Hello community!
I hope your progress is going well. I am facing a recurring issue when solving cases - how to break even. Usually, they come in different formats and types. Two common ones are: how much price we would need to put to break even, and/or how many years we would need. Any general guidelines to solving these?
Hi there,
Q: How much price we would need to put to break even, and/or how many years we would need. Any general guidelines to solving these?
I believe that with the number of years you mean the payback period, that is, the number to recover the investment.
The breakeven point refers to the situation where total revenues are equal to total costs. The question is often related to the quantity required to reach that point but, as you mentioned, it could also be related to price.
I reported below the math definition for both.
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PAYBACK PERIOD
Let’s say that you have the following:
I = Initial investment
CF = Yearly cash flow of the investment
Assume for simplicity that the yearly cash flow is constant and there is no time value of money.
The payback period would be :
Payback period = I / CF
If the cash flow is not constant or there is time value of money, the formula becomes more complex, due to the fact the cash flow changes every year.
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BREAKEVEN POINT
Let’s assume your goal is to find the quantity to reach breakeven.
You can just rearrange the breakeven formula, which is the following:
R-VC-FC=0
⇔ p*q-c*q-FC=0
Where
To calculate the quantity, you can rearrange it as follows:
p*q-c*q-FC=0
⇔ q=FC/(p-c)
For price, you can use the same formula and derive the solution for that variable.
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Hope this helps,
Francesco
Hi!
Would be much better if you could provide a few examples of such mathematical problems as it's much easier to explain such calculations based on real examples.
However, in order to master breakeven calculations, try:
1. Learn all the basic consulting math formulas and try to stick to them while performing calculations.
- For example, if you need to understand which price to put in order to break even the simple formula without applying discounting (some variations are possible, depending on the inputs and the required target metric) could be: (price * quantity sold - total costs) / initial investment = 1
- To calculate the number of years (Payback Period), also disregarding the time value of money here: initial investment / net operating cashflow per year
Those are the basic examples. The calculations get tougher if the costs change in steps based on the volume produced / sold. For those you need to
2. Learn how to put together and solve equations with one or multiple unknowns
And, lastly, if you are having trouble with the first two points,
3. Hire a math tutor (non necessarily with a consulting background) to help you with your sticking points. Oftentimes even a few sessions can make a difference.
Good luck,
Nick
Hi there,
Remember that breakeven is just an algebraic equation. That it!
It is x = y + b
1) Figure out what you need to solve for
2) Setup the equation
3) Plug in the knowns
4) Solve for the unkowns
Hi there!
Yes - it always helps to just lay out the actual equation.
And they first walk the interviewer through the equation before plugging in the numbers.
Make sure that they agree on how to build this actual equation and how it will lead you two to the actual answer.
Once they agree on this, take some time to plug in the actual numbers and then walk them through the computations.
If there are other terms aside from breakeven that you're struggling with, you might find the following resource helpful because it contains all the typical terms from interviews:
Best,
Cristian
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