19 Pricing

The Theory

Prices for products are sometimes determined by demand, in which case management has little control over how much customers pay for the firm’s products. In other cases, however, management has some leeway over how much to charge for the firm’s products. In those situations, the price set will depend on whether the goods are sold to external or internal customers and whether the price is set for the short run or for the long run.

Normally, goods are sold to external customers, and they are priced for the long run. In this situation, the price should be set so that it covers all future fixed and variable costs and provides an appropriate return. A firm can base their desired profit on costs, in which case the profit percentage is called a markup on full costs, or on revenue, in which case the profit percentage is called a profit margin.

Sometimes, goods sold to external customers are priced for the short run, such as when a company is trying to liquidate inventory quickly or when a customer places a special order. In this situation, the minimum price the company could charge just needs to cover any future costs associated with selling the goods. Ordinary fixed costs and sunk costs should be ignored.

When goods are sold internally, from one division of a firm to another, the price set is called a transfer price because goods are basically just transferred within the firm. Setting a transfer price is not always necessary but can be useful if the firm wishes (or is required) to calculate the income of each division separately. Transfer prices do not affect the pre-tax income of the firm as a whole, because they result in a cost to the receiving division equal to the revenue to the transferring division. However, they affect the income of each individual division. If the transfer price is high, income will be shifted from the receiving division to the transferring division. If the transfer price is low, income will be shifted from the transferring division to the receiving division.

Because of this income shifting, transfer prices can affect the income tax paid by the firm, because the divisions may be located in jurisdictions with different tax rates. If the divisions are located in different tax jurisdictions, the company as a whole will prefer a transfer price that shifts income to the division with the lower tax rate. If the transferring division has the lower tax rate, the company will prefer a high transfer price so income will be shifted to the transferring division. If the receiving division has the lower tax rate, the company will prefer a low transfer price so income will be shifted to the receiving division.

Transfer prices can be set in any way the firm wishes as long as they are reasonable. The lower limit on a reasonable transfer price is the variable cost to produce the transferred product, and the upper limit is close to the market price. Transfer prices may be based on variable cost, full cost, or market price, including (or not including) a markup (profit).

Alternatively, the managers of the transferring and receiving divisions may be free to negotiate a transfer price between themselves. In a negotiation, the transferring division will not be willing to accept less than the variable cost to manufacture the goods. If the goods could be sold to other customers, the transferring division will not be willing to accept less than the market price of the goods, minus any costs the division has of selling the goods externally. If the transfer price is lower than that amount, the transferring division would do better to sell to other customers. The receiving division will not be willing to accept more than the market price of the goods plus any costs the division has of buying the goods externally. If the transfer price is higher than that amount, the receiving division would do better to buy from another seller.

The Method

Long-Run Pricing for External Customers

To calculate a long-run price for external customers, first estimate the unit sales and the costs associated with the product over its entire life. If any of the firm’s costs depend on revenue, you will need to use a variable for revenue; you will not be able to calculate total costs numerically because revenue will be unknown until you complete the next step.

Next, calculate estimated total revenue.

• If the firm expresses desired profit as a markup on full costs, multiply full costs by the markup percentage. If all costs are numerical, the result is total revenue.
• If the firm expresses desired profit as a profit margin, divide full costs by one minus the profit margin percentage. If all costs are numerical, the result is total revenue.
• If any of the firm’s costs depend on revenue, the result will equal the variable used to represent revenue. Set up an equation and solve for that variable.

Finally, divide estimated total revenue by total estimated unit sales to calculate the long-run price per unit.

Short-Run Pricing for External Customers

To calculate the minimum short-run price for external customers, identify the costs associated with the product that will occur in the future. The minimum price for the goods should equal the total of these future costs.

Transfer Pricing

To calculate a transfer price using a base such as variable cost, full cost, or market price, calculate the markup by multiplying the base by one plus the markup percentage. Express the transfer price on a per-unit basis.

