## CRU Paper 2 – Further Investigations in to the Cost Structure

In this paper, we highlight a two techniques which can help businesses make more informed decisions. First, we need to determine what is the true profitability of product or service lines and then we use this information to apply peak/off-peak pricing.

#### Calculating Profitability

Let us first take a look at figure 1 below. There are three key elements to this figure, namely the cost line, the revenue line and the break-even point.

Figure 1: cost-volume-profit analysis

You will have noticed that the cost line does not start at zero; this reflects the fixed costs of the business, including staff, premises, electricity and water, suma, and many others.  The most important aspect of the diagramme is the break-even point.  In particular, how many drinks/airline seats/business cards/pairs of shoes do you need to sell before your business enters the green profit zone?  To answer this question, we need to ask how do we calculate prices?

#### Cortados ‘R’ Us: The Concept

Marta has been developing her business plan and has received funding from the banks. “Cortados ‘R’ Us” expects to open in October 2010 and, after undertaking market research, Marta González, the owner expects to sell an average of 100 drinks per day.  Based on this figure, she has calculated that the fixed costs of the business at €20 per day (20 cents per drink), including glasses and the coffee machine.  She has also calculated the ingredient cost per drink at 40 cents per cortado and the labour cost at 35 cents. Now, let‟s look at four pricing options.

Table 1: pricing options for cortados

From this table, it would appear that the only viable decision is to price the cortados at €1.00 or €1.10.  However, this is not true!  At 90 cents, the business is covering its variable costs and is still making a contribution to overheads. Although 90 cents is not viable in the long term or as a permanent price, it is definitely not the case that the owner should pack up and go home. At the 70 cent level, by contrast, the price is lower than the variable costs of 75 cents, and so the owner would be better off doing absolutely nothing rather than serving customers.
So, how do we calculate the breakeven level at each of these prices?

We will eliminate the lowest price from consideration, as we have calculated that such a low price will just lead to ruin. Let us have another look at the price table, but this time with the focus on how much each price contributes to the fixed costs of the business.

Table 2: contribution to fixed costs at each pricing level

We calculate the breakeven volume by dividing the fixed costs (€20 or 2000 cents) by the contribution that each price level makes. So, using price 1 as an example, the break-even volume is 2,000/35, which is 58 (rounded up to the nearest unit, as you cannot serve part of a cortado).

What is interesting in this example is how sensitive price can be to the viability of the business. At €1.00 per drink, our owner needs to sell 80 drinks per day but, by dropping the price to 90 cents, the breakeven volume rises sharply to 134 drinks.

#### Seasonality: making the peaks and troughs of your business work for you

We said previously that Marta expects to be able sell an average of 100 drinks per day but, the motto for this section is: beware the tyranny of averages!  In the graph below, both sales lines have an average of 100 sales per day but the pattern is very different.

Graph 1: Daily sales at “Cortados „R‟ Us”

The green profile in particular shows weak sales of just 40 per day on Sunday and Monday, whereas on Thursday, Friday and Saturday, daily sales reach 140. The blue sales profile, by contrast shows reasonably stable sales throughout the week. Marta expects that her daily sales will be somewhat closer to the green profile than the blue one.  Of course, seasonality can also include hours of the day or months of the year. In this example, we will assume that the only variation is in days of the week.

If, for whatever reason, demand is weak on a couple of days, we can use our knowledge of CVP to try and attract more customers. We know that, at 90 cents per drink, we are still covering all our variable costs and so we can perhaps drop our prices to this level for two days per week to try and generate more customers.  The weekly revenue and contribution using a flat price throughout the week are shown in table 3.

Table 3: Revenue and Profitability – Flat Pricing

Charging the same price per day means that, on busy days, we are probably losing money from people who would place a higher value on a cortado and the €1.10 price might be deterring customers on days of low demand. So, to reflect the variation in demand by day of week, we can increase the price to €1.20 on busy days and have a “25% off” or “Cortados under €1” offer on days when demand is lower.

The results of using seasonal pricing are shown in table 4.

Table 4: Revenue and Profitability – “Seasonal” Pricing

You will have noticed that demand on the busier days has fallen as we have put up the price from €1.10 to €1.20. Indeed, the average number of drinks served per day is now only 91 (640/7). This is because, however many people might be willing to pay the higher price, there will be those who are deterred by the price increase. This is referred to in the jargon as “elasticity of demand”.
But, does this matter in our case here? In a word: no! Our revenue has also decreased but, critically, our contribution to overheads has increased and so the business is €7 more profitable per week. Moreover, as the coffee machine is being used less often, there should be lower maintenance bills which have not been factored into the calculations.

