pv of annuity

[puertoricanninja]

what is the right formula to calculate the pv of an annuity w/ reinvested
interest? Ex:
i receive 10,000 cash / month for 7 years;
i invest all cash @ an interest rate of 5% / year;
i reinvest all the interest;
the discount rate is 9%.

i want the pv of the cash received and reinvested interest.

 

[bpeltzer]

Use FV to calculate the future value of all the investments and
reinvestments, then divide by (1+9%)^n (where n is the number of years) to
get the PV. (For that last part, you could also use the PV function with 0
payments and FV set to the results from part 1).

 

[puertoricanninja]

i have no trouble with the annuity fv and pv, but how do i include the
reinvestments?

 

[joeu2004]

what is the right formula to calculate the pv of an annuity w/ reinvested
interest?

Of course, there are many "right formulas".

i receive 10,000 cash / month for 7 years;
i invest all cash @ an interest rate of 5% / year;
i reinvest all the interest;
the discount rate is 9%.
i want the pv of the cash received and reinvested interest.

Making some simplifying assumptions [1], the FV of the 10000 investment
at 5% with interest reinvested is:

=fv(5%/12, 7*12, -10000)

The PV of that FV at a discount rate of 9% over 7 years is:

=pv(9%, 7, 0, fv(...))

However, that is not the NPV of the cash flows. I wonder if that is
what you really want. The NPV would be:

=pv(9%/12, 7*12, -10000, fv(...), 1)


-----
[1] You do not say whether 5% and 9% are nominal rates or effective
rates. If nominal rates, you do not specify the compounding frequency
of the investment. I make the simplifying assumption that 5% is a
nominal rate. I make varying assumptions about 9% depending on what
makes the formulation convenient ;-). The difference in PV under other
assumptions is less than 0.5%. But if this is a homework assignment,
you might need to make adjustments or clarify the problem statement if
you want further help.

 

[bpeltzer]

FV already assumes reinvestment of the interest earned. Ex:
=FV(10%,2,-100,,1) returns $231. The initial investment is $100. A year
later you've earned $10 and invested another $100 so you'd have $210. That
amount (including the first year's reinvested interest) earns $21 in the
second year, leaving you with $231. If the FV did not assume reinvestment,
you'd only get $230, losing the year 2 interest on the year 1 earnings.