I am trying to figure how to make profit (for a not-for-profit!) in delivering a Forest School program. I am trying to increase the subscriptions by offering a discount, but I am not sure how to calculate this. At what price point are we maximizing our profit?

**For example, for preschool we have three morning sessions per week. Some children attend on just one or two sessions per week, so there are also these variables which makes it hard to anticipate. That’s partly why I’d thought of reducing fees for the winter, and offer a promotion for signing up for the entire stretch.

Also, how to present it clearly to the board of directors so they understand (maybe a graph/spreadsheet?)

Economists are said to know the price of everything and the value of nothing. I actually think that's backward. Figuring out the price is tough. Whenever someone asks me, "What do you think the price for this should be (usually it's a stock)?" I'm stumped. But, there are some tricks to get you started. One easy "back of the envelope" method is called the breakeven price. The breakeven price, as its name suggests, will tell you the minimum you would need to charge so that your costs exactly match your revenues: you are just breaking even. Any penny above that price is profit (and any penny below is loss). You said your school was a non-profit, so this method popped into my head first.

Without knowing exactly what your costs are, I can just give you the basics and you will need to fill in the rest. It's easier to work with some made up numbers.

*Time period.

You said it is weekly, so let's go with that and make this a weekly price (you can adjust it to whatever works for you later.)

*Fixed Costs per week.

Fixed costs are things you have to pay each week even if you don't have any students. I don't know what your fixed costs are (things like rent, electricity, school bus lease, your weekly salary, benefits, etc.), but think about whatever absolutely has to be paid in any given week (guesses are OK) even if you have no kiddos around. This can be easier if things like gas bills or your salary get paid monthly, just divide by 4 to get it weekly. Again, we are mostly guessing here, we just want an educated guess. Let's just say this is $800 a week in total.

*Variable costs per student per week.

This is a bit trickier. Often business owners think all of their costs are fixed: everything has to be paid. But that isn't really true, right? Some costs only get paid when you make your product, in your case, when you have a student in the classroom. Fixed costs have to be paid even over the weekend, right? But a variable cost is something you wouldn't pay for if you didn't have a student there. Variable costs are the costs that go up or down depending on the number of students. This is the one you probably have to think about the most. This is probably something like, for every 5 students you need one teacher aid, so in a week, one aid costs maybe $500 per 5 students making it $500/5 = $100 per student. What other things are costs that vary with the number of students? Art supplies? Snacks? Toilet paper? One way to do this is to look back over your costs from the previous year, highlight the ones that go up or down as student numbers change, add up all these costs and divide by the number of students to get an average and then divide it by the number of weeks (52 for the full year) to get the weekly average. Guessing is fine and again, we are looking for the variable cost per student per week. Let's say it is something like $150 per student.

*The weekly breakeven sales price is:

(Weekly Fixed Cost)/(Number of Students per week) + (Weekly Variable Cost)

In this example, this is:

$800/N + $150

So, this is where you figure out the number of students, N, and how that affects the breakeven price:

10 students, Price = 800/10 + 150 = $230 per student

20 students, Price = $190

50 students, Price = $166

Another way of doing this is to think of a price you want to charge and then you will know how many students you will need in order to just break even. Let's say you want to charge $175 per week.

175 = 800/N + 150

You will need 32 students to break even.

The other part of your question:

You give the example of children attending different days per week, etc. and what if you offered a discount? What the break-even analysis does for you is lets you see what the minimum price would have to be for all students to pay. You could do the analysis for each type of student (2 day per week students versus full-timers), but the tricky thing there is figuring out whether you need to have, for example, aids or snacks or supplies (your variable costs) coming in or out each week...more this week, less the next week...it might just be easier calculating the price as if all the students will attend and then adjusting. For example, let's say you figure out the breakeven for 20 students as above to be $190. If you set the price for the long-run students at $200, you could come down a little bit on the ones who only come twice a week. Conversely, you could set the price on the long-run students at $190 and charge then ones who come fewer days a higher price. After all, you have to cover your fixed costs whether a kid comes Monday through Friday or just on Mondays. You will know best how to manage giving a discount and to whom. Like most business people, you will set a price and then see how you did and probably will have to adjust it next year if it was too high or too low, but at least you won't be guessing.

And, of course, along with the breakeven analysis, you ought to be looking at what other schools in your area are charging. After all, a parent will be doing that too. If you find that you cannot breakeven at the going prices around town, it will really help you figure out where your costs need to adjust.

Good luck.

**Appendix.**

In case you are wondering where the breakeven price comes from, it comes from a profit equation:

Profit = Revenue - Costs

Revenue = price x quantity = PQ

Costs = Fixed Cost + Variable Costs = F + cQ Where c = per-unit cost.

In your case, the quantity or units are the students.

Profit is zero when revenue = costs, so

PQ = F + cQ

P = F/Q +c