Present Value of equal payments of a future value

[Quentin N]

I have a known future value = $300,000 worth of stock options in year 2012.

A third of this value $100,000 will vest on 12/31/2010.
A third of this value $100,000 will vest on 12/31/2011.
A third of this value $100,000 will vest on 12/31/2012.

Estimated rate of increase per year 5%.

How do I find the present value at the end of each year for the vested stock
options and have my present value plus interest earned equal my future value.

I have tried to use PV tables and get a total of PV amounts plus interest
that is greater then my future value.

 

[Joe User]

How do I find the present value at the end of each
year for the vested stock options and have my
present value plus interest earned equal my future
value.

I think you are asking: what amount would be invested on 12/31/2009 that
permits withdrawals of $100,000 on each of the dates 12/31/2010, 12/31/2011
and 12/31/2012 -- a total of $300,000 -- if the investment appreciates at 5%?

That would be PV(5%,3,-100000) -- about $272,324.80.

You can check this several ways. If you put the PV formula into A1, then A2
is =A1*(1+5%)-100000. Copy A2 into A3 and A4.

Alternatively:

A1, PV of 1st $100,000: =PV(5%,1,0,-100000)
A2, PV of 2nd $100,000: =PV(5%,2,0,-100000)
A3, PV of 3rd $100,000: =PV(5%,3,0,-100000)
A4, total PV: =SUM(A1:A3)

Note: I chose the sign of the cash flows so that PV is positive. The
choice is arbitrary, as long as we are consistent. Use 100000 instead of
-100000 if you prefer PV to be negative.


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