Chapter A, Problem 1P

Mary Williams, owner of Williams Products, is evaluating whether to introduce a new product line. After thinking through the production process and the costs of raw materials and new equipment, Williams estimates the variable costs of each unit produced and sold at $6 and the fixed costs per year at $60,000.

1. If the selling price is set at $18 each, how many unit must be produced and sold for Williams to break even? Use both graphic and algebraic approaches to get your answer.
2. Williams forecasts sales of 10,000 units for the first year if the selling price is set at $14 each. What would be the total contribution to profits from this new product during the first year?
3. If the selling price is set at $12.50, Williams forecasts that first-year sales would increase to 15,000 units. Which pricing strategy ($14.00 or $12.50) would result in the greater total contribution to profits?
4. What oilier considerations would be crucial to the final decision about making and marketing the new product?

Summary Introduction

To calculate: The break even quantity using both graphic and algebraic approaches.

Concept Introduction: Break-even point is explained as a point where a company is earning no profits and incurring no losses reflecting that total cost is equivalent to total income.

Explanation of Solution

Given information:

Variable costs: $6 per unit

Fixed costs: $60,000

Selling price: $18 per unit

Break-even quantity: ?

Calculation of break even quantity:

  $\begin{array}{c}\text{Break even quantity}\left(\text{Q}\right)=\left(\frac{\text{Fixed costs}}{\text{Selling price}-\text{Variable costs}}\right)\\ \text{Q}=\frac{\$60,000}{\$18-\$6}\\ \text{Q}=5,000\text{units}\end{array}$

Hence, the break even quantity is 5,000 units.

Graphic approach for calculating break even quantity:

  

  Fig (1)

Summary Introduction

To calculate: The total contribution to profits from this new product.

Concept Introduction: Profit is explained as surplus of total income over total costs.

Explanation of Solution

Given information:

Forecasted sales: 10,000 units

Selling price: $14 per unit

Calculation of total contribution to the profits:

  $\begin{array}{c}\text{Total}\text{Contribution}=\text{Total}\text{revenue}-\text{Total}\text{cost}\\ =\left\{\left(\text{Price}\times \text{Quantity}\right)-\left[\text{Fixed}\text{costs}+\left(\text{variable}\text{costs}\times \text{Quantity}\right)\right]\right\}\\ =\left(\$14\times 10,000\right)-\left[\$60,000+\left(\$6\times 10,000\right)\right]\\ =\$20,000\end{array}$

Therefore, the total contribution from the new product is $20,000.

Summary Introduction

To calculate: The total contribution to profits from this new product if selling price is $12.50.

Concept Introduction: Profit is explained as surplus of total income over total costs.

Explanation of Solution

Given information:

Forecasted sales: 15,000 units

Selling price: $12.50 per unit

Calculation of total contribution to the profits:

  $\begin{array}{c}\text{Total}\text{Contribution}=\text{Total}\text{revenue}-\text{Total}\text{cost}\\ =\left\{\left(\text{Price}\times \text{Quantity}\right)-\left[\text{Fixed}\text{costs}+\left(\text{variable}\text{costs}\times \text{Quantity}\right)\right]\right\}\\ =\left(\$12.50\times 15,000\right)-\left[\$60,000+\left(\$6\times 15,000\right)\right]\\ =\$37,500\end{array}$

Therefore, the total contribution from the new product is $37,500.

If selling price is $14 and forecasted sales are 15,000 units, then,

Calculation of total contribution to the profits:

  $\begin{array}{c}\text{Total}\text{Contribution}=\text{Total}\text{revenue}-\text{Total}\text{cost}\\ =\left\{\left(\text{Price}\times \text{Quantity}\right)-\left[\text{Fixed}\text{costs}+\left(\text{variable}\text{costs}\times \text{Quantity}\right)\right]\right\}\\ =\left(\$14\times 15,000\right)-\left[\$60,000+\left(\$6\times 15,000\right)\right]\\ =\$60,000\end{array}$

It can be concluded that when selling price is $14 then it can get a greater total contribution to Company W.

Summary Introduction

To identify: The other considerations that would be crucial for final decision making for the new product.

Concept Introduction: Decision making is a process in which members of an organization select a particular course of action in response to both problem and opportunity. The objective of decision making is to gain a maximum and profitable result.

Explanation of Solution

Other considerations that would be crucial for final decision making of new product are:

• Company W can identify and evidently state the problems.

• Various other alternatives should be evaluated and for the same information should be collected.

Decisions are taken by organizations on the basis these procedures that are generally performed: break even analysis, decision tree, preference matrix and preference decision tree.