If a firm negotiates transfer prices, the final transfer price will fall within a range. The minimum of that range depends on how much the transferring division would earn by selling the goods on the open market, which falls into one of three situations:

1. If the transferred goods cannot be sold on the open market, the minimum price should be the variable cost of producing the product.
2. If all the transferred goods can be sold on the open market, the minimum price should be the market price minus any additional costs the transferring division would pay to sell on the open market.
3. If some, but not all, of the transferred goods can be sold on the open market, the minimum price should be a weighted average of A (weighted by the number of units that cannot be sold externally) and B (weighted by the number of units that can be sold externally).

The maximum of the negotiated transfer price range depends on how much the receiving division will pay to buy the goods on the open market, which would be the market price of the goods plus any additional costs the receiving division would pay to buy on the open market.

If the transferring division operates in a different tax jurisdiction from the receiving division, the firm will want to maximize income in the division with the lower tax rate. If the transferring division has the lower tax rate, the firm will want the transfer price to be as high as possible. If the receiving division has the lower tax rate, the firm will want the transfer price to be as low as possible.

Illustrative Examples

Long-Run Pricing for External Customers

Omega Company is considering launching a new product. The firm has estimated that the product will have a 5-year life once sales begin, and that as long as the price is below $150, sales will be 10,000 units the first year, increase by 50% the second year, then decrease by 40% each of the following 3 years. The product will require an investment of $500,000 in design and development costs, $800,000 in machinery and equipment, $1,000,000 in advertising costs, and $200,000 in administrative expenses over the course of its life. Manufacturing the product will require $20 per unit in direct materials, $25 per unit in direct labor, and $15 per unit in variable manufacturing overhead. In addition, Omega pays a 5% commission to its salespeople. Omega hopes to earn a profit of 10% of full costs.

What price should be set for the product?

First, estimate the unit sales and the costs associated with the product over its entire life.

• Unit sales:
  • Year 1: 10,000
  • Year 2: 10,000 × 1.5 = 15,000
  • Year 3: 15,000 × .6 = 9,000
  • Year 4: 9,000 × .6 = 5,400
  • Year 5: 5,400 × .6 = 3,240
  • Total unit sales: 10,000 + 15,000 + 9,000 + 5,400 + 3,240 = 42,640
• Costs:
  • Fixed costs: $500,000 + $800,000 + $1,000,000 + $200,000 = $2,500,000
  • Variable costs: ($20 + $25 + $15) × 42,640 = $2,558,400
  • Commission: 5% of revenue = 0.05 R, where R is a variable for revenue
  • Total costs: $2,500,000 + $2,558,400 = $5,058,400 + 0.05 R

Next, calculate estimated total revenue.

• • The firm expresses profit as a markup on full cost, so multiply total costs by one plus the markup percentage: ($5,058,400 + 0.05R) x 110% = $5,564,240 + 0.055R
    • Note: If the firm expresses profit as a profit margin, divide total costs by one minus the markup percentage.

•  The firm has a cost based on revenue, so set up an equation for revenue and solve:
  • R = $5,564,240 + 0.055R
  • R − 0.055R = $5,564,340
  • 0.945R = $5,564,340
  • R = $5,564,340 / 0.945 = $5,888,190.48

Finally, divide estimated total revenue by total estimated unit sales to calculate the long-run price per unit.

• $5,588,190.48 / 42,640 = $138.09 per unit

Short-Run Pricing for External Customers

George’s Emporium sells discount merchandise. The company has decided to clear out their inventory of 200 bouncy balls to make way for new products. Each ball cost George’s Emporium $0.30, and each ordinarily sells for $0.50. In addition, George’s has spent $50 on stocking, storing, advertising, and maintaining the balls so far. George’s will incur costs of approximately $0.05 per ball to sell the balls at this point (the opportunity cost of shelf space).

What minimum price should George’s Emporium charge for each ball?

The company should charge, at minimum, $0.05 per ball, as that cost occurs in the future. All other costs, including the purchase price, are sunk costs.

