CIMA Operational Case Study HTFT Focus Pack Core Activity E

CIMA Operational Case Study

HTFT Focus Pack Core Activity E

© HTFT Partnership – TreadCushy Core Activity E Focus Pack 2

Contents The Competency Framework ............................................................................................................................. 4

Core Activity Area E - Prepare information to support short-term decision making ......................................... 4

Revise and Learn ................................................................................................................................................ 5 Tutor Note – (OCS specific approach) .......................................................................................................... 7

Task 45: Payoff tables using regret ............................................................................................................... 9

Task 46: Payoff tables with probability/Risk Attitudes ............................................................................... 11

Task 47: Linear programming – graph explanation .................................................................................... 13

Task 48: Shadow pricing ............................................................................................................................. 15

Task 49: Multi –product breakeven- graph explanation ............................................................................ 16

Task 50: Multi –product breakeven- usefulness ........................................................................................ 18

Task 51: Relevant costing ........................................................................................................................... 20

Task 52: Decision Trees .............................................................................................................................. 23

Task 53: Decision Tree evaluation .............................................................................................................. 25

Task 45: Suggested Solution ....................................................................................................................... 27










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Core Activity Area E - Prepare information to support short-term decision making Assessment Outcomes

AO E1: I can identify relevant costs and benefits

AO E2: I can apply appropriate techniques that support short-term decision making

AO E3: I can prepare information to support operational decisions

AO E4: I can explain factors that could influence short term decisions

AO E5: I can apply appropriate techniques to deal with situations where there is risk and uncertainty

17 – 25 marks in your paper are from this section.

Core Activity E is commonly examined as Technical Skills

The Competency Framework


Remember OCS is a big theory exam at its heart (with full application expected to TreadCushy)

As per the assumed knowledge ‘Roadmap’ recordings you need to revise and relearn if needed:

Core revision area: Tick

P1: Topic 10 - Relevant costs and Decision making

I can identify relevant costs and benefits

P1: Topic 11 - Break even analysis I can apply appropriate techniques that support short-term decision making

P1 Topic 12 - Linear Programming I can apply appropriate techniques that support short-term decision making

F1: Topic 13 - Risk and uncertainty in the short term

I can apply appropriate techniques to deal with situations where there is risk and uncertainty

Note: Any of these topics can be examined with these I can statements being the angle:

§ I can prepare information to support operational decisions

§ I can explain factors that could influence short term decisions

We recommend revision cards are made based on suggested solutions to each task in this pack and you plan your studies as a mix of:

§ Revision of ‘the knowledge’

§ Review of ‘application of that knowledge’ via these tasks and suggested solutions (includes preparing a revision card. We suggest writing the ‘Question’ on the card front and paragraph headings to form the ‘Answer’ on the back if the card

§ Time spent learning/memorising the revision cards – get someone to test you if possible

§ Every time you have a section test add any knowledge gaps identified to your revision cards

Revise and Learn


Use the answers to the tasks to prepare Q and A style revision cards:

Revision cards needed based on this pack: Tick

Task 45 AO E5 Payoff tables using maximax/ maximin/ minimax regret decision criterion

Task 46 AO E5 Payoff tables with probability/ risk attitudes

Task 47 AO E3 Linear programming- graph explanation

Task 48 AO E3 Shadow Pricing

Task 49 AO E2 Multi product breakeven- graph explanation

Task 50 AO E4 Multi product breakdown- usefulness

Task 51 AO E1 Relevant costing

Task 52 AO E5 Decision trees

Task 53 AO E5 Decision tree evaluation

Also revisit your intro pack as you have Section E content included:

Core Activity E- Revision cards needed based on the intro pack: Tick

Example sub-task

AO E2 Limiting factor analysis

Example Section sub-task (c)

AO E5 Payoff tables using maximax/ maximin/ minimax regret decision criterion



Tutor Note – (OCS specific approach)

OCS Blueprint – AO section E5

“I can apply appropriate techniques to deal with Risk & Uncertainty”

For this assessment outcome, all our usual P1 risk topics are examinable

§ Risk Vs Uncertainty

§ Risk attitudes (risk seeker/ neutral/ averse)

§ Sensitivity analysis

§ Decision trees

§ Pay off tables

§ Expected values/ Standard deviation/ Coefficient of variation

§ Decision rules – maximax/ maximin/ minimax regret

OCS specific guidance : PAYOFF & RISK ATTITUDE QUESTIONS

Recent OCS examiners reports have published guidance on the preferred approach to answering payoff tables with reference to ‘risk attitude types’

OCS examiner advised candidates ( Feb & May2020 OCS examiners report)

When presented with a payoff table and a question concerning risk attitudes then students should be guided by whether probabilities are included in the payoff table.

In the absence of specific question direction, the general rule for payoff & risk attitudes questions should be:

§ If there are probabilities in the payoff table:

This means a calculation of expected value (and/or standard deviation and coefficient of variation values will likely be available) in this case OCS students should use those methods to guide their discussion of risk attitudes.

§ If risk neutral – select option with highest expected value

§ If risk seeking – select option which gives best result irrespective of the probability of that happening

§ If risk averse – select the option which gives the lowest coefficient of variation

However, if a payoff table does not include probabilities:

Then decision making based on risk attitudes can then be discussed with reference to maximax/ maximin and minimax regret


Extract from pre-seen

© CIMA 2021


Task 45: Payoff tables using regret

It is the 22 November 2021 and you have received the following email from Ben Numa, Finance Manager

From: Ben Numa

To: Finance Officer

Subject: Christmas stock levels

Hi FO,

We are trying to make some decisions regarding the amount of inventory to hold in our flagship Keyland store ahead of Christmas sales.

