# Thread: NPV of a Building

1. ## NPV of a Building

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.

2. Originally Posted by njrocket
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.
If you were paying close attention in an earlier math class, you should have noticed somehting about Geometric Series. These are very, very inportant. Make them your friends.

i = 0.14
v = 1/(1+i)

$NPV_{0} = -800000 + 170000(v + v^{2} + v^{3}+...+v^{10})$

Is this what you were describing?

$NPV_{0} = -800000 + 170000\left(\frac{v-v^{11}}{1-v}\right)$

That certainly looks simpler.

$
NPV_{5} = NPV_{0}\cdot v^{-5}
$

3. if the factory costs $800,000.....and i get a present value of doing the calculations you have and get 886,739.66.......do i subtract 800,000 to get a Net Present Value of 86,739,66? 4. ?? It's all in the equation above. Go read it again until you see it. You $DO$ have to acquaint yourself with the notation. Look carefully at the sign of the first term. 5. Originally Posted by njrocket if the factory costs$800,000.....and i get a present value of doing the calculations you have and get 886,739.66.......do i subtract 800,000 to get a Net Present Value of 86,739,66?
Seller: $886,740 Buyer: How do you figure that? Seller: Present value of$170,000 annual profit, 10 years.
Buyer: Bull! I'm offering you \$800,000...

Get my drift?

6. Originally Posted by TKHunny
If you were paying close attention in an earlier math class, you should have noticed somehting about Geometric Series. These are very, very inportant. Make them your friends.

i = 0.14
v = 1/(1+i)

$NPV_{0} = -800000 + 170000(v + v^{2} + v^{3}+...+v^{10})$

Is this what you were describing?

$NPV_{0} = -800000 + 170000\left(\frac{v-v^{11}}{1-v}\right)$

That certainly looks simpler.

$
NPV_{5} = NPV_{0}\cdot v^{-5}
$
Could you help me and elaborate a bit more on this please?

So the formula for the sum of a series (Sn) is: $\frac{a (1-r^{n})}{1-r}$

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!

7. 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?