Speaker A
All right, everyone. Ready for another quantitative analysis case? As you know, I've been building this module with a skill progression logic.
Learn quantitative analysis in case interviews with a B2B SaaS example, focusing on revenue calculation and investment decision-making.
Key Takeaways
- Break complex cases into manageable questions to better understand and internalize concepts.
- Use sales funnel data combined with client retention time to estimate total client base and revenues.
- Investment decisions require sizing benefits relative to costs and understanding payback periods.
- Mathematical shortcuts, like multiplying churn by retention time, can simplify client base estimation.
- Visualizing profits over time helps in evaluating the financial impact of strategic investments.
What the video covers
- This lesson covers a quantitative analysis case focused on a B2B SaaS company selling financial management software to restaurants.
- The case is broken down into three questions to help learners internalize concepts step-by-step.
- The instructor explains how to calculate monthly new clients and total client base using sales funnel data and average client retention time.
- A key lesson is the mathematical trick of multiplying monthly client churn by average retention to estimate total clients.
- The video discusses evaluating a $2 million investment to improve lead segmentation and sales funnel conversion rates.
- Learners are guided through calculating current revenues and projecting revenue increases after the proposed software development.
- The importance of understanding stable revenue assumptions and client retention in modeling is emphasized.
- The instructor highlights how to assess whether the investment pays off within the client’s desired payback period.
- Visual tools like charts and profit functions over time are introduced to analyze investment returns.
- The lesson blends case interview practice with conceptual teaching to enhance problem-solving skills.
Chapters
- 00:00Introduction and Case Setup
- 01:45Client and Sales Funnel Data Overview
- 03:31Calculating Monthly New Clients and Revenue
- 05:16Assumptions and Model Validation
- 07:22Revenue Calculation and Investment Context
- 09:09Key Lesson: Estimating Client Base Using Churn and Retention
- 10:53Applying the Revenue Model and Next Steps
- 14:36Investment Analysis and Payback Period Discussion
- 23:03Profit Function Visualization and Final Insights
Full Transcript — Download SRT & Markdown
Speaker A
So, this case is going to be tougher than the previous ones, but I still want you to learn the concepts that I'm going to bring up, and I don't want them to be cramped. So, I'm going to break it down
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into three different questions. This way, if you want just stuff practice, you're going to have it, but if you want to learn the concepts one by one slowly and internalize them, and if you have more trouble with
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quantitative analysis, you're also going to get a lot of value out of this. But, the end result is that I'm going to treat this more like a lesson than like a drill, but you can still do it like a drill. I just won't be
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answering exactly like I would to an interviewer. Now, I'm going to break this down into three questions. If you're treating this like a drill and getting full practice out of it, what you should do is pause after each one of them, follow the
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four steps, and then listen to each of the steps as I answer them. Of course, as in the other cases, you might need answers from step two to be able to follow along. So, you might want to listen to steps one
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and two after you've drafted yours before moving on to steps number three and four. All right? Let's get right to the case.
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This is a long one. Your client is a software company developing software that helps restaurants, single and small chains, manage their finances and get market insights using aggregate data from all clients they have. They currently charge $2,000 for a yearly subscription to
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their product and sell mostly via cold calls. Here's some data they've provided from their sales process. Their sales team contacts around 4,000 people every month. 30% of those respond to their calls. 1/3 of those who get on the
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phone agree to join a 1-month trial of their software, and 10% of those who join the free trial become paying clients.
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Now, the engineering team has recently come up with an idea to develop a software that will dig up information and segment their leads before they even call, so they can focus only on the ones with greater likelihood of success. They
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want your help deciding whether they should go forward with this or not. The full development process would cost $2 million, and the sales team estimates the following changes in the sales funnel numbers.
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The percentage of calls answered would increase to 40%. The percentage of acceptance of the free trial would increase to 50%, meaning the people who join the free trial.
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And the percentage of free trials that convert to a full subscription would increase to 12%. All right, so this is the full context. Now, the final question would be whether they should do this or not. Okay? But, I
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want to break this down into three questions, and the first question that I want you to answer, and then I'm going to is assuming the average buyer remains a buyer for 3 years, can you figure out what the client's revenues are?
