2. In its first year, “Abol Buna Company” had the following experience
Sales = 25,000 units Selling price = Birr 100
TVC = Birr 1,500,000 TFC = Birr 350,000
Required:
a) Develop revenue, cost and profit functions for the company in terms of quantity.
b) Find the Breakeven point in terms of quantity
c) Convert the cost equation in terms of quantity into a cost equation in terms of revenue
d) Find the Breakeven revenue
e) If profit had been Birr 500,000 what would have been the sales volume (revenue) and the quantity of sales.
f) What would be the profit if sales were Birr 2,000,000?
To solve the given problem, we need to understand some basic concepts and formulas related to revenue, cost, and profit functions.
a) Revenue Function:
The revenue function represents the total income from selling a certain quantity of units. It is calculated by multiplying the quantity of units sold (Q) by the selling price (SP) per unit. In this case, the selling price is Birr 100. Therefore, the revenue function is:
Revenue Function = Q * SP
Revenue Function = Q * 100
Cost Function:
The cost function represents the total cost incurred by the company to produce and sell the given quantity of units. It consists of two components: total variable cost (TVC) and total fixed cost (TFC). The total fixed cost remains constant, while the total variable cost depends on the quantity of units produced and sold. Therefore, the cost function is:
Cost Function = TVC + TFC
Cost Function = (Q * TVC per unit) + TFC
In this case, the TVC is Birr 1,500,000, the TFC is Birr 350,000.
Profit Function:
The profit function represents the difference between revenue and cost. It is calculated by subtracting the cost function from the revenue function. Therefore, the profit function is:
Profit Function = Revenue Function - Cost Function
Profit Function = (Q * 100) - [(Q * TVC per unit) + TFC]
b) Breakeven Point in terms of quantity:
The breakeven point is the quantity of units sold at which the revenue function equals the cost function, resulting in zero profit. To find the breakeven point in terms of quantity, we need to set the profit function equal to zero and solve for Q. Using the profit function obtained in part (a), we have:
(Q * 100) - [(Q * TVC per unit) + TFC] = 0
Simplifying the equation, we get:
Q * (100 - TVC per unit) = TFC
Q = TFC / (100 - TVC per unit)
Substituting the given values, we can find the breakeven point in terms of quantity.
c) Converting the Cost Equation in terms of quantity into a Cost Equation in terms of revenue:
To convert the cost equation in terms of quantity into a cost equation in terms of revenue, we need to substitute the revenue function into the cost function obtained in part (a). The revenue function is Q * 100. Therefore, the cost equation in terms of revenue is:
Cost Equation (in terms of revenue) = (Q * TVC per unit) + TFC
Cost Equation (in terms of revenue) = (100 * Revenue) / 100 + TFC
d) Breakeven Revenue:
The breakeven revenue is the revenue at which the profit function becomes zero, resulting in zero profit. To find the breakeven revenue, we need to substitute Q = (Breakeven Quantity) into the revenue function obtained in part (a). Therefore, the breakeven revenue is:
Breakeven Revenue = (Breakeven Quantity) * 100
e) Finding Sales Volume (Revenue) and Quantity of Sales when Profit is Birr 500,000:
To find the sales volume (revenue) and quantity of sales when the profit is Birr 500,000, we need to set the profit function equal to 500,000 and solve for Q. Using the profit function obtained in part (a), we have:
(Q * 100) - [(Q * TVC per unit) + TFC] = 500,000
Simplifying the equation, we can find the sales volume (revenue) and quantity of sales when the profit is Birr 500,000.
f) Finding Profit when Sales are Birr 2,000,000:
To find the profit when sales are Birr 2,000,000, we need to substitute the given revenue into the profit function obtained in part (a). Therefore, the profit is:
Profit = (Revenue) - [(Q * TVC per unit) + TFC]