Priya and Jenna T-shirt shop flourished
Priya had worked hard at her mother Jenna’s T-shirt shop. With her diligence and effort, the business flourished to the extent that now her mother made Priya an equal partner in the business. Naturally then, now Jenna relied heavily on this young girl for all aspects of the shop.
Sara was in the third year of a four year degree program at a university away from home when she got a call from Priya. Sara was surprised because she didn’t think that she and Priya were that close. She remembered helping Priya once or twice at school and her being super-impressed with the help she got. Sara took the call. They exchanged pleasantries after which the conversation continued.
Priya: I called you because I hadn’t talked to you for a while. Also, we have a special meeting for Jenna and Priya’s T-shirt shop. I am inviting you to come because it was your suggestions that made us grow.
Sara: Thanks for the big honour but as I told you earlier, your success was all due to your entrepreneurship. I didn’t do anything.
Priya twisted Sara’s arm and invited her
Priya: There you go with your modesty again. Our shop will send you the airline ticket if you agree to come and do your same type of nothing again. We have to make a major decision for which we want your opinion. I know that you are in the middle of the semester but you must be missing your Nana. You will get to see her too. How about if you come on the Saturday evening, spend the Sunday here and then go back on the Monday morning? Will that work? I will send you the ticket and also pick you up here at the airport.
Sara was overwhelmed with Priya’s approach but still accepted the invitation and boarded the plane. The flight was short and uneventful. Priya picked her up. Sara wanted to know what the urgency was but was told to go home and relax first, chat with Nana and have a good time. They set up their meeting at Sara’s home for 9 am the next morning. As expected Priya came in the next morning. They exchanged greetings and the conversation continued.
Future of the T-shirt shop and the patent
Priya: The main issue is the future of our T-shirt shop. I value your opinion and your way of thinking makes me comfortable. I am inviting you to come over for the dinner meeting we are having this evening. You, mom, I and two other persons will be at this dinner. The two persons are our patent lawyer and his friend John Q.
Sara: Okay. So what’s happening?
Priya: I think you remember that you helped me with the school fashion show. I also told you how I was super impressed with the pictures from the Trig functions in polar co-ordinates. From these ideas, our shop got someone to make a software to be used by our customers to create their own unique designs to be printed on their T-shirts. We have a utility patent pending on using the software to create these T-shirt designs.
Sara: Yes. I remember all that. Go on.
Priya: It’s been four years and now we have a steady business. We just wanted to celebrate it with a dinner but suddenly our patent lawyer invited one of his friends John Q. John Q works for the Boondoggle – the humungous clothing conglomerate. Apparently Boondoggle people have learned about our patent. Our patent lawyer hasn’t said so but I guess John Q is here to see where we stand. It gives me shivers to think that someone from a multibillion dollar company is here. What does he want? Does he want our patent? I don’t know. My mom is terrified and we don’t know what to do. I already told you how much I value your opinion. My mom thinks you are really smart, and she asked me to call you as our saviour. We will appreciate as much guidance from you as possible.
Sara: Here, calm down. I will get you a cold drink. What does your mom think? It is a family business. How do I fit in? You and your mom have to decide everything. What kind of data do you have about the future outlook of the market?
Priya: Nothing. We don’t even have any future projections of our business – just the past records.
Sara visits Johnny’s parents
Sara: Interesting. I am taking a business course. This is the type of issues why I took the course because it relates to stats. We haven’t covered the topic of licensing patents but we will get to it towards the end of the course. Let me think about it. For now, I want to go to my boyfriend Johnny’s mom and dad for lunch even though Johnny is not in town. His parents are always happy to see me, and I like them too. Besides, you know that Johnny’s dad has a lot of business experience. He might have some ideas.
Priya: Can I come with you?
Sara: No. It would be strange if you suddenly showed up but I am expected to visit them when I am in town. Besides, it’s not good for your shop if others find out what’s going on.
Priya: You are right. This may start false rumors about our shop shutting down. You’re not going to talk to them about the shop, are you?
Sara: No. I will talk to them about my course. So how about if you, your mom and I meet at your shop at 3?
Priya left Sara’s place. Sara then went to have lunch at Johnny’s mom and dad’s house. They were pleasantly surprised to see her. She told them that she came home because she was homesick. They had lunch and talked for over an hour and then Sara left their house. Sara came home, did some quick reading from different sites on the Internet and then went to Jenna and Priya’s T-shirt shop. Priya re-introduced Sara to her mom Jenna.