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Now, pause your video and answer the question using the four-step approach, and then listen to what I have to say to the interviewer.
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So, to find this client's revenues, I would go through three different steps. Number one, I would find the number of new clients that they have every month because I can do that you just but basically multiplying the number of people that they speak to, the
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sales team speaks to, by all of the funnel that leads us to the percentage of them that buy, right? And then, I would find the number of total clients that they have because assuming that their revenues are stable, I might be able to
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assume that the number of old clients leaving the base is equal to the number of new clients coming in.
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And given that I know that the average client stays for a given time in my base, I can get to the number of clients that I have at any given moment simply by multiplying the number of clients that come in every month by the number
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of months that the average client stays in my client base. And then, just by multiplying that by the average price, I would get to the total revenues of my client. I just need to ask a few questions to confirm if the
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structure actually makes sense or if I need to change it a little bit. Would it be fine if I ask these questions now?
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Let's say the interviewer says, "It's okay." So, I basically want to know if revenues have been stable and will remain stable.
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Like, number of clients coming in is equal to the number of clients going out, right? And I also need to know if price has recently changed because if it has, then revenue being stable doesn't mean that I can assume that number of
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clients is the same. And if old clients that are leaving or that have joined a long time ago pay less, for example, than current clients coming in, then I also need to adjust my model for that.
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Let's say that my interviewer says, "No, assume that price didn't change and that all clients pay the same $2,000 per year and that you can assume that number of clients leaving the base is equal to the number of clients coming into the client
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base every month." All right, so I'm going to move on to do my calculations now. What I have is 4,000 leads for a thousand people that we call on the phone. 30% of those pick up, 1/3 of those join the free trial, 10% of
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those actually purchase. And so this is 4K * 3 / 10 * 1 / 3 * 10%. So, I'll cut the threes here and I have 4K / 100, which is 40. Okay, so this is the number of new clients coming in every
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month. Now, since this is also the number of old customers leaving, and I know that they stay 3 years or 36 months. So, basically I have to divide 40 by 1 / 36, which is the same as multiplying 40 by 36.
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And I'm going to call 36 40 minus 10% to make this simpler, as I've done in the other drills a ton of times. So, this is 40 * 40 minus 10% of that, of 40 * 40.
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So, 40 * 40 is 1,600. 10% of that is 160, and so 1,600 minus 160 is 1,440.
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So, this is the number of clients that I currently have. Now, we just need to multiply that by my current price, which is 2,000. So, 1,440 * 2 is 2,880.
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And now I got to add on the thousand, so this is basically 2.88 million.
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So, around $3 million. This is a little bit scary to me. It looks like the investment that we would need to make that we were talking about in the context of this question is almost a year worth of revenue. So, it's 2/3 of a
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year worth of revenues. So, the next thing I would do is definitely size the benefit of this investment to see if it's worth it or if it's even worth looking at because honestly, it's got to be a huge
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difference to make up for 8 months of revenue. All right. Now, I want to before I move on to the next question, I want to go through a quick lesson here with you because I think this is the biggest lesson from this one
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question. It's the reason I broke it down into this specific question. I broke this case down into this specific question because I wanted you to learn this.
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And it is basically the idea that you can find the total revenues of this client just by knowing the size of a small segment and what that small segment represents of the whole. So, now in this case, I know
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that the number of clients coming out of the base were 40 every month. And I also knew that the number of customers leaving the base every month were 1/36 of the base. So, what this means is that there
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the number of clients coming out or going in would fit 36 times into the customer base. So, basically to find the customer base, I multiplied the number of customers coming in or going out, it's the same,
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which is 40, by 36, which is the number of times they would fit in the full client base.
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And I wanted you to learn this because it's not intuitive and it might appear several different times when doing the cases. And if you already know this unintuitive structure, this unintuitive math trick, then you're a lot better off. Okay? A
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places where this could appear is So, basically, let's say you're doing a case on a specific market, and you know that the market growth is 2%. And you also happen to know for other reasons the number the growth of the market in units. And then
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you can just multiply it by 50 or divide it by 2% to find the full market size.
