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FINE 2000 (79)
Chapter 4

CHAPTER 4 THE TIME VALUE OF MONEY.docx

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Department
Finance
Course
FINE 2000
Professor
H A M D I D R I S S
Semester
Summer

Description
CHAPTER 4 THE TIME VALUE OF MONEY 4.1 Future Values and Compound Interest  Future Value (FV): Amount to which an investment will grow after earning interest FV of $I Investment= I X (1+r) t  Compound Interest: Interest earned on interest  Simple Interest: Interest earned only on the original investment; no interest is earned on interest  Future Value Interest Factor: future value of a current cash flow of $1 t FVIF (r, t)= (1+r) 4.2 Present Values  Present value (PV): value today if a future cash flow (a dollar today is worth more than a dollar tomorrow)  How much do we need to invest now in order to get ___ in the future? t PV= future value after t periods/ (1+r) PV= future payment X 1/(1+r) t  Discount Rate: Interest rate used to compute present values of future cash flows **NOTE: time it takes an investment to double in value equals approximately 72/r, where r is expressed as a percentage. (Ex. doubling period is 8 years= 72/8= 9 percent) 4.3 Multiple Cash flows  Future value of multiple cash flows  To find the future value of a stream of cash flows, calculate the future value of each flow and then add them  Present value of multiple cash flows  Present value of a stream of cash flows is the amount you would have to invest today to generate that stream 4.4 Level Cash flows: Perpetuities and Annuities  Annuity: Equally spaced and level stream of cash flows  Annuity factor: present value of a $1 annuity  2 ways to value  Value each cash flow separately and add up the present values or use the formula t t PV= 1/rX 1/(1+r) = 1/ r(r+1)  The general formula or the value of an annuity that pays C dollars a year for each of the t years is Present value of t-year annuity= payment X annuity factor= C X PVA (r, t) t = C X [1/r- 1/r(1+r)  Annuities Dues  Level stream of cash flows s
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