imported>Doug Williamson |
imported>Doug Williamson |
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| ''Financial maths''.
| | The purchase and cancellation of outstanding securities through a cash payment to the holder. |
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| (GAF).
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| Growing annuity factors are used to calculate present values of growing annuities.
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| The simplest type of growing annuity is a finite series of growing future cash flows, starting exactly one period into the future, and growing at a constant percentage rate per period. | |
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| == Present value calculations ==
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| A growing annuity factor can be used to calculate the total present value of a growing [[annuity]].
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| The Growing Annuity Factor is the sum of the adjusted [[Discount factor]]s for maturities 1 to n inclusive, when the [[cost of capital]] is the same for all relevant maturities.
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| The discount factors need to be adjusted because of the growth of the cash flows.
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| By analogy with the simple annuity factor abbreviated as AF(n,r) ''or'' AF<SUB>n,r</SUB>
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| The growing annuity factor can be abbreviated as GAF(n,r,g) ''or'' AF<SUB>n,r,g</SUB>
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| === Present value ===
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| The [[present value]] of the growing annuity is calculated from the Growing Annuity Factor (GAF) as:
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| = GAF x Time 1 cash flow.
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| <span style="color:#4B0082">'''Example 1: Present value calculation'''</span>
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| Annuity factor = 1.842.
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| Time 1 cash flow = $10m.
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| Present value is:
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| = AF x Time 1 cash flow
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| = 1.842 x 10
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| = $'''18.42'''m
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| === Growing annuity factor calculation ===
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| The growing annuity factor for 'n' periods at a periodic yield of 'r' and a periodic growth rate of 'g' is calculated as:
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| AF(n,r,g)
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| = '''('''1 / (r-g) ''')'''
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| ::x '''('''1 - ( (1+g) / (1+r) )<sup>n</sup> ''')'''
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| Where
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| n = number of periods
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| r = periodic cost of capital
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| g = periodic growth rate from Time 1 period in the future
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| <span style="color:#4B0082">'''Example 2: Growing annuity factor calculation'''</span>
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| When the periodic cost of capital (r) = 6%
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| growth rate (g) per period = 1%
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| and the number of periods in the total time under review (n) = 2
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| The growing annuity factor is:
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| = '''('''1 / (r-g) ''')'''
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| ::x '''('''1 - ( (1+g) / (1+r) )<sup>n</sup> ''')'''
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| = '''('''1 / (0.06 - 0.01) ''')'''
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| ::x '''('''1 - ( (1.01) / (1.06) )<sup>2</sup> ''')'''
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| = '''('''20''')'''
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| ::x '''('''0.0921''')'''
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| = '''1.842'''
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| | More specifically, the paying off or buying back of a debt security by the issuer on or before its stated maturity date. The redemption can be made at par value or at a premium, as is the custom when exercising a call option. |
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| == See also == | | == See also == |
| * [[Annuity]] | | * [[Call option]] |
| * [[Annuity factor]] | | * [[Par]] |
| * [[CertFMM]] | | * [[Premium]] |
| * [[CumDF]] | | * [[Puttable]] |
| * [[Discount factor]] | | * [[Sinking fund]] |
| * [[Perpetuity factor]] | | * [[Spens clause]] |
| * [[Present value]] | | * [[Undated]] |
| * [[Instalment]]
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| * [[Equated instalment]]
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| * [[Principal]]
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