It costs $800,000, it will produce an inflow after operating costs of $170,000 a year for 10 years. Opportunity costs of capital is 14%..Whats the NPV of factory, and what will the building be worth after the end of 5 years?
I understand it produces a set 170,000 a year so you could just run the present value after each year. But is this a shorter or way to do it? What would the answer be either way? Thanks alot.
So the formula for the sum of a series (Sn) is:
I'm guessing that a would be 170,000 in this case and I had thought r would be the Cost of Capital at 0.14 but after having read your post I understand it's actually 1/1+r - why is this? Can you show me how the formula you posted related to the general sum of geometric series formula above? If you could walk this through more slowly and explain more closely how NPV calculations relate to geometric series, that would be great!
Are you njrocket, the original poster? If so, why the "disguise"?
The PV of that 170000 10 year flow is:
170000 / 1.14^1 + 170000 / 1.14^2 +....+ 170000 / 1.14^10 = 886739.66
The multiplyer is 1 / 1.14: as example, 170000 / 1.14^5 * (1 / 1.14) = 170000 / 1.14^6
Hence the multiplyer is 1 / (1 + i) ; in this case, i = .14
And formula is:
PV = f[1 - 1/(1+i)^n] / i
In this case, f = 170000, i = .14 and n = 10 : kapish?