Financial Management Annuities

Financial Management

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Timeline

0

I (%)

1 CF1

2 CF2

3 CF3

CF0

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I is the interest rate for the period expressed in %

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Show the timing of cash flows.  Time 0 is today; Time 1 is the end of the first period (year, month, etc.) or the beginning of the second period; and so on.

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The difference between an ordinary annuity and an annuity due

Ordinary Annuity

0 1 PMT 2 PMT 3 PMT

Annuity Due

0

PMT

1

PMT

2

PMT

3

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The PV of ordinary annuity.

0

10%

1 100

2 100

3 100

4 100

90.91 82.64 75.13 68.30 316.98 = PV

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Practice:

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3-Year ordinary annuity of $100 at 10%. What is the future value at end of Yr 3?

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3-Year annuity due of $100 at 10%. What is the future value at end of Yr 3?

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Annuities Rates of Return Amortization

Annuity

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Perpetuity

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An annuity infinitely extended into the future. The present value of an annuity that that pays “PMT’ amount when the interest is “I” is

•

PV = PMT/I.

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Example: an annuity pays $100 at year end, starting from this year, and the I=10%. Its present value is

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PV= $100/0.1 = $1,000.

Annuity

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The perpetuity formula is useful in many contexts

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Other formula can be easily derived with its help See that the PV of a 3-year ordinary annuity is

PM T I  1 (1  I )

3

PV 

PM T I

  1  PM T  1  /I 3  (1  I )  

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Generally, PV of a N-year ordinary annuity is

  1  PM T  1  /I N  (1  I )  

P V AN

Annuity

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Present value and future value formulas

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The FV of an N-year ordinary annuity can be seen to be

F V AN  (1  I ) N  1   PM T    I  

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What about annuity due? You can get them by modifying the above.

F V Adue  F V Aordinary (1  I )

P V Adue  P V Aordinary (1  I )

Annuity

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Solving FV/PV problems not using a...