Question

Cost-volume-profit analysis can also be used in making personal financial decisions. For example, the purchase of a new car is one of your biggest personal expenditures. It is important that you carefully analyze your options.

Suppose that you are considering the purchase of a hybrid vehicle. Let's assume the following facts: The hybrid will initially cost an additional $4,500 above the cost of a traditional vehicle. The hybrid will get 40 miles per gallon of gas, and the traditional car will get 30 miles per gallon. Also, assume that the cost of gas is $3.60 per gallon.

Using the facts above, answer the following questions.

(a) What is the variable gasoline cost of going one mile in the hybrid car? What is the variable cost of going one mile in the traditional car?

(b) Using the information in part (a), if “miles” is your unit of measure, what is the “contribution margin” of the hybrid vehicle relative to the traditional vehicle? That is, express the variable cost savings on a per-mile basis.

(c) How many miles would you have to drive in order to break even on your investment in the hybrid car?

(d) What other factors might you want to consider?

Answer 1

Concepts and reason

Cost-volume-profit analysis: Cost-volume-profit analysis considers the sales price, sales revenue, fixed cost and variable cost of the product.The managerial decisions such as pricing, cost control and profit analysis are based on cost-volume-profit analysis.

Absorption costing: The method of costing where both fixed and variable costs are charged to the products is known as absorption costing. Absorption costing absorbs the costs which are directly related to the product. The fixed overheads are charged to all to units manufactured irrespective of the number of units sold.

Variable costing: The method of costing where only variable costs are charged to the products is called as variable costing. The fixed overheads are charged to the units which are sold.

Fundamentals

Contribution margin: The balance when the sales are deducted by the variable costs is known as contribution margin. The management uses contribution margin to develop the weight of sales mix for multiple products. The contribution margin signifies the profit earned before deducting the fixed costs.

Breakeven point (BEP): The breakeven point or BEP is that level of output at which the total revenue is equal to the total cost. The BEP means that there are no operating income and no operating losses. The management keeps an eye on the breakeven point in order to avoid the operating losses.

Variable cost: Variable cost refers to that cost which gets increased with the increase in the volume of output and decreases along with its decrease.

Fixed cost: The fixed cost is an expense which does not get affected by the level of output or the goods being produced.

(a)

Compute the variable gasoline cost of going one mile in the hybrid car:

$\begin{array}{c}\\{\rm{Variable gasoline cost of going one mile}}\,{\rm{ = }}\,\frac{{{\rm{Cost}}\,{\rm{of}}\,{\rm{gas}}\,{\rm{per gallon}}}}{{{\rm{Number}}\,{\rm{of}}\,{\rm{miles}}\,{\rm{travelled}}\,{\rm{in}}\,{\rm{one}}\,{\rm{gallon}}}}\\\\ = \,\frac{{\$ 3.60}}{{40}}\\\\ = \,\$ 0.09\,{\rm{per}}\,{\rm{mile}}\\\end{array}$

Thus, the variable gasoline cost of going one mile in the hybrid car is $0.09.

Compute the variable gasoline cost of going one mile in the traditional car:

$\begin{array}{c}\\{\rm{Variable gasoline cost of going one mile}}\,{\rm{ = }}\,\frac{{{\rm{Cost}}\,{\rm{of}}\,{\rm{gas}}\,{\rm{per gallon}}}}{{{\rm{Number}}\,{\rm{of}}\,{\rm{miles}}\,{\rm{travelled}}\,{\rm{in}}\,{\rm{one}}\,{\rm{gallon}}}}\\\\ = \,\frac{{\$ 3.60}}{{30}}\\\\ = \,\$ 0.12\,{\rm{per}}\,{\rm{mile}}\\\end{array}$

Thus, the variable gasoline cost of going one mile in the traditional car is $0.12.

(b)

Determine the contribution margin of the hybrid vehicle relative to the traditional vehicle:

$\begin{array}{c}\\{\rm{Contribution margin}}\, = \,\left( \begin{array}{c}\\{\rm{Variable}}\,{\rm{gasoline cost of going one mile in the traditional car}}\,\\\\ - \,{\rm{Variable}}\,{\rm{gasoline cost of going one mile in the}}\,{\rm{hybrid}}\,{\rm{car}}\\\end{array} \right)\\\\ = \,\$ 0.12\, - \,\$ 0.09\\\\ = \,\$ 0.03\\\end{array}$

The variable cost saving on per mile is $0.03 for hybrid car. Thus, the contribution margin of the hybrid vehicle relative to the traditional vehicle is $0.03.

(c)

Compute the breakeven number of miles to be driven by the hybrid car:

$\begin{array}{c}\\{\rm{Breakeven}}\,{\rm{number}}\,{\rm{of}}\,{\rm{miles}}\,\,{\rm{ = }}\,\frac{{{\rm{Fixed}}\,{\rm{investment}}}}{{{\rm{Contribution}}\,{\rm{margin}}}}\\\\ = \,\frac{{\$ 4,500}}{{\$ 0.03}}\\\\ = \,150,000\,{\rm{miles}}\\\end{array}$

Thus, the breakeven number of miles to be driven by hybrid car in order to recover the investment is 150,000.

(d)

Identify the factors which might be considered for analysis:

There can be various other factors which pave impact on cost-volume-profit analysis of the two vehicles. The other factors need to be analysed before making a decision about investment on such vehicles.

Ans: Part a

Part b

The contribution margin of the hybrid vehicle relative to the traditional vehicle is $0.03.

Part c

The breakeven number of miles to be driven by the hybrid car in order to recover the investment is 150,000.

Part d

The other factors which can be considered for analysis include the resale value of vehicles, licensing fees, insurance costs, etc.