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 )
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 = ?
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
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 =
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 =
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
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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