081i - Interpreting Financial Models

Lesson 81 — Interpreting and Communicating Financial Modelling Solutions

Strand: Number | Descriptor: AC9M7N09 | Duration: 45 minutes

Learning Intentions

• To interpret the outputs of a financial model in terms of the situation.
• To communicate a financial recommendation with its justification and limits.

Success Criteria

I can:

1. Translate a model’s numbers into a decision or recommendation.
2. Justify choices about representation (why this model, these assumptions).
3. Write a financial report using the four-part frame.
4. Test how sensitive a recommendation is to its assumptions.

Warmup

(6 minutes — what does the number mean? pairs)

A cake-stall model gives . Interpret each of the following in words, without calculating anything new:

4. The coefficient
5. The constant

Answers: 1. Selling cakes loses 223050$44$2.20$ after its own costs; 5. The fixed costs to be recovered before any profit.

The point: the model’s parts each say something about the stall. Interpretation is reading them back out.

Activities

Activity 1 — From Output to Recommendation (14 min)

The step Year 7s skip: a number is not yet advice.

I do — the subscription decision. From Lesson 78: monthly 12$1159.58$ months.

Poor communication: ”.”

Interpreted communication:

“If you expect to keep the service for months or fewer, pay monthly. From months on, the annual plan is cheaper — over a full year it saves 29$. The recommendation flips on how long you honestly expect to stay, so decide that first.”

Name the three moves made: the raw number became a threshold; the threshold became advice in both directions; the advice named its hinge assumption.

We do — interpret together. A fundraiser model gives break-even at badges.

1. Turn into advice. (Sell or more to profit; still loses.)
2. The badges come in boxes of . Reframe the advice. (Two boxes () clears break-even with margin; one box cannot.)
3. What hinge assumption should be named? (That the sale price and demand estimates hold.)

Activity 2 — The Financial Report (16 min)

Pairs. One full four-part report (Lesson 76 frame) on one scenario. This is the N09 counterpart of Lesson 76’s ratio reports.

Scenario A — The class fundraiser choice. Option 1: sell donuts — buy at 1.10$2.5060$0.70$2.00150120$25$.

Scenario B — The phone plan for a Year 7. Plan X: 25$10$0.0525035012$-month commitment either way.

Socratic prompts to circulate with:

Prompt	Purpose
What is the decision your report must land on?	Reports recommend; they don’t just compute.
Where is the uncertainty, and which option does it punish?	Drives the sensitivity paragraph.
For A: what does the batch-of- constraint do to the comparison?	Quantisation — you buy or , not .
For B: test both ends of the texting range.	: Y costs . : Y costs . The answer flips inside the stated range — the report must say so.
What would you tell the reader to find out?	The report can demand better data.

Reference analysis (teacher):

A — Donuts: profit per unit 1.406084 - 25 = $59120168 - 25 = $143120$1.30120156 - 25 = $13115012030010 + 0.05t = 25 \Rightarrow t = 300$); the student straddles the threshold, so the honest recommendation is X for certainty, or Y with a warning, and one month’s actual count decides it.

Activity 3 — Sensitivity Stress-test (4 min)

Quick, whole class, on Scenario B.

The texting estimate turns out to be /month. Which recommendation survives?

(Y now costs 30300$ as the hinge survives, because the reader knew what to watch.)

The takeaway sentence: a good financial report survives being wrong about its inputs, because it told the reader which input mattered.

Checks for Understanding

(5 minutes — exit ticket, collected)

1. A model gives break-even at tickets. Write the one-sentence advice.
2. In , interpret the and the for a hall-hire context.
3. Plan P costs 18$910$c per call. Find the threshold and write the two-direction advice.
4. Reasoning. Why should a report name its hinge assumption rather than just its recommendation?
5. Reasoning. “The model says Option A, so Option A is correct.” What is wrong with this sentence?

Answers: 1. E.g. “Sell at least tickets to make a profit; still loses money.”; 2. 8$15018 = 9 + 0.1c \Rightarrow c = 9090$ calls, choose Q; more, choose P; 4. If the assumption shifts, the reader can re-decide without redoing the analysis — the advice fails gracefully; 5. The model says A given its assumptions; the recommendation inherits their uncertainty and is a judgement, not a fact.

Common Misconceptions

Misconception	How to pre-empt it
Reporting the raw number as the answer.	The warmup and the “three moves” of Activity 1.
Rounding break-even down.	badges: profits, does not — the direction is forced by meaning.
Ignoring purchase quantisation (batches, boxes).	Scenario A’s batch constraint and Activity 1’s boxes.
Recommending inside an uncertainty range without flagging the flip.	Scenario B straddles its threshold by design.
Treating sensitivity as decoration.	The stress-test shows which reports survive contact with reality.
”The model is correct, therefore the decision is correct.”	Exit Q5; assumptions carry through to conclusions.

Enrichment — Competition-Style Problems

E1 (Kangaroo style). A stall’s model is . What is the smallest giving a profit of at least 60$?

Answer

.

E2 (AMC Junior style). Gym A: 200$5$ per visit. Write the advice as a visits-per-year threshold.

Answer

Equal at visits. Fewer than : pay per visit; more than : the membership; at exactly they tie.

E3 (Challenge). A model recommends Option A by 12200180220$0.90$1.00$. Does the recommendation survive the range?

Answer

The gap changes by 0.10\pm 20\pm$2$12$10$ at worst. A survives comfortably; the report can say so with numbers.

E4 (Challenge). Write the one-paragraph report for: bulk pack of juice boxes at 28.80$0.7540$ boxes.

Answer

Bulk unit price c beats c — but the buyer needs , and singles cost 30$28.80488$ spare; recommend the pack unless the spares are truly worthless, in which case it is nearly a tie and convenience decides.

Homework

1. A model gives . (a) Interpret both constants. (b) Find break-even and write it as advice. (c) Find the profit at .
2. Plan A: 30$148190210$ units — what should your report say?
3. Badges cost 0.9030$2.50$4070$ customers.
4. Reasoning. A break-even of items was reported as ” items”. Explain the error and its consequence.
5. Reasoning. Explain why “the cheaper option” can depend on a quantity the reader must estimate, using one of this lesson’s scenarios.
6. Challenge. Build the full four-part report for: hiring a popcorn machine at 95$1.20$33090130$ serves.

Answers: Q1 — (a) 4.50$11726117/4.5 = 2626P = 02726$15330 = 14 + 0.08u \Rightarrow u = 2002002001617P = an - b16.2P=01617P = 2.7n - 95P = 1.8n0.9n > 95n = 10690130106$ as the hinge.