We have a new furry eco-boot ready to launch for the colder months and can’t be quite sure about the popularity of the new range. If we overestimate demand for the new product, we will have to sell the excess boots in store at a heavily discounted price in the January sales.

Emily Queda, Finance Director, sent me a pay-off table (attached) to cover the choice of inventory levels. She also added a regret table which relates to the pay-off table.

Please prepare a briefing paper which I can circulate at the next meeting which explains:

• An overview of the payoff and regret table and the meaning of maximax, maximin and minimax regret decision criteria. Please explain what level of inventory each decision type would choose to hold based on their risk preference.

(sub-task (a) = 40%)

Ben Numa

Finance Manager

AO:E5

The attachment referred to can be found by clicking on the Reference Materials button above.


Reference Material

Payoff and Regret Information

Payoff table of expected contribution for Christmas sales (Keyland store) all figures are in K$:

PAYOFF TABLE

Customer Demand

Inventory levels

Low Inventory Medium Inventory

High Inventory

K$ K$ K$

Low Demand 1,000 (500) (1,800)

Medium Demand 1,000 1,500 0

High Demand 1,000 1,500 2,000

Regret table relating to the Christmas period (Keyland store) all figures are in K$:

REGRET TABLE

Customer Demand

Inventory levels

Low Inventory Medium Inventory

High Inventory

K$ K$ K$

Low Demand 0 1,500 2,800

Medium Demand 500 0 1,500

High Demand 1,000 500 0

New furry eco-boot ( TreadCushy- Winter 2021 range)


Task 46: Payoff tables with probability/Risk Attitudes

It is the 1 February 2022 and you have received the following email from Sophia Grigg, Managing Director

From: Sophia Grigg

To: Finance Officer

Subject: Summer shoes – material choice

Hi FO,

Brilliant news! TreadCushy are launching a new summer style shoe for next season. The summer shoe will be part of our casual range, but we are unsure which material to choose, wool or wood. Wool being a warmer material than wood.

This is the only decision left to make before we commence production, whether we opt for wood summer shoes or the warmer wool design. We do not have sufficient manufacturing resources to produce both designs. It is inevitable that the success of our summer shoe materials will be somewhat dependent on the weather next season (the temperature in Keyland can vary from mildly sunny to heatwave temperatures).

Emily Queda, Finance Director, has consulted a big data analyst who combined past weather records with perception of customer demand and our selling prices & production costs to provide the attached analysis.

The results provide us with figures for expected values/ standard deviations and coefficient variations for both design choices, all of which Emily has assured me will be very useful to SMT, given their different risk attitudes.

Please can you prepare some briefing notes which.

• Explains the meaning of expected value, standard deviation and coefficient of variation and what type of different risk attitudes may exist across the senior management team. Please use the data provided in the attached schedule to identify the decision made for each possible risk attitude.


Sophia Grigg

Managing Director

AO:E5

The attachment referred to can be found by clicking on the Reference Materials button.


Reference Material

Summer shoes (new TreadCushy Casual Range)

Forecast presented from Big Data Analyst

Estimated Profits based on raw material choice

Product Choice Wool based Wood based

Keyland summer weather Probability $’000s $’000s

Mildly sunny 0.3 180 (200)

Moderately sunny 0.2 355 490

Heatwave 0.5 650 1100

Wool-based Shoe: Expected Value Profit ($000’s)

(0.3*180) + (0.2*355) + (0.5*650) = $450

Wood-based: Expected Value Profit ($000’s)

(0.3*(200)) + (0.2*490) + (0.5*1100) = $588

Wool Based Wood-Based

Standard deviation 209 565

Coefficient of variation

0.46 0.96

Summer-Shoe design (in wool)


AO E3: I can prepare information to support operational decisions

Task 47: Linear programming – graph explanation

It is the 1 November 2021, and you receive the following email from Ben Numa, Finance Manager:

From: Ben Numa

To: Finance Officer

Subject: Linear Programming

Hi FO,

TreadCushy are always keen to compete with the big-brand trainers, so we have updated our designs for both casual and performance shoe types. We are referring to them as Casual version 2.1 and Performance version 2.1 both launching for the peak autumn/winter season Unfortunately, we’ve come across some production complications that means we need to think carefully about the optimum number of batches to make based on the various restrictions that we face.

The problem here is that we are short of hours for two of the additional skills needed to produce the new shoe designs. We need specialist sewing hours and additional inspection hours to ensure quality before these products reach our customers. The two new show types different amounts of these resources and bring in different levels of contribution.

We therefore need to make some urgent decisions about how many batches of each new shoe type we should produce.

Emily Queda (finance director) has put together a linear programming graph (attached) relating to our first week of production which I would like you to send to SMT along with an interpretation of its meaning.

Please prepare a report relating to the graph, which provides:

• An explanation of each axis, the lines, and the key points also a description of how we find our optimum production point.


Ben Numa

Finance Manager

AO: E2

The attachments referred to can be found by clicking on the Reference Materials button.


