**Essential F5 and F9 skills for P3**

#### Some important methods and techniques that were introduced in the F5 and F9 syllabuses are assumed knowledge in the P3 syllabus. This article provides five simple examples to help revision of some of these topics.

Details of brought forward techniques can be found in the Study Guide. Extracts are as follows:

**Section A**

Requires candidates to evaluate methods of business forecasting used when quantitatively assessing the likely outcome of different business strategies. The examiner’s article of August 2010 said that this requirement would include the key techniques of linear regression, the coefficient of determination, time series analysis and exponential smoothing.

**Section E**

Requires candidates to describe a process for establishing a pricing strategy for products and services that recognises both economic and non-economic factors.

**Section G**

Includes: funding strategies, sources of finance, capital management, budgeting, variance interpretation, risk and uncertainty, decision trees, marginal costing techniques, activity based costing, ratio analysis.

It is expected that the importance of these techniques will increase in P3 examinations, and the purpose of this article is to provide some revision placed in the context of strategic decision-making and implementation. It is probable that combinations of techniques will be needed rather than their stand-alone application.

For example:

- Activity based costing could be combined with pricing using a cost-plus approach.

- Interpretation of variances could lead into marginal cost decisions to discontinue a product.

- Linear regression forecasts could be combined with expected value techniques to make decisions about future action.

Generally it can be expected that emphasis will be placed on interpreting calculations already prepared and presented in the question. If calculations have to be performed then these will be relatively simple. In both cases it will be important to approach any analyses with an understanding of their assumptions, simplifications and limitations and with an idea of what further information might be useful.

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**Example 1**

A company manufactures two products with the following cost structures:

| Product A | Product B |

Expected sales volume | 10,000 units | 2,000 units |

$ | $ | |

Marginal cost | 20 | 50 |

Fixed costs | 50 | 100 |

Total absorption cost | 70 | 150 |

Selling price (50% mark-up) | 105 | 225 |

Product B is more complex to manufacture than Product A, taking twice the amount of production time and requiring more expensive components. It sells in a much lower volume than Product A. Production is carried out in a highly automated factory. The annual fixed production costs of $700,000 have been absorbed on a simple production time basis.

However, whereas Product A is produced in batches of 1,000 units, Product B is produced in batches of only 100 units. Set-up is very complex and it is estimated that 30% of fixed costs are set-up costs incurred every time production of a batch has to be organised. The company is considering costing its products using an activity based costing approach for set-up costs.

Competing products from other manufacturers sell at $100 for Product A competitors, and $250 for product B competitors.

**Required**

- Calculate each product’s cost and selling price using activity based costing and comment on any changes from the original results and any implications there might be for future production strategies.
- Comment on the company’s current and future pricing policies.

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**Solution**

Under ABC, $210,000 of fixed costs will be driven by set-ups (30% x $700,000). The remaining 70% will be absorbed as present over 12,000 units.

For set-ups:

Total number of set-ups driving (causing) the set-up cost of $210,000 is:

10,000/1000 + 2,000/100 = 30

Cost/set-up = $210,000/30 = $7,000

The set-up cost in a production run of 1,000 units of A = $7,000/1000 = $7

The set-up cost in a production run of 100 units of B = $7,000/100 = $70.

The new cost structures under ABC would be:

| Product A | Product B |

$ | $ | |

Marginal cost | 20 | 50 |

Set-up costs | 7 | 70 |

Fixed costs (70% of original) | 35 | 70 |

Total absorption cost | 62 | 190 |

Selling price (50% mark-up) | 93 | 285 |

ABC has therefore pushed more costs towards the less efficient production used for Product B. Under ABC, set-up costs absorbed into Product B cost 10 times those of Product A (previously these costs were apportioned 1:2 on the basis of time in production).

Product B is very inefficient to set-up and produce, and its costs would be radically decreased if batch sized could be increased. It is not clear why Product B is produced in such very small batches, but an obvious reason is that Product B is perishable. If it were produced in the same batch size as Product A, only two production runs per year would be needed, but that implies high, slow-moving inventory.

(b)

Summary selling prices are:

Product A | Product B | |

$ | $ | |

Market prices of close competitors | 100 | 250 |

Original cost + 50% mark-up | 105 | 225 |

New cost + 50% mark-up | 93 | 285 |

If the markets and products are very competitive, then market prices will have to be, or should be, charged. So, under the original approach Product A would not have sold well at $105 if competing products could be bought for $100. If the company were able to introduce a degree of differentiation into its products, then it has more options. Differentiation allows non-price competition to be used. For example, a strong brand name can allow companies to charge premium prices for otherwise identical products. So, if Product A is selling well at $105, it might be worthwhile exploring what would happen with even higher prices and more advertising.

