Final answer:
Closing the Rhode Island store would lead to a net gain in operating income of $32,000 due to the avoidance of variable costs and a reduction in overhead. Opening an additional store with the same financials would not be advisable as each store operates at a loss. The decision is based on an analysis of operating income, variable costs, and corporate overheads.
Step-by-step explanation:
The question asks us to analyze a business decision for a Yoga Center with respect to its operating income, which involves understanding the impact of closing or opening a store on the company's finances.
If the Rhode Island store is closed, the center's revenues will be $0, but it will also not incur any variable costs. The only cost would be the fixed costs of $10,000, but the company will save $42,000 in corporate overhead costs. Therefore, operating income, in this case, would be a negative $10,000 plus the $42,000 saved, resulting in a net gain of $32,000.
On the other hand, if the store remains open, and another identical store is opened, the overall operating income would be additionally impacted by the revenues and costs of the new store, including the $18,000 equipment cost with no salvage value and a $2,000 increase in corporate overhead costs. Assuming the new store has identical financials to the Rhode Island store, with $10,000 in revenue and $15,000 in variable costs, each store would operate at a loss before considering the overhead savings or additional costs.