Planning for the meeting
Jenna: Sara, I am so glad to see you. I am sure you are a star at your university too. Priya must have told you that as soon as our business got stable, we have to deal with a major concern.
Sara: Yes, Priya told me that but we did not discuss any numbers.
Jenna: Priya is good with numbers. She will tell you.
Priya: Last year, we sold about 30,000 shirts, our total revenue was $400,000, and the total income was about $120,000 which mom and I split evenly. I don’t expect it to change much in the next year.
Sara: What do you think is the total value of the store including your brand and all the equipment?
Priya: I would say that the equipment is worth around $250,000, and I will add $150,000 for being well known for the unique service we provide. I don’t know the value of the patent. We don’t have any capital to expand this business. Mom doesn’t think that we need it. She has a line of credit from the bank. We will use it only if needed.
Sara: One of the things they recommend is that you should consider the different scenarios with all the risk factors.
Priya: One of the major risk factors is that a company like Boondoggle developing a similar service. I don’t think it would be difficult for them. They have deep pockets.
Sara: What other competition do we need to think of?
Priya: There are two T-shirt shops 6-10 kilometers away from us. The same guy owns them. They could open a store near us. I think they have the money but they don’t have our unique service.
Jenna: No one knows when a Walmart opens up anywhere. They could undercut our business.
Priya: Mom, do you remember the flood about 10 years ago? It slowed down every business in town.
Sara: I didn’t mean for everyone to get all negative and scared. We are only talking about the different scenarios we should consider? Let’s list them first and then think of the odds for each one to get an overall picture. Let’s not make any commitments without talking to a professional. By the way, did your patent lawyer invite John Q under a confidentiality clause which would hold up in a court of law?
Jenna: We have no plans to change. The answer to your confidentiality clause question is yes.
Sara: Priya, good thing that I went for lunch with Johnny’s mom and dad. Don’t worry, your shop was not mentioned. They gave me three obvious additional scenarios to consider. These are: license Boondoggle to use your technology, sell the patent to Boondoggle, and sell the patent to Boondoggle with the provision of permitting you to continue using it at the current level for a limited period. So we can look at all of them.
Jenna: I would have never thought the last one. You can have your cake and eat it too!
Values of the different risk factors
Sara: First, let’s look at the values of the three risk factors we talked about. We don’t know the exact risk for any of them nor do we have the time to determine it but we do have our gut feelings. What do you think are the chances that someone will imitate your unique service in Year 1 which is the coming year.
Priya: May be 20 %. Do you agree mom?
Jenna: May be but our store will only lose some customers. We should still keep at least half of the customers even if we lose the benefit of our unique technology. So the chance of loss of income is only 10%.
Sara: Okay. So the odds are 0.8/1 that your unique service will survive for Year 1. If the same probability continues, the odds for survival of the unique service for year 2 are 0.8 x 0.8 or 0.64. The same way we can multiply by 0.8 to get the odds for the years 3,4,5 to be 0.51, 0.41 and 0.33, respectively. One can get the exact odds for the loss of income from these and the actual calculations are quite complex. But it’s clear that in year 5, the odds of survival of your unique service are about 0.33. That means that there is a 67% chance that you will not have the unique service and hence you will lose about 33% of your income which is roughly half of 67%.
Priya: The chance of another store opening nearby next year is no more than 5%. If another store were to open, our business may go down by only 20%. Then should we list the risk at 1%. I would you say the same thing for a Walmart opening up.
Sara: You can say that but the other store will not come in if a Walmart opens. Both will not happen. So I should say list the total risk due to competition of a new store as 1%. So, the odds for survival from this competition in year 1 are 0.99 which is quite good.
Jenna: A year with a bad flood may cut the business into half.
Sara: I checked once that historically the city gets a bad flood once every 20 years or so. Also, the effect of the flood will be only for that year. So I will put this risk at 5% but the loss of income at 2.5% per year. This would not be repeated year after year. I take it that the shop has flood insurance to protect its contents. I would say that the odds for survival from this risk are quite good. Remember these are only odds for a scenario. They do not include unique incidents that could change the business one way or the other. Nothing has actually happened. The most severe risk is that of the loss of technology. Let’s focus on that risk at this time.
