Chapter 7, Problem 1MTC

Cost-Volume-Profit Analysis, Single-Product Setting

Use CVP analysis to calculate the break-even point in units for

1. a. The canoe product line only (i.e., single-product setting)
2. b. The paddle product line only (i.e., single-product setting)

To determine

Calculate per unit variable costs and total fixed costs for canoe product line by using high-low estimation method.

Explanation of Solution

High Low Method:

High and low points of data when used to classify the mixed cost into fixed and variable cost then this method is known as high low method. This is one among the three costs of separation methods.

The costs of canoes and paddle include manufacturing and marketing costs. Direct and variable cost includes a part of both manufacturing and marketing costs. The records for both marketing and manufacturing cost are kept separately which emphasizes on the requirement of four different high-low analyses. The variable cost of both marketing and manufacturing can be added to get variable cost per unit for both the product line. The same can be done for fixed costs of both the product line.

Use the following formula to calculate variable manufacturing cost:

$\mathrm{Variable}Rate=\frac{\left(\mathrm{High}PointCost–\mathrm{Low}PointCost\right)}{\left(\mathrm{High}PointOutput–\mathrm{Low}PointOutput\right)}$

Substitute $140,000 for high point cost, $108,000 or low point cost, 400 for high point output and 240 for low point output in the above formula.

$\begin{array}{c}\mathrm{Variable}Rate=\frac{\left(\$140,00–\$108,00\right)}{\left(400-240\right)}\\ =\frac{\$32,000}{160}\\ =\$200\end{array}$

Therefore, total manufacturing variable cost per unit is $200.

Use the following formula to calculate total manufacturing fixed cost:

$\mathrm{Total}fixed\cos t=Total\cos t-Totalvariable\cos t$

Substitute $140,000 for total cost and $80,000¹ for total variable cost in the above formula.

$\begin{array}{c}\mathrm{Total}fixed\cos t=\$140,000-\$80,000.\\ =\$60,000\end{array}$

Therefore total fixed cost is $60,000.

Use the following formula to calculate variable marketing cost:

$\mathrm{Variable}Rate=\frac{\left(\mathrm{High}PointCost–\mathrm{Low}PointCost\right)}{\left(\mathrm{High}PointOutput–\mathrm{Low}PointOutput\right)}$

Substitute $60,000 for high point cost, $44,000 or low point cost, 400 for high point output and 240 for low point output in the above formula.

$\begin{array}{c}\mathrm{Variable}Rate=\frac{\left(\$60,000–\$44,000\right)}{\left(400-240\right)}\\ =\frac{\$16,000}{160}\\ =\$100\end{array}$

Therefore, total manufacturing variable cost per unit is $100.

Use the following formula to calculate total manufacturing fixed cost:

$\mathrm{Total}fixed\cos t=Total\cos t-Totalvariable\cos t$

Substitute $44,000 for total cost and $24,000² for total variable cost in the above formula.

$\begin{array}{c}\mathrm{Total}fixed\cos t=\$44,000-\$24,000.\\ =\$20,000\end{array}$

Therefore total fixed cost is $20,000.

Use the following formula to calculate variable cost per unit of canoe:

$\mathrm{Variable}\cos tperunit=Manufacturing\mathrm{unit}variable\mathrm{cost}+Marketing\mathrm{unit}variable\mathrm{cost}$

Substitute $200 for manufacturing unit variable cost and $100 for marketing unit variable cost in the above formula.

$\begin{array}{c}\mathrm{Variable}\cos tperunit=\$200+\$100\\ =\$300\end{array}$

Therefore, per unit variable cost of canoe is $300.

Use the following formula to calculate fixed cost of canoe:

$Fixed\cos t=Manufacturingfixed\mathrm{cost}+Marketingfixed\mathrm{cost}$

Substitute $60,000 for manufacturing fixed cost and $20,000 for marketing fixed cost in the above formula.

$\begin{array}{c}Fixed\cos t=\$60,000+\$20,000\\ =\$80,000\end{array}$

Therefore, fixed cost of canoe is $80,000.

Working Note:

1.

