve for FV n . We will, however, often 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 3 of the four values and find the 4th. Finding future values (moving to the right along the time line) is called compounding . Note that there are 3 ways of finding FV 3 : using a regular calculator, financial calculator, or spreadsheets. For simple problems, we show only the regular calculator and financial calculator methods. (1) regular calculator: 1. \$100(1.10)(1.10)(1.10) = \$133.10. 10%
2. \$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, pmt = 0, and solve for FV = \$133.10. 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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