Mathematics • Year 10 • Unit 1 • Lesson 7
Depreciation and Smart Money Decisions
Use straight-line and reducing balance depreciation to compare real Australian assets: a new car, a tradie's ute, a gaming PC, factory equipment, and a "buy vs lease" decision. Then explain your reasoning.
1. Word problems
Each problem uses one (or both) of the methods from Lesson 7: straight-line (constant dollars per year) or reducing balance (Book Value = P(1 − r)ⁿ). Read carefully — sometimes the question tells you which method to use; sometimes you choose. Show your working.
1.1 — New car (reducing balance). Hamish buys a new Hyundai i30 for $32,000 from a Sydney dealer. The ATO's diminishing-value rate for passenger cars is around 25% p.a.
(a) What is the book value of the car after 1 year? After 3 years?
(b) The lesson says new cars typically lose 15–20% in the first year and 10–15% afterwards. Does a flat 25% feel high or low for year 1? Explain in one sentence. 3 marks
1.2 — Tradie's ute (straight-line, with scrap value). A plumber buys a Toyota Hilux for $55,000 to use for 8 years. At the end she expects to sell it as a used work ute for around $15,000 (scrap value).
(a) Using straight-line depreciation, what is the annual depreciation?
(b) What is the book value after 5 years?
(c) Why might the ATO suggest a tradie use reducing balance instead for the first few years? 3 marks
1.3 — Gaming PC (reducing balance, fast obsolescence). Mei builds a gaming PC for $3,200. Because technology becomes outdated quickly, she uses reducing balance with r = 30% p.a.
(a) What is the book value after 4 years?
(b) Roughly how many whole years until the PC is worth less than $500? (Try n = 4, 5, 6, ...) 3 marks
1.4 — Factory equipment (straight-line, decision making). A clothing factory has two CNC machines.
Machine A: cost $80,000, scrap value $10,000, useful life 10 years.
Machine B: cost $50,000, scrap value $5,000, useful life 6 years.
(a) Find the annual straight-line depreciation for each machine.
(b) Which machine has the higher annual depreciation cost? Justify with your numbers. 3 marks
1.5 — Buy vs lease decision. A small business is choosing between two options for a $20,000 piece of equipment used for 4 years.
Option A — Buy: pay $20,000 upfront; reducing balance at 15% p.a.; sell at the end-of-year-4 book value.
Option B — Lease: pay $5,500 per year for 4 years (no resale, no ownership).
(a) Find the book value of the equipment after 4 years (Option A).
(b) Net cost of Option A over 4 years = purchase − resale value. Compute it.
(c) Total cost of Option B = annual lease × 4. Compute it.
(d) Which option is cheaper, and by how much? 4 marks
2. Explain your thinking
This question is about communication, not just answers. Use full sentences. 4 marks
2.1 A friend says "Straight-line and reducing balance must give the same answer over the same useful life — they're both just depreciation." Using a worked example of your own choice (clearly stated), explain (i) why this is wrong in general, (ii) what is true only when the scrap value is zero, and (iii) which method the lesson recommends for cars and technology, and why.
How did this worksheet feel?
What I'll revisit before next class:
1.1 — New car at 25% reducing balance
(a) After 1 year: 32,000 × 0.75 = $24,000. After 3 years: 32,000 × (0.75)³ = 32,000 × 0.421875 = $13,500.
(b) A flat 25% in year 1 is slightly above the lesson's 15–20% range for new cars — so the ATO's diminishing-value rate is somewhat aggressive for a small hatch but realistic for tax purposes.
1.2 — Hilux straight-line $55,000 → $15,000 over 8 years
(a) Annual depreciation = (55,000 − 15,000) ÷ 8 = 40,000 ÷ 8 = $5,000 per year.
(b) Book value after 5 years = 55,000 − (5,000 × 5) = 55,000 − 25,000 = $30,000.
(c) Reducing balance gives a much bigger depreciation amount in the early years, so the tradie can claim more on her tax return sooner — useful when cash flow matters.
1.3 — Gaming PC at 30% reducing balance
(a) Book value after 4 years = 3,200 × (0.70)⁴ = 3,200 × 0.2401 = $768.32.
(b) Try n = 5: 3,200 × (0.70)⁵ = 3,200 × 0.16807 = $537.82 — still above $500.
Try n = 6: 3,200 × (0.70)⁶ = 3,200 × 0.117649 = $376.48 — below $500.
Answer: 6 years.
1.4 — Two factory machines
Machine A: (80,000 − 10,000) ÷ 10 = 70,000 ÷ 10 = $7,000/year.
Machine B: (50,000 − 5,000) ÷ 6 = 45,000 ÷ 6 = $7,500/year.
Machine B has the higher annual depreciation cost ($7,500 vs $7,000), even though Machine A is more expensive — because Machine B has a shorter useful life.
1.5 — Buy vs lease ($20,000, 4 years)
(a) Book value after 4 years (15% reducing balance) = 20,000 × (0.85)⁴ = 20,000 × 0.522006 = $10,440.13.
(b) Net cost of buying = 20,000 − 10,440.13 = $9,559.87.
(c) Total cost of leasing = 5,500 × 4 = $22,000.
(d) Buying is cheaper by 22,000 − 9,559.87 = $12,440.13 over 4 years. (Assuming the business can pay the $20,000 upfront and has somewhere to store the equipment.)
2.1 — Explain your thinking (sample response)
My friend is wrong in general because the two methods only have to agree on total depreciation when the scrap value is zero and the reducing-balance rate is chosen to bring the book value down to zero — which essentially never happens, since reducing balance never reaches zero in finite time. The pattern of depreciation is always different: straight-line loses the same dollar amount each year, while reducing balance loses a percentage of a shrinking balance (so the dollar loss starts large and gets smaller).
Worked example. A $10,000 asset, 4-year life. Straight-line with scrap = 0 → $2,500/year, book values: $7,500, $5,000, $2,500, $0. Reducing balance at 40% → book values: $6,000, $3,600, $2,160, $1,296 — never reaches zero.
The lesson recommends reducing balance for cars and technology because those assets actually lose value faster in early years — the model matches reality.
Marking: 1 mark for noting the pattern differs; 1 for the scrap-value subtlety; 1 for a worked example; 1 for the correct recommendation with a reason.