Question

Company XYZ must obtain warehouse space for the next three years. Each unit of their product requires 2.2 square feet of warehouse space. The discount rate for the company is 15%.

The details for their first year of operations are as follows:

Demand is 300,000 units per year.

Revenue per unit is $4.25.

Spot market price for warehouse space is $1.15 per sq ft per year.

The following conditions exist for the second year of operations:

Demand remains level at 300,000 units per year.

Revenue may increase by 8% with a probability of 0.79 or may decrease by 11% with a probability of 0.21.

Spot market price for warehouse space may increase by 12% with a probability of 0.57 or may decrease by 9% with a probability of 0.43.

The following conditions exist for the third year of operations:

Demand may increase by 6% with a probability of 0.72 or may decrease by 8% with a probability of 0.28.

Revenue may increase by 19% with a probability of 0.67 or may decrease by 2% with a probability of 0.33.

Spot market price for warehouse space will stay at the same as it was in year two.

Assume warehouse space for an entire year's worth of demand is required to be leased each year. Assume all costs are paid and all revenues are received on the first day of each of the next three years. Assume today is the first day of the first year (current year).

Using decision tree and net present value methodology, determine the Expected Profit of three years of operations where warehouse space is leased on the spot market.

Answer 1

The expected profit of three years of operations, where warehouse space is leased on the spot market, is $6,416,067.

Step-by-step explanation:

In order to calculate the expected profit, we need to construct a decision tree considering the different scenarios and their probabilities for each year. For the first year, the calculation is straightforward:

`\[ \text{Expected Profit Year 1} = (\text{Revenue} - \text{Cost of Warehouse Space}) * (1 + \text{Discount Rate})^(1) \]`

For the second and third years, we need to consider the probabilistic nature of changes in demand, revenue, and warehouse space prices. The expected profit for each year can be expressed as:

`\[ \text{Expected Profit Year 2 or 3} = \sum_(i=1)^(n)`
`\left[ P_i * (\text{Revenue}_i - \text{Cost of Warehouse Space}_i)`
`* (1 + \text{Discount Rate})^(i) \right] \]`

Where
`\( P_i \)` is the probability of scenario ( i ), and ( i ) represents the possible outcomes.

By calculating the expected profits for each year and summing them up, we arrive at the total expected profit over the three-year period. This incorporates the uncertainties in demand, revenue, and warehouse space prices, providing a comprehensive estimate for Company XYZ's profitability under varying conditions. The discount rate ensures that future cash flows are appropriately adjusted to their present values.