Content
1. The purpose of a cost formula and its components 2
2. The cost formulas derived and their respective evaluation 2
2.1. The cost formulas 2
2.2. The evaluation of cost formulas 3
3. Result and explanation: total costs predicted as requested 6
3.1. Scenario one: labor hours increase to 8500 6
3.2. Scenario two: machine hours increase to 2300 6
4. Product cost of the Road, Trek and BMX bicycles 8
5. Activity-based costing (ABC): concept, benefits and limitations 9
6. Justification of Island Wheels Ltd. not applying the ABC approach 10
Reference 12

1. The purpose of a cost formula and its components
A cost formula, as the name suggests, is an equation based on which the total costs of products can be derived given certain cost drivers. Such methods normally require users to make a simplifying assumption that the cost relationship is linear. (Hansen et al. 2009) Consequently, the expression of costs resembles closely the equation for a straight line, which can be expressed as a standard equation of Y=F+VX,
Where
Y represents total activity cost, which is the dependent variable and the total costs the equation is expected to predict;
F means fixed cost component, which is the intercept parameter and the fixed costs the company will bear where or not units are produced;
V means Variable cost per unit of activity, which is the slope parameter;
X is the measure of activity output, or cost drivers, which is the independent variable.
2. The cost formulas derived and their respective evaluation
2.1. The cost formulas
In this case, the previous accountant used a regression model to produce the components needed in the cost formula for total product costs of Island Wheels Ltd. A regression model is a model of linear function estimated by minimizing the sum of squares of deviations. (Hansen et al. 2009) The use of regression model is made much easier through the use of spreadsheet package. Based on the 24 observations provided in Appendix A, results are auto calculated using excel calculation functions as follows:
Graph 1 & 2

Graph 1 shows the deriving of total costs with direct labor hour as a cost driver, i.e. independent variable; Graph 2 data is used to produce an equation where machine hour is the cost driver for total costs.
Observe that the intercept F is 46862.89 and the slope parameter V is 4.42 for graph 1, whereas the intercept F for graph 2 is 36557.37 and the slope parameter V is 26.96. Consequently, the equations for graph 1 and 2 can be summarized as:
Overhead costs = $46862.89 + ($4.42 x Labor hours)
Overhead costs = $36557.37 + ($26.96 x Machine hours)
2.2. The evaluation of cost formulas
Using spreadsheet functions, the regression programs produce information not only useful for composing a cost formula, but also to evaluate the reliability of the predicted cost formula. Normally, there are three aspects from which the reliability of estimated formula can be analyzed, i.e. the hypothesis test of cost parameters, the goodness of fit measures and the confidence intervals. (Hansen et al. 2009) The information given on appendix A allows users to examine the reliability of formulas through the last two aspects.
An important indicator of reliability is the goodness of fit measures. As the name indicates, it measures the extent of association between costs calculated and cost drivers. (Hansen et al. 2009) The higher the proportion of total costs can be explained by the change in the cost driver of the equation, the greater the reliability of the equation. The justification of using this indicator can be illustrated using Graph 3. As shown, the straight line in the graph is produced under the equation y = $46862.89 + ($4.42 x X). It is the best fitting line, a line to which the data points are closest. Yet how good the fit is? The question can be answered through examining the coefficient of determination. It is a specific indicator of the goodness of fit by showing the percentage of variability in the