In class discussion :
Budding entrepreneurs
Let’s start with a small trivia question:
Do you know any of these individuals? What’s common in them?
Reveal:
Bill Gates, Warren Buffet, Jeff Bezos. They are all really very rich!
Ask the student: Would you want to get rich someday? What would you do if you were a billionaire? Where would you spend your money?
But how did these people got rich? Do you have any ideas what do they do?
Reveal:
Bill Gates created Microsoft which is probably the operating system running your laptop
Jeff Bezos created Amazon which is probably the place where you shop things from:
Warren Buffet is special in this case because he majorly owns a company which invests in companies that other people make and when they make money, he makes money too:
Discussion:
But you might ask, what do all of these things have to do with Mathematics right? Let’s take a case and try to understand how mathematics is involved in becoming rich.
Ask the student: Let’s think about a new business idea- Do you have any business ideas that you would want to set up some day?
Let’s say you decide that you want to someday create a chain of “Theatres” because you love movies and you would want to make places where people can watch them.
Ask the student- Can you think of the last time when you went to a theatre? Where did you go to? Recollect the experience of watching a movie in the theatre.
Now, think about what all would you want if you were to create a theatre? What are the different questions that come to your mind? Let’s discuss.
Now, have a look at a tour of a theatre to refresh your memory:
https://www.youtube.com/watch?v=1ltQycMLO-4
Some questions that might come up during the discussion:
- Where would the theatre be located? Where should we set it up?
- How many people will it be able to hold?
- How large will the screen be? How many screens?
- What will be the ways to earn money from the theatre?
- How much money will be required to make a theatre? Where to get the money from?
- What other facilities will it need to have? (Bathrooms, shops to buy popcorns)
- How many people will need to work there? How much will they need to be paid?
- How much to charge people for one ticket?
- Will there be a profit?
Do you think the answer to any of these questions will require mathematics? Which ones?
Let’s tackle this large problem by splitting it up into simpler ones and looking at the mathematics involved, if any in each of them:
- Where would the theatre be located? Where should we set it up?
Do you know where the theatres in your city are located?
Mumbai Bangalore
Teacher can ask the student to do a google search for their city and the theaters in them.
How do people decide the location to put up a theatre? What factors do you think it could depend on?
- How remote the location is? (If a location is way too far from where large number of people live, will it be a good idea to put up a theatre there?)
- Are there other theatres nearby? (Too much competition for the same audience?)
- How much the land/ space costs to buy/rent? (A busy area will have high costs of land/ space as compared to a remote place)
They could also look up to other theatres in different areas and understand the demand from the people who already own it?
The decision does involve mathematics because we are thinking about a potential location that depends on the population of a locality (a number) and average distance to the theatre from any place in the city (another number). Comparing costs which is again using numbers.
Let’s try to understand it better by taking a decision- Which location is a better idea for your city and why? Open Google maps and try to deduce based on the factors. Trainer can help them to deduce.
Let’s say we go to the location that you chose to buy that land. You meet a real estate agent who is selling it and ask him that you want this land/property. Can you tell the price for it?
The real estate agent asks you the following:
“How much land/space do you require?” I am selling it for 4000 per meter square.
Do we know the answer to this question yet?
For that, we need to go back and answer the following question first.
- How much land/space do you require?
Land or space should be an area. How do we begin thinking about this? Any ideas?
What if we thought about this:
How many people will be able to watch movies in it ?
If we know, how many people we want to make it for, we will know the area of the land that we want because we know how wide roughly a seat is. So the question becomes how large is a theatre in terms of its area. Let’s try.
You have gone to a movie theatre right? How many people do you think it can have? Can you estimate? Show them the image and ask them to try:
Reveal:
Let’s do some estimates.
As per the image, each row has some 10 seats and there are roughly 12-15 rows. 150 seats? But how do we get to a number for area from a number of seat? Can you try to think of a model to think of this problem?
How about this model? (the picture is used for the model, the number of seats is not the same as the theatre image being used). We can think each of the seat as a square when looked from the top. We will be able to calculate the area of a square if we know it’s side.
Now, the question is how wide each of the seat is? What do you estimate it to be?
0.5 m (Half a meter wide)? What will be the area of one square in that case? Remind them of the area of a square which is side length squared.
0.25 meter square! Now, we just need to multiply it to the number of seats.
150 times 0.25. Can they multiply this? If not, ask them to use a calculator.
37.5 meter square.
But is that all there is to the theatre? Is there no other space?
What about the space in between seats?
What about the space that’s used to walk from the sides or the centre?