Reference Material

Marketing literature for the new casual 2.1 and performance 2.1 shoes

(TreadCushy Marketing Literature 2021/22)

New casual 2.1 and new performance shoe 2.1

Linear programming graph

Note

• Let X = the number of new performance shoe batches to produce • Let Y = the number of casual shoe batches to produce • There are 100 hours of sewing hours available per month • There are 80 hours of quality inspection hours available per month


Task 48: Shadow pricing

It’s the 21 November 2021 and you meet Emily Queda, Finance Director in the corridor, she says:

“Hi FO,

Thank you for the excellent report you delivered for SMT on linear programming with regards to production of our two new athletic shoe types (casual 2.1 and performance 2.1).

Sara Gomez (our HR director) has been talking to a recruitment agency today and managed to locate an agency that has sewing workers available to hire including ones that can start immediately. However, they will command a high hourly rate.

Please can you prepare some additional notes to explain:

• The meaning of the term shadow price, which is, in this case, a K$30 premium per sewing hour. Please explain the implications of this shadow price in terms of the hourly pay amount. Also, please provide two other practical considerations to make before hiring the temporary labour”

[sub-task (a) = 32%]

AO:E3


AO E2: I can apply appropriate techniques that support short-term decision making

Task 49: Multi –product breakeven- graph explanation

Today is the 1 November 2021 and you receive the following email from Jack Tang, Sales & Distribution Director:

From: Jack Tang

To: Finance Officer

Subject: Breakeven Analysis

Hi FO,

In preparation for a senior team meeting next week, I asked Emily Queda, our Finance Director, for her thoughts on our current product range sales and she sent me a ‘multi product breakeven’ chart with some notes (See reference materials attached). Unfortunately, Emily is now on holiday, and I must confess that I am not sure what this chart is showing me!

From what I can tell, I think this analysis could be quite useful. Normally I would talk to Ben Numa, Finance Manager, but he is tied up with the auditors today and so he suggested I speak to you.

Please send me an email which explains the following:

• The meaning of the points A, B, C, D, E and F and the two lines shown on the chart, items labelled point 1 and point 2 and the term ‘margin of safety’ (No further calculations will be necessary).


Jack Tang

Sales & Distribution Director

AO: E2



Reference Material:

Breakeven Analysis – TreadCushy – Budgeted Sales Year ended June 2022

NB: Graph approximately to scale.

Table below provides full details:

Figures based on 2021/ 22 Budgeted Sales

TreadCushy Budgeted Figures (K$ 000's)

Casual - Wool

Casual -Wood

Performance Hill

Performance Flat TOTALS

Revenue $ 29,580 $ 16,660 $ 9,840 $ 17,760 $ 73,840

Contribution $ 19,231 $ 10,317 $ 6,489 $ 12,144 $ 48,181

Individual C/S Ratio 65% 62% 66% 68% 65%

Fixed Costs $ 7,977

Budgeted Profit for year ending June 2022

$ 40,204


AO E4: I can explain factors that could influence short term decisions

Task 50: Multi –product breakeven- usefulness

Today is the 18 November 2021 and you receive a follow-up memo from Jack Tang, Sales & Distribution Director:

From: Jack Tang

To: Finance Officer

Subject: Extra task –Breakeven analysis

Hi FO,

Thank you so much for getting me up to speed on the multi-product breakeven chart, I think I understand this now.

Please can you prepare some more notes for me to discuss,

• The usefulness of this multi-product breakeven analysis in terms of decision making at TreadCushy.

(sub-task (b) = 32%)

I have reattached this to the email for your convenience.

Thanks

Jack Tang

Sales & Distribution Director

AO: E4



Reference Material:

Breakeven Analysis – TreadCushy – Budgeted Sales Year ended June 2022

NB: Graph approximately to scale.

Table below provides full details:

Figures based on 2021/ 22 Budgeted Sales

TreadCushy Budgeted Figures (K$ 000's)

Casual - Wool

Casual -Wood

Performance Hill

Performance Flat TOTALS

Revenue $ 29,580 $ 16,660 $ 9,840 $ 17,760 $ 73,840

Contribution $ 19,231 $ 10,317 $ 6,489 $ 12,144 $ 48,181

Individual C/S Ratio 65% 62% 66% 68% 65%

Fixed Costs $ 7,977

Budgeted Profit for year ending June 2022

$ 40,204


AO E1: I can identify relevant costs and benefits

Task 51: Relevant costing

It is the 15 November 2021 and an email has arrived from Sophia Grigg, Managing Director

From: Sophia Grigg

To: Finance Officer

Subject: Relevant Costing

Hi FO,

I have just been in an e-meeting with the owners of Green-Org. charity. They are a privately run charity based in Keyland, who educate the public on environmental sustainability. They are planning a huge campaign in which they will be handing out leaflets and informing people on ways they can reduce their carbon footprint.

They have asked if we can produce a special order for sport-shoes which their campaigners to wear during the campaign. They want the shoes to be eco-friendly and have requested a specific design which includes an ‘air-sole’ to reduce fatigue and spine pressure.

I want this order to be the lowest possible price, so we can show our support for this deal. Emily Queda, (finance director) suggested I ask you to prepare a relevant cost schedule so I can decide a minimum price for the order.

I have attached a list of the costs which I think will be involved, there is no need to recalculate a total, but I’m wondering if they are classed as relevant or not.

Please can you produce a report for me that:

• Explains relevant costing principles and explains with reasons, which of the costs in the attached schedule would be relevant or irrelevant to this special-order pricing decision.


