break even point by net income

[ohffs]

What I am trying to figure out is if I do a complete buyout of a particular business then how long would it take in net income for me to break even on my investment assuming a certain rate of income growth each year.

The variables I know in this equation are 1. the cost to buy the business 2. the current yearly net income of the business 3. the assumed yearly growth rate of net income. The variable I am solving for is the number of years it would take for the accumulated net income to equal the cost of the business.

A simple compound interest formula will not work on this problem because it will only say when the net income for one year (not the accumulated net income) is the same as the cost of the business which will obviously take many years. Can anyone help me solve for this?

 

[tkhunny]

Please never use the word "simple" to describve a compound interest methodology. It is VERY confusing.

You should be able to solve this directly.

P = Purchase Price
F = First Year Net Income
g = Annual Growth Rate of Net Income --- Year 2 Net Income is F(g)

The difficulty with your problem statement is that it fails to offer an investment rate or rate of return.

i = Rate of Return --- You must selelct this, somehow. Often it is stated as a profit goal. It can be expressed many ways.
v = 1/(1+i) = The annual Discount Rate associated with the Rate of Return

Now we can write the solution.

P = F(1 + gv + (gv)^2 + (gv)^3 + ... + (gv)^(n-1))

That's it. Now what? I'll wait to see how you feel about the Rate of Return before dragging any farther through it. Just for the record, though, it IS almost done.