Question

Trips Logistics manager considers signing a flexible lease with a minimum charge that allows variable usage of warehouse space up to a limit, with additional requirements from the spot market. The general manager at Trips Logistics has been offered a contract in which, for an upfront payment of $20,000, Trips Logistics will have the flexibility of using between 80,000 square feet and 100,000 square feet of warehouse space at $1 per square foot per year. Trips Logistics must pay $80,000 per year for up to the first 80,000 square feet and can then use up to another 20,000 square feet on demand at $1 per square foot. One thousand square feet of warehouse space is required for every 1,000 units of demand, and the current demand at Trips Logistics is for 90,000 units per year.

The manager forecasts that from one year to the next, demand may go up by 20 percent, with a probability of 0.4, or go down by 20 percent, with a probability of 0.6. The probabilities of the two outcomes are independent and unchanged from one year to the next. Warehouse space is currently available on the spot market for $1.40 per square foot per year. From one year to the next, spot prices for warehouse space may go up by 10 percent, with probability 0.5, or go down by 10 percent, with probability 0.5. The probabilities of the two outcomes are independent and unchanged from one year to the next. The general manager believes that prices of warehouse space and demand for the product fluctuate independently. Each unit Trips Logistics handles results in revenue of $1.3, and Trips Logistics is committed to handling all demand that arises. Trips Logistics uses a discount rate of k=0.2. The lease agreement spans two years (T=0, T=1). What is the expected profit with this lease option? Draw the decision tree and show your calculations.

Answer 1

The expected profit with the lease option can be calculated using a decision tree and the given information about demand, spot market prices, and lease terms.

Step-by-step explanation:

The expected profit with this lease option can be calculated by creating a decision tree using the given information. At time T=0, Trips Logistics has the option to sign the flexible lease contract with an upfront payment of $20,000. At time T=1, demand can either increase by 20% or decrease by 20% with probabilities 0.4 and 0.6 respectively. The spot market price for warehouse space can either go up by 10% or go down by 10% with probabilities 0.5 and 0.5. Using this information and the given revenue and cost data, we can calculate the expected profits at each branch of the decision tree and multiply them by their respective probabilities to find the overall expected profit over the two-year lease period.