Pricing methods — practice questions

Recommend penetration pricing — launch near $20 (undercut rivals) to build volume quickly in elastic market.

Cost constraint: Price must exceed variable cost ($12) in short run for positive contribution. At $20, contribution = $8 per unit toward fixed costs (5.4.4 break-even).

Risk: If price stays below full cost ($18) long term, business unsustainable unless scale cuts unit cost. Plan to raise price or cut costs once share secured.

The solution involves calculating the full cost per unit and then adding the desired mark-up.

Step 1: Calculate the fixed cost per unit. $\text{Fixed Cost per Unit} = \frac{\text{Total Fixed Costs}}{\text{Expected Sales Volume}}$ $\text{Fixed Cost per Unit} = \frac{\text{\textdollar}6,500}{5,000 \text{ units}} = \text{\textdollar}1.30 \text{ per unit}$

Step 2: Calculate the full cost per unit. $\text{Full Cost per Unit} = \text{Variable Cost per Unit} + \text{Fixed Cost per Unit}$ $\text{Full Cost per Unit} = \text{\textdollar}1.80 + \text{\textdollar}1.30 = \text{\textdollar}3.10 \text{ per unit}$

Step 3: Calculate the mark-up amount. $\text{Mark-up Amount} = \text{Full Cost per Unit} \times \text{Mark-up Percentage}$ $\text{Mark-up Amount} = \text{\textdollar}3.10 \times 75\% = \text{\textdollar}2.325$

Step 4: Calculate the final selling price. $\text{Selling Price} = \text{Full Cost per Unit} + \text{Mark-up Amount}$ $\text{Selling Price} = \text{\textdollar}3.10 + \text{\textdollar}2.325 = \text{\textdollar}5.425$

Final Answer: The calculated selling price is $5.43 (rounded to two decimal places). Artisan Bakes might choose to set the final price at $5.45 or $5.49 for practical and psychological reasons.