Sue runs a small independent bookshop. She pays a lease of $20,000 per year. Each year, she earns revenues of $100,000, and her cost of goods (and other operating expenses) is $10,000 per year.
If she were not running the store, she would instead work in a local bookshop and earn a salary of $40,000 per year.
It is currently the beginning of 2010. She has not yet paid any of her expenses for 2010. She learns that in one year's time (at the beginning of 2011), the lease on the store will increase and so it will no longer be profitable for her to run the store. The store will have no value at that time.
At the beginning of 2010, a potential buyer (Buyer A) approaches Sue with an offer for the store.
What is the minimum price that she should accept? (For this question and all following questions, assume she will accept an offer that leaves her equally happy with either option
Q 1: What is the minimum price that she should accept? (You can assume she will accept an offer that leaves her equally happy with either option.)
Q 2: Suppose Sue has already signed her lease, and cannot get this money refunded. (However, she can allow Buyer A to use the premises.) What is the minimum offer she should accept?
Q 3: For this and all future questions, suppose that Sue has not yet signed the lease. However, now suppose that Sue faces uncertainty about her cost of goods. She thinks that: there is a 50% chance that her cost of goods in 2010 will be $10,000 and there is a 50% chance that her cost of goods will be $20,000.
Assuming that Sue is risk-neutral, what is the minimum price that she should accept for the store (as before, at the beginning of 2010)?
Q4: Go back to the assumption that the cost of goods is $10,000. However, Sue now thinks that she might get another offer (Offer B) for the store next week. She thinks there is a 50% chance that she will receive an offer of $20,000, and a 50% chance that she will receive an offer of $40,000. She has to decide on the current offer (A) before she knows about the offer (B) next week. What is the minimum price for the store that she should be willing to accept now
Q 5: Suppose that Sue also values being her own boss. Specifically, she places a value of $10,000 on this aspect of her job. Go back to the original situation (Question 5). What is the minimum price she should accept for the store?
Q6: Suppose Sue values being her own boss at $10,000, and we are in the situation of Question 8 (she might get an Offer B next week). What is the minimum Offer A she should accept?