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Or let's say that you know the market leader's revenues and you know their market share. With that, using the same logic, you can find the total market size. So, let's say the leader of the market has 10 billion in revenues and it represents
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10% of the market. So, you can tell that the total market size is 100 billion. Okay?
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So, basically, the formula here is that we're reversing a simple equation. A simple equation which is a part divided by the whole is equal to the percentage of that part on the whole. Like, 3 / 100 is 3%. And
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we're reversing this equation to a part divided by the percentage that that part represents is equal to the total. So, 3 / 3% would be 100. That's the reverse.
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And as I said, this can appear in many different cases. So, take note of it, write it down, and once you see that in a case again, you're going to remember me.
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Another quick thing that I want you to learn here is that the there's a technical term for a concept that we used, which is the percentage of clients leaving the recurring revenue client base every year. So, we have, you
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know, 1,440 clients, and every year we have leaving uh a third of those clients, right? Because they stay in for 3 years on average. And we call that the churn rate.
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The churn rate is the percentage of clients leaving the client base every year. Net churn would be the net number of clients leaving the base every year. So, in this case, it'd be zero because the number coming in is
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equal to the number going out. But, here you go. If you didn't know it before, now you know the concepts of churn and net churn, what they mean, if they appear, you know what they're talking about.
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Now, let's move on to question number two. Basically, what we want to know is can you figure out what the revenues would be with this new software once revenues reach stability, assuming that nothing else changes, prices, capacity, anything.
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Okay? Now, pause the video, get to your answer, and then listen to mine. I would solve this case for the future revenues in two simple steps. First, I'd find the multiple of change of the revenues simply by finding the change in each of the
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drivers of revenues cuz I calculated the revenues simply by using the numbers in the sales funnel, right?
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And then dividing it by the average time the customer stays in the base. And since the average time didn't change as per the case question, then I can just find how each of the drivers changed, and then I'll find the multiple that I
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can multiply my revenues by and find the future revenues. Of course, step two will be multiplying this multiple by the current revenues that I found, and then I'll get to the final answer.
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So, let's move on to step number two, asking questions. And I don't really have any questions in this case. I if the interviewer hadn't stated that everything else was staying the same, I had to confirm that all the other drivers
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other than the sales funnel were not changing. And let since they already said they're the same, so I don't have any questions. Now, I'm moving on to step number three, calculating my answer.
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So, here I have the funnel numbers from before that I'd already written. And now I know that after this change, I will be still talking to 4,000 clients, but the percentage of those that answer the the get on the phone is 40% now. The
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percentage that is joins the free trial is 1/2 now, and the percentage that buys now 12%. So, the change here, no change to the number of people we call, but the percentage that get on the phone with us
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changes by 4/3, right? Which is 40% / 30% 4/3. The percentage that get into the free trial changes by 3/2. It's 50% larger.
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Right? 1/2 over 1/3 is 3/2. And the percentage that buy increases by 20% or it's a multiplied by 1.2.
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And so, 4/3 * 3/2 * 1.2 is 2.4. So, this is by how much the revenues are going to increase because basically what I have is an equation, and I'm going to write it down here for you. So,
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calls * percentage responded * percentage free * percentage that buy equals revenue. And if I multiply each of these by a different number, then my new revenues are going to be multiplied by a number that is the product of those. So, here I have 4/3
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multiplied by 3/2 multiplied by 1.2, and this is 2.4. My previous revenues were 2.88 million.
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Would you mind if I rounded this to 2.9 million or maybe 3 million? 2.9 would be just a 0.02 change. It's just a little bit, almost nothing. And even 3 million would be less than a 3% change.
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And let's say the interviewer says they will only allow me to to round it to 2.9 million. So, 2.9 million * 2.4. I'm going to break this down. 3 million * 2.4 0.1 * 2.4. Okay? So, 3 million * 2 is 6 million. 3 million *
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0.4 is 1.2 million. So, this is 7.2 million. 7.2 million - 0.24 million is 6.96 million. So, this is my new revenues after the change. When they're stable, they will be 6.96 million or around 7 million.
