# Calculations

## Introduction

### The job of a calculation

Calculations serve many different purposes, but all have in common that they determine costs related to a certain job. Based on this principle, this chapter will deal with a very important job within a given firm, i.e. to establish or approach the cost function for the production activities in a firm where:

o More than one good is produced

o The time horizon is realistic

o Going concern is a main point of view (if not necessarily the only one). Going concern means that the company is expected to continue its activities in the near future.

o The production is carried out on a more or less know facility with more or less known technology etc.

Calculations on costs etc. are used in many different places within the financial system of the firm, therefore it is no surprise that the calculations can solve many different jobs. Some of these include:

o Control: For instance concerning pre and post calculations, controlling that a given production has the expected financial consequences. At the same time, a basis for future calculations is built upon these experiences. Examples of this relational dynamic are calculations concerning public capital investments such as: bridges, roads, metros, or calculations involved in building a house, or sewing clothes.

o Inspiration: Major cost entries could be investigated in order to rationalize, whereas major cost divergence, in a seemingly constant production flow, would generate extreme decision-maker curiosity.

o Production: Knowledge and understanding of the costs of several different alternatives is necessary, before it is possible to assess how a product is to be produced at the lowest possible cost.

o Decisions: Cost calculations are, for instance, used in relation to pricing and choice of product mix.

In short, the calculation tasks are everyday workings aspects of a firm.

To solve this complicated calculation task requires knowledge about a huge number of methods and terms, some of which are introduced in this chapter. In this text, it is naturally impossible to go in depth with all of the issues, but a number of the most important chains of reasoning will be discussed. The final part of the chapter presents some concrete methods of dividing costs, each method representing an approach to dealing with the calculation task.

### Definition of a calculation

In the most traditional sense a calculation can be defined as follows:

"A calculation is a financial estimate of the costs attributed to the purchasing, manufacturing and sales of a company's goods."

Or "A calculation is an estimate of the financial consequences of a given action, ex­ante or ex-post. It could be for a single product unit or a comprehensive alternative action (e.g. construction of a new factory). It can be a pure cost calculation or a calculation that incorporates (expected) future earnings." The tool "a calculation" adapts, to a large extent, to this job.

Pre-calculation is a way of drawing up the expected costs per product unit. The pre­calculation focuses on production that has yet to take place (ex-ante). Post-calculation seeks to establish the costs that were actually involved in a completed production (ex-post).

By combining a pre- and post-calculation for the same product unit, it is possible to control whether or not the production has proceeded as expected, as well as identifying locations of cost deviations.

### Costs vary with the purpose and the job.

Due to a number of factors costs can not be determined unambiguously, but have to be defined with relation to the issue at hand.

Costs and marketing/sales:

o Principally speaking, costs and marketing-conditions have to treated independently. They are not to be connected before optimization of the job has taken place. In practice however, a correlation may occur between the two disciplines, for instance, sales knowledge and marketing could inspire possibilities as to the size of a realistic production. As such, it is superfluous to calculate on the basis of output levels that are impossible to market and sell. At the same time, the time horizon should be established with regard to both cost and marketing conditions.

Costs and dependency on quantity:

o The classic cost definition states that costs are a function of the consumed factors of production, multiplied with the price for production factors. The consumption of production factors is directly connected to the produced lot.

o Jumps in capacity are either "hard" or "soft," reversible or irreversible, and can thus result in different cost related considerations, including both expansion and reduction in production. In this way, uncertainty or fluctuations in production levels is a cost factor.

o Temporary reductions in capacity produce great difficulties using or integrating the use of factors of production, including individuals possessing key knowledge and technological set-up, which could result in overly optimistic assessments.

o Because of gradual adaptations, the marginal costs and average costs have both a tendency to avoid listing the so-called sneaking costs, whereby the dependency on quantity is underestimated. Examples of this are petty theft, power, and having % an extra employee.

o Production risks are not typically included in cost calculations, e.g. competitive tendering in major public works.

Costs and time dependency:

o Short-term and long-term defined as technology choice. In the short-term, existing facilities are employed. While in the long-term, it is possible to adjust to the most appropriate configuration of production and technology.

o Short-term as basis for operations decisions mean that relatively few of the fixed costs are variable. Concerning a long-term perspective, it is possible to adjust the costs, including various reversible, and irreversible cost developments.

o Learning curves, efficiency development, etc. are also included.

Costs and situation dependency:

o Costs can vary with the degree of capacity utilization. In a situation with over capacity in a business sector, businesses are inclined to assess the overhead fixed costs as being higher than in a situation with a shortage of capacity, as the variable costs are lower.

o Costs vary in accordance with the competitive situation found in a business sector. If the competition is fierce, the businesses will, when listing the calculations, assess the overhead fixed costs to be higher than if the competitive situation makes room for more long-term calculations.

o Non-going concern is a perspective where the assets are realized/sold as a result of crisis or normal phasing out, e.g. because of expectations that the firm will not exist in the near future.

o Opportunity costs, depreciation vs. real loss of value caused by wear and tear, financial life-span, alternative usage of capital, or new technology.

o Subcontracting and outsourcing both nationally and internationally, international division of labor, etc.

o Conditions inherent to returns to scale, rationalizing, management effort, technology level, etc.

o The firm's strategic situation, ownership, the industrial competitive situation, capacity of profit, and loss, etc.

The sum of all these issues influences cost estimations.