CVP Analysis – Key Points (Last-Minute Review)

Overview

• CVP (Cost–Volume–Profit) analysis assesses how changes in sales volume affect costs, revenue, and profit.
• Aim: aid decision-making to improve profitability and shareholder value.

Key Terms

• Contribution margin variables
• Breakeven Point (in sales units)
• Breakeven Point (in dollars)
• Safety margin
• Weighted average contribution margin (WACM)

Core Formulas

• Unit contribution margin (UCM): $ext{UCM} = p - v$ where $p$ = unit selling price, $v$ = unit variable cost.
• Total contribution margin (TCM): $ext{TCM} = ext{Sales} - ext{Variable costs}$
• Alternative: $ext{TCM} = ext{UCM} imes ext{Units sold}$
• Contribution margin ratio (CMR): $ext{CMR} = \frac{ ext{UCM}}{p}$
• Contribution margin percentage (CMP): ext{CMP} = ext{CMR} imes 100 ext{%}
• Breakeven (units): $BE_{ ext{units}} = \frac{F}{ ext{UCM}}$
• Breakeven (dollars): $BE_{ ext{dollars}} = \frac{F}{ ext{CMR}}$

Breakeven (step-wise)

• Step 1: calculate Unit Contribution Margin (UCM).
• Step 2: use BE formulas above:
  • $BE_{ ext{units}} = \frac{F}{ ext{UCM}}$
  • $BE_{ ext{dollars}} = \frac{F}{ ext{CMR}}$

Safety Margin

• Definition: difference between budgeted (or actual) sales and breakeven sales.
• Formula: $ext{Safety margin} = ext{Budgeted sales} - BE_{ ext{dollars}}$
• Interpretation: reflects how much sales can drop before profits reach zero.

Target Net Profit (and Taxes optional)

• Target sales volume (units): $ext{Target units} = \frac{F + ext{Target profit}}{ ext{UCM}}$
• Target sales (dollars): $ext{Target dollars} = \frac{F + ext{Target profit}}{ ext{CMR}}$
• Including income taxes:
  • Target profit before tax: $ext{Target profit before tax} = \frac{ ext{Target net after tax profit}}{1 - t}$ where $t$ = tax rate.
  • Then use the same BE/Target formulas with the before-tax figure.

CVP with Multiple Products

• Key term: Sales mix (relative proportions of each product sold).
• Weighted average unit contribution margin (WACM): ext{WACM} =
  ext{(weight of product 1)} imes ext{UCM}1 + ext{(weight of product 2)} imes ext{UCM}2 + \, ext{…}
• Steps:
  • Compute UCM for each product: $ext{UCM}<em>i = p</em>i - v_i$
  • Compute WACM using sales mix weights (by units or revenue): e.g. weights sum to 1.
  • BE units (in total): $BE_{ ext{units}} = \frac{F}{ ext{WACM}}$
  • Allocate BE units to products in the sales mix proportion.

Example Highlights (condensed from slides)

• Example 1 (single product): UCM = $35$; CMR = $0.35$; CMP = 35 ext{%}; TCM = $210000$.
• Example 2 (breakeven): BE units = $10000 ext{ units}$; BE dollars = $1000000 ext{ dollars}$.
• Example 3 (breakeven & safety): BE dollars = $512000$; Safety margin = $2800$.
• Example 4 (target profit): Target units = $13334\text{ units}$; Target dollars = $1333334$.
• Example 6 (multiple products): UCM (Beef) = $5$; UCM (Pork) = $4.5$; UCM (Chicken) = $4$; WACM = $4.55$.
• Example 7 (two prices): Weighted average UCM = $213$; BE seats ≈ $1456$; VIP ≈ $146$, Normal ≈ $1311$ (rounded).

Taxes in CVP (overview)

• When evaluating after-tax profit, convert to pre-tax profit first:
  • $ext{Target profit before tax} = \frac{ ext{Target net after tax profit}}{1 - t}$
  • Use BE/target formulas with pre-tax profit.

Limitations

• CVP is a simplified model with assumptions that may not hold in reality:
  • Linear cost and revenue behavior within the relevant range.
  • Fixed costs remain constant; variable costs per unit remain constant.
  • Selling price remains constant.
  • Only holds within the relevant range of activity; external factors ignored.

Quick reference formulas

• UCM: $ext{UCM} = p - v$
• TCM: $ext{TCM} = ext{Sales} - ext{Variable costs} = ext{UCM} imes ext{Units}$
• CMR: $ext{CMR} = \frac{ ext{UCM}}{p}$
• BE (units): $BE_{ ext{units}} = \frac{F}{ ext{UCM}}$
• BE (dollars): $BE_{ ext{dollars}} = \frac{F}{ ext{CMR}}$
• Safety margin: $ext{Safety margin} = ext{Budgeted sales} - BE_{ ext{dollars}}$
• Target (units): $ext{Target units} = \frac{F + ext{Target profit}}{ ext{UCM}}$
• Target (dollars): $ext{Target dollars} = \frac{F + ext{Target profit}}{ ext{CMR}}$
• Taxes (pre-tax target): $ext{Target profit before tax} = \frac{ ext{Target net after tax profit}}{1 - t}$
• WACM (multi-product): ext{WACM} =
  igl(w1 igr) ext{UCM}1 + igl(w2 igr) ext{UCM}2 + \,igr)