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And now this is looking a lot better for this investment. Not only did the revenues increase by over 200%, but the increase is also a lot greater than the investment. The investment was 2 million if I recall correctly, and
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revenues increased from around 3 million to around 7 million. So, it's around double the investment. Next thing I would look at is the profit margin that we have, or rather the marginal profit margin of this change, to see whether it
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would pay off this investment or not. And before I we move on to question number three, I want to touch on just a single lesson here. Again, the reason I divided this case into these three questions and specifically into this
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question number two, and that is in this case finding the deltas or the multiplier for each of the drivers was so much faster than calculating the full revenue again. Right, I could have done the same thing as I did in the case
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before. Right, had the 4,000 multiplied by all of those percentages. So, by 40%, by 1/2, by 2% and then divide multiply that by 36 and I'd get to a number that is the same. But, since I knew that
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I could find simply the changes in the drivers and multiply the revenue that I had before, I could do this so much faster. And this question is not actually unfeasible even though it was very simple, the interviewer might want to see if
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you're able to find this quicker path because it's something that it's a skill that if you hone and if you have, once you're in consulting it might be super useful cuz if you can do an analysis that could take a week in only
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one day or anything any kind of savings in this order of magnitude, you're saving the client a ton of money and you're making them a lot more satisfied.
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And so, this means a lot to the partner and to the firm. And so, basically this is something that they are actively looking for.
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Now, let's finally move on to question number three which is should your client move on with this investment or not? And of course, the questions that we've answered before are going to help answer this one, but there's still a long way to go.
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And before you and I start solving this case, I want to make a quick comment here because this is the first and only investment analysis question that we're doing in this in this short course.
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Basically, there are several ways to decide if an investment is worth doing or not, right? You don't want to simply see if profits are positive or negative because you want to take into account value of money in time, which means
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money today is worth more than money tomorrow. And of course, you also want to take into account that there are other stuff you could do with that money as well.
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And among the several ways to benchmark your investment returns and see if it's worth doing, some of them are payback time. So, a client might say, "My money must be back into my account, the full money that I invested in 2 or 3
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or 5 years." Right? There's a discount rate method. So, you could discount the cash flows into all to the present value, compare it to the value of the investment that you're making, discount the all of the future investment as well, and get to the net
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present value. This is basically the discounted cash flow method. Or you could have a return rate expected. So, you'll see based on the discount rate and the cash flows, what is the return rate that you can expect? And if it's greater than
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your cost of capital, then you can do it. If it's not, then you won't do it.
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And I would definitely suggest you ask your interviewer even before structuring your all of your investment analysis if they haven't mentioned it. If they have a preferred method, if they have a benchmark. So, you might ask them if they have a
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preferred method or you might ask them if they have a specific payback time that they want or a specific return rate that they expect. Okay? And in this case, the reason I'd ask this as soon as possible is because it
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completely determines what structure you're going to use. If it's a more complex case or if it's a more complex method like the discounted cash flow, you might need a more complex structure.
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Usually in case interview, you're not going to get a very complex cash flow, you know, with ups and downs all the way which you have to discount entirely.
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You're hardly ever going to have to do a ton of compound math with pen and paper.
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That hardly ever makes sense. But, sometimes that might be what the interviewer wants. And of course, the interviewer appreciates you giving them the choice and you showing them that you know that these exist, you know it can be more complex, you know it can be less
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complex. And usually they're going to give you a simple method and you're also going to get a simple cash flow structure.
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And one thing that you should know is that many times the interviewer is not going to give you a an answer to this.
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They're not going to prefer anything. They just want you to tell them whether they should do it or not. And then, you've got to choose your own method and then you've got to create your own structure based on that. But let's say
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that in this specific case, I did get an answer and that answer is the client wants their money back in 2 years.
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All right. So, let's move on to the answer. Pause the video right now and come up with your answer.
