Chapter 3, Problem 32E

Basic Decision Analysis Using CVP

Refer to the data for Warner Clothing in Exercise 3-30. Assume that the company plans to sell 5,000 units per month. Consider requirements (b), (c), and (d) independently of each other.

Required

1. a.      What will be the operating profit?
2. b.      What is the impact on operating profit if the sales price decreases by 10 percent? Increases by 20 percent?
3. c.       What is the impact on operating profit if variable costs per unit decrease by 10 percent? Increase by 20 percent?
4. d.      Suppose that fixed costs for the year are 10 percent lower than projected, and variable costs per unit are 10 percent higher than projected. What impact will these cost changes have on operating profit for the year? Will profit go up? Down? By how much?

To determine

Calculate the operating profit of Company W per month.

Answer to Problem 32E

The operating profit of Company W is $18,000 per month.

Explanation of Solution

Operating profit: The operating profit is the excess of total revenues over total expenses after adjusting for depreciation and taxes.

Compute the operating profit per month:

$\begin{array}{c}\text{Operating}\text{profit}\text{=}\text{Total}\text{revenue}\text{(1)}-\text{Total}\text{costs}\text{(2)}\\ \text{=}\text{\$75,000}\text{-}\text{\$}\text{57,000}\\ \text{=}\text{\$}\text{18,000}\end{array}$

Thus, the operating profit of Company W is $18,000 for every month.

Working note 1:

Compute the total revenue:

$\begin{array}{c}\text{Total}\text{revenue}\text{=}\text{Sales}\text{price}\times \text{Units}\text{sold}\\ \text{=}\text{\$15}\times \text{5,000}\\ \text{=}\text{\$75,000}\end{array}$

Working note 2:

Compute the total cost:

$\begin{array}{c}\text{Total}\text{costs}\text{=}\text{Variable}\text{cost}\text{+}\text{Fixed}\text{cost}\\ \text{=}(\text{units}\text{sold}\times \text{variable}\text{cost)}+\text{Fixed}\text{cost}\\ \text{=}(5,000\times \$3)+\$42,000\\ =\$57,000\end{array}$

To determine

Calculate the impact of a 10% decrease and a 20% increase in sales price on operating profit.  

Answer to Problem 32E

The change in operating profit when the sales price decreases by 10% is ($7,500).

The change in operating profit when the sales price increases by 20% is $15,000.

Explanation of Solution

Target volume: the level of sales which need to be achieved during a particular period of time is termed as target volume.

Target profit: the amount of profit which needs to be achieved during a particular period of time on a particular level of sales is termed as target profit.

Compute the impact of a 10% decrease in sales price on operating profit:

$\begin{array}{c}\text{Change}\text{in}\text{operating}\text{profit}\text{=}\text{Profit}\text{after}\text{decrease}-\text{Profit}\text{before}\text{decrease}\\ =\$10,500-\$18,000\\ =(\$7,500)\end{array}$

Thus, operating profit decreases by $7,500 when sales price decreases by 10%.

Compute the impact of 20% increases in sales price on operating profit:

$\begin{array}{c}\text{Change}\text{in}\text{operating}\text{profit}\text{=}\text{Profit}\text{after}\text{decrease}-\text{Profit}\text{before}\text{decrease}\\ =\$33,000-\$18,000\\ =\$15,000\end{array}$

Thus, operating profit increased by $15,000 when the sales price increases by 20%.

Working note 3:

Compute the operating profit, revised sales price and total revenue when the sales price decreases by 10%:

Operating profit:

$\begin{array}{c}\text{Operating}\text{profit}\text{=}\text{Total}\text{revenue}\text{(3)}-\text{Total}\text{costs}\text{(4)}\\ \text{=}\text{\$67,500}\text{-}\text{\$}57\text{,000}\\ \text{=}\text{\$10,500}\end{array}$

Revised sales price:

$\begin{array}{c}\text{Revised}\text{sales}\text{price}\text{=}\text{Sales}\text{price}\text{(unit)}-\text{Change}\%\\ =\$15-\left(\$15\times 10\%\right)\\ =\$13.5\end{array}$.