Thanks

Sophia

AO: E1



Reference Material

Schedule of Costs

Schedule of Costs:

Green-Org Charity Sports Shoe Order

Notes K$

Direct Materials 1 250,000

Keyring Logos 2 19,000

Labour Costs 3 55,000

Manufacturing overheads 4 78,000

Design & development costs 5 10,000

Shoe air-sole moulds 6 30,000

Specialist 3D printing machine for inner sole components

7 12,000

Total cost 454,000

Notes:

1) Direct materials include all wool, wood pulp and natural rubber materials needed. We use this type of inventory regularly and have current stock which is valued at K$200,000. We need to buy in some additional dual-branded eco-packaging which will cost K$50,000. The existing raw material inventory has a replacement cost of K$240,000.

2) The keyring logos have been requested by Green-Org charity and are embossed with their logo. They can be attached to the shoes or worn separately. They will be purchased from a local Keyland supplier and will be produced especially for the charity sports shoe order.

3) The labour includes K$25,000 salaries of warehouse management who are normally on site throughout the week. The other K$30,000 relates to production worker pay, some of the production must take place at the weekend therefore K$20,000 relates to overtime payment relating to the weekend work. The other K$10,000 relates to normal production time, in which there is spare capacity to produce the charity sports shoes.

4) Manufacturing overheads includes K$28,000 variable overheads relating to extra electricity needed to manufacture the charity shoes. The other K$50,000 is total fixed general overhead absorbed at our normal factory OAR rate.

5) Design and development costs represents the time that was spent the board while negotiating whether to go ahead with the deal.

6) The moulds for air-soles will be purchased especially for this order and cannot be reused for any other shoe types.


7) The different inner-sole components require a specialist 3D printer which was purchased by us two years ago for K$12,000 and has remained unused due to its specialist nature. We were planning to dispose of this printer and sell it for K$5,000 to a local factory however, its resale value by the time the special charity order is finished will be K$1,000 which is its recycled scrap value.

We should also bear in mind that due to the time and focus needed for the charity order, TreadCushy will have to reduce sales of other shoe types and will lose contribution of K$40,000 in total.

Photos of 3D printed parts for cushioned soles

Design prototype: Sports-Shoe for Green-Org Charity



Task 52: Decision Trees

Today is the 1 December 2021 and you have received the following email from Ben Numa, Finance Manager:

From: Ben Numa

To: Finance Officer

Subject: Campaign Selection – Marketing choice

Hi FO,

Recently the management team have been discussing the launch and advertising of an exciting new product range, Eco-clothing. This is obviously quite a big diversification away from our shoe-collection, but will be based on the same environmental and quality principles. A picture from our marketing material is attached (exhibit 2).

Our researchers have been working hard to create this product, which we hope will tap into the trend for environmentally sound fashion, which uses organic cotton and friendly colour dyes.

Jack Tang, our sales and distribution director, has suggested two possible campaigns to promote the new clothing range. One is to pay Eco-Monthly for a featured campaign. We have done this for shoe launches in the past and it seems a plausible suggestion because they specialise in eco-friendly choices. The other is to use our past customer data to conduct an email campaign which promotes our new clothes range to all our previous TreadCushy website and app customers. We haven’t got the time or resources to do both.

I have put together some estimated costs and sales forecasts which contain some probabilities that Jack has provided.

I thought it helpful to present this information as a decision tree (see exhibit 1 attached). However, as you can imagine, the rest of the SMT board will not be familiar with this technique, so would like further explanation.

Please can you draft me a report which explains:

• The elements of a decision tree diagram and their meaning with reference to the choice of promotional campaigns. There is no need to mention which decision to select at this point.


Ben Numa

Finance Manager

AO: E5



Reference Material


Task 53: Decision Tree evaluation

Later that day you receive a follow-up email from Ben Numa, Finance Manager:

From: Ben Numa

To: Finance Officer

Subject: Campaign Selection - continued

Hi FO,

Really good work on the decision tree. I know I asked you to omit which decision should be selected here but SMT would now like to know. I’ve attached it again for your convenience.

Please can you create further notes to explain:

• The campaign you would select based on the decision tree evaluation; also, please add any other considerations you think we should discuss before making our final decision.

(sub-task (b) = 32%)

Ben Numa

Finance Manager

AO: E5



Reference Material


Task 45: Suggested Solution

Explanation of the payoff and regret table and the meaning of maximax, maximin and minimax regret decision criteria. Including which level of inventory each decision type would choose to hold based on their risk preference.

Payoff table

The payoff table attached shows us the contribution and losses which could occur relating to our decision to hold a low, medium, or high level of inventory in our flagship Keyland store. We are unsure of customer demand (this also ranges from low to high levels) and if we stock too much inventory ( high level) and the range is not popular (customer demand is low) according to this table we will make a loss of K$1800. Alternatively, if we decided to stock only a low level of inventory, we have effectively ‘capped’ our potential contribution level at K$1,000 (regardless of customer demand). This is because we will only have a low level of inventory available in store to sell, so $1,000 is the maximum we could earn from that quantity. The payoff table alone doesn’t tell us which choice to make, this will depend on risk preference.

Maximax

One decision making option is maximax. This is the decision made by a risk seeker and an optimist. A maximax decision will select the best potential payoff regardless of the likelihood of receiving. They are not concerned with the downside outcomes associated with the choice. In this case, a maximax decision maker will choose to hold a high level of inventory in store. They will be hoping for a high level of customer demand, in which case they will earn the maximum contribution possible which is K$2,000.

