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This answer results from incorrectly treating variable overhead costs as fixed costs. See the correct answer for a complete explanation.
The flexible budget is the budget developed for the actual achieved level of activity rather than the master budget level. To compute the flexible budget we must use the standard costing system, i.e. we need to determine the budgeted selling price, budgeted variable cost per unit, and budgeted total amount of fixed costs. The budgeted selling price minus the budgeted cost per unit equal the contribution per unit, so we can use the budgeted contribution per unit and need not calculate the first two items. The budgeted contribution per unit is $6.50 ($975,000 ÷ 150,000). Fixed costs for the flexible budget are the same as for the static budget, since fixed costs do not fluctuate with the level of output. The flexible budget contribution margin for sales of 180,000 is $1,170,000 ($6.50 × 180,000). Subtracting the fixed costs from the expected contribution margin for the actual level of sales, we arrive at a flexible budget operating income of $420,000 ($1,170,000 ? $250,000 ? $500,000 = $420,000).
This is the static budget operating income not adjusted for the actual level of output.
This is calculated using the static budget operating income per unit of $1.50 ($225,000 ÷ 150,000) and multiplied by the actual level of sales of 180,000. This gives the operating income of $270,000 ($1.5 × 180,000), but it ignores the fact that fixed costs do not vary with the level of activity.