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So, I would solve this case in four different steps. Step number one, I would find the difference in profits between the client with the investment when stable and without the investment when stable. And then, I'm going to chart that into a formula
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because those profits are going to grow steadily. Every month we're going to get a little bit more clients than than are leaving our base for 3 years until the clients that we acquired 3 years before are leaving the base and that
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brings us to stability again except with a lot more clients like we calculated in question number two.
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Right? And so, I've I would charge that into a steady increase and draw formula for it where I plug in the time and I get the difference in profits or the monthly profits.
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And then I would use that formula to find the profits in 2 years that our client would have.
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Because that's how that's when we want the investment to be paid back. And then I would add up all of the profits during those 2 years or the increase in profits of those 2 years and I would see if it paid off the
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investment or not. All right. Now, I do have just a couple of questions that I would need to I would need to have the answer to to start doing this case. So, would you mind if I ask them now? And
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let's say the interviewer says that's okay. And question number one is do we know what is the profit margin that our client has and if that profit margin will change over the years?
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Because of course, we can only pay our investments with our profits, not with our revenues. Of course, we don't it wouldn't work to only know the difference in revenues. We need to know the difference in profits.
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And let's say that the interviewer tells me that the profit margin is 75% but I also want to know if that will be different because we're going to scale this company a lot. So, profit margin might increase because we
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now have more customers to scale. And let's say the interviewer tells me no profit margin's not going to change.
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It's always going to be 75%. Now, the second question I have is whether our customers pay us in advance or if they pay us in the end of the year because that totally changes how much revenues we're going to get in those 2
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years since it's seem like it's an yearly payment. And let's say that the interviewer tells me that we can assume that they pay monthly even though we gave me they gave me a yearly price. Assume that the new customers and old customers pay
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monthly. All right. So, I think I'm ready to move on to calculate. So, now is the time to pause the video and solve the case by yourself if you haven't done this yet.
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All right, step one. Finding the difference in profits between right now and what profits will be once we've implemented this change.
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So, basically what I'm going to do is find the difference in revenues and multiply it by the profit margin.
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Since revenues are now would you mind if I approximated or rounded the new revenues to 7 million and the old revenues to 3 million. And let's say the interviewer says that is fine. So, the difference between 7 million and
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3 million is 4 million. That's a difference in revenues times the profit margin of 75%.
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That is 3 million. So, right now profits are zero. If we implement the change right now, it will take 3 years, actually 3 years and 1 month because there's the free trial month.
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And then our profits will be 3 million more than our profits are today. For now, I'm going to forget about this free month and then I'm going to take it back into consideration in the end of the of the problem. So, what I'm going
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to do right now is step number two. I'm going to actually draw a chart with the Y axis being the difference in profits.
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So, it starts in zero cuz difference in profits from right now to right now is zero.
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And on the X axis, I'm going to have time. So, profits are going to slowly grow from the moment I implement change until the moment revenues and profits start stable again.
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And so what I have here is that in 3 years our increase in profits will be 3 million. And this is going to be a straight line, forgetting about the free trial month, okay?
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Which is only going to move this line a little bit to the right, anyway.
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So this is basically the formula here. Given that I'm assuming that they pay monthly, then this would be a a bunch of dots instead of a a straight line, but I'm going just going to assume that this is a linear function
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rather than a bunch of dots. And basically the accumulated profits are the area of the triangle, right?
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Mhm. First, I want to find what the profits are going to be in year number two. And since in 3 years it's going to be 3 million in revenues in difference in profits, I know that in 2 years it's going to be 2
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million, right? This is a simple chart. And so to get to the accumulated profits, as I said, I just need to find the area of this triangle, because it's the sum of the yearly profits from each moment, okay?
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And so this is basically the basis times the height of the triangle divided by two. And so 2 years times 2 million divided by two, this gives me 2 million.
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That's the accumulated profits over these 2 years. But I do have to consider that this 1 month of free trial.
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And honestly, I would go back and reconsider my approximations because now that we are right on top of the of the goal, we need to figure out if it's a little bit above or a little bit below.
