Numerical Ability: Catering Order Break-Even
Mama Nangula runs a small catering business. A client orders lunch for 180 delegates at N$85 per plate, excluding 15% VAT. She plans to prepare 10% extra plates because some plates may be damaged or returned, but she will charge only for 180 plates. Ingredients cost N$38 per plate prepared. Fixed costs for the event are N$450 for transport, N$300 for gas, and N$600 for staff overtime. She will add 15% VAT to the invoice and remit it to the revenue authority; the VAT is not her income. The client asks whether she can reduce the price to N$75 per plate, excluding VAT, if the same 180 delegates are confirmed. Mama Nangula has no other booking that day and her staff are already scheduled.
1. Calculate Mama Nangula's profit on the N$85 order. Show revenue excluding VAT, ingredient cost, fixed cost, and profit. Explain why the VAT is not included in profit.
Read the worked answer
Revenue excluding VAT = 180 × N$85 = N$15,300. VAT = 0.15 × 15,300 = N$2,295; the invoice total is N$17,595, but the N$2,295 is collected for the revenue authority, not earned. Plates prepared = 180 × 1.10 = 198. Ingredient cost = 198 × N$38 = N$7,524. Fixed cost = 450 + 300 + 600 = N$1,350. Total cost = N$8,874. Profit = 15,300 − 8,874 = N$6,426. Including VAT in revenue would overstate profit by N$2,295 and would confuse cash collected with income earned.
2. Calculate the number of charged plates Mama Nangula needs to break even at N$85 per plate. Use the fact that she prepares 1.1 plates for every charged plate. Round up and explain the result in one sentence.
Read the worked answer
Let n be charged plates. Revenue = 85n. Ingredients = 38 × 1.1n = 41.8n. Fixed = 1,350. Break-even: 85n − 41.8n − 1,350 = 0, so 43.2n = 1,350, giving n = 31.25. She must round up to 32 charged plates. At 32 plates she plans to prepare 35.2 plates; in practice she would prepare 36, so the exact break-even may be slightly higher, but 32 is the minimum whole-number order under the 1.1 planning rule.
3. Should she accept the client's N$75 offer? Calculate the profit at N$75 and give one condition under which accepting is reasonable.
Read the worked answer
At N$75, revenue = 180 × 75 = N$13,500. Costs are unchanged at N$8,874, so profit = N$4,626. That is N$1,800 less than at N$85, but still positive. Because she has no other booking and staff are already scheduled, the fixed costs are committed once she accepts; the relevant comparison is whether the offer covers the extra ingredient cost and contributes something to fixed costs. It does: contribution = 13,500 − 7,524 = N$5,976, which exceeds the N$1,350 fixed cost. Accepting is reasonable if she expects no better booking, the client will not resell at N$85, and the lower price will not become her standard rate. She should also confirm that the 10% extra preparation still applies.