Same bottom line as the functional statement; only this one answers "what if"

One season, two statements

Northlake Nordic Centre Inc.'s season at 20,000 skier-days, built from the cost list in L9.3. The functional statement — the one the bank receives — sorts the 495,000 of costs by what they were for:

Revenue                                   600,000
Trail and lodge operations                330,000
Administration                            165,000
Operating income                          105,000

The contribution-margin statement sorts the same 495,000 by how they behave:

Sales                                     600,000
Less: variable costs (20,000 × 9)         180,000
Contribution margin                       420,000
Less: fixed costs                         315,000
Operating income                          105,000

The foot is the same 105,000, because the same dollars have been re-sorted, not changed. Trail and lodge operations held fuel (variable) and the lease (fixed); administration held card fees (variable) and salaried staff (fixed). Pull the variable pieces out of both functional lines and they sum to 180,000; the fixed pieces sum to 315,000. The subtotal that the CM statement has and the functional one lacks is contribution margin — and the subtotal the functional statement has and the CM one lacks is nothing, because a service business has no gross profit.

The foot is operating income, before interest on the bank loan and before tax. US textbooks label it net income; on this paper the CM statement stops at operating income.

The question only one statement can answer

What if skier-days rise 10 %, to 22,000? The functional statement is silent: nothing on it says how much of trail and lodge operations will move. The CM statement answers in one line, because every line on it is either per unit or fixed:

Sales                    22,000 × 30     660,000
Less: variable costs     22,000 × 9      198,000
Contribution margin      22,000 × 21     462,000
Less: fixed costs                        315,000
Operating income                         147,000

Volume rose 10 %; operating income rose from 105,000 to 147,000 — 40 %. Contribution margin rose 10 % (every skier-day brings its 21), but the 315,000 did not move, so the whole 42,000 of extra contribution fell to operating income. Run it the other way — 18,000 skier-days — and contribution margin is 378,000, operating income 63,000: down 40 % on volume down 10 %. Fixed costs make operating income swing more than volume, in both directions; Module 10 gives that swing a name.

Two things the restated statement never does

It never restates fixed costs per unit. At 20,000 skier-days the fixed cost is 15.75 a skier-day; at 22,000 it is 14.32. Neither figure appears on the statement and neither should be multiplied by anything — the 315,000 goes in as 315,000 (L9.1). And it never changes the price or the variable cost per unit unless the case says so: a 10 % volume change is 10 % more skier-days at the same 30 and the same 9. The three inputs — price 30, variable cost 9, fixed cost 315,000 — are Module 10's entire dataset, and every break-even, target and what-if there is this statement rebuilt at a different volume.