Chapter 3, Problem 29E

a.

To determine

Calculate the operating profit for Company D.

Answer to Problem 29E

The operating profit is $450,000 for Company D.

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:

Operating profit:

$\begin{array}{c}\text{Operating}\text{profit}\text{=}\text{Total}\text{revenue}\text{(1)}-\text{Total}\text{costs}\text{(2)}\\ \text{=}\text{\$1,350,000}-\text{\$}\text{900,000}\\ \text{=}\text{\$450,000}\end{array}$

Thus, the operating profit for company D is $450,000.

Working note 1:

Compute the total revenue:

$\begin{array}{c}\text{Total}\text{revenue}\text{=}\text{Sales}\text{price}\times \text{Projected}\text{units}\text{sold}\\ \text{=}\text{\$270}\times \text{5000}\\ \text{=}\text{\$1,350,000}\end{array}$

Working note 2:

Compute the total cost:

$\begin{array}{c}\text{Total}\text{costs}\text{=}\text{Variable}\text{cost}\text{+}\text{Fixed}\text{cost}\\ \text{=}(\text{Units}\text{sold}\times \text{Variable}\text{cost)}+F\text{ixed}\text{cost}\\ \text{=}(5,000\times \$120)+\$300,000\\ =\$900,000\end{array}$

b.

To determine

Calculate the impact on operating profit if the sales price decreases by 10 per cent and increases by 20 per cent.

Answer to Problem 29E

The change in operating profit when sales price decreases by 10% is ($135,000).

The change in operating profit when sales price increases by 20% is $270,000.

Explanation of Solution

Given:

$\begin{array}{c}\text{Sales}\text{price}\text{=}\text{\$270}\text{per}\text{unit}\\ \text{Variable}\text{cost}\text{=}\text{\$120}\text{per}\text{unit}\\ \text{Fixed}\text{cost}\text{=}\text{\$300,000}\text{per}\text{month}\\ \text{Projected}\text{units}\text{sold}\text{=}\text{5,000}\text{units}\end{array}$

When the sales price decreases by 10%:

Compute the operating profit:

$\begin{array}{c}\text{Operating}\text{profit}\text{=}\text{Total}\text{revenue}\text{(4)}-\text{Total}\text{costs}\text{(5)}\\ \text{=}\text{\$1,215,000}-\text{\$}\text{900,000}\\ \text{=}\text{\$315,000}\end{array}$

Thus, the operating profit decreased by $135,000. Earlier, operating profit was $450,000 and now current profit is $315,000.

When the sales price increases by 20%:

Operating profit:

$\begin{array}{c}\text{Operating}\text{profit}\text{=}\text{Total}\text{revenue}\text{(6)}-\text{Total}\text{costs}\text{(7)}\\ \text{=}\text{\$1,620,000}-\text{\$}\text{900,000}\\ \text{=}\text{\$720,000}\end{array}$

Thus, operating profit increased by $270,000.

Working note 3:

When sales decrease by 10%:

Compute the operating profit:

Revised sales price:

$\begin{array}{c}\text{Revised}\text{sales}\text{price}\text{=}\text{Sales}\text{price}-\text{10\%}\\ \text{=}\text{\$270}-\left(\text{\$270}\times \text{10\%}\right)\\ \text{=}\$\text{243}\end{array}$

Working note 4:

Total revenue:

$\begin{array}{c}\text{Total}\text{revenue}\text{=}\text{Sales}\text{price}\times \text{Units}\text{sold}\\ \text{=}\text{\$243}\times \text{5,000}\\ \text{=}\text{\$1,215,000}\end{array}$

Working note 5:

Total cost:

$\begin{array}{c}\text{Total}\text{costs}\text{=}\text{Variable}\text{cost}\text{+}\text{Fixed}\text{cost}\\ \text{=}(\text{units}\text{sold}\times \text{variable}\text{cost)}+\text{fixed}\text{cost}\\ \text{=}(5,000\times \$120)+\$300,000\\ =\$900,000\end{array}$

When the sales price is increased by 20%:

Compute the operating profit:

Revised sales price:

$\begin{array}{c}\text{Revised}\text{sales}\text{price}\text{=}\text{Sales}\text{price}+2\text{0\%}\\ \text{=}\text{\$270}+2\text{0\%}\\ \text{=}\$324\end{array}$

Working note 6:

Total revenue:

$\begin{array}{c}\text{Total}\text{revenue}\text{=}\text{Sales}\text{price}\times \text{Units}\text{sold}\\ \text{=}\text{\$324}\times \text{5,000}\\ \text{=}\text{\$1,620,000}\end{array}$

Working note 7:

Total costs:

$\begin{array}{c}\text{Total}\text{costs}\text{=}\text{Variable}\text{cost}\text{+}\text{Fixed}\text{cost}\\ \text{=}(\text{Units}\text{sold}\times \text{Variable}\text{cost)}+\text{Fixed}\text{cost}\\ \text{=}(5,000\times \$120)+\$300,000\\ =\$900,000\end{array}$

c.

