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Case Interview Fundamentals: Lesson 7 [Drill: Personal trainers in London] — Transcript

by CraftingCases · 2,202 words · 389 segments · language en · Watch on YouTube

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0:00Hey guys, how are you doing? In this
0:02drill, we're going to estimate how many
0:03personal trainers there are in London.
0:06I want you to try solving this by
0:08yourself before listening to my answer
0:11and watching my answer.
0:12Uh
0:13do it on paper. Also, say it out loud so
0:16you can compare everything to what I do.
0:18And remember to watch carefully for the
0:21steps that you've learned in the
0:23step-by-step and do them carefully with
0:25the lessons that I told that I taught
0:27you in the last video. Okay? So,
0:32this question is how many personal
0:34trainers are there in London?
0:36Uh and first
0:39the first step is clarifying the scope.
0:41And honestly, in this case, I don't
0:44think there are many relevant questions
0:45to be asked. You could have asked uh do
0:49I want to know those who are working or
0:51those who are apt to work, maybe?
0:53Uh maybe you could ask if it's
0:56just in London or in the entire
0:58metropolitan area.
1:00But honestly, I don't think those are
1:02really that relevant. It wouldn't be a
1:03problem if you asked, but those are not
1:05necessary.
1:06Now,
1:07uh I want to structure my problem. And
1:10the way I want to do this is
1:12the number of personal trainers in
1:13London is the number of hours of
1:16training demanded per year divided by
1:20the number of hours supplied per trainer
1:22per year.
1:23And the number of hours of training
1:25demanded per year is the number of
1:27clients times the number of hours per
1:30client per year.
1:31And the number of clients is the
1:34population
1:35uh times the percentage that uses the
1:38service.
1:39And the percentage that uses the service
1:41is the percentage that is not of
1:44population that is non-sedentary times
1:46the percentage of those who work out in
1:49gyms times the percentage of those that
1:51actually have trainers.
1:53And now, let's go to the number of hours
1:55supplied per trainer. And that is the
1:57number of hours worked per week per
2:00trainer
2:01times the number of active weeks.
2:04And the number of worked hours worked
2:06per week is their total capacity times
2:09their actual utilization rate, which is
2:13might not be 100%. They might not be
2:15full all the time. Okay?
2:18Now, let's
2:19choose some assumptions for this. All
2:21right?
2:22I want to start with the number of
2:24active weeks. So, there are 52 weeks in
2:27a year. I'm assuming they'll take two or
2:29three weeks off for vacations.
2:31And I can assume that their other
2:34two weeks off for holidays or sick days
2:37that they have to take. So, I'm going to
2:39go with 48 active weeks. And
2:44now
2:45to the utilization rate, I guess this is
2:47the most complicated assumption here.
2:49So, I'm going to assume clients cancel
2:51their appointments.
2:53Uh
2:53I cancel probably between 5 and 10% of
2:57this kind of appointment. So, I'm going
2:58to assume that those are
3:00the canceling
3:01uh non-peak hours
3:04not always have client schedule.
3:06So, I'm assuming 50% I'm going to assume
3:0850% of vacancy
3:11at non-peak hours, which I'm going to
3:13assume are 50% of the hours.
3:16So, there's
3:1720% of vacancy here.
3:20And 5 to 10%
3:23uh
3:24because
3:26and 5 to 10% of vacancy because clients
3:28cancel, so that's 5 to 10%.
3:31And uh there's another source of
3:34vacancy, which is
3:36uh clients
3:37don't want to work out with that
3:39personal trainer anymore for whatever
3:41reason. They want to work out anymore or
3:42they don't like that person or they
3:44can't, they're hurt, anything. And it
3:47takes some time
3:49to
3:50find another client. So, I'm going to
3:52get another 5% of vacancy here. So, 25%
3:57+ 10% + 5% gives me 40% of vacancy rate.
4:03So, 60% of utilization rate.
4:07Now, I want to go to the total capacity
4:10and I'm assuming they work around 10
4:12hours per day
4:13uh based on what I've seen and uh other
4:16people who work independently. So, they
4:19either start very early, so from 6 6:00
4:22a.m. to 4:00 p.m., or finish very late
4:25from like 2:00 p.m. to 12:00 p.m. And
4:27that's probably because I'm assuming
4:29that because most people want to work
4:31out uh not in regular working hours and
4:35so personal trainers have to adapt to
4:36that.
4:37And I'm assuming that they work 5 days a
4:40week. So, that gives me
4:42uh 50 hours per week.