Clearly, the example shown is hypothetical and simple – after all, what business has only one product line? – but the principles of CVP and seasonal pricing can be applied to any business.  Marta is looking forward to her first year in business and is interested to see just how much these techniques might help her improve. For her first year, though, she intends to “play it safe” and focus on just generating awareness for her new business.

## CRU Paper 1 – Converting data to information

Converting Data to Information

Marta Gonzaléz has been considering setting up a new business. One of her good friends in Tenerife, Consuela Martín, has been operating a café for a few years and she is interested in finding out the cost structure of the business. As Marta is thinking of establishing her business in the Costa Blanca, Consuela sees no threat from Marta‟s proposed operation and provides her with the following information.

Table 1: costs and volume of business at Consuela’s coffee bar

From this table, Marta can see that the cost of a cortado is roughly 75 cents (1,520/2,000 for example) but this does not really give her any indication of the cost structure of the business. So, she decides to plot the data and see how it looks. This is shown in the following graph.

Graph 1: Scatter diagramme of costs and volume at Consuela’s coffee bar

Two things are immediately apparent to Marta. First, the costs increase in a reasonably straight line. This makes intuitive sense, as the more drinks served means more labour, coffee beans and milk. What the graph does not tell her, however, is how the costs are split been fixed and variable costs. To get an idea of the type of costs involved, she undertakes an exercise in linear regression, a technique she remembers from her undergraduate days. The main purpose of this technique is to fit the best straight line through the data so that she can see how the costs are structured.
Although regression analysis has many parts, the most important part of the output is the equation of the line through the points in graph 1. The equation for total costs, as given in the output is:

Total Costs = €1,123 + €0.21 * (cortados sold)

So, from this equation, we can see that €1,123 are the average monthly fixed costs of Consuela‟s business and each time a cortado is served, total costs increase by €0.21. It is interesting to note at this point that around 70% of Consuela‟s costs are fixed (€1,100 out of a monthly average of around €1,600) and the remainder variable. She is a little concerned about this, but she knows that, based on Consuela‟s figures, she needs to budget €13,500 (€1,123 per month for 12 months) in the first year of operation just to keep the business afloat.

Using the equation, Marta checks how well the model performs. For the January figures, for example, she multiplies the number of cortados (2,000) by €0.21 and adds on the modelled fixed costs of €1,123. This gives a total of €1,542. This figure is very close to the actual figure of €1,520 with an error of only 1½%. In fact, this is the largest error of the 12 months. The full results are shown in table 2.

Table 2: Actual and modelled costs for Consuela’s coffee bar

After judging these results, Marta has decided to investigate opening a coffee bar more thoroughly, as we shall see in later papers in the series. The business will be called “Cortados „R‟ Us”.

## Case Study – Cortados ‘R’ Us

### Introduction and Abstract

Many people regard numbers with the same pleasure as a trip to the dentist to have all their teeth extracted. Frankly, this is a great shame, as the applied use of business data can help owners understand their business so much better and guide them in deciding what products to stock, what pricing decisions to take and when to undertake promotional activity, amongst many others.

To help illustrate how data analysis can help with business decisions, we have developed a very simple business called “Cortados ‘R’ Us”.  In the course of five papers, we show how the owner, Marta González, of the business can apply various numerical techniques to keep her informed both on how her business is progressing and also how to improve her decision-making skills.

In paper 1, Marta gets an overall view of the cost structure of the business.  What proportion of costs are fixed and variable is critical to determining how robust a business case can be, since in times of recession, only variable costs can be tackled in an attempt to reduce overall business costs.

Paper 2 introduces techniques which will help Marta find the most appropriate (i.e. profitable) price for her drinks.  Like many businesses, she faces a good deal of seasonal variation in her business and she is keen to use pricing as a means to improve her profitability.

In paper 3, having been in business for a year, she examines how her demand fluctuates from day to day and whether, over the course of the year, her business has grown and if so by how much. When there is a great deal of fluctuating demand, the paper shows that it is not immediately apparent how well a business is actually performing but presents techniques to help with this problem.

Paper 4 introduces concepts to aid a decision common to many businesses: whether to buy equipment new, second hand or to rent it.  The paper explains how the concepts of discounted cash flow can help Marta in deciding what to do about acquiring an extra espresso machine for her business.

After tirelessly serving nothing but cortados, Marta investigates diversifying into other types of coffee in paper 5. The paper focuses on maximising the profitability of her business with a mix of products, taking into account the constraints on time, labour and materials.

We recommend that the papers are read in strict order, as the business decisions she needs to make are presented in chronological order from paper 1 to paper 5.