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The St
The St. Thomas Winery plans to open a new production facility in the Napa Valley of California. Based on information provided by the accounting department, the company estimates fixed costs of $250,000 per year and average variable costs of AVC = $10 + $0.01Q, where AVC is average variable cost (in dollars) and Q is output measured in cases of output per year.
a. Estimate total cost and average total cost for the coming year at a projected volume of 4,000 cases.
b. An increase in worker productivity because of greater experience or learning during the course of the year resulted in a substantial cost saving for the company. Estimate the effect of learning on average total cost if actual total cost was $522,500 at an actual volume of 5,000 cases.
Expert Solution
The fixed estimated cost of new production is $250,000 and the average variable cost is:
AVC = $10 + $0.01Q
where Q = Output
(a)
The total cost (TC) and average total cost (ATC) at quantity 4,000 can be calculated as:
TC = FC + VCTC = $250,000 + $10Q + $0.01Q2TC = $250,000 + $10 × 4,000 + 0.01 × 4,0002TC = $450,000TC = FC + VCTC = $250,000 + $10Q + $0.01Q2TC = $250,000 + $10 × 4,000 + 0.01 × 4,0002TC = $450,000
Average total cost at 4,000 quantities is:
ATC =TCQATC =$450,0004,000ATC = $112.5ATC =TCQATC =$450,0004,000ATC = $112.5
(b)
With greater productivity, the total cost was $522,500 at volume of 5,000 cases. The effect of learning on average total cost (AC) can be calculated as:
Learning effect = Actual AC - Estimated AC
The estimated average cost at 5,000 cases is:
AC =TCQAC =$522,5005,000AC = $104.5AC =TCQAC =$522,5005,000AC = $104.5
The estimated average cost at 5,000 cases is:
TC = $250,000 + $10 × 5,000 + 0.01 × 5,0002TC = $550,000AC =550,0005,000AC = $110TC = $250,000 + $10 × 5,000 + 0.01 × 5,0002TC = $550,000AC =550,0005,000AC = $110
Learning effect = $104.5 - $110
Learning effect = - $5.5 per case
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