What the model assumes; how the answer is written for the owner

What the straight lines assume

Every answer in this module came from three numbers and a straight line. The line holds only while six things stay true, and a case is built by breaking one of them:

1. Price per unit is constant — every skier-day sells for 30. A volume discount to schools (L10.5) breaks it: the 1,500 at $18 are on a different line.
2. Variable cost per unit is constant — 9 at any volume. A fuel contract that gives a discount above 20,000 skier-days breaks it.
3. Total fixed costs are constant — 315,000 at any volume inside the range.
4. Activity stays inside the relevant range (L9.2) — above 30,000 skier-days Northlake needs a second lodge, and assumption 3 fails with it.
5. The sales mix is known and constant — the 60/20/20 of L10.6. If the café grows faster than the passes, the blended ratio and the break-even move.
6. A single period, with no change in inventory — what is produced is sold. Northlake sells skier-days, which cannot be stockpiled; a manufacturer's unsold units would carry cost into the next period and break the equation.

Under these, revenue and total cost are straight lines and the model is exact. When a case says "state the assumptions", it wants the specific one its facts strain — "CVP assumes constant total fixed costs, and a second lodge at 30,000 skier-days would breach it" — not "it's only an estimate".

Operating leverage, named

L9.6 found that a 10 % rise in volume moved Northlake's operating income 40 %. The multiplier has a name, the degree of operating leverage:

$$\text{DOL}=\frac{\text{Contribution margin}}{\text{Operating income}}=\frac{420,000}{105,000}=4.0$$

At 20,000 skier-days, every 1 % change in volume moves operating income 4 %. The figure is specific to the volume — at 30,000 skier-days it is 630,000 ÷ 315,000 = 2.0 — and it is what the automation decision (L10.5) was really about: more fixed cost means a higher DOL and bigger swings.

The recommendation sentence

The final's managerial question ends "recommend" or "advise the owner", and the marking scheme (L1.2) gives its marks for three things, in three sentences:

1. The number. Northlake breaks even at 15,000 skier-days; at the expected 20,000 the margin of safety is 5,000 skier-days, 25 %.
2. The condition. That holds at a $30 pass and $9 of variable cost; the school contract at $18 and any rise in fuel both move it.
3. The risk. A poor-snow season of 15,000 skier-days wipes the cushion out entirely, and with a DOL of 4 every further 1 % of volume lost costs 4 % of income.

Written as advice to an owner, not as a formula to a marker. Cedar Ridge Golf Club Ltd. breaks even at 6,443 rounds and expects 8,000: the number is a margin of safety of 1,557 rounds, 19.5 %; the condition is the 55 green fee and 3.00 of variable cost; the risk is a rained-out August — for a course, weather is the assumption most likely to fail.