The Cold Chain That Wasn't
A family vegetable operation near Manjimup packs 12 tonnes of broccoli per week for a Perth supermarket chain. The contract specifies a maximum of 48 hours from harvest to store delivery and a reject rate below 3%. Last month the reject rate hit 7% because the old cool room struggled to pull field heat out on hot days; broccoli arrives at the store at 9°C instead of the specified 4°C. A new blast chiller costs $85,000 and would cut the reject rate to about 1.5%. The supermarket pays $4,200 per tonne but applies a 20% penalty deduction on rejected tonnes. The operation's gross margin is thin: total weekly revenue is $50,400 and weekly costs are $46,000. The bank will lend at 7.5% over five years.
1. Calculate the current weekly cost of rejects and the expected weekly cost after installing the blast chiller, then assess whether the investment is justified on reject savings alone.
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Current rejects: 7% of 12 t = 0.84 t rejected. Rejected tonnes still incur the 20% penalty deduction, so the loss per rejected tonne is the full $4,200 value plus the 20% penalty on that tonne? Careful: the penalty is a deduction applied to rejected tonnes, meaning the producer receives 80% less - effectively the rejected tonne returns $4,200 × (1 − 0.20) = $3,360, but the tonne is not sold as premium product. The cleanest framing: rejected tonnes earn nothing of the premium price and attract a 20% deduction, so the revenue lost per rejected tonne is $4,200, and the penalty adds 20% × $4,200 = $840. Total loss per rejected tonne = $5,040.
Weekly loss now: 0.84 × $5,040 = $4,233.60.
After chiller: 1.5% of 12 t = 0.18 t rejected. Weekly loss = 0.18 × $5,040 = $907.20.
Weekly saving = $4,233.60 − $907.20 = $3,326.40.
Annual saving ≈ $3,326.40 × 52 = $172,972.80.
Loan repayment: $85,000 at 7.5% over 5 years. Annual repayment ≈ $85,000 × 0.075 / (1 − 1.075⁻⁵) ≈ $85,000 × 0.2472 ≈ $21,012 per year.
The saving massively exceeds the repayment, so on reject savings alone the investment is strongly justified - payback is roughly $85,000 / $172,973 ≈ 0.49 years, or about six months.
2. The supermarket offers a choice: keep the current contract, or accept a new contract with a 2% lower price but a relaxed reject threshold of 5%. Advise the operation, showing your reasoning.
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Current contract: price $4,200/t, threshold 3%, actual 7% reject. Weekly revenue on 12 t = $50,400 gross, but rejects cost $4,233.60, so net ≈ $46,166.40.
New contract: price $4,200 × 0.98 = $4,116/t. Gross weekly revenue = 12 × $4,116 = $49,392. Reject threshold 5%; at current performance of 7%, rejects are 0.84 t, but the penalty only applies above the threshold? The threshold defines what counts as a reject breach. If the threshold is 5%, then rejects up to 0.6 t are tolerated and only the excess 0.24 t attracts the penalty. Loss = 0.24 × ($4,116 × 1.20) = 0.24 × $4,939.20 = $1,185.41.
Net new contract ≈ $49,392 − $1,185 = $48,207, which is better than the current $46,166.
But this depends on the chiller decision. If the chiller is installed, rejects fall to 1.5%, well under both thresholds, and the current contract's higher price is better: 12 × $4,200 = $50,400 with minimal reject loss. The judgement is sequencing: install the chiller first, then stay on the higher-price contract. Accepting the lower price to buy tolerance is only rational if the chiller is not installed, and even then the margin is thin and leaves the operation exposed to further quality drift.