Payback period math

Math problem
New answer on Oct 24, 2021
4 Answers
949 Views
Anonymous A asked on Oct 23, 2021

Option 1: build a plant, investment cost = $52.5M, VC  = $2/bottle

Option 2: Outsource production, VC = $2.25/bottle for first 20M bottles. $2.5/bottle for any production above 20M bottles.

Annual production level required = 40M bottles. What is the payback period of option 1 given the alternative is outsourcing? Answer: 3 years, 7.5 months.

Is there a simple way to get this answer?

Overview of answers

Upvotes
  • Upvotes
  • Date ascending
  • Date descending
Best answer
Pedro
Expert
replied on Oct 23, 2021
30% off in March 2024 | Bain | EY-Parthenon | Roland Berger | Market Sizing | DARDEN MBA

You have to go by semesters…

1st Semester Difference: 20M * 2.25 - 20 * 2 = 5M

2nd Semester Difference: 20M * 2.5 - 20 * 2 = 10M

So to get to payback you have:

52.5 = 45 (3 years) + 5 (1st semester) + 2.5/10 (part of second semester) = 3Y + 6 monts + 25% * 6 months (1.5 months) = 3Y + 7.5 months.

Was this answer helpful?
Anonymous B on Oct 24, 2021

Thanks, if I try to find the savings per year it is 0.25 x 20M for 1st 20 M bottles and then 0.5x20M for the next 20M bottles = $15M. Can I just divide the investment cost 52.5M by this savings (15M)? You get 3.5 years. How would you know if you need to find it on a semester by semester basis or can just divide by additional savings like you typically do for payback period calculations?

Pedro on Oct 25, 2021

That formula works only is profitability per unit is constant over time. This is not the case. You have lower profitability for the first 20M units, and then higher profitability for the remainder. While in this case it was pretty easy to equate the 20M with the semester, but what I am actually doing is "plotting" the first 20M and then the second 20M to get to the payback.

(edited)

Clara
Expert
Content Creator
replied on Oct 24, 2021
McKinsey | Awarded professor at Master in Management @ IE | MBA at MIT |+180 students coached | Integrated FIT Guide aut

Hello!

+1 to the previous answers and to the importance of breakeven. It´s probably the most important concept when looking into econ/math for consulting interviews. If you master it, you have done a great 80-20

Hope it helps!

Cheers, 

Clara

Was this answer helpful?
Ian
Expert
Content Creator
replied on Oct 24, 2021
#1 BCG coach | MBB | Tier 2 | Digital, Tech, Platinion | 100% personal success rate (8/8) | 95% candidate success rate

Hi there,

Pedro has already provided an answer here, but I just wanted to flag how important it is that you fully understand how to use breakeven.

Payback period is just one form of breakeven (i.e. solving for years), so make sure you get a good amount of exposure to the other types of breakeven across cases (i.e. price, quantity, FC, VC, etc.)

Was this answer helpful?
Antonello
Expert
Content Creator
replied on Oct 24, 2021
McKinsey | NASA | top 10 FT MBA professor for consulting interviews | 6+ years of coaching

Hi!

Pedro gave a great answer here!

I highly recommend reading more about consulting math and recurring concepts like payback, NPV, etc. There are several useful articles here on PrepLounge.

Best,

Anto

Was this answer helpful?
Pedro gave the best answer

Pedro

CoachingPlus Expert
Premium + Coaching Expert
30% off in March 2024 | Bain | EY-Parthenon | Roland Berger | Market Sizing | DARDEN MBA
128
Meetings
14,966
Q&A Upvotes
52
Awards
5.0
21 Reviews
How likely are you to recommend us to a friend or fellow student?
0
1
2
3
4
5
6
7
8
9
10
0 = Not likely
10 = Very likely