Chapter 4 Notes

# Chapter 4 Notes - Chapter 4 Time Value of Money(TVM(1/3...

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Chapter 4: Time Value of Money (TVM) (1/3) Recommended Questions: a. You are expected to solve every question behind the chapter 4. b. However, for this lecture (TVM 113),the following questions are recommended: Self-Test questions on page 140 & #4-1 - #4-6 on page 167 . Overall description about today's lecture: This lecture provides the materials to understand the following concept: "The sooner cash is received, the more valuable it is" or "One dollar today is more valuable that the same amount in the future" More in detail, "The same amount of money (say one dollar) has different time values of money for different time period of investment (maturity) and interest rates." Let's think about the following question: Question) Which amount is worth more at 14 percent: \$1,000 in hand today or \$2,000 due in six years? (this question is #4-5 on page 167) -l-

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1. A single (or Lump-sum) cash flow (PV' FV, N, r) a -L-
c o

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Answer the following questions using the derived formulas and examples of (4), (5) and (6). The following three questions will be handled after (4), (5) and (6). These questions are the same topics of Figures 4-2 and 4-3 on page p. 134 and 137 (1) Given constant r and PV,what happen to FV if n/increases? (2) Given constant n/ and, PV, what happen to FV if r increases? (3) Given constant N and, FV, what happen to PV if r increases? -4-
Calculator (TI BA II PLUS) Calculator setting for TVM: 1) 2"o TFORMAT t 9t ENTER) CE/C You have just set nine digit decimal. 2) 2"d> P/Y)l) ENTER> CEIC You have just set annual compounding. 3) Whenever you do the time value of money, you have to clear the previous calculatorions in your calculator by doing: 2"d t CLR TVM. Note: a. For all the computations in Time value of money, you will use the following five variables: N, I/Y, PV, PMT, and FV. b. Look at the third row of your calculator (BAII PLUS). N is the number of (remaining) (holding) periods. I/Y is interest rate (We use r or I for interest rate). PV is present value. PMT is payment. FV is future value. To enter -\$1000, enter 1000 and press the key @. c. For'single' (or'lump-sum') cash flow analysis, PMT:0 always. d. For 'single' (or 'lump-sum') cash flow analysis, one of either PV or FV should be entered followed UV E4 whenever you compute N or I/Y. 5

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Example questions for the sinsle (or lump-sum) cash flows (4) PV:\$1,000, r:0.05 (5" ), FV2:? (5) FV2:51,000, r-0.05, PV:? Draw time lines for (a) and (5) in the above. Solve (4) and (5) using formula: Solve (4) and (5) using Calculator: (6) which \$1,000 do you want to choose in the above questions (4) and (5)? why? Implication: A dollar today is worth more than a dollar in the future. A dollar today earns interest. Since time earns interest or returns on investment, time has value. It's called ,Time value of money.' -6-
(7) You have \$1000 currently. You want to buy a Benz which costs \$40,000. When you deposit your money, the bank will give you 57" interest rate. How many years do you have to wait until your account becomes equal to or lager than \$40,000?

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