- 25 Marks
Question
Agorwu Company produces office chairs. The price per chair is GHe99.75 and the variable cost per chair is GHe49.75. The following fixed costs are incurred:
| Depreciation of plant and equipment per year | GHe20,000 |
|---|---|
| Property taxes per year | GHe12,000 |
| Manager’s salary and fringe benefits per month | GHe5,200 |
Perform a breakeven analysis of this company:
a. What is the total revenue function? (2 marks)
b. What is the total cost function? (2 marks)
c. What is the profit function? (2 marks)
d. What is the breakeven point in number of chairs? (2 marks)
e. What is the revenue at the breakeven point? (2 marks)
f. What is the income at the breakeven point? (2 marks)
g. Determine the profit when 1,500 chairs are produced in a year. (8 marks)
h. How many chairs must be sold for the company to make GHe75,000 in a year? (5 marks)
Answer
First, annual fixed costs: Depreciation GHe20,000 + Property GHe12,000 + Manager (GHe5,200 × 12 = GHe62,400) = GHe94,400.
Contribution per unit = 99.75 – 49.75 = GHe50.
a) Total revenue function: R(Q) = 99.75Q, where Q is number of chairs.
b) Total cost function: C(Q) = 94,400 + 49.75Q.
c) Profit function: P(Q) = R(Q) – C(Q) = 99.75Q – (94,400 + 49.75Q) = 50Q – 94,400.
d) Breakeven point: Set P(Q)=0: 50Q = 94,400; Q = 94,400 / 50 = 1,888 chairs.
To arrive: Fixed costs / Contribution per unit.
e) Revenue at breakeven: 99.75 × 1,888 ≈ GHe188,400.
Calculation: 99.75 × 1,888 = (100 × 1,888 – 0.25 × 1,888) = 188,800 – 472 = 188,328 (wait, precise: 99.75 = 399/4, but approx GHe188,328).
f) Income (profit) at breakeven: GHe0, by definition.
g) Profit at 1,500: P(1,500) = 50 × 1,500 – 94,400 = 75,000 – 94,400 = -GHe19,400 (loss).
To arrive: Substitute into profit function.
h) For P(Q)=75,000: 50Q – 94,400 = 75,000; 50Q = 169,400; Q = 169,400 / 50 = 3,388 chairs.
In banking analogies, breakeven applies to product volumes, e.g., minimum accounts for profitability, ensuring compliance with BoG’s profitability thresholds post-recapitalization.
- Tags: Breakeven Point, Cost Function, Profit Calculation, Profit Function, Revenue Function
- Level: Level 2
- Series: JULY 2020
- Uploader: Samuel Duah