E5 Performance with Data Analysis

A. Data analysis techniques and the learning curve

Cost forecasts can be made from data in several ways. The high-low method separates fixed and variable costs using the highest and lowest activity levels. Correlation measures the strength of the linear relationship between two variables, from -1 to +1, and regression finds the line of best fit, y = a + bx, which can be used to forecast, provided that the correlation is strong, that the forecast is within the range of the data, and that the relationship has not changed. Time series analysis splits data into the trend, seasonal variations, cyclical variations and random variations, and uses them for forecasts. Each technique has benefits and limits: the high-low method is simple but uses only two points, regression uses all the points but assumes linearity, and all forecasts depend on past data.

The learning curve model describes how the time to make each unit falls as workers become more experienced. In the cumulative average time model, the average time per unit for the first X units is Y = a x X to the power b, where a is the time for the first unit and b is the log of the learning rate divided by the log of 2. A learning rate of 80 percent means that the cumulative average time per unit falls to 80 percent each time the cumulative output doubles. The total time for X units is X times the average. The time for a particular unit is the difference between the totals for X and X - 1 units. After a number of units, the learning effect stops, and the time per unit becomes constant. This is called the steady state, and costs for output beyond that point use that time per unit. Learning curve models are useful for pricing, budgeting and scheduling, but they assume a stable workforce and repetitive work.

Data collection issues. Cost forecasts need reliable and relevant data. The issues include the cost and time of collection, the quality, the age of the data, changes in conditions, and bias in the way data is collected or interpreted. Predictions are only as good as the data.

Worked figures

An 80 percent learning curve with a first unit time of 100 hours has b = log 0.8 / log 2 = -0.3219. The cumulative average for 4 units is 100 x 4^-0.3219 = 64.0 hours, so the total for 4 units is 256.0 hours. The cumulative average for 3 units is 70.21 hours, so the total is 210.6 hours. The time for the fourth unit is 256.0 - 210.6 = 45.4 hours.

Key terms

• Steady state: The point at which the learning effect ends and the time per unit becomes constant.
• Correlation coefficient: A number from -1 to +1 that shows the strength of a linear relationship.
• Learning rate: The percentage to which the cumulative average time falls each time output doubles.

Study tip: For learning curve questions, find the total time for X and X - 1 units and subtract. Do not apply the curve to the single unit.

Practice questions for section A

B. Cost analysis, constraints and sustainability

Quality costs fall into four categories: prevention (costs of stopping defects, such as training and design), detection or appraisal (costs of finding defects, such as inspection and testing), internal failure (costs of defects found before delivery, such as scrap and rework) and external failure (costs of defects found after delivery, such as warranty claims, returns and lost reputation). Spending more on prevention and detection normally reduces failure costs, and reduces total costs of quality over time.

Environmental costing. Environmental management accounting helps to identify and manage the costs and benefits of an entity's effect on the environment. Environmental costs can be grouped as conventional costs (such as energy and raw materials), hidden costs (costs that are not separately identified, such as waste disposal and regulatory compliance in overheads), contingent costs (costs that may arise in the future, such as clean-up or fines) and reputational costs (loss of customers and the cost of rebuilding trust). Techniques include life-cycle costing, input-output analysis, flow cost accounting and ABC. Collecting data for sustainability is hard because the costs are spread through overheads, and there may be no system to measure them.

Constraints. The Theory of Constraints of Goldratt and Cox says that the output of a system is limited by its bottleneck, so effort should go into finding the bottleneck, using it fully, subordinating everything else to it, and lifting it. With one limiting factor, products are ranked by contribution per unit of the scarce resource. With several scarce resources, the simplex method of linear programming is used, and a computer package gives the optimal plan. The output shows the shadow (dual) price of each constraint (the extra contribution from one more unit of the resource), the slack (the unused amount of a resource that is not fully used) and the surplus (the amount by which a minimum requirement is exceeded). A resource with slack has a shadow price of zero.

Other considerations in decisions include non-financial factors (quality, staff, supplier relations, reputation), the effect of sustainability, and the attitude of the decision maker to risk, which affects the choice between expected values, maximax, maximin and minimax regret. Data collection and interpretation also create problems, such as the cost of data, bias and data overload.

Worked figures

Linear programming: maximise contribution 5x + 4y subject to machine time 2x + y <= 100 and labour 1x + 2y <= 80. The corners of the feasible region are (0,0), (50,0), (40,20) and (0,40), with contributions 0, 250, 280 and 160, so the optimum is x = 40 and y = 20 with a contribution of $280. Solving the dual, 2a + b = 5 and a + 2b = 4 gives shadow prices of $2 for a machine hour and $1 for a labour hour.

Key terms

• Hidden cost: An environmental cost that is included in overheads and not separately identified.
• Slack: The unused part of a resource that is not fully used.
• Shadow price: The extra contribution from one more unit of a scarce resource.

Study tip: A resource with slack has a shadow price of zero, because more of it would not increase the contribution.