Maximin

Maximin is a risk-averse decision-making method (in addition to mini-max regret). This is the decision choice of a pessimist and wants to choose the best outcome in the event of the worst possible outcome occurring. Maximin would choose to hold a low level of inventory in store because whatever the sales demand level, the contribution will be $1,000. This is the minimum that will be earned, in all outcomes. The other higher inventory levels could result in losses. For example, if demand is low and we hold medium or high levels of inventory, we will be making a loss on the new range.

Regret table

The regret-table is based on the payoff table and represents the outcomes from the perspective of a risk-averse, sore loser decision maker. This type of decision-maker is concerned about the opportunity lost from making the wrong decision and will select the choice that results in the smallest amount of ‘regret’. Where there is a zero in the table this represents ‘no regrets’ and is the best outcome for each decision choice. The higher the regret figures, the more the decision/ outcome combination represents a bad choice from this perspective.

Choice using regret-table.

A decision-maker using the regret-table would be looking for the column (the decision) which results in the least regret. The maximum regret from each decision would be noted and the smallest of these


chosen. In this case, the lowest maximum regret relates to holding the lowest inventory levels. Here the most regret the decision-maker can experience, in the event of uncertain customer demand will be K$1,000. The other columns result in potentially higher possible regret values, for example, we could face a regret of K$2,800 if we chose to hold a high inventory level and customer demand turns out to be low.



Explanation of the meaning of expected value, standard deviation and coefficient of variation and type of different risk attitudes existing senior management team. Includes the decision made for each possible risk attitude based on data given.

Expected value (EV)

Expected value is a long-term, weighted average result. It is the sum total of each product’s outcome multiplied by the associated probabilities. It is not an ‘absolute’ result that will occur, more that it represents a longer-term average result if the decision is repeated multiple times. So as per the data, when we take the probabilities relating to summer weather ( e.g. 30% chance of it being mild, 20% chance of it being moderately sunny and 50% chance of it being a heatwave), we can then multiply each one of those by the profit outcome for each shoe-material type to get an ‘average’ value for wool-based shoes, which is EV of K$450,000 and for wood-based shoes it is an EV of K$588,000.

Standard deviation

The analyst has also provided us with a value for standard deviation for each shoe material type. Standard deviation compares each of the outcomes with the expected value and calculates the average deviation from the mean. This gives an indication of the ‘range’ of profits that may result. From these results we can see that the spread or the volatility of the profit from wood-based shoe is largest. This is because it has the highest standard deviation of the two products, so a wood-based summer shoe range could result in a profit outcome that deviates much further from its expected value average figure, than the wool-based product.

Co-efficient of variation (CoV)

The co-efficient of variation compares the standard deviation of the project relative to its mean (EV) which illustrates the trade-off between risk and return. For both the wool and wood shoe types, we would take each standard deviation and divide it by that product’s expected value (CoV = SD/EV). This formula shows how we are comparing the standard deviation, relative to the average EV return (how much variation is there compared to the average return level each product earns). When the CoV is high (as with the wood-based material choice) we are accepting quite a large variation in relation to the average expected return. For example, for wood-based the CoV of 0.96 tells us that the standard deviation is 96% the size of the mean (EV) value.

Risk attitudes

When making a decision such as this, there are 3 potential risk attitudes which we may find amongst our senior board members: risk neutral, risk seeking and risk averse. These will affect the decision relating to the summer-shoe material, because of the risk level that they are prepared to accept. Our choice between the raw material choice is a mutually exclusive decision (we can only choose one of the two materials) and the table shows there is a quite a wide variation of potential profit and loss outcomes. The choice of which material to use is ‘controllable’ whereas the ‘uncontrollable’ element is the weather temperature in Keyland. The table shows that if there is a heatwave, then the wood-based summer shoes will be most profitable (profit is K$1,100,000), whereas if the weather is mildly sunny, we would be


better to choose the warmer wool-based materials (which earns a profit of K$180,000 (compared to the loss of (K$200,000) which could occur if we launch the wood-based product and weather is mild.

Choice using risk attitudes

If we take a risk neutral attitude, we will use the expected values figures to make our decision. Here we will choose the highest expected value, which gives us the highest long run average profit, so we would select, wood-based shoe (highest EV is K$588). If we adopt a risk seeking attitude, we want the best figure in the payoff table, regardless of likelihood or potential downside outcomes, therefore we will select wood-based shoes because we are hoping for the K$1,100 ( in the event of a heatwave). If we are a risk averse decision maker then we would choose the lowest coefficient of variation, the wool-based shoe. This gives us less range or difference in the actual outcome compared to the EV figure stated – so suits a risk averse profile better.



An explanation of each of the axis, the lines and the key points on the graph including a description of how we find our optimal production point

Linear Programming

The attached graph is a linear programming solution which shows the optimum value for x and y (our new performance shoe v2.1 and new casual shoe v2.1 respectively) while satisfying a number of constraints. In this case, the constraints are a shortage of sewing hours and inspection hours. So, we are trying to find the optimum number of batches of performance v2.1 and casual v2.1 to produce.

Axis

The linear expressions refer to X and Y axis as per standard graphical notation. However, we can determine that performance v2.1 batches are represented by X and the casual v2.1 batches are represented by Y because these are written on the appropriate axis.

