. A firm manufactures and markets a product that sells for Birr 20 per unit. Fixed costs associated with activity total Birr 40,000 a month, while variable cost per unit is Birr 10. A maximum of 10,000 units can be produced and sold.Required:
a) Drive the TR, TC and Total profit functions.
b) Sketch the TR, TC and Total profit functions in the same coordinate system.
c) What is the Break-even point (in terms of quantity and sales volume)?
d) Drive the new TC, Total profit functions given that FC is increased by Birr 10,000 a month, and calculates the new break-even point.
e) Drive the new TC and Total profit functions given that unit variable costs aredecreased by 20% and calculate the new Break-even point.
f) Drive the new TR and Total profit functions given that the unit selling price increases by 20% and calculates the new break-even point.
g) What is the relationship that you may inter from BEP& FC, P& BEP and V& BEP?
h) Assume selling prince increases by 10% and at the same time V increases by 10% what is the effect of these changes on the BEP - calculate the new breakeven point. What lesson can we drive from this?
i) Suppose there is no any change in FC, V and P, What is the maximum profit the firm can generate, and at what level of output?
j) Keeping P and FC constant, what is the maximum unit variable cost for the firm to break even (at its maximum out put level)?
k) Keeping all things as they are, what is the quantity level at which the company:
i. Makes a profit of Birr 100,000?
ii. Looses Birr 10,000?
l) Had there been no capacity limitation, how would your answer have changed in part (i)
To answer the given questions, we need to understand the concepts of Total Revenue (TR), Total Cost (TC), and Total Profit.
a) Total Revenue (TR) = Selling Price per Unit x Quantity Sold
TR = 20 x Quantity Sold
Total Cost (TC) = Fixed Costs + (Variable Cost per Unit x Quantity Sold)
TC = 40,000 + (10 x Quantity Sold)
Total Profit = Total Revenue - Total Cost
Total Profit = TR - TC
b) To sketch the TR, TC, and Total profit functions in the same coordinate system, we need to plot the values of these functions against the quantity sold. The x-axis represents the quantity sold, while the y-axis represents the TR, TC, and Total Profit values.
c) The Break-even point is the quantity at which Total Revenue equals Total Cost, resulting in zero profit or loss. To calculate the break-even point:
Set TR = TC (20 x Quantity Sold = 40,000 + 10 x Quantity Sold)
Simplify the equation to find the break-even quantity.
d) To calculate the new Total Cost (TC) and Total Profit functions when the Fixed Costs (FC) increase by Birr 10,000 a month, simply add Birr 10,000 to the original Fixed Costs in the TC function. Calculate the new break-even point.
e) To calculate the new Total Cost (TC) and Total Profit functions when the unit Variable Costs (V) decrease by 20%, subtract 20% of the original Variable Cost per Unit from the original TC function. Calculate the new break-even point.
f) To calculate the new Total Revenue (TR) and Total Profit functions when the unit Selling Price (P) increases by 20%, multiply the original Selling Price per Unit by 1.2 in the TR function. Calculate the new break-even point.
g) From the Break-even Point (BEP) and Fixed Costs (FC), we can infer that a higher FC will increase the BEP. From the Profit (P) and BEP relationship, we can understand that the profit increases as the quantity sold exceeds the BEP. From the Variable Cost (V) and BEP relationship, we can infer that a higher V will increase the BEP.
h) Calculate the new break-even point when the Selling Price (P) increases by 10% and the Variable Cost (V) increases by 10%. Analyze the effect of these changes on the BEP and draw conclusions from the results.
i) When there are no changes in FC, V, and P, we can calculate the maximum profit by finding the quantity level at which Total Revenue - Total Cost is maximized.
j) Keeping P and FC constant, calculate the maximum unit variable cost for the firm to break even (at its maximum output level). This can be done by finding the unit variable cost that makes the TC equal to the FC when the maximum output level is reached.
k) Calculate the quantity level at which the company makes a profit of Birr 100,000 and the quantity level at which the company loses Birr 10,000. This can be done by setting the Total Profit equal to the desired profit or loss amount and solving for the quantity.
l) If there were no capacity limitations, the answer to part (i) would change as the company could produce and sell an unlimited quantity of the product, potentially resulting in a higher maximum profit.