You must be looking in the wrong places.
NPV is merely the present value of spme sequence of future payments. Why is that dark? It is easy enough when the payments are level or increasing by some predictable amount. When payments vary all over the place, there is a formula for each arrangement and none can be written succintly.
IRR is merely the level rate of return that brings some sequence of future payments to a given present value. Only in VERY SPECIFIC circumstances can there be a nice, closed formula for such a thing. Indeed, if you go over four cash flows, you really connot expect to find a formula, per se.
Where does that leave us? "Basic Principles".
In your example:
[quote]1. A company is considering whether to spend £1100 on equipment. It is expected that profits from the project will be £1000 after one year, and £100 after each of the second and third years.
Management are only interested in projects yielding at least 9% per annum.
What is the Net Present Value of this investment (to the nearest pound)? (NPV answer)]/quote]
We have given i = 0.09
This gives v = 1/(1+i) = 1/1.09 = 0.91743119
Then we can write:
That is easily solved. I get NPV = -21.18246000
This seems to indicate that 9% is a bit too far a stretch for this investment.
In your other example:
4000 = Number/1.09^n
1000 = Number/1.12^n
Number = 325843.10560611775609
n = 51.058705734532394527
I leave it to you to read the definition of IRR and finish the solution.
Or do we get to approximate? +3% decreased NPV by $3000 Perhaps another +1% will drop it to zero?
What are your definitions?
What are your tools?
Don't take it out on your poor calculator.