Harborlight Printing is pricing a new contract that will use its production equipment and support team, so the bid needs a defensible forecast of monthly support cost at the expected workload.
The operations manager estimates that the contract will run about 1,250 machine-hours in a month, and we have two recent cost observations for the same support cost pool. At 1,000 machine-hours, total support cost was $38,000. At 1,400 machine-hours, total support cost was $46,000. The decision is whether the bid should carry a support cost forecast closer to $38,000, closer to $46,000, or somewhere between based on how costs behave as activity changes.
A quick way to picture that behavior is to treat total cost as a line where the vertical change in cost follows the horizontal change in machine-hours. Before we calculate anything, commit to the direction and rough size of that slope by inspecting the two points shown here:
Support costs for a contract are often mixed costs, meaning one part does not change with machine-hours and one part moves with machine-hours within the relevant range of activity for the bid.
The high-low method uses the highest and lowest activity observations to estimate the variable rate per machine-hour and the fixed monthly amount. With our data, the change in cost is $46,000 minus $38,000 which equals $8,000, and the change in activity is 1,400 MH minus 1,000 MH which equals 400 MH. The estimated variable cost per machine-hour is $8,000 divided by 400 MH which equals $20 per MH.
With the variable rate, we back into the monthly fixed cost using either point. Using the low point, total cost $38,000 equals fixed cost plus $20 times 1,000 MH, so fixed cost equals $38,000 minus $20,000 which equals $18,000. Using the high point gives the same check. $46,000 minus ($20 times 1,400 MH) equals $46,000 minus $28,000 which also equals $18,000.
We now have a simple cost formula for the bid range that matches both observations. Total support cost equals $18,000 plus $20 times machine-hours, where fixed cost is the $18,000 monthly amount that stays the same as machine-hours change and variable cost is the $20 per machine-hour that scales with the contract’s activity.
Common error Treating the entire $38,000 or $46,000 as variable makes the bid too high or too low when activity differs from the month observed.
Before calculating, decide which component will drive most of the change from 1,000 MH to 1,250 MH. Is it the fixed $18,000, or the variable portion tied to the extra 250 MH?
The forecast uses the estimated linear cost function for total support cost at 1,250 MH.
| Input | Amount |
|---|---|
| Fixed cost per month | $18,000 |
| Variable cost per MH | $20 |
| Forecast machine-hours | 1,250 MH |
| Variable portion | $20 × 1,250 = $25,000 |
| Forecast total support cost | $18,000 + $25,000 = $43,000 |
| Check | $43,000 is between $38,000 and $46,000 |
So the bid-relevant forecast for monthly support cost at 1,250 MH is $43,000, which includes $18,000 of monthly capacity type support and $25,000 that scales with machine-hours. It excludes any contract specific direct materials or direct labor that would be traced separately rather than pooled into support, because this estimate is only for the defined support cost pool.
A linear cost formula is most useful when we are forecasting within a reasonable band of activity near the observed data, because we are assuming the same fixed cost and the same variable rate still apply. To see how much the bid number moves when machine-hours differ from plan, we compute the forecast at 1,150 MH, 1,250 MH, and 1,350 MH using the same $18,000 fixed cost and $20 per MH variable rate. Use the inputs below to produce the three totals: