The company expects that sales volume will increase at a rate of 5% annually, and it needs to sell 10,000 units every year in order to start achieving profits, noting that current sales are 8,000 units, and the break-even point is 10,000. How many years does it take to break even?

Estimating the year evolution:

• Year 0: 8000 units
• Year 1: 8000 + 5% = 8000 + 400 = 8400
• Year 2: 8400 + 5% = 8400 + 420 = 8820
• Year 3: 8820 + 5% = 8820 + 440 = 9260 
• Year 4: 9260 + 5% = 9260 + 460 = 9720
• Year 5: 9720 + 5% = 9720 + 480 = 10200

It takes 5 years to reach 10000.

Note a couple of things:

1. These are estimates. I did not multiply the full number, I only took the first two digits and multiplied those by 5 (e.g., 5% increase of 8000 is calculated as 5*80 = 400 and 5% increase of 9260 is calculated as 5*92 = 460).

2. I stopped multipying after year 3. The increase every year is always the same increase plus 20 (e.g., 400, 420, 440, etc.). So I just wrote those and simply focused on doing the sums. 

These are two strategies you can always follow in estimation cases. First, focus on the bigger numbers that make the difference and forget about being precise. Second, look for patterns in the data that can help you avoid computations.

I hope this helps! 


 

Hi there,

I would be happy to share my thoughts on your question:

• First of all, if you want to maximize your own development instead of using the forum as a “calculator”, it would be good to see your proposal first so that coaches can give you feedback on it.
• Moreover, it takes until the 5th year to reach unit sales of 10,000 (just solve the equation 8,000×1,05^x=10,000).

If you would like a more detailed discussion on how to best prepare for your upcoming interviews, please don't hesitate to contact me directly.

Best,

Hagen

Hi,
Assuming you are asking how to approach this in a case interview. I would simplify the calculation in this manner. 

8K ((1+.05) ^ N) = 10k ; N= number of years to breakeven
(1.05)^N = 1.25

Now ,since 1.05 is close to 1. We can approximate it to below : 
1.05^5 = 1+ .05*5 = ~1.25 

This means it will take around ~5 years (most likely lesser than 5 yrs because we have approximated down)  for sales to reach 10K and breakeven. 

Thanks

Ashwin 

I see you received great answers here already. 

Adding an additional resource that might help you if you are preparing for case maths:

Cheatsheet: The Must-Know Consulting Terms for Interviews

Best,
Cristian

10000 / 8000 = 1 + 25%

If you ignore compounding, it will take 25% / 5% = 5 years.

Since you have compounding, it will take a bit less than 5 years.

This is how you are expected to get to an answer in a case interview (by estimating… not by doing perfect math that takes much longer), unless precision is specifically requested.