Two Stall Contracts, One Cash Constraint
Meera runs a small catering unit. She has been offered a three-day stall at a college fest and must choose one of two contracts before paying anything.
Under Contract A she pays the organisers a fixed rent of Rs 18,000 and keeps every rupee of sales. Under Contract B there is no rent, but the organisers take a 10% commission on revenue.
In both cases the food materials cost her 40% of the selling price, and all other costs (staff, transport, gas) are fixed at Rs 9,000 for the three days. She plans to sell a single combo plate priced at Rs 150.
Her best estimate is 900 plates. The fest committee has told her that if the headline music act confirms, footfall could push sales to 1,500 plates; she puts that chance at 30%. She has Rs 25,000 of cash available and must pay the Rs 18,000 rent in advance if she chooses A.
1. Calculate the plate volume at which the two contracts give Meera the same profit, and her profit under each contract at 900 plates.
Read the worked answer
Contribution per plate. Materials are 40% of Rs 150 = Rs 60.
- Contract A: 150 - 60 = Rs 90 per plate. Fixed outgoings = 18,000 + 9,000 = Rs 27,000. Profit = 90Q - 27,000.
- Contract B: 150 - 60 - 15 (10% commission) = Rs 75 per plate. Fixed outgoings = Rs 9,000. Profit = 75Q - 9,000.
Indifference point. Set the two equal: 90Q - 27,000 = 75Q - 9,000 15Q = 18,000 Q = 1,200 plates.
At 900 plates.
- A: 90 x 900 - 27,000 = 81,000 - 27,000 = Rs 54,000
- B: 75 x 900 - 9,000 = 67,500 - 9,000 = Rs 58,500
B is ahead by Rs 4,500. The intuition is that at low volume the Rs 18,000 rent is spread over too few plates: it costs Rs 20 per plate at 900 units but only Rs 12 at 1,500.
2. Using her 30% probability for the 1,500-plate outcome, compare the two contracts on expected profit and recommend one. State any constraint that could override the arithmetic.
Read the worked answer
High-demand profits (Q = 1,500).
- A: 90 x 1,500 - 27,000 = 135,000 - 27,000 = Rs 1,08,000
- B: 75 x 1,500 - 9,000 = 1,12,500 - 9,000 = Rs 1,03,500
Expected profit.
- A: 0.70 x 54,000 + 0.30 x 1,08,000 = 37,800 + 32,400 = Rs 70,200
- B: 0.70 x 58,500 + 0.30 x 1,03,500 = 40,950 + 31,050 = Rs 72,000
B is better by Rs 1,800 - under 3% of the expected profit, so this is a close call, not a clear one.
The constraint that decides it. Contract A requires Rs 18,000 rent plus Rs 9,000 of other fixed costs = Rs 27,000 out before the first plate is sold. She has Rs 25,000, a shortfall of Rs 2,000. Borrowing or dipping into a buffer to chase an expected gain of Rs 1,800 is not a rational trade, and if the music act falls through she is down Rs 54,000 of profit and has already sunk the rent.
Recommendation: take Contract B. It is ahead on expected value, ahead in the likely (70%) state, and requires no upfront cash. Revisit only if the music act confirmation is near-certain.
3. At what probability of the 1,500-plate outcome does Contract A become the better choice? Does the cash shortfall change that threshold?
Read the worked answer
The gap between the two contracts in each state is:
- Low state (900): A - B = 54,000 - 58,500 = - Rs 4,500
- High state (1,500): A - B = 1,08,000 - 1,03,500 = + Rs 4,500
Let p be the probability of the high state. Expected advantage of A: p(4,500) - (1-p)(4,500) = 9,000p - 4,500. Setting this to zero gives p = 0.50.
Because the two gaps are equal and opposite, the threshold is exactly 50%, not something requiring a calculation beyond the midpoint. At her 30% estimate A is clearly behind; at 55% it would be ahead.
The cash gap does not move the threshold - expected value is unaffected by how the Rs 27,000 is financed. It changes feasibility and risk: at p just above 0.50, A offers a slightly higher expected profit but a worse downside for someone with Rs 25,000 in hand. In exam terms: the arithmetic sets the indifference point, the cash constraint sets whether she is entitled to play that game at all.