Hi!!
Present Value (PV) for cash flows made at the end of each period
(ordinary annuities):
CF1 CF2 CFn
PV = --------- + ---------- + ... + ----------
(1 + r)^1 (1 + r)^2 (1 + r)^n
Where r is the required return and n is the number of periods.
If all the cash flows are equal (like in this problem):
CF 1
PV = ---- * [1 - ---------]
r (1+r)^n
1 1
Where ---- * [1 - ---------] is the the annuity discount factor.
r (1+r)^n
The annuity discount factor is useful for using tables to facilitate
calculations, its value is function of the rate (r) and number of
periods (n):
PV = CF * Discount Factor(r,n)
For Reference see:
"Annuities" at NetMBA:
http://www.netmba.com/finance/time-value/annuity/
Now we can solve the problem:
r = 0.07
n = 10
CF = $10,000
Discount Factor(r,n) = 1/0.07 * [ 1 - 1/((1.07)^10 ] =
= 7.024
PV = CF * Discount Factor(r,n)
= $10,000 *7.024 =
= $70,240
The present value of an annuity of $10,000 to be received at the end
of each year for 10 years at a discount rate of 7% is $70,240 .
I hope that this helps you. Feel free to request for a clarification
if you need it.
Best regards.
livioflores-ga |
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