1 Chapter 9 Quantitative analysis in budgeting 梁志轩 周杰 熊琭

Variable cost / unit= Quantitative analysis in budgeting Analysing fixed and variable cost—high-low method Approach Select the highest and lowest activity level and their costs. Find the variable cost / unit cost at high level of activity – cost at low level activity High level activity – low level activity Find fixed cost using either the high or low activity level. Fixed cost = total cost at activity level – total variable cost Use the variable and fixed cost to forecast the total cost for a specified level of activity. 2

Quantitative analysis in budgeting 3 Analysing fixed and variable cost—high-low method Advantages: It is simple. It is easy to understand and easy to use. Disadvantages: It assumes the only factor on costs is activity. It assumes the historical costs are reliable to predict future costs. It only uses highest and lowest value. This assumes fixed costs remain unchanged and variable costs per unit are constant. However, this will not always be the case

Quantitative analysis in budgeting 4 Learning curve theory When new working practices or products are introduced, the theory is that as a workforce gains experience in a task, it will come to perform that task quicker. This means that labor costs and variable overheads (if labor hour driven) will be lower in later periods of production than when the new product or production technique is introduced.

Quantitative analysis in budgeting 5 Learning curve theory Principles: As cumulative output doubles, the cumulative average/unit falls to a given percentage of the previous cumulative average time per unit.

Quantitative analysis in budgeting 6 Learning curve theory Method 2 –The algebraic approach Y = a X b where Y is the cumulative average time per unit taken to produce X units. a is the time taken to produce the first unit. X is the cumulative number of units. b is the index of learning (log LR/log 2 ). LR = the learning rate as a decimal

Quantitative analysis in budgeting 7 Learning curve theory Example Afirm‘s workforce experiences a 75% learning rate. The budgeted time for the first batch is 100 hours. Required Using the formula Y= aX b, calculate the time to produce: (a) the first 10 batches in total (b) the 10th batch only.

Quantitative analysis in budgeting 8 Learning curve theory Answer: (a) Y = aX b a = 100 X = 10 b = log 0.75/log 2 = /0.301 = Y = 100× = hrs Total time taken to produce 10 batches:10× = hrs (b)Y = aX b a = 100 X=9 b = Y = 100× = hrs Total time to produce 9 batches:9× = hrs ∴ Time to produce 10 th batch = – = hrs

Quantitative analysis in budgeting 9 Learning curve theory Steady state production Eventually the learning curve will reach a steady state where no further improvements will be made. reasons for the learning effect to cease are: (a) When machine efficiency restricts any further improvement. (b) The workforce reach their physical limits. (c) There is a ‘go-slow’ agreement among the workforce.

Quantitative analysis in budgeting Learning curve theory Practical application a. b. c. d. Calculate the marginal cost of making extra units of a product Quote selling prices for a contract Prepare realistic production budget Prepare realistic standard costs for cost control *Material costs and fixed overhead should be unaffected by the learning curve 10

Quantitative analysis in budgeting 11 Learning curve theory Limitations Breaks in production may result in losing the learning effect. The learning effect will not apply if machines limit the speed of labor in a machine intensive manufacturing environment. Learning curve effect will be reduced if the process is not repetitive. The more complex the product, the more probable that the learning effect will be significant and longer. The introduction of a new product makes it more probable that there will be a learning effect.

12 Quantitative analysis in budgeting Expected values in budgeting Probabilistic budgeting It assigns probabilities to different conditions to derive an EV of budgeted profit Advantage Combine several outcome into one Easy to calculate and understand Assist decision making Disadvantage More time consuming than fixed budget Represent a weighted average outcome rather than an actual one Little practical value

Quantitative analysis in budgeting 13 Using spreadsheets in budgeting A spreadsheet is a type of general purpose software with many business application, not just accounting ones. It contains many techniques(eg. “what if “ analysis). It can be used to build a model and can present information in various forms. The most widely used spreadsheet packages are lotus and Excel

Quantitative analysis in budgeting Using spreadsheets in budgeting AdvantageDisadvantage Managers can prepare budgets The validity of data throughout the away from office Budget can be prepared quicker and more accurately spreadsheet Over-dependence on spreadsheets Enable managers to consider different options and perform Take no account of qualitative data sensitivity analysis Security problems 14