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Date Submitted: 10/04/2013 08:59 PM
Financial Management
Mon 10:00 – 11:50 D404 Fri 17:00 – 17:50 C407
Recap
Timeline
0
I (%)
1 CF1
2 CF2
3 CF3
CF0
I is the interest rate for the period expressed in %
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.
Recap
Recap
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
Recap
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
Recap
Practice:
3-Year ordinary annuity of $100 at 10%. What is the future value at end of Yr 3?
3-Year annuity due of $100 at 10%. What is the future value at end of Yr 3?
Roadmap
Annuities Rates of Return Amortization
Annuity
Perpetuity
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.
Example: an annuity pays $100 at year end, starting from this year, and the I=10%. Its present value is
PV= $100/0.1 = $1,000.
Annuity
The perpetuity formula is useful in many contexts
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 )
Generally, PV of a N-year ordinary annuity is
1 PM T 1 /I N (1 I )
P V AN
Annuity
Present value and future value formulas
The FV of an N-year ordinary annuity can be seen to be
F V AN (1 I ) N 1 PM T I
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
Solving FV/PV problems not using a...