. In its first year, “Abol buna” Company had the following experience.
Sales = 25,000 units Selling price = Birr 100
Total variable cost = Birr 1,500,000 TFC = Birr 350,000
Required:
Develop revenues, cost, and profit functions for the company in terms of quantity.
Find the break-even point in terms of quantity.
Find the break-even revenue.
If profit had been Birr 500,000 what would have been the sales volume (revenue) and the quantity of sales.
What would have been the profit if sales were Birr 2,000,000?
Well, well, well, let's dive into the numbers and crunch some calculations, shall we?
First things first, let's develop the revenue function. Revenue is simply the product of the selling price and the quantity sold. So, the revenue function in terms of quantity (Q) is:
Revenue = Selling price * Quantity
Plugging in the given values, we get:
Revenue = 100 * Q
Now, let's move on to the cost function. Total variable cost (TVC) is given as Birr 1,500,000. The variable cost per unit is TVC divided by the number of units sold. So, the variable cost per unit (VCu) is:
VCu = TVC / Quantity
Plugging in the given values, we get:
VCu = 1,500,000 / 25,000
Next, we can calculate the total fixed cost (TFC), which is given as Birr 350,000.
The cost function in terms of quantity (Q) is:
Cost = VCu * Quantity + TFC
Plugging in the values we calculated earlier, we get:
Cost = (1,500,000 / 25,000) * Q + 350,000
Finally, let's find the break-even point in terms of quantity. The break-even point is where the revenue equals the cost, so we can set the revenue and cost functions equal to each other:
100 * Q = (1,500,000 / 25,000) * Q + 350,000
Solving for Q, we find:
Q = 25,000 units
Now, let's find the break-even revenue. We can plug the break-even point (25,000 units) into the revenue function:
Break-even Revenue = 100 * 25,000
And voila, the break-even revenue is Birr 2,500,000.
Now, let's move on to the next scenario. If the profit had been Birr 500,000, we can set the profit function equal to 500,000 and solve for the sales volume (revenue) and quantity of sales:
Profit = Revenue - Cost
500,000 = 100 * Q - [(1,500,000 / 25,000) * Q + 350,000]
Solving for Q, we find:
Q = 32,000 units
Plugging this value into the revenue function, we find:
Sales Volume (Revenue) = 100 * 32,000
Now, for the last scenario, if sales were Birr 2,000,000, we can plug this value into the revenue function:
Profit = 2,000,000 - [(1,500,000 / 25,000) * Q + 350,000]
Remember, my dear friend, profit is revenue minus cost. So, go ahead and calculate that profit.
I hope this adds a dash of humor to your number-crunching adventure!
To develop the revenue, cost, and profit functions in terms of quantity, we need to understand a few concepts:
1. Sales Revenue: This is the total income generated from selling a specific number of units. It is calculated by multiplying the selling price per unit by the quantity sold.
Sales Revenue = Selling Price * Quantity
In this case, the selling price is Birr 100 per unit, and the quantity sold is given as 25,000 units. Therefore, the Sales Revenue function can be expressed as:
Revenue = 100 * Quantity
2. Total Variable Cost (TVC): This is the total cost that varies with the number of units produced or sold. To calculate the TVC, we need to know the variable cost per unit and multiply it by the quantity.
TVC = Variable Cost per Unit * Quantity
The variable cost is not provided directly, but we are given the total variable cost (TVC) as Birr 1,500,000. The quantity is given as 25,000 units. Therefore, we can express the Total Variable Cost function as:
TVC = (1,500,000 / 25,000) * Quantity
3. Total Fixed Cost (TFC): This is the cost that remains constant regardless of the number of units produced or sold.
TFC = Birr 350,000
4. Profit: Profit is the difference between the total revenue and the total cost (variable and fixed). It is calculated by subtracting the total cost from the total revenue.
Profit = Revenue - Total Cost (Variable Cost + Fixed Cost)
Now let's answer the specific questions:
1. Break-Even Point in terms of quantity:
The break-even point is the sales volume at which the company neither makes a profit nor incurs a loss. In other words, the revenue equals the total cost (fixed and variable costs). To find the break-even point in terms of quantity, we set the profit equal to zero and solve for the quantity.
