Problem #$1(35$ Points$)$

Consider that U$-$Haul is offering to store ergonomic chairs for Hardrockers Medical Furniture Company.

The manager of U$-$Haul has to decide whether to lease fixed amount of warehouse space for two years

and get additional space from the spot market.

Demand Uncertainty$-$ The current demand at U$-$Haul is for $200,000$ units per year. The manager

forecasts that from one year to the next, demand may go up by $25$ percent, with a probability of $0\mathrm{.}6,$ or go

down by $25$ percent, with a probability of $0\mathrm{.}4.$ The probabilities of the two outcomes are independent and

unchanged from one year to the next.

Spot Market Uncertainty$-$ Storage space is currently available on the spot market for $$2\mathrm{.}20$ per square

foot per year. From one year to the next, spot prices for storage space may go up by $20$ percent, with

probability $0\mathrm{.}9,$ or go down by $20$ percent, with probability $0\mathrm{.}1.$ The probabilifies of the two outcomes are

independent and unchanged from one year to the next.

Determine the Net Present Value$($NPV$)$ if U$-$Haul were to sign a two$-$year lease

warehouse space $(200,000sq.ft)$ and get additional requirements from the spot narket as needed. The two$-$year

lease makes available $200,000$ sq$.$ft at $$2$ per square foot per year. Draw the decision tree diagram as part of

your solution. Each unit U$-$Haul handles results in revenue of $$2\mathrm{.}22,$ and U$-$Haul is committed to handling all

demand that arises. U$-$Haul uses a discount rate of $k=0\mathrm{.}2$ for each of the two years. Assume $1,000$ sq$.$ft of

storage space is required for every $1,000$ units of demand.