Estimate the revenue that a multiplex makes in a week
Candidate (C) - I’ll pick up a multiplex in a metro city, as that is one I’m most familiar with. Is it safe to assume that an average multiplex has 4 screens and each screen runs 4 shows a day? I have seen some with more, and some with fewer.
Interviewer (I) - Sure, let’s go with 4 screens with 4 shows each.
C - All right. There are multiple sources of revenue for a multiplex:
Tickets
Food & beverages
Advertising
Parking
Let me begin with figuring out the Ticket revenue. I’m going to try and estimate the number of seats, look at the price of tickets and the occupancy rate and then determine the revenue. Roughly, the ticket revenue is:
Total # seats * # shows * occupancy rate * price per seat
I - Sounds good.
C - When I try to book tickets online, I notice there are approximately 20 seats in a row and about 15 rows. That makes it about 300 seats. I have seen smaller and larger theatres too, but I’ll go with 300 as an estimate. For 4 screens, that’s about 1200 seats in the multiplex.
Now, I would think the occupancy is different through the different days of the week. Weekends are more crowded - I’d say almost a hundred percent occupancy for prime time shows on the weekend although early morning shows might see lesser occupancy. So let me average it out to 80%. Weekdays would see much lesser occupancy, say even half of the occupancy of weekdays, so I’m going to average it to 40%.
Let’s now look at prices. I’ve seen weekday prices range from Rs 110 to Rs 200 depending on time of day, I’ll average it out to Rs 150. Weekend prices are higher, and I’ve seen significant variation between cities too - Bangalore seems to be more expensive than Delhi. Let me go with my city, where I pay Rs 250 on average for a weekend show.
With these estimates, let me now calculate how much revenue is made with tickets.
On a weekday:
40% occupancy * 1200 seats * 4 shows * Rs 150 = Rs 288K
On a weekend:
80% occupancy * 1200 seats * 4 shows * Rs 250 = Rs 960K
Total ticket revenue for the week = (Rs 288K * 5 days) + (Rs 960K * 2 days) = Rs 3,360,000
I - Are there any other assumptions you’ve made along the way?
C - Yes, for one, occupancy is also a factor of how hit or flop a movie is. Hit movies might see increased occupancy through the week and not just on weekdays. There are also holidays apart from the weekends that would see increased occupancy and therefore revenue.
And of course, I have considered everything pre-COVID.
I - Excellent. Let’s also quickly estimate one more revenue stream. Let’s pick parking.
C - Sure. I think a multiplex would try to optimize their parking space on occupancy. They wouldn’t want to allocate more space than necessary and have that space go unused. Luckily, we’ve already established occupancy above.
Again, I’ll make a few more assumptions along the way. One, while I do see people go alone for movies, I will assume it is an insignificant number of people and not consider them for my calculations. That means any bike parked would have 2 people watching a show. A car would have 2-4 people, I’ll take an average of three.
Now, India has way more bikes than cars. Out on the streets on a busy day, I see roughly 3 times as many bikes than cars. Would you say that’s an accurate assumption?
I - I believe the share of bikes in India is 5-6 times that of cars.
C - Understood. If I had to determine the ratio of cars to bikes in the multiplex, I’ll go with 4 bikes for every car. Since cinema as a source of entertainment is likely to be consumed more by the above average income households, I cannot take the same ratio as what’s out on the streets. Again, I’m basing this on theatres I’ve been to like Inox or PVR, and this may be different for local theatres, just like ticket prices may differ too.
Considering 2 people on a bike, and 3 in a car, let's calculate the car and bike occupancy.
Imagine X cars in the parking lot. Then the number of bikes would be 4X.
Maximum capacity of one show is 1200.
3 people * X + 2 people *4X = 1200 people
X (number of cars) = 109 roughly, let’s say the multiplex is optimized for 100 cars
And number of bikes = 400
If the multiplex is not in a mall, the parking fees are fixed. I’ve seen Rs 50 per car and Rs 20 per bike, so let’s calculate revenue from parking for the week.
Potential revenue = Rs 50 * 100 + Rs 20 * 400 = Rs 13000 per show
Per day, potential revenue = Rs 13000 * 4 shows = Rs 52000
On a weekday:
40% occupancy means 0.4 * 52000 = Rs 20,800
On a weekend:
80% occupancy means 0.8 * 52000 = Rs 41,600
For the entire week, the revenue from parking becomes Rs 1,87,200.
I - Excellent.
Note: In Estimation questions, it’s important to remember that the interviewer is not looking for the right answer, or one that’s very accurate. Here’s what they are looking for, though:
Structured thinking
Creativity
Logic
Thinking outside the box (this is where all those edge cases come in)
It is important to talk through your logic, break down the problem into manageable chunks and keep talking through all the assumptions you are baking into your solution.