082i - Consolidation Financial Modelling

Lesson 82 — Consolidation and Check: Modelling with Rational Numbers and Percentages

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

Learning Intentions

• To complete an extended financial modelling task independently.
• To demonstrate the full cycle: formulate, solve, interpret, communicate.

Success Criteria

I can:

1. Build a financial model from a realistic brief, stating assumptions.
2. Use fractions, decimals and percentages accurately within it.
3. Round correctly for the context and interpret every figure.
4. Deliver a recommendation with sensitivity and limits.

Warmup

(6 minutes — whole-block retrieval, mini whiteboards)

1. A price of 77$ includes GST. Find the GST.
2. Interest on 4005%2$ years?
3. Interpret the in “selling price cost”.
4. Break-even for ? State it as advice.
5. =B2*C2 in a spreadsheet does what?

Answers: 1. 7$4060%3485 \div 2.5 = 343435$); 5. Multiplies cells B2 and C2, updating automatically.

Activities

Activity 1 — The Main Task (30 min)

Individual or pairs. The N09 assessment piece — a four-part report. Calculators (or spreadsheets, if the room allows) encouraged; the thinking, not the arithmetic, is being assessed.

The Year 7 Movie Fundraiser.

Your class will screen a movie to raise money for camp. The facts:

• Licence fee: 180$ flat.
• The hall is free, but the school requires supervising adult per attendees; each adult receives a 15$ thank-you voucher.
• Tickets: you must choose the price — market research suggests attendance of about at 5120$790$9$.
• Snacks: popcorn cups cost 0.60$2.5034$ attendees buy one.
• GST: ticket and snack prices are GST-free for school fundraisers (no GST work needed — stated so the report can say so).

Produce a report recommending a ticket price, with the full expected profit calculation for your chosen price, at least a summary comparison of all three options, correct rounding with reasons, and a sensitivity note.

Reference analysis (teacher):

For attendance : adults ; popcorn sales (round sensibly).

The designed punchline: 5$7$2$5$7$9$ is clearly worse. Marking rewards recognising the tie, not picking the “right” price.

Marking emphases: assumptions stated (attendance figures trusted; buy popcorn; adults sourced); ceilings used for adults ( attendees would need , not ); popcorn count rounded and the choice named ( or at ); sensitivity — e.g. “if only come at 5788 - 100 - (\text{popcorn} -15 \times 1.9 \approx 28.50) \approx $660$9$ option.”

Extension for early finishers: the P&C offers to underwrite the licence for of profits. Should you accept? (At : keep of ? No — recompute: without licence cost, profit becomes ; giving leaves . Decline — but only just, and the answer flips if attendance is weak, since the underwriting removes a fixed risk.)

Activity 2 — Peer Audit (9 min)

Swap reports; audit against the checklist:

Check	✓ / ✗ / ?
All three prices compared, not just one computed
Adults counted with a ceiling, vouchers costed
Popcorn take-up applied to attendance, not to ticket revenue
Every rounding has a direction and a reason
The near-tie between 5$7$ is acknowledged
The recommendation names its hinge assumption

Audit debrief — the popcorn trap: some reports will compute revenue instead of attendees. Surface it: take-up rates apply to people, and the units (600$ “popcorn buyers”?) expose the error — units-checking is the fastest audit tool.

Checks for Understanding

(6 minutes — exit ticket, collected)

1. Why does the adult count use a ceiling rather than nearest rounding?
2. At 7120$ attendees, verify the popcorn profit figure.
3. The 5$7$2$. What should a report conclude?
4. State one hinge assumption of the whole model and how you would test it.
5. Reasoning. Which single input, if optimistic, hurts the recommendation most — and why?

Answers: 1. attendees legally require adults; rounding to breaks the requirement; 2. cups 171$ ✓; 3. That the model cannot separate them at this precision — decide on secondary grounds and say so; 4. E.g. the attendance-vs-price estimates; test against a similar past event or pre-sales; 5. Attendance — it drives tickets and popcorn and the adult count together, so its error propagates through every line.

Common Misconceptions

Misconception	How to pre-empt it
Applying the popcorn rate to dollars instead of people.	The audit’s named trap; units-checking.
Nearest-rounding the supervising adults.	Exit Q1 — the requirement forces the ceiling.
Computing only the favourite option.	Checklist row 1: comparison is the task.
Declaring a winner inside the noise.	The designed 2$ tie; marking rewards honesty about it.
Fixed costs scaled with attendance (licence “per person”).	Warmup Q4’s structure and the L78 cost sort.
Presenting profit without the working that survives audit.	The audit is the immediate consequence.

Enrichment — Competition-Style Problems

E1 (Kangaroo style). With attendees, how many supervising adults are needed, and what do the vouchers cost?

Answer

adults; 75$.

E2 (AMC Junior style). Popcorn margin is 1.90\tfrac34aa = 144$.

Answer

; at : 205.20$.

E3 (Challenge). The three research points , , do not lie exactly on one line. Using just the outer two points, find a linear model and predict attendance at 6$7$?

Answer

; . So ; at : . At the model predicts against the researched — off by . Models smooth data; the discrepancy is worth a sentence in any report that uses the model.

E4 (Challenge). Ticket revenue under the E3 model is . Tabulate for and find the revenue-maximising price.

Answer

: 800$855$875$860$810p = 7p \approx 7.07$; the table finds it well enough, and popcorn pulls the best overall price slightly lower.)*

Homework

1. Complete any unfinished report sections, incorporating one audit comment.
2. Recompute your chosen option with attendance lower. Present the two profit figures side by side and state whether your recommendation survives.
3. A rival class proposes a quiz night: entry 680$120$1.10$ per person with everyone eating. Build the profit model and compare its expected profit with your movie night’s.
4. Reasoning. Explain why attendance uncertainty matters more than popcorn-price uncertainty in the movie model.
5. Reasoning. The licence underwriting offer (extension) removes risk but costs expected profit. Explain the trade-off in one paragraph — when is it worth accepting?
6. Challenge. Using E3’s demand model , include popcorn () and adults () and the 180p = 59$. Does the best price move from E4’s revenue answer?

Answers: Q2 — e.g. at 5a = 1447204 \to 60108 \times 1.9 = 205.20P = 685.20$9P = 6 \times 80 - 120 - 1.10 \times 80 = 480 - 120 - 88 = $272\approx $788\approx $14a = 247.5 - 17.5pp=5a=160P = 800 + 228 - 180 - 60 = $788p=6a=142.5P = 855 + 203.06 - 180 - 60 \approx $818p=7a=125P = 875 + 178.13 - 180 - 60 \approx $813p=8a=107.5P = 860 + 153.19 - 180 - 45 \approx $788p=9a=90P = 810 + 128.25 - 180 - 45 \approx $713$6a > 120$) reward the fuller hall.