What about the space between the seats and the Screen?
Can we very roughly say then the space will be at least 150 square meters?
Let’s move ahead for the sake of simplicity with this number and estimate how much will that space cost!
Remember the real estate agent said that the space he is selling is at 4000 per square meter and we will at least require 150 square meters for just one theatre alone. Leave alone the space for selling popcorns/drinks, or other utilities like a bathroom, water etc.
How much does the cost come out to be? How do you find it out?
Yes, we multiply them: 4000x150= Rs. 6,00,000
This is usually a rental cost per month in real life for a mall space in a metro city!
3) How much money will be required to make a theatre? Where to get the money from?
The cost that we calculated is just the monthly rental. Add to it the costs of equipment, projector, furnishing the place, sound systems and a lot more construction and civil work.
That’s going to be a lot of money. Do you have any ideas where you can get all that money from? Banks! Is there any mathematics involved while getting the money from the bank?
Let’s have a look-
You go to the bank and ask for a loan of 1,00,00,000 from them.(Rough estimate considering rental for all months in a year and other costs) They tell you this:
“We will give you the money but you will need to keep something with us in return in case you don’t pay back.” (Banks keep a security in the form of cars, house, land etc. )
They also say that the money that we give you, we will need that back of course but along with an additional amount when you pay back. That additional money will be called an interest!
What’s an interest? Whatever amount you have to pay back, a percentage of it acts as an interest. If they give you 100 rupees, they might charge you an extra 10-20% depending on the bank as interest. So, in total you will need to pay 100+20= Rs. 120.
Interest is the place where the banks earn from, pay their employees and also how they give incentives to the customers who deposit their money with them.
Mathematics is required to calculate percentages and the amount of money that you have to repay to a bank as a business!
Let’s say, you have the money now taken from the bank and you have put everything into place, the construction is finished, theatre is ready, equipment is in place and people are also excited to watch movies in your theatre. Now the question is, when they come to buy a ticket- at what price should you sell the ticket for and why?
4. How much to charge people for one ticket?
You know that running a theatre is a costly business and you would want to recover the amount you have put into the business and also make a profit to get richer! But can you charge a lot? What would happen if you charge a lot?
How do you decide the cost of a ticket of a show? Discuss.
Many possible things to think about:
- Are people excited to watch that movie? (Is the demand high or low?)
- What are the competitors charging?
- What is it that’s new about your theatre?
- Are the customers getting any additional services?
- Position of the seat from the screen- better view from the back so higher cost.
Some movies are hit, some are flop!
Screenshot from the app book my show. Check out the prices for seats at the top vs seats at the bottom. You may ask them to check it in real time too using this website:
https://in.bookmyshow.com/explore/home/mumbai
Considering all such factors, the cost of a ticket is decided.
Let’s say it’s decided at Rs.200 roughly.
You have started your business now, tickets are selling. When do you expect to start making profits. How many tickets need to be sold to start making a profit? Remember, there is a loan that you have to pay aback along with interest.
A simple division gives you the number of tickets that you need to sell to pay back the loan:
If the loan amount was 1,00,00,000 at 10% per year, at the end of 1 year you need to pay back
1,00,00,000 + 10% of 1,00,00,000 which is 1,10,00,000 on total!
Each ticket is Rs. 200.
Hence, 1,10,00,000 divided by 200 gives you the total tickets needed to be sold in a year to just earn enough to pay back to the bank. The number comes out to 55,000 tickets!
How many full house shows does it mean? How would you calculate that?
Again a division: 55,000 divided by 150 tickets per house full show. The number comes out to 367 shows!
That seems feasible right? To calculate whether it is doable, you can again back-calculate the total number of shows in a year that you will be opening. If you have 3 shows in a day, how many shows will the theatre be showing in a year? (consider all day working)
Simple, 3 multiplied by 365. The number comes to 1,095 shows.
Out of those 1,095 shows, you just want to have 367 full house shows to at least pay back to the bank.
Of course, this was a very simple calculation and real life has a lot more complications, lot more costs to think of- For example salaries of people who work for you, maintenance costs, taxes that have to be paid to the government and a lot of other things!
Mathematics helps us think about everything by sitting and working on a piece of paper. Whether the business looks like a feasible idea or not, mathematics can offer lot of insights!
Conclusion:
Every business requires a lot of basic mathematics, from thinking about the expenses, salaries, inventory to be purchased, profit margins, losses, interests, loans, areas, volumes, time, length etc. As a budding entrepreneur, the better the hold you have on your arithmetic, the better your chances to join the big leagues!
