ACCG2000 Week 2 – Cost-Volume-Profit Analysis

Cost–Volume–Profit (CVP) Analysis

• Technique linking changes in sales volume to changes in
  • Costs (variable & fixed)
  • Revenue
  • Profit $\text{(Profit = Revenue – Costs)}$
• Managerial aim: inform decisions that lift profitability & shareholder value.

Key Concepts & Terminology

• Contribution Margin (CM)–related
  • Unit CM (UCM): $\text{UCM = Selling\ price\ per\ unit – Unit\ variable\ cost}$
  • Total CM (TCM): \text{TCM = Total\ sales – Total\ variable\ costs = UCM \times \text{Units}}
  • Contribution Margin Ratio (CMR): $\text{CMR = UCM / Selling\ price\ per\ unit}$
  • Contribution Margin Percentage (CMP): \text{CMP = CMR \times 100\%}
• Breakeven Point (BEP)
  • In units: $\text{BEP}_{units} = \dfrac{\text{Fixed\ costs}}{\text{UCM}}$
  • In dollars: $\text{BEP}_{\$} = \dfrac{\text{Fixed\ costs}}{\text{CMR}}$
• Safety Margin
  • Measures buffer between budgeted sales and BEP: $\text{Safety\ margin} = \text{Budgeted\ revenue – BEP\ revenue}$
• Target Profit (before tax)
  • Units required: $\text{Units} = \dfrac{\text{Fixed\ costs}+\text{Target\ profit}}{\text{UCM}}$
  • Dollars required: $\text{Sales}_{\$}= \dfrac{\text{Fixed\ costs}+\text{Target\ profit}}{\text{CMR}}$
• After-tax Target Profit
  • Convert after-tax goal to pre-tax using $\text{Target\ before\ tax} = \dfrac{\text{Target\ after\ tax}}{1-\text{Tax\ rate}}$
  • Plug into usual formulas.
• Sales Mix (multi-product): relative share of each product in expected sales.
• Weighted-Average UCM (WACM): $\text{WACM}=\sum (\text{UCM}<em>i \times \text{Sales-mix}</em>i)$

Contribution Margin Illustration (Lecture Example 1)

• Data (per handbag)
  • Selling price $=\$100$
  • Direct material $=\$28$
  • Direct labour $=1.5\text{h} \times \$14 = \$21$
  • Variable MOH $=\$16$
  • Variable cost total $=28+21+16 = \$65$
• Results
  • $\text{UCM}=100-65=\$35$
  • $\text{CMR}=35/100=0.35$ (→ CMP $=35\%$)
  • Total CM (6000 units): $35\times 6000 = \$210{,}000$
  • Practical link: $\text{CM}$ pays first for fixed costs (\$48,000) then profits.

Breakeven Computation (Lecture Example 2 – The Voice Concert)

• Parameters: $P=\$100$, $V=\$25$, $\text{FC}=\$750{,}000$
• $\text{UCM}=100-25=\$75$
• BEP (units): $750\,000/75 = 10\,000\text{ tickets}$
• BEP (revenue): $750\,000/(75/100)=\$1{,}000{,}000$

Safety Margin (Lecture Example 3 – Theatre Company)

• Capacity: $330\text{ seats} \times 30 \text{ performances}$
• Attendance 65 % → Expected units $=330\times30\times0.65=6435$
• $P=\$80$, $V=\$30$, $\text{UCM}=50$, $\text{FC}=\$320{,}000$
• BEP ($): $320\,000/(50/80)=\$512\,000$
• Budgeted revenue: $80\times6435 = \$514\,800$
• Safety margin: $514\,800-512\,000 = \$2\,800$ (2.7 k buffer before zero profit)

Target Profit (Lecture Example 4 – The Voice)

• Same costs as Example 2, target after-tax ignored.
• Desired pre-tax profit $=\$250\,000$
• Required units: $(750\,000+250\,000)/75=13\,333.3\rightarrow13\,334$
• Required revenue: $(750\,000+250\,000)/(75/100)=\$1\,333\,334$

CVP With Income Taxes (Lecture Example 5 – ABC Ltd)

• $P=\$10$; Variable $=5+1.4 = 6.4$ ⇒ $\text{UCM}=3.6$
• Fixed costs: $240\,000+380\,000=\$620\,000$
• After-tax target $=\$126\,000$, tax rate 30 %.
  • Pre-tax target: $126\,000/(1-0.3)=\$180\,000$
• Units required: $(620\,000+180\,000)/3.6 \approx 222\,223$

Multi-Product CVP

• Need sales-mix assumption & WACM.
• General BEP units: $\dfrac{\text{Fixed\ costs}}{\text{WACM}}$
• Split back into individual products in proportion to sales-mix.

Weighted-Average UCM Illustration (Lecture Example 6 – HealthyLife)

• Beef: $UCM=8-3=5$ ; Pork: $7-2.5=4.5$ ; Chicken: $6-2=4$
• Mix: 30 %, 50 %, 20 %.
• $\text{WACM}=0.30\times5+0.50\times4.5+0.20\times4=\$4.55$

BEP With Two Price Tiers (Lecture Example 7 – Opera House)

1. UCMs
   • VIP: $700-100=\$600$
   • Normal: $270-100=\$170$
2. Sales mix (capacity 2,500 seats): 10 % VIP, 90 % Normal.
3. $\text{WACM}=0.10\times600+0.90\times170=\$213$
4. BEP seats: $310\,000/213 \approx 1\,456$
   • VIP: $1456\times0.10\approx146$
   • Normal: $1456\times0.90\approx1\,310$
   • Rounding leads to 1,457 total for exact BEP.

Assumptions & Limitations of CVP

• Linear revenue & cost functions within relevant range.
• Single product or constant sales-mix.
• Constant selling price, variable cost/unit & total fixed cost.
• Inventory levels unchanged (units produced = units sold).
• Simplified; more reliable for small firms or discrete projects.
• For large, diversified firms: good for preliminary project screening but requires sensitivity & scenario analysis.