4:45Now,
4:46let's go to the percentage that uses the
4:48service and I want to start with the
4:49percentage of population that is
4:51non-sedentary. Uh I'm going to assume
4:5350% of the population is non-sedentary.
4:56And the percentage of those that work
4:59out in gyms, I'm going to assume
5:01something like 25%. So, 75% of
5:04non-sedentary people of are doing
5:07anything else like playing sports or
5:10something like that and not going to the
5:11gym.
5:12And that's that's what I see based on my
5:15friends
5:17and family and people who I know. Like
5:19not many of them are going to the gym
5:21out of those who are not sedentary.
5:23And
5:24the percentage that actually uses
5:26trainers
5:27is probably only
5:30uh the richest part of the population
5:33and those who want to do that. So,
5:36probably not much at all. I'm going to
5:38go with 5%. Okay?
5:41And now, the number of hours per client,
5:45so I can assume that clients
5:48work out 1 to 2 hours per week with
5:50their personal trainers. So, that's 1.5
5:52hour per week. They probably take 2
5:55weeks off, so that is only 50 weeks in a
5:58year.
5:59And they probably cancel 10% of the
6:02time.
6:03Uh like I said before. So,
6:06that gives me 50 * 1.5
6:1075 hours minus 10%
6:1367.5
6:15hours per year. And the population of
6:17London is 9 million. Uh if you didn't
6:20know that, you could have asked the
6:22interviewer. You could have probably
6:23researched since you're just doing a
6:25drill. And you can assume that the
6:27interviewer is probably going to give
6:28you that number if you're not familiar
6:30with the city of London.
6:32Now, let's go to calculations.
6:36Now,
6:38to get to the number of hours worked per
6:40week, I'm going to do 50 * 60% and that
6:43is 30.
6:44Um to get to the hours supplied per
6:47trainer,
6:48that's 30 * 48. 30 * 40 is 1,200.
6:5330 * 8 240. So, that's 1,440.
6:58And
6:59now, to get to the percentage that uses
7:02the service, this is going to be a
7:03little bit complicated. So,
7:0550 * 25% is 50 / 4. So, 12.5%
7:11and
7:13that times 5%. So, I'm going to get 10%
7:17of 12.5% and then divided by 2. So,
7:20that's 1.25%
7:23Half of that is 0.625%
7:270.625%
7:29* 9 million.
7:31Uh okay.
7:34Let me just see what I'm going to do
7:36with these zeros. Okay. So, this should
7:37be
7:39I'm going to multiply 0.625%
7:42by 10 million and then I'm going to take
7:4410% away. So, this is 62.5
7:48thousand
7:50minus 6.25 thousand that's 56
7:540.25 thousand.
7:56Uh I'm going to round that down to 56
7:59thousand.
8:00Uh of course I'd have to ask the
8:01interviewer and in a perfect world
8:03scenario I would say
8:05uh I'm rounding down less than 1% around
8:09half percent. Is that okay? And then the
8:11interviewer is going to say fine cuz
8:13I can control what the interviewer is
8:15going to answer me in this case.
8:17Um hopefully. And so now 56 thousand
8:21times 67.5
8:23this is going to be a little bit
8:24complicated. So, I want to reality check
8:27this first.
8:28Uh so 60 thousand times 60
8:31should give me around 3.6 million. So,
8:34my answer should be close to that.
8:38And now let's do the boring part. So,
8:4156 thousand times 60 67.5
8:46uh I'm going to do 60 thousand times 70
8:51minus 4 thousand times actually 60
8:54thousand times 67.5 minus 4 thousand
8:57times 67.5.
8:59So, 60 thousand times 70
9:03um
9:04is
9:0642 0 0 thousand. So, 4.2 million
9:11minus
9:13um 60 thousand times 2.5 which is 150
9:18thousand.
9:20And minus 4 thousand times 67.5. So, 4
9:24thousand
9:25si- times 70
9:28is 280
9:294 thousand. 4 thousand times 2.5 10
9:33thousand. One minus the other 270
9:36thousand.
9:37So, I have 4.2 million minus 150 minus
9:41270. So, that's 4.2 million minus
9:45420,000.
9:47And that gives me
9:493 million
9:51point 78. So, three
9:543,078
9:56thousands.
9:57All right. Now,
9:59um
10:003.78 thousand 3.78 million time divided
10:04by 1.44 thousand.