The recalculation of the selling price under ABC shows that Product A is made more cheaply than originally thought and it would be worthwhile for the company to explore whether it was the cost leader. That would give access to a cost leadership strategy where the company can make very good profits whilst selling at the market price, or it could reduce its prices in the hope of pushing less efficient competitors from the market.

Under the conventional approach, the cost Product B, appears to have been understated and its selling price set too low – both with respect to a cost plus approach (which hopes to cover costs by a mark-up) and with reference to the market prices that seem to have been available. Under ABC, the company would like to charge $285. That might be possible if the product could be differentiated sufficiently. Even if a selling price of only $250 could be achieved, this is still in excess of the new total cost and well in excess of the marginal cost of production. Product B would be worth discontinuing only if the expected contribution at market price of:

2000 x (250 – 50) = 400,000

were compensated for by a reduction in fixed costs of that amount. Given that total fixed costs are $700,000 and most production effort is spent on Product A, it is unlikely that these savings could be achieved.

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**Example 2**

A company buys and sells goods and has a sales budget of 10,000 units selling at $100 each. The standard purchase price of a unit is $70, and fixed costs (which include all costs except the purchase price of goods) are budgeted at $200,000.

Actual results for the period show that 12,000 units were sold at a selling price of $68. Fixed costs were $220,000 which includes an additional $10,000 spent on advertising.

The operating statement is therefore:

$ | $ | |

Budgeted contribution 10,000 x (100 – 70) | 300,000 | |

Sales price variance (A) 12,000 x (70 – 68) | (24,000) | |

Sales volume contribution variance (F) 2,000 x (100 – 70) | 60,000 | |

336,000 | ||

Budgeted fixed costs | 200,000 | |

Fixed overhead expenditure variance (A) | 20,000 | |

(220,000) | ||

Actual profit | 116,000 |

Note: budgeted profit was $100,000 ($300,000 contribution – $200,000 fixed costs)

**Required**

Outline what might have caused the three variances and include comments about the potential interdependencies of variances and what the strategies the company might therefore adopt to improve profits in the future.

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**Solution**

**Adverse sales price variance**

This could simply be caused by market forces such as competitors dropping their selling prices, or a poor economy forcing companies to maintain or increase sales volumes by decreasing prices.

Alternatively it could be part of a more deliberate strategy to gain market share, to put pressure on competitors and to make the market less attractive to new entrants.

Potential interdependencies with other variances are discussed below.

**Favourable sales volume variance**

This could simply be caused by increased demand for the company’s products. For example, a better economy, a competitor withdrawing or an increase in advertising.

**Fixed overhead variance**

It is assumed that the $10,000 increase in advertising was deliberate, either to make a play for a higher market share or to defend the company’s current position if a competitor had become more aggressive.

**Interdependencies**

There is probably a connection between the favourable volume variance, the unfavourable price variance and the unfavourable $10,000 additional advertising spend. It is not possible to separate out the causes and effects using the data provided and this is something that the company should investigate further.

The most favourable outcome of the investigation would be that the company deliberately spent $10,000 more on advertising, reduced its price as part of the campaign, and that these changes boosted demand by 2,000 units.

That was clearly a worthwhile effort because contribution increased by $36,000 and after the additional advertising profits would have increased by $26,000. As part of future strategies, the company should try to predict the effect of reducing selling costs further and of increasing advertising as it might be worthwhile pursuing those polices even further.

There is, of course, a danger that competitors will retaliate and that a price war begins.

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**Example 3**

A new factory will cost a company $7.5 million and is expected to produce cash inflows for each of the next 10 years with the following probabilities:

p | Cash flow per year,times 1 – 10 ($m) |

0.5 | 0.8 |

0.4 | 1.0 |

0.1 | 1.6 |

Alternatively, the company could spend only $5 million. This would restrict potential inflows to:

p | Cash flow per year,times 1 – 10 ($m) |

0.5 | 0.8 |

0.5 | 1.0 |

**Required**

Using both risk and uncertainty approaches, what investment should be made with respect to a risk averse, risk neutral or risk-seeking stakeholder?

Comment on your results

Note: The 10 year 10% discount factor is 6.145

**Solution**

The first thing to do is to produce a simple pay-off matrix setting out all the things that could happen

Initial investment. $7.5m | Initial investment. $5m* | |

0.5 | NPV = 6.145 x 0.8 – 7.5 = -2.58 | -0.08 |

0.4 | NPV = 6.145 x 1.0 – 7.5 = -1.36 | 1.14 |

0.1 | NPV = 6.145 x 1.6 – 7.5 = 2.33 |

*NPVs are $2.5m greater because of $2.5m less expenditure and the high income of $1.6 per year is not available.

**Uncertainty (makes no use of probabilities)**

Maximin (risk averse approach):

If investment is $7.5m, the worst outcome is -2.58; if investment is $5.5m, the worst outcome is -0.08. Therefore invest $5 to minimise the potential bad news.

