XYZ company’s cost function for the next four months is
C = 500,000 + 5Q
a) Find the BE dollar volume of sales if the selling price is br. 6 / unit
b) What would be the company’s cost if it decides to shutdown operations for
the next four months
c) If, because of strike, the most the company can produce is br. 100,000
units, should it shutdown? Why or why not?
(a) BE is when cost = revenue, so
500,000+Q = 6Q
(b) C(0) = 500,000
(c) is 6*100,000 >= C(100,000)?
a) To find the breakeven dollar volume of sales, we need to equate the cost with the revenue and solve for Q:
Cost (C) = 500,000 + 5Q
Revenue = Selling Price (P) * Quantity Sold (Q)
Since we know the selling price is br. 6/unit, the revenue equation can be written as:
Revenue = 6Q
Setting the cost equal to the revenue, we get:
500,000 + 5Q = 6Q
To solve for Q, we subtract 5Q from both sides:
500,000 = Q
The breakeven quantity (Q) is br. 500,000.
To find the breakeven dollar volume of sales, we multiply this quantity by the selling price:
Breakeven Dollar Volume of Sales = breakeven quantity * selling price
Breakeven Dollar Volume of Sales = 500,000 * 6 = br. 3,000,000
Therefore, the breakeven dollar volume of sales is br. 3,000,000.
b) If the company decides to shutdown operations for the next four months, it means they will not produce any units. Hence, the cost would be zero:
Cost = 500,000 + 5(0) = 500,000
Therefore, the company's cost would be br. 500,000 if it decides to shutdown operations for the next four months.
c) If the company can produce a maximum of br. 100,000 units due to a strike, we need to calculate the total cost for producing these units:
Cost = 500,000 + 5Q
Plugging in Q = 100,000:
Cost = 500,000 + 5(100,000)
Cost = 500,000 + 500,000
Cost = br. 1,000,000
Since the cost of producing the maximum units is br. 1,000,000 and the company's cost if it shuts down is br. 500,000, it would be more cost-effective for the company to continue operations and produce the limited quantity of 100,000 units.
a) To find the break-even (BE) dollar volume of sales, we need to determine the quantity (Q) at which the total revenue (TR) equals the total cost (TC). Since we are given the cost function C = 500,000 + 5Q, we also need the revenue function.
The revenue function can be found by multiplying the selling price (P) by the quantity (Q):
TR = P * Q
Given that the selling price is br. 6 per unit, we can substitute it into the revenue function:
TR = 6Q
Setting the revenue equal to the cost, we get:
TR = TC
6Q = 500,000 + 5Q
Subtracting 5Q from both sides:
Q = 500,000
Therefore, the break-even dollar volume of sales is br. 500,000.
b) If the company decides to shut down operations for the next four months, it would not incur any variable costs during that time. However, it would still need to cover its fixed costs.
With the given cost function C = 500,000 + 5Q, we need to determine the cost when Q is zero (assuming no production):
C = 500,000 + 5 * 0
C = 500,000
Therefore, the company's cost if it decides to shut down operations for the next four months would be br. 500,000.
c) To evaluate whether the company should shut down due to a strike, we need to compare the cost of production with the potential revenue.
Given that the most the company can produce is br. 100,000 units, we can calculate the cost of production by substituting this value into the cost function:
C = 500,000 + 5 * 100,000
C = 500,000 + 500,000
C = 1,000,000
To assess if the company should shut down, we compare the cost of production (br. 1,000,000) with the potential revenue. As we do not have information regarding the selling price during the strike, we are unable to make a definitive decision. If the potential revenue from selling the 100,000 units is higher than the cost of production, it may be more beneficial for the company to continue operations.