Steepest Line - 16x + 12y = 100

The steep line which is labelled 16x + 12y = 100 represents all the production points which would utilise all the sewing hours that we have available. All points on this line are potential production points, in that we have sufficient sewing hours to produce the associated quantity of X and Y (Performance v2.1s and Casual v2.1s batches). However, before we can find the point, we need to be aware of the other constraint too, see next. The equation of this line tells us that we need 16 sewing hours to produce one batch of performance v2.1 and 12 sewing hours to make one batch of casual v2.1. Together, the combined quantity we make of both new shoe types cannot utilise more than the maximum available sewing time of 100 hours in the period.

Red line - 8x + 16y = 80

The other less steep line is the constraint for quality inspection time. We only have a limited amount of these hours and all points on this line are possible in terms of inspection hours. The equation of this line tells us that we need 8 inspection hours to process one batch of performance v2.1s and 16 inspection hours to process one batch of casual v2.1s. Presumably, there are more potential quality failures with casual shoes v2.1s product because it takes twice as long to test each batch compared to the performance v2.1 batches. Together, the number of batches we produce must be limited to an amount that can be inspected within a maximum total of 80 hours between them.

Feasible Region - Points 0, A, B, C

These are the vertexes of the feasible region. This is the area that lies inside the various production constraints and contains all possible combined quantities of X and Y. One of the corners A, B or C will be the optimal production point. To find which requires us to use the iso-contribution line.

Dotted line - Iso-contribution


The dotted line is the iso-contribution line and is shows levels of contribution at each point. This is a moveable line because it is not a production constraint and should slide away from origin point 0, at the same angle, until it touches the last vertex of our feasible region; in this case, point B.

Optimal point

Point B represents the optimal production quantity of batches for both new shoe types. By reading from our graph at point B it appears 4 batches of performance v2.1s and 3 batches of casual v2.1s is the best solution. This production level maximises contribution and does not exceed any of the constraints. The values of x = 4 and y = 3 fits into both labour constraints exactly.



Explanation of the meaning of the term shadow price, which is, in this case, a $30 premium per sewing hour. Please explain the implications of this shadow price in terms of the hourly-pay amount. Also, two other practical considerations to make before hiring the temporary labour

Shadow Price

A shadow price represents the premium we would pay over and above the amount already being paid for a scarce resource – in this case, the sewing hours. The shadow price is also equal to the extra contribution that will be generated from one extra unit of resource being made available (i.e. one extra sewing hour, assuming all sewing hours have been fully utilised up to that point). We can see from the previous linear programming graph that at optimum point, we are utilising all our sewing hours because this line crosses at optimum point B.

Implications for hourly pay rate

Assuming the figure of K$30 shadow price is correct, then this tells us we would be prepared to pay K$30 extra per hour to obtain one additional hour of sewing time. This means the shadow price of K$30 per hour represents the maximum additional premium we could agree to when hiring the temporary staff, which would be on top of our standard hourly wage rate.

Practical Consideration – skills and experience

It seems unlikely that the recruitment agency will have specialist sewing workers on hand who are able to stitch our footwear and are available to start immediately. It is possible that these temporary workers do not have the specific sewing skills required for our shoes or that the agency has misunderstood the job description. It would be a better plan to speak to our existing sewing staff and try to negotiate an overtime rate (of less or equal to K$30 premium per hour), rather than risking taking on temporary workers who are lacking skills needed.

Practical Consideration – effect on other staff

It may be demotivating to the existing staff if we hire in temporary workers to increase production hours. Our workers may discover that the temporary staff are on a higher hourly rate than they are. We need to consider the well-being of our existing staff and by talking to them, we may find there are sewing trained staff available in other production areas (perhaps where previously trained staff have moved roles). It could also be disruptive for our current workers to have new staff join our business who are not committed to TreadCushy’s concern for environmental impact and quality, this could increase wastage and undermine the final product.



Explanation of the meaning of the points A, B, C, D, E, F and G and the two lines shown on the chart, items labelled point 1 and point 2 and the term ‘margin of safety’.

Multi-product breakeven

The graph shown is a multi-product break-even chart. The horizontal axis here shows cumulative sales revenue, while the vertical axis shows the resulting profit or loss at different levels of sales. The chart is based on our budgeted costs and revenues for year ending June 2022. This shows values planned for our four main shoe types using the average figures which we used to create the main budget.

Point A

Point A is the point at which there is no revenue and where sales volumes are nil. At this point, fixed costs for TreadCushy will still be incurred because, by their very nature, they are fixed regardless of production levels. The graph shows that if sales revenue is nil, a loss will be generated equal to K$7.98 million, which is the amount of our fixed costs.

Point F

At the other extreme, point E represents the total revenue and profit that is expected for the year as a result of the expected sales volumes, the contribution, and the fixed costs for our athletic shoes. The chart and accompanying table indicate that sales revenue of approximately K$73.8m is expected for the next financial year, which would generate an operating profit of approximately K$40m (as per the accompanying table).

Points B, C, D and E

The crooked line which includes points B, C, D and E was drawn to represent sales and profits that would be earned from selling our shoes in the order of highest c/s ratio first. The c/s ratio is essentially the margin of contribution to sales price for each show type and indicates for every K$1 of revenue generated, how much that will contribute towards the fixed costs of the business. The section of the line labelled ‘B’ on the chart assumes we will be selling our Performance, ‘Flat’ shoe type (these shoes have the highest c/s ratio of the range at 68%). The next section labelled ‘C’ shows the sales for Performance ‘Hill’ shoes, our next highest C/S ratio product. Point D and E show the budgeted sales of Casual Wool shows, followed by Casual Wood shoes, again sold in order of c/s ratio (65%, 62% respectively).