Total revenue:

$\begin{array}{c}\text{Total}\text{revenue}\text{=}\text{Sales}\text{price}\times \text{Units}\text{sold}\\ \text{=}\text{\$13}\text{.5}\times \text{5,000}\\ \text{=}\text{\$67,500}\end{array}$

Working note 4:

Compute the total costs when the sales price decreases by 10%:

$\begin{array}{c}\text{Total}\text{costs}\text{=}\text{Variable}\text{cost}\text{+}\text{Fixed}\text{cost}\\ \text{=}(\text{Units}\text{sold}\times \text{Variable}\text{cost)}+\text{Fixed}\text{cost}\\ \text{=}(5,000\times \$3)+\$42,000\\ =\$57,000\end{array}$

Compute the operating profit and revised sales price when the sales price increases by 20%:

Operating profit:

$\begin{array}{c}\text{Operating}\text{profit}\text{=}\text{Total}\text{revenue}\text{(5)}-\text{Total}\text{costs}\text{(6)}\\ \text{=}\text{\$90,000}\text{-}\text{\$}57\text{,000}\\ \text{=}\text{\$33,000}\end{array}$

Revised sales price:

$\begin{array}{c}\text{Revised}\text{sales}\text{price}\text{=}\text{Sales}\text{price}\text{(unit)}+\text{Change}\%\\ =\$15+\left(\$15\times 20\%\right)\\ =\$18\end{array}$

Working note 5:

Compute the total revenue:

$\begin{array}{c}\text{Total}\text{revenue}\text{=}\text{Sales}\text{price}\times \text{Units}\text{sold}\\ \text{=}\text{\$18}\times \text{5,000}\\ \text{=}\text{\$90,000}\end{array}$

Working note 6:

Compute the total costs:

$\begin{array}{c}\text{Total}\text{costs}\text{=}\text{Variable}\text{cost}\text{+}\text{Fixed}\text{cost}\\ \text{=}(\text{Units}\text{sold}\times \text{Variable}\text{cost)}+\text{Fixed}\text{cost}\\ \text{=}(5,000\times \$3)+\$42,000\\ =\$57,000\end{array}$

To determine

Calculate the impact of a 10% decrease and a 20% increase in Variable cost on operating profit.

Answer to Problem 32E

The change in operating profit when variable cost decreases by 10% is $1,500.

The change in operating profit when variable cost increases by 20% is ($3,000).

Explanation of Solution

Target volume: the level of sales which need to be achieved during a particular period of time is termed as target volume.

Target profit: the amount of profit which needs to be achieved during a particular period of time on a particular level of sales is termed as target profit.

Compute the impact of a 10% decrease in variable cost on operating profit:

$\begin{array}{c}\text{Change}\text{in}\text{operating}\text{profit}\text{=}\text{Profit}\text{after}\text{decrease}-\text{Profit}\text{before}\text{decrease}\\ =\$19,500-\$18,000\\ =(\$1,500)\end{array}$

Thus, operating profit decreases by $7,500 when sales price decreases by 10%.

Compute the impact of 20% increases in variable cost on operating profit:

$\begin{array}{c}\text{Change}\text{in}\text{operating}\text{profit}\text{=}\text{Profit}\text{after}\text{decrease}-\text{Profit}\text{before}\text{decrease}\\ =\$15,000-\$18,000\\ =(\$3,000)\end{array}$

Thus, operating profit increased by $15,000 when the sales price increases by 20%.

Compute the operating profit, revised sales price, total revenue and total cost when the variable cost decreases by 10%:

Operating profit:

$\begin{array}{c}\text{Operating}\text{profit}\text{=}\text{Total}\text{revenue}\text{(7)}-\text{Total}\text{costs}\text{(8)}\\ \text{=}\text{\$75,000}\text{-}\text{\$}55\text{,500}\\ \text{=}\text{\$19,500}\end{array}$

Revised variable cost:

$\begin{array}{c}\text{Revised}\text{variable}\text{cost}\text{=}\text{Variable}\text{cost}\text{(unit)}-\text{Change}\%\\ =\$3-\left(\$3\times 10\%\right)\\ =\$2.7\end{array}$

Working note 7:

Total revenue:

$\begin{array}{c}\text{Total}\text{revenue}\text{=}\text{Sales}\text{price}\times \text{Units}\text{sold}\\ \text{=}\text{\$15}\times \text{5,000}\\ \text{=}\text{\$75,000}\end{array}$

Working note 8:

Total costs:

