First Principles Structuring 2026: Deriving the Tree

First principles start from the identity the business obeys

The identity is a sentence with an equals sign in it, written in the units the business is constrained by. For a scheduled airline that is seat-miles. For a hospital ward it is bed-days. For a law firm it is billable hours. For a parking garage it is space-hours.

Four steps, and the order matters because each one narrows the next.

1. Name the scarce thing. What runs out first: floor space, machine time, licensed capacity, engineer hours.
2. Write the capacity of that thing per period. Count times availability times periods, in one unit.
3. Write yield per unit of capacity. Revenue divided by capacity, which is different from revenue divided by customers.
4. Read the branches off the identity. Each term becomes a branch. Nothing else becomes a branch.

Deloitte's published five-step approach puts the assumption hunt second, right after understanding the issue: the step is named "Identify the underlying assumptions", checked 30 September 2026 at deloitte.com. Step one above is that hunt, applied to the unit. A borrowed framework arrives with its unit already chosen, which is why it skips the step.

The parking garage, in space-hours

A downtown operator runs one garage with 620 spaces. It opens 18 hours a day, 365 days a year. Revenue last year was about 4.4 million dollars. The owner wants to know whether to sign more monthly contracts or fewer.

Capacity first. 620 spaces times 18 hours is 11,160 space-hours a day, times 365 days is 4,073,400 space-hours a year. That is the entire inventory, and it is the only thing the garage sells.

Now split the inventory by how it is sold, because that is where the two businesses inside this garage separate.

• Contract spaces. 180 spaces let on monthly contracts at 185 dollars a month. Those spaces are reserved around the clock, so they consume all 18 hours whether or not a car is in them.
• Transient spaces. The remaining 440 spaces are sold by the hour at an average of 2.53 dollars, and they run at 55 percent occupancy.

Contract revenue is 180 times 185 times 12, which is 399,600 dollars. The capacity those spaces consume is 180 times 18 times 365, which is 1,182,600 space-hours. So the yield is 399,600 divided by 1,182,600, which is 0.338 dollars, or about 34 cents per space-hour.

Transient capacity is 440 times 18 times 365, which is 2,890,800 space-hours. At 55 percent occupancy that is 1,589,940 paid hours, at 2.53 dollars each, which is 4,022,548 dollars. Yield against capacity is 4,022,548 divided by 2,890,800, which is 1.3915 dollars, so about 1.39 per space-hour.

Total revenue is 399,600 plus 4,022,548, which is 4,422,148 dollars. That closes on the 4.4 million the owner reported.

What a revenue split misses that first principles catch

Split the same garage the way a revenue tree would, and the contract business looks small and harmless: 399,600 of 4,422,148 dollars is 9 percent of revenue. Nothing about that number suggests a problem.

The contract business takes 29 percent of the capacity and returns 9 percent of the revenue. Per space it earns 2,220 dollars a year against 9,142, which is a ratio of 4.1 to 1. The identity made that visible because capacity is a term in it. A revenue split has no capacity term, so it cannot produce the comparison at all.

This is the payoff of derivation, and it is narrow and real. The recommendation reverses. A revenue tree says protect the 91 percent. A space-hour tree says look hard at the 29 percent of inventory earning a quarter of the going rate.

The assumption that decides it

Convert 60 contract spaces to transient and the arithmetic looks easy. Those 60 spaces carry 60 times 18 times 365, which is 394,200 space-hours. Moving them from 34 cents to 1.39 dollars is a gain of 1.05 dollars per hour, so 394,200 times 1.05 is 413,910 dollars a year.

That figure holds only if transient demand grows with transient supply. Test the opposite. Suppose demand is fixed at the 1,589,940 paid hours already observed. Spread across 500 transient spaces instead of 440, capacity becomes 500 times 18 times 365, which is 3,285,000 space-hours, and occupancy falls from 55 percent to 1,589,940 divided by 3,285,000, which is 48.4 percent. Paid hours are unchanged, so transient revenue is unchanged at 4,022,548 dollars.

Under that assumption the conversion earns nothing and gives up 60 times 185 times 12, which is 133,200 dollars of contract revenue. Same operator, same garage, same 60 spaces: plus 413,910 dollars or minus 133,200 dollars depending on one unobserved quantity.

So the recommendation is a test rather than a decision. Release 20 spaces, not 60, and measure whether paid transient hours rise. Oliver Wyman's published method asks candidates to pick an approach and then "Show your client why it's better than the alternatives", checked 30 September 2026 at oliverwyman.com. A staged release is the approach that survives being wrong.

Kearney publishes the same instruction

The firm that says this most plainly says it without using the word derivation. Under a tip it calls thinking top down, Kearney writes: "As you analyze the information you receive, begin with the big picture. Understand the overriding issues, and use them to prioritize and organize issues that have lesser consequences. Try to avoid forcing your solution to fit a standard framework. The only things it needs to fit are the problem, the business, and the objectives", checked 30 September 2026 at kearney.com.

Three things have to fit, in the firm's own list: the problem, the business, and the objectives. A space-hour identity fits all three for a garage and none of them for a software company. That is what makes it derived.

The same page carries a second warning that reads differently once you have worked an identity: "Try to avoid searching for a silver bullet. Complex problems rarely have simple solutions." An identity works as a constraint on what the answer can be made of, and it usually reveals that two things matter at once, which is the space-hour and the yield here.

Not every firm takes this line. Case interview frameworks sets Kearney's position against the firm that publishes the opposite one, because a candidate reading both needs to know they disagree.

The unit is where a first principles structure pays

Getting the unit wrong produces a wrong answer delivered confidently, and it happens at the top of the tree where nobody checks.

An associate at L.E.K. describes his own case on the firm's careers blog. He sized the wedding market as though each person married separately instead of two people per wedding, and he notes that the interviewer credited the method while pointing out the error, checked 29 September 2026 at lek.com. Every multiplication below that point was correct and every result was double.

Three units that produce three different garages, from the same accounts.

1. Per customer. Suggests loyalty programs and monthly passes, because a contract holder is a repeat customer.
2. Per space. Suggests filling empty spaces, which is the 45 percent of transient hours nobody paid for.
3. Per space-hour of capacity. Suggests repricing the contracts, because capacity is what they consume.

Only the third one is the thing the garage runs out of. The first two are real measurements of something the business does not sell.

Practicing the first principles derivation

The drill is unit substitution, and it takes five minutes. Take the garage and rebuild it per square foot instead of per space. At 320 square feet per space including aisles, the garage has 198,400 square feet, and revenue per square foot is 4,422,148 divided by 198,400, which is 22.29 dollars a year. Now the comparison is against retail rent on the same block, which is a different question and a better one when selling the building is on the table.

Then rebuild it per car. At 2.6 hours of average transient stay, 1,589,940 paid hours is 611,515 transient parkings a year, at an average ticket of 2.53 times 2.6, which is 6.58 dollars. That version supports a pricing conversation and cannot support a capacity conversation, because cars are not scarce and spaces are.

Build the structure itself against a timed prompt in the case structure builder, and check a capacity threshold in the breakeven calculator. Both are free and need no account. Neither will tell you what a business runs out of first, which is the judgment the whole method rests on. For the version of this tool that decomposes a question, see issue trees; for the arithmetic identity worked as a tree of quantities, see driver trees. The four weights our grader applies to a structure are ours alone, read from the rubric code, and the reasoning behind them sits on how an answer is assessed.