Points 1 and 2

Point 1 shows where TreadCushy will breakeven in terms of sales revenue. This is also represented by point 2, because they are calculated under two different assumptions (see next). Where we intersect the horizontal axis is the point at which our total sales revenue is precisely equal to total costs (fixed and variable) so that no profit or loss is made at that point. Moving upwards and rightwards past this point means the company is earning a positive contribution and making a profit.


Two Lines ( AF and ABCDEF)

As mentioned above we have two lines which represent two different sales assumptions. The straight-line which runs from point A to F, represents the expected profit or loss at different revenue levels assuming that the sales mix of product category sales is kept constant. The crooked line which connects points A, B, C, D, E and F is the line that represents the relationship between revenue and profit or loss on the assumption that we sell our product categories in order of profitability (i.e. we sell in order of highest individual c/s ratio first, starting with Flat-Performance range – as discussed above). We can see from the crooked line that we breakeven (point 1) just by selling our Flat-Performance shoes alone. The contribution from just that range is in excess of our fixed costs. This is reassuring and confirms that our product margins are high and fixed costs are relatively low.

Margin of Safety

The difference between the breakeven point on either of the two lines and the estimated total sales revenue (point F) is known as the margin of safety. This is the amount that sales can fall before we reach the point where fixed costs are not covered by contribution. Therefore, the margin of safety shows us how far our sales can fall before a loss is made. We are told that the graph is only approximately to scale but the relative gap between the budgeted sales of $73.8 million and Point 1 or Point 2 shows our margin of safety is relatively large and so we are far from loss making here. The line ABCDE has a different break-even point to the straight-line AF. Without further calculations, I cannot give a reliable estimate of the exact breakeven revenue at either point, however, breakeven revenue will always be lower with the crooked line; this is because when we sell our products in order of profitability and we breakeven much sooner in terms of the value of sales required.



Discussion of the usefulness of this multi-product breakeven analysis in terms of decision making at TreadCushy.

Benefits and use of multiproduct breakeven chart

Overall, the chart is useful because it gives an idea of the level of revenue at which we will make neither a profit nor a loss. We need to know when we have exceeded that point that we are working towards earning profits. It is quite useful to know our minimum sales volumes for our shoes. As it happens from the graph, we can see that TreadCushy has a margin of safety that is relatively large here. We have enough contribution in our most profitable Performance ‘Flat’ range alone, to cover breakeven point. Therefore, concerns about making a loss seem unlikely. However, the graph could be used to emphasise the need to prioritise sales in terms of profitability, especially if future sales volume did start to fall.

Limitations– sales in order of prioritisation of products ( c/s ratio)

In terms of the crooked line A,B,C,D,E,F and the principles on which it is drawn. This assumes that we sell the most profitable shoe types first. This is very unrealistic our shoes are designed for different customer needs and demand will vary, so we cannot restrict our sales to offer only Performance Flat shoes, before we allow sales of our Performance Hill shoes etc. Our customers will select the shoes which meet their needs and are able to choose freely from any of our products from our stores/ website app or website. However, there is a small advantage in selling our Performance flat range in terms of profitability, so we could consider marketing this one or displaying more prominently to encourage sales of the higher margin shoe.

Limitations – Assumptions of straight line and standard sales mix

The multi-product straight line AF is also quite unrealistic. This assumes we make sales in a pre-determined product sales mix, proportions of which are estimated in our budget but may vary considerably. It is more likely that actual sales will conform to these proportions rather than follow the assumptions of the crooked line (where sales are made in sequence). But even so, the margin of safety in this more realistic case shows our breakeven sales point is still a very large distance from our budgeted total sales so concerns about loss-making don’t seem relevant.

Other Limitations

There are other factors which limit the usefulness of break-even analysis. The figures are from our budget which was set at the beginning of financial year, so some figures and standard costs and selling prices may already be out-of-date. We also use selling prices and variable costs which are averages and assume that they will be constant throughout the year. In addition, our estimated fixed costs is assumed to be correct and will remain the same throughout the year. We could prepare a what-if analysis perhaps to test different levels of selling prices and other costs to see how break-even may be affected.



Explanation of relevant costing principles and explains with reasons, which of the costs in the attached schedule would be relevant or irrelevant to a special-order pricing decision.

Criteria for relevant costs

Relevant costs are those which are directly caused by a specific management decision, such as the decision to go ahead with this special order for Green-org charity. We will only classify costs as relevant if they are incurred, saved, or changed in the future as a direct result of our decision to go ahead with the charity deal. Relevant costs should be future, incremental, and cash-based, along with opportunity costs.

Materials and packaging

The materials required to produce the charity sports shoe are our frequently used raw materials such as wool, wood pulp and natural rubber. The inventory valuation cost given here of $200,000 for existing materials is irrelevant because that cost has been paid and is historic. The relevant cost to us of using these materials is the replacement cost of the existing inventory which is stated as $240,000. This is relevant because although we have the materials in stock, we will have to replace and buy materials in again for other orders. The additional cost of buying the dual-branded packaging for $50,000 is being purchased especially for this order and therefore is a direct cost incurred by the deal. This means the $50,000 is a relevant cost and must be included in the schedule.

Keyring logos

Similarly, as with the dual-branded packaging, the embossed keyrings are being purchased specifically for this order and therefore are a relevant cost. We don’t have these keyrings in stock and therefore the full cost of purchasing the inventory will be directly attributable to the charity order.