Revenue - Total Cost = 0
Using the earlier equations, we substitute Revenue and Total Cost:
100 * Quantity - ((1,500,000 / 25,000) * Quantity + 350,000) = 0
Simplifying the equation, we get:
100 * Quantity - 60 * Quantity - 350,000 = 0
Combining similar terms, we have:
40 * Quantity = 350,000
Solving for Quantity:
Quantity = 350,000 / 40
Therefore, the break-even point in terms of quantity is 8,750 units.
2. Break-Even Revenue:
The break-even revenue is the total income required to cover all the costs (variable and fixed costs) and result in zero profit. To find the break-even revenue, we can substitute the break-even quantity (8,750 units) into the Revenue function:
Revenue = 100 * 8,750
Therefore, the break-even revenue is Birr 875,000.
3. If the profit was Birr 500,000:
To find the sales volume (revenue) and quantity of sales that would result in a profit of Birr 500,000, we can set the Profit equal to 500,000 and solve for Quantity and Revenue:
100 * Quantity - ((1,500,000 / 25,000) * Quantity + 350,000) = 500,000
Simplifying the equation, we have:
100 * Quantity - 60 * Quantity - 350,000 = 500,000
Combining similar terms, we get:
40 * Quantity = 850,000
Solving for Quantity:
Quantity = 850,000 / 40
Substituting the found quantity into the Revenue function:
Revenue = 100 * (850,000 / 40)
Therefore, the sales volume (revenue) would be Birr 2,125,000, and the quantity of sales would be 21,250 units.
4. If the sales were Birr 2,000,000:
To find the profit when the sales are Birr 2,000,000, we can substitute the sales volume (revenue) into the Profit function:
Profit = 2,000,000 - ((1,500,000 / 25,000) * Quantity + 350,000)
Substituting the known values:
Profit = 2,000,000 - ((1,500,000 / 25,000) * (2,000,000 / 100) + 350,000)
Calculate the above equation to find the profit.
Please note that the profit is calculated differently based on the given information and the specific case. Adjustments may be required based on the provided formulas and equations.
To develop revenues, cost, and profit functions for the company in terms of quantity, we need the following information:
Sales = 25,000 units
Selling price = Birr 100
Total variable cost = Birr 1,500,000
TFC = Birr 350,000
1. Revenues function:
Revenues = Sales * Selling price
Revenues = 25,000 * 100
Revenues = Birr 2,500,000
2. Total variable cost function:
Total variable cost = Total variable cost per unit * Sales
Total variable cost per unit = Total variable cost / Sales
Total variable cost per unit = Birr 1,500,000 / 25,000
Total variable cost per unit = Birr 60 per unit
Total variable cost function: Total variable cost = Birr 60 * Sales
3. Fixed cost function:
Fixed cost = TFC = Birr 350,000
4. Profit function:
Profit = Revenues - Total variable cost - Fixed cost
Profit = Birr 2,500,000 - (Birr 60 * Sales) - Birr 350,000
To find the break-even point in terms of quantity, we need to find the sales volume where the profit is zero.
Break-even point:
0 = Birr 2,500,000 - (Birr 60 * Sales) - Birr 350,000
Solving the equation for Sales:
60S = 2,500,000 - 350,000
60S = 2,150,000
S = 35,833 units
Therefore, the break-even point in terms of quantity is 35,833 units.
To find the break-even revenue, we can use the break-even quantity and selling price.
Break-even revenue:
Break-even revenue = Selling price * Break-even quantity
Break-even revenue = Birr 100 * 35,833
Break-even revenue = Birr 3,583,300
Therefore, the break-even revenue is Birr 3,583,300.
If the profit had been Birr 500,000, we can use the profit function to find the sales volume (revenue) and quantity of sales.
Birr 500,000 = Birr 2,500,000 - (Birr 60 * Sales) - Birr 350,000
Solving the equation for Sales:
60S = 2,500,000 - 350,000 - 500,000
60S = 1,650,000
S = 27,500 units
Therefore, if the profit had been Birr 500,000, the sales volume would have been 27,500 units and the quantity of sales would be the same.
To find the profit if sales were Birr 2,000,000, we can substitute the sales value into the profit function.
Profit = Birr 2,000,000 - (Birr 60 * Sales) - Birr 350,000
Profit = Birr 2,000,000 - (Birr 60 * 2,000,000) - Birr 350,000
Let's calculate it:
Profit = Birr 2,000,000 - (Birr 120,000,000) - Birr 350,000
Profit = Birr -118,350,000
Therefore, if sales were Birr 2,000,000, the profit would be Birr -118,350,000.