Practice questions for section B

C. Pricing, budgeting and control

Pricing. The price of a product depends on costs, demand, competition, the market, the strategy and legal factors. Price elasticity of demand shows how demand responds to price. A straight-line demand equation, P = a - bQ, has a marginal revenue of a - 2bQ, and the profit-maximising output is where marginal revenue equals marginal cost, with the price read from the demand equation. The tabular method lists prices, quantities, total revenue and total cost to find the combination with the highest profit. Cost-plus pricing adds a margin to cost, and relevant cost approaches set a minimum price at the incremental cost. Strategies such as skimming, penetration, premium pricing and price discrimination reflect the market environment.

Budgeting. The performance hierarchy runs from the mission through objectives and strategies to the budgets and targets that are used for control, and critical success factors are used to develop key performance indicators. Budgets can be fixed, flexed or flexible, and approaches include incremental, zero-based, rolling and activity-based budgeting. Which one is suitable depends on the business environment: rolling budgets suit uncertain or volatile conditions, and zero-based budgeting suits discretionary costs. Green budgeting builds sustainability goals into the budget, for example by setting targets and assigning budgets to emissions reductions. Behavioural issues include imposed or participative budgets, the difficulty level of targets (too easy and there is no motivation, too hard and managers give up) and the way in which targets can lead to unethical behaviour, such as manipulation of results.

Control and reporting. Variances are calculated under absorption or marginal costing, for sales (price, volume, mix and quantity), materials (price, usage, mix and yield), labour (rate and efficiency), variable overhead (expenditure and efficiency) and fixed overhead (expenditure and volume). They are interrelated, so an adverse variance in one area can come with a favourable variance in another. Variance analysis has limits because it ignores non-financial and external factors such as quality, customers, sustainability and competition. Control reports should be based on the principle of controllability: managers should be held accountable for what they can influence, or motivation suffers. Where the standard has been revised, planning and operational variances separate the effect of changes outside the manager's control. A good control report analyses the data and recommends how to improve future performance.

Worked figures

Demand is P = 80 - 0.01Q and marginal cost is $20. Marginal revenue = 80 - 0.02Q. Setting 80 - 0.02Q = 20 gives Q = 3,000. The price is 80 - 0.01 x 3,000 = $50, and the profit before fixed costs is (50 - 20) x 3,000 = $90,000.

Key terms

• Tabular method: Listing prices, quantities, revenue and cost to find the most profitable combination.
• Green budgeting: Building sustainability goals and targets into the budget.
• Controllability: The principle that managers are judged only on what they can influence.

Study tip: Find the quantity from marginal revenue = marginal cost, then substitute it in the demand equation to get the price.

Practice questions for section C

D. Performance management

Performance indicators. Financial indicators (for profitability, liquidity, efficiency and operational gearing) are mainly lagging indicators, because they report what has already happened. Non-financial indicators (for example customer satisfaction, quality, delivery times and employee turnover) are often leading indicators, because they give early warning of future financial results. A balance of both helps to avoid short-termism, which means putting short-term profit ahead of long-term value, for example by cutting training or maintenance. The results of financial and non-financial indicators are related, so that, for example, a fall in service quality may lead to lower revenue. Performance analysis must also consider external factors such as stakeholders, market conditions, competitors and regulation. Collecting non-financial data is hard, because it may not be recorded, may be subjective, and costs money to collect.

The Balanced Scorecard of Kaplan and Norton looks at four perspectives, financial, customer, internal business process, and innovation and learning, and each has goals and indicators linked to the strategy. Its benefits are a broad view and the link to strategy, and its challenges include the cost and complexity, the choice of indicators and the problem of data overload.

Divisional performance. Return on investment (ROI) is divisional profit divided by capital employed, and residual income (RI) is profit less a charge for capital. A manager judged on ROI may reject a project that earns more than the cost of capital but less than the division's current ROI, which is bad for the company, and RI avoids this because any project earning above the cost of capital increases RI. RI is an absolute figure, so it is harder to compare divisions of different sizes. Transfer pricing aims to give goal congruence, fair performance measures, divisional autonomy and good tax management. A transfer price can be market-based or cost-based (variable cost, full cost or cost plus), and it affects the profit of each division and the decisions they take. In a multinational group, the issues include tax rate differences, exchange controls and the rules on arm's-length prices.

Worked figures

A division has an ROI of 20 percent and a cost of capital of 12 percent. A project of $500,000 would earn 16 percent. Under ROI the manager would reject it, because 16 percent is below the division's 20 percent. Under RI the project adds (16% - 12%) x 500,000 = $20,000 a year, so it should be accepted.

Key terms

• Leading indicator: An indicator that gives early warning of future performance.
• Lagging indicator: An indicator that reports past results.
• Short-termism: Putting short-term results ahead of long-term value.

Study tip: If a question asks you to recommend a transfer price, give the range (minimum and maximum) and say where in it the price should fall.

Practice questions for section D