Choosing a courier: break-even, annual cost and contract risk
Ngaio runs Pōhutukawa Prints from her garage, posting art prints nationwide. In a normal week she sends about 190 parcels, but this swings from about 30 in quiet weeks (January, exam season) to 210 in the pre-Christmas rush. Over a year she sends roughly 8,500 parcels.
Two courier options:
- Kōwhai Couriers: $60 per week account fee, plus $4.20 per parcel. 96% of parcels arrive on time.
- Tūī Freight: no weekly fee, $6.80 per parcel. 89% of parcels arrive on time.
Late parcels cost Ngaio $12 each in refunds and replacement printing, plus damage to her feedback rating. Kōwhai requires a 12-month contract with a $250 exit fee; Tūī is rolling week to week. Ngaio expects her volumes to grow by about 15% next year.
She must sign before the busy season starts.
1. Find the weekly parcel volume at which the two couriers cost the same, ignoring late-parcel costs. Explain what the number means for a quiet week.
Read the worked answer
Let n be the parcels in a week.
- Kōwhai: 60 + 4.20n
- Tūī: 6.80n
Set them equal: 60 + 4.20n = 6.80n → 60 = 2.60n → n = 23.08
Break-even is about 23 parcels a week; at 24 parcels Kōwhai is already cheaper. Check n = 24: Kōwhai = 60 + 100.80 = $160.80; Tūī = $163.20.
What it means: the $60 weekly fee is a fixed cost that has to be absorbed by the margin of $2.60 per parcel. In a week with only 20 parcels, Kōwhai costs $144.00 and Tūī costs $136.00, so Tūī wins by $8. Ngaio's quiet weeks (about 30 parcels) sit just above the break-even, so the fee is only marginally justified in those weeks - and this calculation ignores reliability entirely, which is the next step.
2. Using the annual volume of 8,500 parcels, compare the total annual cost of each courier, including the $12 cost for every late parcel. Show your figures.
Read the worked answer
Kōwhai
- Weekly fees: 52 × $60 = $3,120
- Parcels: 8,500 × $4.20 = $35,700
- Late parcels: 4% × 8,500 = 340 → 340 × $12 = $4,080
- Total = $3,120 + $35,700 + $4,080 = $42,900
Tūī
- Parcels: 8,500 × $6.80 = $57,800
- Late parcels: 11% × 8,500 = 935 → 935 × $12 = $11,220
- Total = $57,800 + $11,220 = $69,020
Kōwhai is cheaper by $69,020 − $42,900 = $26,120 per year.
Worth noting: reliability contributes $7,140 of that gap on its own ($11,220 − $4,080), so even if Tūī dropped its parcel rate to $4.20 the on-time difference would still favour Kōwhai. The per-parcel rate is the dominant factor here, but the quality gap is not trivial - it is roughly 27% of the total advantage.
3. Ngaio's weekly volume in January falls to 30 parcels and could fall further if the print market slows. Recommend a courier and explain what evidence or condition would change your recommendation.
Read the worked answer
Recommendation: sign with Kōwhai, because it is cheaper across almost the whole plausible volume range and its reliability protects her feedback rating, which drives future sales.
Checking the risk case. At 30 parcels a week, including late costs:
- Kōwhai: 60 + (30 × 4.20 = 126) = $186; late ≈ 1.2 parcels → $12–24 → about $198–$210
- Tūī: 30 × 6.80 = $204; late ≈ 3.3 parcels → $36–48 → about $240–$252
Kōwhai still wins. Volumes would have to drop below about 20 parcels a week for Tūī to be cheaper once late costs are counted, and 15% growth moves her further from that point, not closer.
What would change the recommendation:
- A sustained fall below ~20 parcels a week. The $60 fee is fixed, so a long slow period makes the no-fee option better. The 12-month contract plus $250 exit fee locks her in, so she should ask for the exit fee to be waived or reduced.
- A Tūī on-time guarantee. If Tūī lifted on-time delivery to about 96% or agreed to cover the $12 refunds, the reliability argument disappears and only the rates matter.
State the assumption plainly: the comparison assumes her 4% and 11% late rates hold for her own parcels, which she should verify from a month of tracking data rather than trusting the headline averages.