my problem states that a natural preserve would yield a net benefit stream of $5 per year, forever and to calculate the net present value when r= .04… im so stuck because the formula doesn’t make any sense to me…
how do you calculate net present value for continuous payments over many years??
30
Jul
Kelley Anne
July 30, 2010 at 4:42 am
I’m not sure what r is (I believe the rate of return or interest rate) but this is how to derive those problems.
Let PV = Present value and i = annual interest rate.
PV*(1+i) = 5[(1+i) + 1 + 1/(1+i)^2 + 1/(1+i)^3 + ... + ]
PV = 5[1 + 1/(1+i) + 1/(1+i)^2 + 1/(1+i)^3 + ... + ]
Now substracting the second equation from the first all terms drop out except PV*i = 5(1+i) Therefore,
PV = 5*(1+i)/i
Note: I assumed the first payment was at the beginning of the year, If at the end of the first year you would omit the first term Then PV*i = 5; PV = 5/i
In that case if i= r = 0.04 then PV = 125