Priya: Most of the risk comes from the loss of the unique service. Also, the patent is only pending. We may need to spend some money for its approval. We already figured that we cannot afford the scary scenario of no change of plans. Should we look at the licensing possibility?
Sara: In the licensing possibility they would give you a royalty.
Priya: They are big. They could use it for tens of thousands of T-shirts within the first year and then continue using it.
Sara: What would you ask them per shirt?
Priya: They may sell a shirt for $12-15 with a margin of $5 per shirt. So asking them for 10% of the margin would be reasonable – say 50 cents per shirt. What do you think mom?
Jenna didn’t know but agreed with this assessment.
Sara: We can make the assumption that they will use it for 100,000 shirts in the first year and give you 50 cents per shirt. Does your patent pertain only to the use of designs on T-shirts?
Priya: No our patent lawyer made sure that it was for all clothing and similar materials.
Basis of the proposal to Boondoggle
Sara: So, you have to convince John Q that the patent is of a broader use to Boondoggle. They have lines of T-shirts, neckties, socks, jackets, sweaters, lingerie and other items. So they would have to pay you royalties for use with any of the items.
Priya: Let’s say that they will pay us the same 50 cents per use for any item. I would think that they would use the license for sell 100,000 items the first year, and keep increasing the total number of items by 20% each year.
Sara: So would this mean a royalty of $50,000, 60,000, 72,000, 86,400 and 103680 for the years 1,2,3,4 and 5, respectively?
Priya: Yes. I like these numbers.
Sara: Not so fast. Remember, we said that the odds that the unique service will survive for years 1,2,3,4 and 5 were 0.8, 0.64, 0.51, 0.41 and 0.33, respectively. Why would Boondoggle pay you if they can get it for free or at a better cost elsewhere? They may have the license for your technology but not actually use it. Accordingly, the numbers for the expected royalty should be adjusted down to $40,000, 38,400, 36864,35389 and 33974 for years 1,2,3,4 and 5 respectively. That’s a total of $186,627.
Priya: That’s not as much as the other numbers I liked. So should we sell the patent to them instead?
Sara: If you sell it to them, tell them that their lawyers will have the advantage of blocking others from developing a similar technology, and that they themselves could modify it for their own use. For example, they could make an App for a wider use by online customers. Ask for $300,000 and settle for $200,000. But remember, in that case your store income will drop to about $60,000 per year immediately.
Priya: What about the possibility that Boondoggle will own the patent but allow us to use the unique service at our current level as part of the deal for 5 years?
Jenna: Why would they do that?
Sara: Quid pro quo. As a part of the bargain, you make them the offer that you will be happy to train someone from their company in how best to use and benefit from your unique service. Make this as a goodwill gesture to make them agree to the deal. Also, tell them that with this provision, you will drop the price of the patent by another $50,000.
Priya: Mom, isn’t she a fox? Sara, I think, mom will go for it if you tell her the full benefits of this deal.
Sara: The risk of someone else using your technology will decrease because Boondoggle lawyers will protect the patent. Let’s say, it will decrease annually from 20 % to 5 %. The odds that you will have the unique technology in year 5 will be 0.95 x 0.95 x 0.95 x 0.95 x 0.95 which is 0.77. That means that there is only a 23% chance of losing the unique service. This would come to a chance of the income loss of only 11.5 % in year 5 rather than the 33% with the plan of no change. You will also retain the competitive edge better. The money from the sale of the patent will increase your capital and the value of the company.
The business meeting
Jenna: So, let’s plan. Sara, what do you suggest?
Sara: Priya really knows how to trap people.
Priya: What do you mean?
Sara: You know that you are good at coercing people. You got me here on a two day’s notice. In the same one minute you asked me to come over, and also said that you would send me the plane ticket. How would you go about dealing with John Q? Be nice to him and a little less pushy.
Priya: I haven’t even met him. I will think of it at the dinner. If it turns out that he has any interest in the patent, I will request him to stay for another day. I will ask him to come watch what we do and how our system works. Then we can talk at the shop. I’ll ask him for advice, and also to teach me the meager teen girl about business dealings. How’s that?
