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Q: Finance ( Answered,   0 Comments )
Question  
Subject: Finance
Category: Miscellaneous
Asked by: pheifer-ga
List Price: $2.00
Posted: 14 Oct 2003 10:44 PDT
Expires: 13 Nov 2003 09:44 PST
Question ID: 266151
At the end of each year for the next ten years you will recieve cash
flows of $50. If the appropriate discount rate is 5.5%, how much would
you pay today for the annuity?
Answer  
Subject: Re: Finance
Answered By: livioflores-ga on 14 Oct 2003 22:12 PDT
 
Hi pheifer!!

An annuity is a constant cash flow that occurs at regular intervals
for a fixed period of time. You want to know the present value of this
annuity. To calculate it you must take each cash flow and discounting
it back to the present (using the appropiate discount rate), and
adding up the present values.
The formula for present value of an annuity is:

                         1
              1 - --------------
                     (1 + r)^n
PV = CF . ---------------------------  = CF . PVAF(r,n)
                       r
Where:
CF = periodic cash flow
PV = present value
r = discount rate
n = number of periods
PVAF(r,n) = present value annuity factor for r and n (you must use
tables for this factor)

Present Value Annuity Factor Tables:
You can opent this file with Microsoft Word or with the Wordpad
program included in almost version of Windows.
http://www.finance.cch.com/tools/downloads/presvalfuturepayseries.rtf

Now the problem:

PVAF(r,n) = 7.5376 (just use the table or simply do the calculations
with a calculator).

PV = $50 * 7.5376 = $376.88

For more reference on this topic visit the following pages:
"Present Value of Annuities":
http://www.getobjects.com/Components/Finance/TVM/pva.html

"Derivation of the Annuity Formula":
http://secure.webstation.net/~ftsweb/texts/bondtutor/appendix1a.htm

"Present Value Annuity Example" prepared by Pamela Peterson:
http://garnet.acns.fsu.edu/~ppeters/fin3403/work/pvanex.html 

I hope this helps you.

Best regards.
livioflores-ga
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