Mr.Kedir milk manufacturing company has started producing and selling a product. In its first year it has the following operations:
Unit selling price--------Birr 2.00
Unit variable cost--------Birr 1.25
Total revenue------------Birr 550,000
Total cost ----------------75% of total revenue
Assuming linearity, answer the following
What is the amount of fixed cost?
Develop total revenue, total cost and total profit functions in terms of quantity.
To find the amount of fixed cost, we can use the contribution margin formula:
Unit selling price - unit variable cost = contribution margin
Birr 2.00 - Birr 1.25 = Birr 0.75
Contribution margin ratio = contribution margin / unit selling price = Birr 0.75 / Birr 2.00 = 0.375
The contribution margin ratio represents the portion of each sale that contributes towards covering the fixed costs and generating profit. We can use this ratio to find the fixed cost:
Fixed cost = (total revenue x (1 - contribution margin ratio)) / contribution margin ratio
Fixed cost = (Birr 550,000 x (1 - 0.375)) / 0.375 = Birr 733,333.33
To develop the total revenue function, we can use the formula:
Total revenue = unit selling price x quantity
Total revenue = Birr 2.00q
To develop the total cost function, we can use the information given in the question:
Total cost = 75% of total revenue
Total cost = 0.75(Birr 2.00q) = Birr 1.50q
To develop the total profit function, we can use the formula:
Total profit = total revenue - total cost
Total profit = Birr 2.00q - Birr 1.50q = Birr 0.50q
Therefore, the total revenue function is Birr 2.00q, the total cost function is Birr 1.50q, and the total profit function is Birr 0.50q.
To find the amount of fixed cost, we need to subtract the total variable cost from the total cost.
Total variable cost = Unit variable cost x Quantity
Total variable cost = Birr 1.25 x Quantity
Total cost = Total revenue - Total variable cost
Total cost = Birr 550,000 - (Birr 1.25 x Quantity)
But we are given that the total cost is 75% of the total revenue.
Thus, Total cost = 75% x Total revenue
Therefore, we can write the equation as:
Birr 550,000 - (Birr 1.25 x Quantity) = 75% x Birr 550,000
Simplifying the equation, we get:
Birr 550,000 - Birr 1.25 x Quantity = 0.75 x Birr 550,000
Now, let's solve for Quantity:
Birr 550,000 - Birr 1.25 x Quantity = Birr 412,500
Birr 1.25 x Quantity = Birr 550,000 - Birr 412,500
Birr 1.25 x Quantity = Birr 137,500
Quantity = Birr 137,500 / Birr 1.25
Quantity = 110,000 units
Now, we can substitute the value of Quantity back into the equation for Total cost:
Total cost = Birr 550,000 - (Birr 1.25 x 110,000)
Total cost = Birr 550,000 - Birr 137,500
Total cost = Birr 412,500
The amount of fixed cost is the difference between the total cost and the total variable cost:
Fixed cost = Total cost - Total variable cost
Fixed cost = Birr 412,500 - (Birr 1.25 x 110,000)
Fixed cost = Birr 412,500 - Birr 137,500
Fixed cost = Birr 275,000
Therefore, the amount of fixed cost is Birr 275,000.
Now let's develop the total revenue, total cost, and total profit functions in terms of quantity:
Total revenue = Unit selling price x Quantity
Total revenue = Birr 2.00 x Quantity
Total cost = Fixed cost + Total variable cost
Total cost = Birr 275,000 + (Birr 1.25 x Quantity)
Total profit = Total revenue - Total cost
Total profit = Birr 2.00 x Quantity - (Birr 275,000 + Birr 1.25 x Quantity)
Simplifying further, we get:
Total profit = Birr 0.75 x Quantity - Birr 275,000