T-shirt quote: GST, a conditional discount and a budget-inclusive rule
At the student council meeting at Ōpāwa College, the treasurer and the chair are checking a quote for 60 event T-shirts.
The supplier's quote: $18.50 per shirt, freight $45.00, and all prices exclude GST (15%). The council has $1,200 to spend, GST inclusive, and the school cannot claim GST back.
The chair calculates: 60 × $18.50 = $1,110, plus $45 freight = $1,155, which is under $1,200, so he moves to sign the order. The treasurer stops him. She points out that the supplier's terms also include an 8% discount on the shirt price (but not the freight) once the shirt subtotal exceeds $1,000.
Council policy is that every purchase must sit inside the budget GST inclusive, and the quote is valid for only five days. The shirts must be ordered before the end of term or the event will not have them in time.
1. Identify the error in the chair's reasoning and calculate the true GST-inclusive cost of the 60-shirt order.
Read the worked answer
The error: the chair compared a GST-exclusive figure ($1,155) with a GST-inclusive budget ($1,200). That is comparing two different currencies. The school cannot claim GST back, so GST is a real cost and must be added.
Correct working, with the discount
- Shirts: 60 × $18.50 = $1,110.00. This exceeds $1,000, so the 8% discount applies to shirts only.
- Discounted shirts: $1,110.00 × 0.92 = $1,021.20
- Add freight (no discount): $1,021.20 + $45.00 = $1,066.20 excl GST
- Add GST: $1,066.20 × 1.15 = $1,226.13
That is $26.13 over the $1,200 budget.
For comparison, ignoring the discount gives $1,155.00 × 1.15 = $1,328.25, which is $128.25 over - so the discount is worth having but is not enough on its own. The chair's $1,155 is the pre-GST, pre-discount subtotal and is not the amount the council actually pays.
2. The chair proposes ordering 58 shirts instead, arguing the 8% discount still applies because 58 × $18.50 = $1,073 is over $1,000. Check this arithmetic and state whether it fits the budget.
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Working
- Shirt subtotal: 58 × $18.50 = $1,073.00. Over $1,000, so the discount condition is met.
- Discounted: $1,073.00 × 0.92 = $987.16
- Add freight: $987.16 + $45.00 = $1,032.16 excl GST
- Add GST: $1,032.16 × 1.15 = $1,186.98 → $1,187.00
$1,187.00 is under $1,200, with $13.02 to spare. The chair's arithmetic is correct and the plan fits the budget.
But it is tight, and two shirt sizes will be missing. Also check the boundary: the freight is unchanged, so freight is now 4.4% of the order; if the supplier adds any surcharge, or if GST is applied before the discount (it is not), the margin disappears. A $13 buffer on a $1,200 order is about 1% - smaller than a single reprint.
3. Recommend a course of action to the council and state one assumption that, if wrong, would change your recommendation.
Read the worked answer
Recommendation: order 58 shirts only if the council can confirm the discount still applies at that quantity; otherwise ask the supplier to waive or reduce the $45 freight, which alone brings the 60-shirt order to $1,021.20 × 1.15 = $1,174.38 - under budget with $25.62 spare. A third option is to keep 60 shirts and move $26.13 from another council budget line. All three are better than signing the chair's original $1,155 figure.
Assumption that matters most: that the 8% discount is triggered by the dollar value of the shirt subtotal ($1,000), not by quantity (for example, 60 units). If the discount is actually quantity-based, the 58-shirt plan collapses: $1,073.00 + $45.00 = $1,118.00 × 1.15 = $1,285.70, which is $85.70 over budget. The treasurer should get the trigger condition in writing before the five-day quote expires - this is exactly the assumption the whole decision hinges on.