10:07Uh let me just do a quick reality check
10:09here that 4 million divided by 1.5
10:12thousand should give me something around
10:152.5 thousand. So, my answer should be in
10:18that ballpark.
10:19Now, the actual math here. I want to
10:22still round this a little bit. So, I'm
10:24going to do 3.8 million divided by 1.5
10:28thousand.
10:29And then I'm going to subtract the 4%
10:32because I'm changing 1.44 thousand to
10:361.5 thousand. Okay?
10:39So, 3.8 million divided by 1.5 thousand,
10:43that is 38 divided by 15
10:46thousands.
10:48Um 38 divided by 15
10:51is here.
10:54Oh, just so you know, I'm actually doing
10:55this on paper 38 divided by 15 and that
10:58is completely fine. Uh this is
11:01absolutely okay. So, two and then
11:04there's eight.
11:05Uh point 6333.
11:08So, that gives me 2.63
11:12thousand. And that is my final number.
11:15Let me just
11:16do a quick check to make sure that this
11:19is actually the number I trust. So,
11:232.63 thousand, this means that 3.3
11:26thousand divided by 9 million
11:29one in every 3,000 people in London
11:32uh is a personal trainer.
11:35And at least I can tell that this is not
11:37too much, but it still could be too
11:39little.
11:40So, I want to do a different check here.
11:43So, at £50 an hour, that means that
11:48uh
11:4914
11:5014 40 * 50 around £75,000
11:54a year, which sounds about right. That
11:56sounds like what a personal trainer
11:58would make in London. Maybe they would
12:00make a little bit less. So,
12:02I would say if anything, there might be
12:05a little bit more than 2.6 thousand
12:07personal trainers, but it shouldn't be
12:09way off.
12:11And now let's assume the interviewer
12:13said, "Okay, um we've made some research
12:16and we found out that there are actually
12:19uh 1,300
12:22personal trainers in London. Where do
12:24you think you made a mistake?" And this
12:26is a quite common question for them to
12:27ask. This is a usual follow-up question
12:29for first estimation questions. Even if
12:31you did get the number correctly, what
12:34they want to see, like I said in the
12:35step-by-step, is
12:37can you actually find the variables that
12:40are most sensible in your in your model?
12:44Cuz you're going to have to do that all
12:45the time in your quantitative models in
12:47the consulting job. And so, what I want
12:49to do here is get my structure
12:52and find the variables that are the most
12:55sensible and that could be the most
12:56wrong. Uh
12:58why don't you do this before listening
13:00to my answer?
13:01Uh
13:02come up with your own answer and then
13:03listen to me.
13:04So, now here I go.
13:07I think that the first variable that
13:09could be very wrong is the percentage
13:11that actually has trainers, percentage
13:13of people that work out in gyms that
13:15actually has trainers. It could be half
13:17of that. It would I would believe if you
13:20told me that that's half of that. And
13:24uh
13:24because
13:26oh
13:27uh 5% is already very little little and
13:30I don't know that many people that have
13:32personal trainers. Like my assumption
13:34could be off.
13:36And the next one is the utilization
13:38rate. So,
13:40uh I don't think that this would explain
13:43all of the change, but the utilization
13:45rate could be
13:46uh higher enough that
13:50uh at least we would get to a 1.8 number
13:54or something like that.
13:55Um
13:57so, it
13:58since the utilization rate is on the
14:01denominator and not in the numerator, a
14:03little change in it would cause a larger
14:06change in the final answer. So, there
14:09could be it could be wrong. And also, I
14:12don't trust my observation that much in
14:14the utilization rate. So, there would
14:16have to be other factors there, but I
14:18think that the utilization rate could be
14:21uh off and could make a significant
14:23difference in my final in the final
14:25answer.
14:26Okay? Well, this was this this was the
14:29drill for today. Uh I hope this helped
14:31you. I just want to call your attention
14:33for one thing, aside from practicing all
14:36the skills that you'll you've learned in
14:38a step-by-step, which is the most
14:39important part here, I want to I want
14:42you to pay attention to the utilization
14:43rate cuz it's present in many many
14:45situations and many estimations. You're
14:47going to find
14:48the utilization rate to be very
14:50important. So, something like the number
14:52of Uber drivers or cab drivers or
14:55hairdressers or gas stations somewhere,
14:57in all of those the utilization rate is
14:59going to play an important role.
15:01Uh so, don't make the mistake of
15:03assuming that any of those are always
15:06full. And it's also going to show up in
15:08many many other estimations. Pay
15:10attention to that. All right? See you in
15:12the next video.

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