Labour

The salary of the supervisors is not a relevant cost. These supervisors will be paid anyway and on site regardless of this special order, so should be ignored. Similarly, the labour cost of $10,000 which relates to ordinary production time during which there is spare capacity should also be excluded and is not relevant. This is because the staff will be paid anyway and if they have spare time in their working week to produce the charity shoe order then no extra cost is being caused because of this. The weekend work, on the other hand, is an additional cost that is a direct result of the order going ahead so is relevant. Therefore, only the $20,000 weekend work will be classed as relevant labour cost for this order.

Manufacturing Overheads

As with the above, we need to decide if the overhead costs are directly caused by the special order, or are going to be paid regardless of the extra activity. The variable cost of the electricity for the machine will be relevant because they will be directly caused by making the charity shoe order, whereas the general fixed overheads are a committed cost relating to overall running of the factory and are irrelevant.


Design & development

Time spent negotiating or designing the special order before the agreement was made to accept the special order are irrelevant to the decision. These costs are sunk and not related to the future decision we are making, so should be ignored.

Air-sole moulds & 3D printer

The air-sole moulds relate to the specific requirements of the charity shoes, so should be included as a relevant cost of the order here. The cost of purchasing the 3D printing machine is sunk because the decision to buy the printer was made a long time ago and not connected to the charity order. Therefore, the historic cost of $12,000 is not relevant and should be ignored. The reduction in the disposal proceeds is relevant though. We will no longer get $5,000 from the disposal of the machine and will only receive $1,000; therefore, we have forgone $4,000 cash proceeds. This is an opportunity cost and should be included as a relevant cost of the charity deal going ahead.

Lost contribution

The agreement to focus on this customer has meant we have had to sacrifice contribution from any other shoe sales, therefore, this lost contribution of $40,000 should be added to the relevant costs because it is an opportunity cost of the decision caused as a result of accepting this deal.

Customer pricing

It is important to mention that the relevant costing schedule will show TreadCushy the true, additional costs which will be incurred by accepting this charity deal. Because this is an environmental cause that we would like to support, the actual price we charge to Green-Org charity could be equal just to cover these costs or potentially we could discount below the cost, by way of contributing to the cause. Relevant cost schedule will help with making this decision when we are deciding the minimum selling price.



Elements of decision tree and meaning with reference to the choice of promotional campaign

Square

A square in a decision tree is a point at which the decision-maker, TreadCushy, has control over the choice. For example, here at the beginning of the decision-making process, TreadCushy has the option to select a marketing campaign which involves an Eco-Monthly featured advertisement or conduct an email campaign. Reading from left to right the decision tree then visually displays the potential outcomes and results of each decision based on likelihoods and decisions made.

Circle

A circle in a decision tree is an outcome over which the decision-maker does not have control. Probabilities may be available for the various outcomes. These are written on the branches which lead from the circles. In our example, we can see that the chance of a good or bad response from either an email or Eco-Monthly campaign is equally split with 50% chance of being bad and 50% chance of being good. This is something we cannot control directly which is why this is portrayed as a circle in this decision tree diagram.

Branches

These show the potential direction or results from each decision or outcome. The descriptions of these are written along the branch. For example, we can see that the outcome of an Eco-Monthly feature campaign may have a good or a bad response. Where there is a value given below the branch there is a cost or revenue associated with that direction or outcome occurring. For example, the cost of an Eco-Monthly feature is shown as K$300,000, whereas an email campaign has an associated cost of K$150,000.

Resulting Figures

The figures at the end of the branches represent the estimated revenues, contributions or profits associated with each decision-related outcome. For example, in the event that we choose an Eco-Monthly campaign and the public reception to the campaign is good, we will earn extra contribution of K$750,000 from our new clothing range.



Explanation of the campaign to select based on the decision tree evaluation along with other considerations to be discussed before making a final decision

Expected Value & Selection

We can use expected value to weigh up these outcomes and probabilities and will select the decision which has the highest expected value overall. These calculations are provided on the original attachment and show that we should opt for the Eco-Monthly campaign because this has the highest expected value of K$345,000 compared with the expected value of the email campaign of K$250,000.

Other Considerations - using expected value as a decision-making tool

By using expected value, we are assuming that TreadCushy is a risk-neutral decision maker whereas our risk appetite may be a bit braver or more cautious than this. It also assumes that the decision being made here will be repeated many times and with this being a one-off promotional campaign for a new clothes range product, this is not the case so may not be the most appropriate method of decision making.

Other Considerations - Email Campaign

It is likely that, may be of interest to our previous web-based /app customers who we could easily obtain name and address for, based on past shoe orders. This is a new but related product so eco-clothes could be a potential purchase for those who are fans of our eco-shoes. Before we send off an email, we do need to consider data protection regulation, whether our past customers have consented for us to use their emails for future, promotional campaigns. If not, then we need to make sure we are selecting to send only to those customers who have agreed to receive future email correspondence from us.

Other Considerations - Estimated Figures

We should also bear in mind that these figures are mostly estimates. It is likely that the Eco-Monthly campaign is an actual quote that has been obtained, however, the cost of an email campaign will not really be known and therefore is an estimated figure. The impact on the contribution levels as a result of the campaigns cannot be known with certainty either and may well be affected by different aspects such as price of the clothing range, competitor actions or the response to our product by others in the market, such as reviewers and customer feedback sites.

Documents

CIMA Operational Case Study HTFT Focus Pack Core Activity E