Coastal Cold Chain Cost Estimation
Coastal Cold Chain is preparing its 2026 distribution cost budget. Finance has 24 months of delivery data but the cost formula is disputed. The lowest month had 10,000 deliveries and total cost $420,000. The highest had 26,000 deliveries and total cost $790,000. The high month includes $60,000 for an accident repair that is not expected to recur and $40,000 of fuel surcharge caused by a temporary price spike. At 18,000 deliveries the company added a second dispatch supervisor shift, which adds $35,000 of fixed cost per year; the low month is below this step and the high month is above it. A regression on all 24 months gives total cost = $310,000 + $12.90 per delivery, with R-squared 0.86. Residuals are large in the fuel-spike months. The 2026 plan is 22,000 deliveries, within the existing depot capacity but above the supervisor step. The operations director wants a single formula; the CFO wants to know which estimate is defensible.
1. Derive a high-low cost formula after adjusting the observed costs for the non-recurring items and the step cost. Show the variable rate, the fixed cost below and above 18,000 deliveries, and the 2026 estimate at 22,000 deliveries.
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Adjusted high cost = $790,000 - $60,000 accident - $40,000 temporary fuel surcharge - $35,000 supervisor step = $655,000 at 26,000 deliveries. Low cost = $420,000 at 10,000 deliveries. Variable rate = ($655,000 - $420,000) / (26,000 - 10,000) = $235,000 / 16,000 = $14.6875 per delivery. Fixed cost at the low range = $420,000 - (10,000 x $14.6875) = $273,125. The step cost is then added above 18,000 deliveries: fixed cost above the step = $273,125 + $35,000 = $308,125. For 22,000 deliveries, total cost = $308,125 + (22,000 x $14.6875) = $631,250. The high observation must be adjusted before differencing; otherwise the accident, fuel spike and step would be embedded in the variable rate and then double-counted. The formula is only valid within the relevant range and assumes the step remains a single $35,000 increment.
2. Compare the high-low estimate with the regression and recommend which to use for the 2026 budget. Address the R-squared and the omitted variables.
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The regression estimate at 22,000 deliveries is $310,000 + (22,000 x $12.90) = $593,800. That is $37,450 lower than the adjusted high-low estimate of $631,250. R-squared of 0.86 means delivery volume explains a large part of cost variation, but it does not prove the model is correctly specified. The residuals are large in fuel-spike months, which suggests a missing fuel-price variable, and the regression does not explicitly include the $35,000 supervisor step. Because the 2026 plan is above the step, the regression may average the pre-step and post-step periods and understate the fixed cost. High-low is also limited because it uses only two observations and ignores the middle months. My recommendation is to use the adjusted high-low plus step as the conservative budget estimate, while re-estimating a multiple regression with a step dummy and a fuel-price index. The board should see a range of $594k to $631k and understand that the higher figure protects cash flow if fuel and step costs behave as expected.
3. What data checks would you perform before presenting the formula to the board?
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I would verify that the cost data are on the same basis for every month: no capital items, no prepayments, no allocated group charges and no changes in fleet ownership. I would confirm the timing and permanence of the supervisor step and whether the 18,000 threshold is measured in deliveries or cases. I would test whether the fuel surcharge is truly temporary or has become a permanent cost. I would examine delivery size, route density and fleet mix, because a 22,000-delivery plan with smaller drops could cost more per delivery. I would check inflation, wage rates, depot capacity and overtime. I would also test outliers, restate the regression on normal months, and run sensitivity analysis on the variable rate and step. Finally, I would confirm that the 2026 volume forecast is achievable and consistent with the sales plan.