What is the formula to calculate total sales for a year when you have CM%, BE point in Sales$ with X Net income after tax of 50%??

We'll answer the question using the given constants, by walking through the logic one step at a time. Afterwards, you can generalize those same concepts into a formula, if you like.

First we'll have to determine Total Fixed Costs, and we'll use the given breakeven data to do so. Hopefully you're familiar with the fundamental breakeven concept, which can be expressed in "income statement" form as

Total Revenue less Total Variable Costs less Total Fixed Costs = 0

(Income tax can be ignored in this phase, since there is no tax expense at breakeven. Both pre- and post-tax net income is zero, so we can safely work with pre-tax net income--and disregard tax rates--in finding our total fixed costs.)

Since Tot Rev - Tot Var Cost is frequently expressed as "Gross Margin", which is Total Revenue x CM%, the breakeven equation becomes

(Tot Rev x CM%) - Tot FC = 0

... or in this case, ($200K x 0.40) - TotFC = 0

(This is where you take over and solve that one to determine total fixed costs. I'll hold... )

Part 2. With Fixed Costs in hand you can now answer the question. If the post-tax net is 50K, and the effective tax rate is 50%, then pre-tax net must be??

Now you'll just solve for "Tot Rev", where

(Tot Rev x 40%) - TotFC = Pre-tax Net

Of course, you'll replace TotFC and Pre-tax Net with the actual dollar amounts you determined previously. That just leaves Tot Rev as the only unknown in the equation. Solve for Tot Rev, and you're done. Have fun!

OK, we're not quite ready to stamp "case closed" on this one just yet. (I do appreciate your appreciation, tho' :))

The breakeven equation (one form of it, anyway)...

(Sales x CM%) - Fixed Costs = 0

... is just another way of saying that when gross margin (Sales x CM%) exactly equals total fixed costs, the resulting net income is zero. A simple rearrangement shows that at breakeven,

(Sales x CM%) = Total Fixed Costs

In your case, then, Tot FC = 200K x 0.4 = 80K.

Now let's see where our after-tax net income would be, if total sales were 500K:

Pre-tax net is (500K x 40%) - 80K = 120K.

At a tax rate of 50%, 120K of pre-tax net results in 60K of after-tax net profit. According to your original post, though, the question is asking for the Sales amount that will produce 50K of after-tax net.

So warm up the calculator, and have another go at it.