$\begin{array}{c}\text{Total}\text{costs}\text{=}\text{Variable}\text{cost}\text{+}\text{Fixed}\text{cost}\\ \text{=}(\text{units}\text{sold}\times \text{variable}\text{cost)}+\text{Fixed}\text{cost}\\ \text{=}(5,000\times \$2.7)+\$42,000\\ =\$55,500\end{array}$

Compute the operating profit, revised sales price, total revenue and total cost when the variable cost increases by 20%:

Operating profit:

$\begin{array}{c}\text{Operating}\text{profit}\text{=}\text{Total}\text{revenue}\text{(9)}-\text{Total}\text{costs}\text{(10)}\\ \text{=}\text{\$75,000}\text{-}\text{\$}60\text{,000}\\ \text{=}\text{\$15,000}\end{array}$

Revised variable cost:

$\begin{array}{c}\text{Revised}\text{variable}\text{cost}\text{=}\text{Variable}\text{cost}\text{(unit)}+\text{Change}\%\\ =\$3+20\%\\ =\$3.6\end{array}$

Working note 9:

Total revenue:

$\begin{array}{c}\text{Total}\text{revenue}\text{=}\text{Sales}\text{price}\times \text{Units}\text{sold}\\ \text{=}\text{\$15}\times \text{5,000}\\ \text{=}\text{\$75,000}\end{array}$

Working note 10:

Total costs:

$\begin{array}{c}\text{Total}\text{costs}\text{=}\text{Variable}\text{cost}\text{+}\text{Fixed}\text{cost}\\ \text{=}(\text{Units}\text{sold}\times \text{Variable}\text{cost)}+\text{Fixed}\text{cost}\\ \text{=}(5,000\times \$3.6)+\$42,000\\ =\$60,000\end{array}$

To determine

Calculate the impact of a 10% decrease in fixed cost and a 10% increase in Variable cost on the operating profit.

Answer to Problem 32E

The operating profit increases by $2,700, when fixed cost decreases by 10% and Variable cost increases by 10%.

Explanation of Solution

Target volume: the level of sales which need to be achieved during a particular period of time is termed as target volume.

Target profit: the amount of profit which needs to be achieved during a particular period of time on a particular level of sales is termed as target profit.

Compute the impact of a 10% decrease in fixed cost and a 10% increase in variable cost on operating profit:

$\begin{array}{c}\text{Change}\text{in}\text{operating}\text{profit}\text{=}\text{Profit}\text{after}\text{change}-\text{Profit}\text{before}\text{change}\\ =\$20,700-\$18,000\\ =\$2,700\end{array}$

Thus, operating profit increased by $2,700 when fixed cost decreases by 10% and variable cost increases by 10%.

Working note:

Compute the operating profit, revised sales price, total revenue and total cost when fixed cost decreases by 10% and variable cost increases by 10%.

Operating profit:

$\begin{array}{c}\text{Operating}\text{profit}\text{=}\text{Total}\text{revenue}\text{(11)}-\text{Total}\text{costs}\text{(12)}\\ \text{=}\text{\$75,000}\text{-}\text{\$}54\text{,300}\\ \text{=}\text{\$20,700}\end{array}$

Revised fixed cost:

$\begin{array}{c}\text{Revised}\text{fixed}\text{cost}\text{=}\text{Fixed}\text{cost}-\text{Change}\%\\ =\$42,000-(\$42,000\times 10\%)\\ =\$37,800\end{array}$

Revised variable cost:

$\begin{array}{c}\text{Revised}\text{variable}\text{cost}\text{=}\text{variable}\text{cost}+\text{Change}\%\\ =\$3+(3\times 10\%)\\ =\$3.3\end{array}$

Working note 11:

Total revenue:

$\begin{array}{c}\text{Total}\text{revenue}\text{=}\text{Sales}\text{price}\times \text{Units}\text{sold}\\ \text{=}\text{\$15}\times \text{5,000}\\ \text{=}\text{\$75,000}\end{array}$

Working note 12:

Total costs:

$\begin{array}{c}\text{Total}\text{costs}\text{=}\text{Variable}\text{cost}\text{+}\text{Fixed}\text{cost}\\ \text{=}(\text{units}\text{sold}\times \text{variable}\text{cost)}+\text{Fixed}\text{cost}\\ \text{=}(5,000\times \$3.3)+\$37,800\\ =\$54,300\end{array}$