I have an investment that pays me $19.50 per year for the next 40
years. The 19.50 increases 3% per year as a cost of living increase. I
want to sell the cash flow and the buyer expects a 10% return. What is
the current day value? How muc is it worth if the buyer want 8% or 12%
return respectively?

Hi!!


This is a Growing Annuity case and you need to find the present value
of it according to the required discount rate, to solve this problem
you need to use the following formula:
            {1 - [(1+g)/(1+r)]^t} 
PV = A *  ------------------------- 
                   (r-g)

where:
PV = Present Value of the growing annuity 
A = Initial annuity value
r = Interest rate 
g = Growth rate 
t = number of time periods 


In this case (10% rate):
A = $19.5
r = 0.1
g = 0.03 
t = 40 

Then:
PV = $19.5 * {1 - [(1+0.03)/(1+0.1)]^40} / (0.1-0.03) =
   = $19.5 * {0.92792551} / 0.07 =
   = $258.49


For the 8% case:
PV = $19.5 * {1 - [(1+0.03)/(1+0.08)]^40} / (0.08-0.03) =
   = $19.5 * {0.849845356} / 0.05 =
   = $331.44


For the 12% case:
PV = $19.5 * {1 - [(1+0.03)/(1+0.12)]^40} / (0.12-0.03) =
   = $19.5 * {0.964943538} / 0.09 =
   = $209.07


For references see:
"GROWING ANNUITIES" by Albert L. Auxier and John M. Wachowicz, Jr.:
http://web.utk.edu/~jwachowi/growing_annuity.pdf

"Growing Annuity":
http://www.pitt.edu/~schlinge/fall99/example_growth.htm


Search strategy:
"present value" "Growing Annuity"


I hope this helps you. Feel free to request for a clarification if you need it. 


Regards,
livioflores-ga