Sara: Great. Jenna that’s the plan if you agree. Everybody should be comfortable but please don’t get too relaxed and ink the deal at the dinner. Get a professional to negotiate. Ask your patent lawyer about it.
Jenna: Thanks Sara.
Sara: Even if you get this deal, it’s only for 5 years. So you can’t afford to get too complacent. Priya would have to think of newer innovations for the shop to keep an edge over the competition.
Priya: I hope it will be with Sara’s help. I love working with you. It’s so comforting. I will drop you home and pick you up at 6:30 to go for the dinner.
They all had a nice dinner as planned and Priya convinced John Q to spend the next day with her at the shop. Throughout the dinner Priya and Jenna couldn’t help but continue admiring Sara for her modesty and for her helping them for the last four to five years.
Sara took her flight back to school the next morning.
John Q spent the day with Priya at the T-shirt shop and then left.
A month later, Boondoggle called Jenna
Lawyer: Hello Jenna. Is Priya there? I have good news for you. Boondoggle has agreed for a patent price of $150,000 with the conditions you wanted. They will let you use the technology at the level of a maximum of 40,000 shirts per year for the next 5 years with no carry over from year to year. They will send staff whom you will train. One person will work with you for 6 months. The second person will be a technology guy who will come for a few days to learn about your selection and the ordering systems. This is conditional to their talking to Sara because they think that she may have some undeclared rights. Can you please give me Sara’s contact?
Jenna: That’s great news. I want to make sure that Sara doesn’t mind talking to you because she doesn’t expect it. I will ask Priya to check with Sara and then give you the contact information.
Priya told Sara about the phone call. Sara was so thrilled for them and agreed to talk to the lawyer to release any rights.
The patent lawyer then called Sara.
Lawyer: At the dinner the other night, Priya convinced John Q that you had a hand in developing the technology of the Jenna and Priya’s T-shirt shop.
Sara: No. Priya came for some help with a school project and we chatted. I had fun showing her how Math could be used for arts and fashion. I will relieve them of any rights. Send me the papers to sign.
Lawyer: I wish I could convince John Q. He wants you to sign the rights off but will give you a cheque for $10,000 to make it official. This is on top of the $150,000 that the T-shirt shop would get.
Sara: Thanks, as a student I could use the money. Please, send the papers to sign.
Lawyer: Yes. Then I will send you the papers
Sara phoned Priya about the call from John Q.
Priya: When you came here, you admonished me for my complacency. I have decided to buy a 3-D printer and develop a new service for our shop.
Sara: Way to go! I will have to see that service when I come. Bye for now.
Challenge
Aron, age 14 was a very good base ball player, may be even one of the best in his team. He was now going to enter grade 9. His dad was trying to convince Aron that he may have to study a little bit harder in high school. Aron argued that he didn’t have to study harder because he would become a major league baseball player (MLB) with a salary of millions of dollars per year. Because Aron was so adamant, his dad asked Aron what he thought were the odds that he would be selected in the school baseball team. Aron countered around 0.8:1 (80% chance). His dad showed him a baseball magazine that showed that in high school the odds of a starting baseball player entering the senior baseball team were only 0.28:1. From there, the odds for these athletes getting into a freshman NCAA team were only 0.14 and then only 70% (odds 0.7:1) of these athletes became senior NCAA athletes. Only 10% (odds 0.1:1) of the senior NCAA athletes were drafted into the MLB. When in MLB, only 15% (0.15:1) of them made it to the level of getting over a million dollar a year contract. Then together they figured out the odds of Aron making million dollar salaries in MLB. What do you think these odds were? Express them as a fraction of 1 and as a percent chance.
Solution: The overall odds of a number of sequential events are the product of odds of success at each stage. Aron would have to be selected for the school team for which the odds are around 0.8:1. If selected he would have to enter the senior baseball team for which the odds are 0.28:1. From there, his odds getting into a freshman NCAA team would be 0.14:1 and then 0.7:1 of becoming a senior NCAA athlete. Once he has reached this stage, the odds for being drafted are 0.1:1. If drafted the odds for getting the over a million dollar a year contract would be 0.15:1. From these since Aron his not even in the high school team yet, his overall odds for obtaining over a million dollar contract would be:
0.8 x 0.28 x 0.14 x 0.7 x 0.1 x 0.15 = 0.00032: 1 = 0.032 %.
Math Stories For You 