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But to be honest, this is not the point. I think this Doing this would completely miss the point. And even considering the free trial month would completely miss the point, especially if we didn't make the investment because even if it's a little bit more than 2
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years that it takes to repay the investment, let's say it's 2 year and 2 months or something.
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Right? If you look at it, the profits are still growing and they're growing a lot. And so, in 2 years we might accumulate around $2 million in profits. But, in year three, look at the area of the of this triangle. It's
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3 * 3 / 2. It would give me 4.5 million, the accumulated profits in year until year three.
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If I subtract the profits until then, which are $2 million, just year three would give me $2.5 million in profits.
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This means that only year three in year three alone would pay the investment and have an extra.
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And in 3 years, we would have uh 4.5, it's over two times the revenues of the investment back. And then, from then on, we would have $3 million more of profits every single year, which is more than the investment. So, even if the
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payback time is a little bit more than 2 years, unless this is a hard no from our client for some reason, I would definitely recommend going forward with this investment. And if it is a hard no for some reason, like we have specific
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debt that we need pay by those 2 years, I would probably recommend that the client go find a way to be able to make this investment anyway, because it sounds like a really, really good investment, a really good opportunity.
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Okay? Now, I want to talk about three lessons from this third question. So, you got two important lessons from the previous two questions, but here there are a few more. Number one, notice that the interviewer in the case question
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omitted the profit margin and the existence of a profit margin in general. We're talking about revenues, revenues, revenues, never mentioned profits, but then when they started doing the investment analysis, I absolutely needed to come up with this. And of course, you can only pay
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for your investment using profits. You can't pay using revenues, otherwise you don't have any money to pay for your costs.
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And it was not a coincidence that this happened. This is something that you need to be wary of when you're in consulting. Like everyone's seeing a problem, everyone in the client firm is seeing a problem one way, right? They're talking about it in
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their own terms. And a consulting firm needs to come and be able to give an outsider look from first principles with a clear mind.
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And that means also thinking from the problem not only in the terms that they are talking about, not only in the terms and in the variables that they're using, but in all the terms and variables that are relevant. So, if you're able to come up
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with the idea that you should use the profit margin here and only consider profits rather than revenues in the payment of the investment, you are showing that you will be a consultant who gets to the client side and can think about the
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problem in your own terms and perhaps come up with a solution that they haven't thought of, which is super important to do as a consultant. Lesson number two, and this is this might be repetitive cuz I talked about in the beginning of the
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case, but I it needs to be re-emphasized. Every investment analysis needs a method to analyze an investment. You need to use a method. And it can be multiples, it can be the payback time, it can be the the rate, it can be discount cash
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flow, and asking the interviewer which one they want you to use and what their benchmark is, like what their return rate expected is or what the payback time that they want is is a good idea. You should always do
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this, but beware, many times they are not going to give you an answer to that.
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They are going to say, "Just tell me if I need to do it or not." And then, of course, you are going to have to pick one, okay? And it's going to depend on the complexity of the cash flows and on
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the complexity of the case. But generally, in case interviews, the cash flow structure is not going to be very complex. And of course, you need to have an idea in your mind of what is a good return rate and what is not.
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And lesson number three is this idea of drawing a chart and finding the function for profits in terms of time. Once we do the change and using a little graph, drawing on the paper and finding the area of a
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triangle, this is definitely a tool that you will benefit if you have it in your toolkit because sometimes it's just going to be so much easier to draw than to make formulas or explain things with words. This is something that you need
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to have. And even if you're doing Zoom interviews or video call interviews, have pen and paper with you. Have a few spare papers so that you can draw large charts on it or large tables and then show them to
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your interviewer on your camera. All right. Everyone, this is it for today's video. I hope this was helpful to you. I guess this is it for the quantitative analysis module as a whole.
Speaker A
So, I hope this was fun to you. I hope it was helpful as well, most importantly. And I'll see you in the next one.
Topics:case interviewquantitative analysisB2B SaaSsales funnelclient retentionrevenue calculationinvestment analysispayback periodlead segmentationCraftingCases
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