Calculation of total variable cost of manufacturing:

$\begin{array}{c}Totalvariable\cos t=Unitvariable\cos t\times Numberofunits\\ =\$200\times 400\\ =\$80,000\end{array}$

2.

Calculation of total variable cost of marketing:

$\begin{array}{c}Totalvariable\cos t=Unitvariable\cos t\times Numberofunits\\ =\$100\times 240\\ =\$24,000\end{array}$

To determine

Calculate per unit variable costs and total fixed costs for paddle product line by using high-low estimation method.

Explanation of Solution

Use the following formula to calculate variable manufacturing cost:

$\mathrm{Variable}Rate=\frac{\left(\mathrm{High}PointCost–\mathrm{Low}PointCost\right)}{\left(\mathrm{High}PointOutput–\mathrm{Low}PointOutput\right)}$

Substitute $66,500 for high point cost, $38,500 or low point cost, 1,700 for high point output and 900 for low point output in the above formula.

$\begin{array}{c}\mathrm{Variable}Rate=\frac{\left(\$66,500–\$38,500\right)}{\left(1,700-900\right)}\\ =\frac{\$28,000}{800}\\ =\$35\end{array}$

Therefore, total manufacturing variable cost per unit is $35.

Use the following formula to calculate total manufacturing fixed cost:

$\mathrm{Total}fixed\cos t=Total\cos t-Totalvariable\cos t$

Substitute $38,500 for total cost and $31,500¹ for total variable cost in the above formula.

$\begin{array}{c}\mathrm{Total}fixed\cos t=\$38,500-\$31,500.\\ =\$7,000\end{array}$

Therefore total fixed cost is $7,000.

Use the following formula to calculate variable marketing cost:

$\mathrm{Variable}Rate=\frac{\left(\mathrm{High}PointCost–\mathrm{Low}PointCost\right)}{\left(\mathrm{High}PointOutput–\mathrm{Low}PointOutput\right)}$

Substitute $11,500 for high point cost, $7,500 or low point cost, 1,700 for high point output and 900 for low point output in the above formula.

$\begin{array}{c}\mathrm{Variable}Rate=\frac{\left(\$11,500–\$7,500\right)}{\left(1,700-900\right)}\\ =\frac{\$4,000}{800}\\ =\$5\end{array}$

Therefore, total manufacturing variable cost per unit is $5.

Use the following formula to calculate total manufacturing fixed cost:

$\mathrm{Total}fixed\cos t=Total\cos t-Totalvariable\cos t$

Substitute $7,500 for total cost and $4,500² for total variable cost in the above formula.

$\begin{array}{c}\mathrm{Total}fixed\cos t=\$7,500-\$4,500.\\ =\$3,000\end{array}$

Therefore, total fixed cost is $3,000.

Use the following formula to calculate variable cost per unit of paddle:

$\mathrm{Variable}\cos tperunit=\left(\begin{array}{l}Manufacturing\mathrm{unit}variable\mathrm{cost}\\ +Marketing\mathrm{unit}variable\mathrm{cost}\end{array}\right)$

Substitute $35 for manufacturing unit variable cost and $5 for marketing unit variable cost in the above formula.

$\begin{array}{c}\mathrm{Variable}\cos tperunit=\$35+\$5\\ =\$40\end{array}$

Therefore, per unit variable cost of paddle is $40.

Use the following formula to calculate fixed cost of canoe:

$Fixed\cos t=Manufacturingfixed\mathrm{cost}+Marketingfixed\mathrm{cost}$

Substitute $7,000 for manufacturing fixed cost and $3,000 for marketing fixed cost in the above formula.

$\begin{array}{c}Fixed\cos t=\$7,000+\$3,000\\ =\$10,000\end{array}$

Therefore, fixed cost of paddle is $10,000.

Working Note:

1.

Calculation of total variable cost of manufacturing:

$\begin{array}{c}Totalvariable\cos t=Unitvariable\cos t\times Numberofunits\\ =\$35\times 900\\ =\$31,500\end{array}$

2.

Calculation of total variable cost of marketing:

$\begin{array}{c}Totalvariable\cos t=Unitvariable\cos t\times Numberofunits\\ =\$5\times 900\\ =\$4,500\end{array}$