Target Costing and Pricing Dino's, Inc., makes a variety of...

Target Costing and Pricing Dino's, Inc., makes a variety of T-shirts with logos. The company has discovered a new market for sweatshirts with logos. Market research indicates that a sweatshirt like this would sell well in the market priced at $$\$ 36$$ each. Dino's desires an operating profit of 25 percent of costs. Required What is the highest acceptable manufacturing cost for which Dino's would be willing to produce the sweatshirt?

Target Costing and Pricing
Dino's, Inc., makes a variety of T-shirts with logos. The company has discovered a new market for sweatshirts with logos. Market research indicates that a sweatshirt like this would sell well in the market priced at $$\$ 36$$ each. Dino's desires an operating profit of 25 percent of costs.

Required
What is the highest acceptable manufacturing cost for which Dino's would be willing to produce the sweatshirt?

Key Concepts

Target Costing

Target costing is a pricing strategy in which a company determines the planned selling price based on market conditions and then subtracts the desired profit margin to arrive at a target cost. This method ensures that new products are designed with cost efficiency in mind so that production costs do not exceed the amount available to achieve the desired profitability.

Pricing Strategy

Pricing strategy involves setting the selling price of a product based on various factors such as consumer demand, competition, and market research. When a market price is predetermined or highly competitive, companies use target costing to ensure that their production costs align with the price to maintain overall profitability.

Operating Profit Margin

Operating profit margin is the percentage of cost or revenue that is planned to be retained as profit after covering operating expenses. In target costing, this margin is a critical parameter used to determine the maximum allowable cost for production, ensuring that the company's desired level of profitability is maintained after all costs are incurred.

Transcript

00:01 So we have an equation for how much it's going to cost them to produce x shirts, and that's 2x plus 26, when x is greater than or equal to zero.

00:09 And then we have a price demand equation, a little p sub x, and that is 30 minus 2x.

00:19 And this would be the price that they're going to sell them at.

00:24 And we know that profit, capital p of x, will be how many shirts they sell, times the amount.

00:33 That they're going to charge for the shirt less the cost and so our function will end up being negative 2x squared and then we're going to have plus 30x minus 2x minus 26 so our profit equation is negative 2x squared plus 28 x minus 26 and this is where you're going to make how much profit you're going to make and we want to find what the maximum profit is and how many shirts do we have to sell.

01:09 So we know that this will happen at the vertex, and this parabola is going to open downward.

01:14 And we know that the x value of the vertex occurs at negative b over 2a, so negative 28 over 2 times negative 2, negative 4.

01:28 So seven shirts is where they will maximize their profit.

01:36 And the amount of profit they'll make for seven shirts is negative two times seven squared plus 28 times seven minus 26.

01:48 And i just put that in my calculator and that comes out to be $72.

01:55 And then we want to know, well, how much should you charge for the shirt? so that little p of seven is what the price will be for that demand.

02:05 And so we're going to take that 30 minus 2 times 7 and 2 times 7 is 14.

02:13 So $16 per shirt is what we would charge to get that maximum profit.

02:21 And we would sell 7 shirts.

02:23 And then we do want to find that break -even point.

02:27 So we know again that this parabola basically looks like this.

02:32 So the y intercept down here at negative 26 and it's going to come up and it's going to come down.

02:37 We want to know where are you going to break even...

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