# Cost-plus pricing

Cost-plus pricing

Cost-plus pricing is a pricing method used by companies to maximize their profits.

The firms accomplish their objective of profit maximization by increasing their production until marginal revenue equals marginal cost, and then charging a price which is determined by the demand curve. However, in practice, most firms use cost-plus pricing, also known as markup pricing. There are several varieties, but the common thread is that one first calculates the cost of the product, then adds a proportion of it as markup. Basically, this approach sets prices that cover the cost of production and provide enough profit margin to the firm to earn its target rate of return.It is a way for companies to calculate how much profit they will make. Cost-plus pricing is often used on government contracts (cost-plus contracts), and has been criticized as promoting wasteful expenditures.

The method determines the price of a product or service that uses direct costs, indirect costs, and fixed costs whether related to the production and sale of the product or service or not. These costs are converted to per unit costs for the product and then a predetermined percentage of these costs is added to provide a profit margin.

Cost-plus pricing is used primarily because it is easy to calculate and requires little information. Information on demand and costs is not easily available, managers have limited knowledge as far as demand and costs are concerned. This additional information is necessary to generate accurate estimates of marginal costs and revenues. However, the process of obtaining this additional information is expensive. Therefore, cost-plus pricing is often considered the most rational approach in maximizing profits. This approach relies on arbitrary costs and arbitrary markups.

## Mechanics of cost-plus pricing

There are two steps which form this approach. The first step involves calculation of the cost of production, and the second step is to determine the markup over costs.

1. Calculation of cost of production

The total cost has two components: Total Variable cost and Total fixed Cost.In either case,costs are computed on an average basis. That is

AC = AVC + AFC

Where

In this approach, the quantity is assumed.In cost-plus pricing we use quantity to calculate price but price is the determinant of quantity.To avoid this problem, the quantity is assumed.This rate of output is based on some percentage of the firm's capacity.

2. Determining the markup over costs

The objective of this approach is to set prices in a manner that a firm earns its targeted rate of return.Now, if that return is Rs.X of total profit then the markup over costs on each unit of output will be X/Q and then the price will be: P = AVC + AFC + X /Q

## Reasons for wide use

Firms vary greatly in size, product range, product characteristics etc. Firms also face different degrees of competition in markets for their products. So, a clear explanation cannot be given for the widespread use of cost-plus pricing. However the following points explain as to why this approach is widely used:

• Even if a firm handles many products, this approach provides the means by which fair prices can be found easily
• This approach involves calculation of full cost. Prices based on full cost look factual and precise and may be more defensible on moral grounds than prices established by other means
• This approach reduces the cost of decision-making. Firms which prefer stability use cost-plus pricing as a guide to price products in an uncertain market where knowledge is incomplete
• Firms are never too sure about the shape of their demand curve neither are they very sure about the probable response to any price change.So, it becomes risky for a firm to move away from cost-plus pricing
• Unknown reaction of rivals to the set price is a major uncertainty.When products and production processes are similar competitive stability is achieved by usage of cost-plus pricing. This competitive stability is achieved by setting a price that is likely to yield acceptable returns to other members of the industry
• Management tends to know more about product costs than any other factors which can be used to price a product
• Insures seller against unpredictable, or unexpected later costs
• Ethical advantages (see just price)
• Simplicity
• Price increases can be justified in terms of cost increases

## Usefulness

Cost-plus pricing is specially useful in the following cases:

• Public-utility Pricing
• Finding out the design of the product when the selling price is predetermined i.e. product tailoring.By working back from this price,the product and the permissible cost is decided upon.This means that market realities are taken into account as this approach considers the viewpoint of the buyer in terms of what he wants and what he will pay
• Pricing products that are designed to the specification of a single buyer-the basis of pricing is the estimated cost plus gross margin that the firm could have got by using facilities otherwise
• Cost-plus pricing is useful in cases like 'Monopsony Buying' - here, the buyers have enough knowledge about suppliers' costs.Thus, they may make the product themselves if they do not comply with the offered prices. So, relevant cost would be the cost which a buying company would incur if it made the product itself

## Cost-plus pricing and Economic Theory

Cost-plus pricing might appear to be inconsistent with the economic theory of profit maximization. Analysis based on marginal cost equals marginal revenue decision rule may appear to have become irrelevant due to the wide use of cost-plus pricing.However, this conflict is more apparent than real.A comparison of the two approaches to pricing starts with a consideration of costs. Cost-plus pricing is based on average costs and not marginal costs.However, in economic theory long-run marginal and average costs are not very different. Thus, it can be said safely that usage of average costs for pricing may be considered a reasonable approximation of marginal cost decision making.

Second step in comparison involves the target rate of return and the resulting markup. Determination of the target rate of return depends on certain factors. Basically, the decision involves management's perception of demand elasticity and competitive conditions. This can be explained with an example,consider grocery stores.Profits are held down to the intense competition that exists among these firms. Due to this intense competition the markup for most food items is only about 12 percent over cost. If the markup over cost is based on demand conditions,cost-plus pricing may not be inconsistent with profit maximization. This can be shown mathematically.

Marginal revenue is the derivative of total revenue with respect to quantity. Thus

MR = d (TR)/ dQ = d (PQ)/ dQ = P + dP*Q /dQ

(P + dP *Q /dQ) can also be written as P (1 + dPQ /dQP) .Here, (dP /dQ) (Q /P) is 1/EP, where EP is price elasticity of demand. Thus

MR = P (1 + 1/EP ) (equation 1)

In order to maximize profit MR should be equal to MC.To simplify the assumption let MC=AC. Thus the profit maximizing price is the solution to

P (1 + 1/EP) = AC

which can be written as

P (EP + 1 /EP) = AC

Solving for P yields

P = AC (EP /EP + 1) (equation 2)

Equation 2 can be interpreted as a cost-plus pricing or markup pricing scheme.That is the price of the product is based on markup over average costs. (EP + 1 /EP) which is the markup is a function of the price elasticity of demand. From the equation we can see that the markup and the price elasticity of demand are inversely related, as the demand becomes more elastic the markup becomes smaller.

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