Transfer Pricing

Dunham Company has two divisions: the Parts division is located in Argentina, where the tax rate is 35%, and the Assembly division is located in the United States, where the tax rate is 20%. The Parts division manufactures parts at a variable cost of $50 per part, which are transferred to the Assembly division, who uses them to manufacture the final product. Each unit of final product requires 10 parts. In addition to the cost of the parts, the Assembly division incurs $300 in variable costs per unit to manufacture the final product. The Parts division produces 100,000 parts per year, and the Assembly division produces 10,000 units of final product per year. Fixed costs are $2,500,000 for the Parts division and $3,000,000 for the Assembly division. The market price for parts is $100 per unit. Market demand is unlimited, but if the Parts division wants to sell on the outside market, they will incur marketing costs of $1,000,000 that they would not incur if they transfer the goods to the Assembly department. The selling price of the final product is $1,500 per unit.

1. Calculate the transfer price if it is based on:
   1. Variable cost with a 10% markup
   2. Full cost with a 10% markup
   3. Market price
2. Would the company prefer a high or low transfer price?
3. What range would the transfer price fall into if it were negotiated between the two divisions?

 

1. Multiply the base by one plus the markup percentage.
   1. Variable cost with a 10% markup
      1. Variable cost = $50.00
      2. Transfer price = $50.00 × 110% = $55.00
   2.  Full cost with a 10% markup
      1. Full cost = ($50 + $2,500,000 / 100,000) =$75.00
      2. Transfer price = $75.00 × 110% = $82.50
   3. Market price
      1. Market price = $100; there is no markup, so the transfer price is $100.00
2. Parts has a higher tax rate than Assembly, so the company would prefer a low transfer price. This price shifts the most income from Parts to Assembly, maximizing profit in the country with the lower tax rate and minimizing profit in the country with the higher tax rate.
   1. Note: If Parts had a lower tax rate than Assembly, the company would prefer a high transfer price to shift income from Assembly to Parts.
3. Minimum of the range:
   1. Demand is unlimited, so the Parts division can sell all their goods on the open market. The minimum price should be the market price, $100, minus any additional costs the transferring division would pay to sell on the open market. The additional cost per unit is $1,000,000 / 100,000 = $10, so the minimum of the negotiated range would be $100 – $10 = $90.
   2. The maximum price should be the market price plus any additional costs to the receiving division of buying on the open market. The Assembly division has no additional costs of buying on the open market, so the maximum of the range is $100.
   3. The range if the transfer price is negotiated will be $90 – $100.

 

Lecture Examples

Long-Run Pricing for External Customers

Your firm is considering developing a new product. The product will cost $7,000,000 to develop. Product-related costs will be $250,000 per year plus $15 per unit. Your firm plans to manufacture an average of 40,000 units per year over the product’s 8-year life.

1. What price should be set for the product if your firm wishes to earn a profit margin of 10%?

Short-Run Pricing for External Customers

Your firm is liquidating their inventory, which cost $20 per unit to purchase. Selling costs will be $5 per unit, and the opportunity cost of holding the inventory until it is sold will be $3 per unit.

1. What minimum price should be set for the product?

Transfer Pricing

Your firm has two divisions. West Division manufactures 100,000 bearings per year at a variable cost of $5 per unit, which they transfer to East Division, who uses 10 bearings in each of the 10,000 machines they produce. Each machine costs an additional $250 in variable costs to manufacture, and East Division sells them for $500 per unit. Fixed costs are $300,000 per year for West Division, and $800,000 per year for East Division. The bearings sold by West Division have a market price of $10 per bearing, but West Division would have to spend $100,000 per year in advertising to sell on the market.

1. Calculate the transfer price if it is based on variable cost with a 20% markup. Then calculate the net income of each division and the firm as a whole with this transfer price.
2. Calculate the transfer price if it is based on full cost with a 20% markup. Then calculate the net income of each division and the firm as a whole with this transfer price.
3. Calculate the transfer price if it is based on market price. Then calculate the pre-tax income of each division and the firm as a whole with this transfer price.
4. If the two divisions were to negotiate the transfer price, what would be the minimum price acceptable to West Division? The maximum acceptable to East Division?
5. West Division is located in a state with a tax rate of 25%, and East Division is located in a state with a tax rate of 20%. Would the firm prefer a high or low transfer price?