Chapter 4_Part II

Chapter 4_Part II - Chapter 4 The Time Value of Money (Part...

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1 Chapter 4 The Time Value of Money (Part II)
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2 Plan of the lecture Annuities due Inflation and the time value of money Effective annual interest rates Examples of time value of money ( TVM )
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3 Annuities due Annuities due Ordinary annuity : a level stream of cash flows starting one period (e.g. one year) from now Annuity due : a level stream of cash flows starting today Examples of annuity due : rent , tuition , and car lease etc.
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4 Annuities due Annuities due Consider the following cash flows stream: 0 1 3 2 4 5 4% 4% 4% 4% 4% $100 $100 $100 $100 $100 PV = ? FV = ?
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5 Annuities due Annuities due The cash flows inside the red oval are a 4- year ordinary annuity Plus a $100 paid immediately So the PV of this cash stream = PV of a 4-year annuity + $100 99 . 462 $ 100 $ 99 . 362 $ 100 $ ] %) 4 1 %( 4 1 % 4 1 [ 100 $ PV 4 = + = + + - × =
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6 Annuities due Annuities due An annuity due of t periods paying $C per period is equivalent to $C plus a corresponding ordinary annuity of t-1 periods (see also Figure 4.12 on p. 101 ) In our previous example, t = 5, C = $100, and t-1 = 4
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7 Annuities due Annuities due ] ) r 1 ( r 1 r 1 [ C $ ) r 1 ( ... ] ) r 1 ( r 1 r 1 [ C C $ t 1 t + - × × + = + - × + = + = - periods t of due annuity an of PV that shown be can it ons, manipulati some After periods 1 - t of annuity ing correspond a of PV $C periods t of due annuity an of PV PV of an annuity of t periods
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8 Annuities due Annuities due PV of an annuity due of t periods = (1+r) × PV of an annuity of t periods In our earlier example: t = 5, C = $100, and r = 4% 99 . 462 $ 18 . 445 $ ) 04 . 0 1 ( ) 04 . 0 1 ( 04 . 0 1 04 . 0 1 100 $ ) 04 . 0 1 ( 5 = × + = + - × × + PV of annuity due =
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9 Annuities due Annuities due Similarly, FV of an annuity due of t periods = (1+r) × FV of an annuity of t periods: - + × × + r 1 ) r 1 ( C $ ) r 1 ( t FV of annuity due = FV of an annuity of t periods
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10 Annuities due Annuities due We continue with our earlier example: t = 5, C = $100, and r = 4% 30 . 563 $ 63 . 541 $ ) 04 . 0 1 ( 04 . 0 1 ) 04 . 0 1 ( 100 $ ) 04 . 0 1 ( 5 = × + = - + × × + FV of annuity due =
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11 Inflation and the time value of money Inflation is a significant variable in any long-term financial planning (e.g. retirement planning, tuition saving plans etc.). Even a low rate of inflation can have a major negative impact on people who receive fixed nominal incomes, e.g. pensioners
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12 Inflation and the time value of money Current or nominal dollars : the face value of dollars Constant or real dollars : the amount of goods and services that the nominal dollars can buy (i.e., the purchasing power of dollars) The difference between these two dollars is due to inflation
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13 Inflation and the time value of money Nominal interest rate : the interest rate in terms of current or nominal dollars Real interest rate : the interest rate in terms of constant or real dollars
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This note was uploaded on 01/26/2010 for the course ADMS 3530 taught by Professor Unknown during the Spring '09 term at York University.

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Chapter 4_Part II - Chapter 4 The Time Value of Money (Part...

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