Maximax (risk seeking approach):

The best of the best is achieved by investing $7.5m and earning $2.33m

**Risk (uses probabilities)**

Expected values (risk neutral approach)

Invest $7.5m: PV = 0.5 x (-2.58) + 0.4 x (-1.36) + 0.1 x 2.33 = -1.6

Invest $5m: PV = 0.5 x (-0.08) x 0.5 x 1.14 = 0.53

The higher expected value is achieved by investing $5m.

**Comments**

Relevant comments could include the following:

- Investing $7.5 million is very risk seeking. Although there is a possibility of netting $2.33 million, there is also a possibility of losing $2.58m and that loss could destroy the organisation. Investing only $5.5m is almost devoid of risk as any loss is expected to be small.

- In once-off decisions, expected values will not usually be the result obtained.

- It is unlikely that all stakeholders will have the same attitude to risk even within a single stakeholder group. Both power and ethical considerations will be relevant when choosing which strategy to follow.

4 Probabilities are usually very difficult to estimate accurately.

**Example 4**

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A business has performed a regression analysis between sales revenue and advertising. Data was used from the past three years during which the economy was growing strongly and where each year the advertising spend and revenue increased. The result of the analysis is:

y = 500,000 + 10x

where y = sales revenue ($), and x = advertising spend ($).

The coefficient of determination (r^{2}) was calculated as 0.8.

The company wants a prediction of next year’s sales revenue based on the assumptions that the economy will not grow and that advertising spend will be $50,000.

**Required**

Advise the company on the use of its linear regression results to predict next year’s sales revenue.

**Solution**

Relevant points are as follows:

- The regression data is based on only three sets of advertising and revenue figures, so any conclusions are inevitably rather weak because of the low quantity of evidence.
- The coefficient of determination figure of 0.8 can be interpreted as meaning that 80% of the change in revenue can be associated with the change in advertising expenditure. However, that does
*not*mean that increased advertising is causing the increased sales. The scenario stated that the economy had been growing strongly and that might be the sole cause of the sales increase, with the advertising being incidental and completely ineffective. - Next year’s economy will show no growth, and this creates a huge prediction problem as the company’s environment has changed. Although the regression line suggests that:

Sales = 500,000 + 10 x 50,000 = $1,000,000

almost certainly this will be wide of the mark.

**Example 5**

A company has $24 million cash available and could spend this on three of Ansoff matrix quadrants.

- Project 1: Market penetration: Cost $8m; inflows $2.4m pa for 10 years
- Project 2: Market development: Cost $10m; inflows $3.5m pa for 10 years
- Project 3: Diversification: Cost $12m; inflows $3.2m per year for 10 years

The company has dicided to use a discount rate of 10% when evaluating their net present value.

**Required**

- Determine which combination of projects would maximise the company’s NPV if the projects are indivisible.

- Comment on using 10% for all three evaluations.

- Recalculate the answer on the assumption that projects were divisible.

Note the 10 year 10% cumulative discount factor is 6.145

**Solution**

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- Project 1 NPV = -$8m + 6.145 x 2.4 = $6.7m

Project 2 NPV = -$10m + 6.145 x 3.5 = $11.5m

Project 3 NPV = -$12m + 6.145 x 3.2 = $7.7m

Possible combinations | NPV |

Project 1 + project 2 | 6.7 + 11.5 = 18.2 |

Project 1 + project 3 | 6.7 + 7.7 = 14.4 |

Project 2 + project 3 | 11.5 + 7.7 = 19.2 |

The best combination using the company’s assumptions is to undertake Project 2 + Project 3 which are predicted to result in an NPV of $19.2m

- Generally, the different quadrants in Ansoff’s matrix are expected to have different risk return characteristics.

Market penetration means the organisation is on its home ground (same products and markets) so risk should be low.

Market development means that the company is launching into a new, relatively unknown market, so risks are higher.

Diversification is riskiest of all and companies have a very high chance of failure.

Given the three risks characteristics of the different options, it might not be wise to evaluate all NPVs using 10%. For example, it might be appropriate to evaluate Project 3 using a 15% (a 3% risk premium). That would reduce that project’s NPV to:

NPV = -$12m + 5.019^{*} x $3.2m = 4.1

(* the 10 year 15% cumulative factor)

Project 1 and Project 2 would then show the highest NPV.

- If the projects were infinitely divisible, then the approach would be to calculate the NPV per $ needed in the capital restricted period. This gives an ‘earning rate’ per $ invested and money would be allocated to the highest earning rate projects first.

Project 1 NPV/$ = 6.7/8 = 0.84

Project 2 NPV/$ = 11.5/10 = 1.15

Project 3 NPV/4 = 7.7/12 = 0.64

So Project 2 then Project 1 would be done in preference, leaving $6m that would be enough to undertake 50% of Project 3.

NPV = 6.7 + 11.5 + 0.5 x 7.7 = 22.05.

Piao says

very valuable and concise answer.