To determine

Calculate the impact on operating profit if variable costs per unit decreased by 10 per cent and increase by 20 per cent.

Answer to Problem 29E

The change in operating profit when variable cost is decreased by 10% is $60,000

The change in operating profit when variable cost is increased by 20% is ($120,000)

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.

Operating profit:

When variable cost is decreased by 10%:

$\begin{array}{c}\text{Operating}\text{profit}\text{=}\text{Total}\text{revenue}\text{(9)}-\text{Total}\text{costs}\text{(10)}\\ \text{=}\text{\$1,350,000}-\text{\$}84\text{0,000}\\ \text{=}\text{\$510,000}\end{array}$

Thus, operating profit is increased by $60,000.

When variable cost is increased by 20%:

$\begin{array}{c}\text{Operating}\text{profit}\text{=}\text{Total}\text{revenue}\text{(9)}-\text{Total}\text{costs}\text{(12)}\\ \text{=}\text{\$1,350,000}-\text{\$}1,02\text{0,000}\\ \text{=}\text{\$330,000}\end{array}$

Thus, operating profit is decreased by $120,000.

Working note 8:

When variable cost is decreased by 10%:

Compute the revised variable cost:

$\begin{array}{c}\text{Revised}\text{variable}\text{cost}\text{=}\text{Variable}\text{cost}-1\text{0\%}\\ \text{=}\text{\$120}-1\text{0\%}\\ \text{=}\$108\end{array}$

Working note 9:

Compute the total revenue:

$\begin{array}{c}\text{Total}\text{revenue}\text{=}\text{Sales}\text{price}\times \text{projected}\text{units}\text{sold}\\ \text{=}\text{\$270}\times \text{5,000}\\ \text{=}\text{\$1,350,000}\end{array}$

Working note 10:

Compute the total cost:

$\begin{array}{c}\text{Total}\text{costs}\text{=}\text{Variable}\text{cost}\text{+}\text{Fixed}\text{cost}\\ \text{=}(\text{Units}\text{sold}\times \text{Variable}\text{cost)}+\text{Fixed}\text{cost}\\ \text{=}(5000\times \$108)+\$300,000\\ =\$840,000\\ \end{array}$

When variable cost is increased by 20%:

Working note 11:

Compute the revised variable cost:

$\begin{array}{c}\text{Revised}\text{variable}\text{cost}\text{=}\text{Variable}\text{cost}+2\text{0\%}\\ \text{=}\text{\$120}+2\text{0\%}\\ \text{=}\$144\end{array}$

Working note 12:

Compute the total costs:

$\begin{array}{c}\text{Total}\text{costs}\text{=}\text{Variable}\text{cost}\text{+}\text{Fixed}\text{cost}\\ \text{=}(\text{Units}\text{sold}\times \text{Variable}\text{cost)}+\text{Fixed}\text{cost}\\ \text{=}(5000\times \$144)+\$300,000\\ =\$1,020,000\end{array}$

d.

To determine

Calculate the change in operating profit when fixed cost is reduced by 20% and variable cost is increased by 10%.

Answer to Problem 29E

There is no change in operating profit when fixed cost is reduced by 20% and the variable cost is increased by 10%.

Explanation of Solution

Operating profit:

$\begin{array}{c}\text{Operating}\text{profit}\text{=}\text{Total}\text{revenue}\text{(15)}-\text{Total}\text{costs}\text{(16)}\\ \text{=}\text{\$1,350,000}-\text{\$}900\text{,000}\\ \text{=}\text{\$450,000}\end{array}$

Thus, there is no change in the operating profit as the profit is the same in both situations.

Working note 13:

Compute the revised fixed cost:

$\begin{array}{c}\text{Revised}\text{fixed}\text{cost}\text{=}\text{Fixed}\text{cost}-\left(\text{Fixed}\text{cost}\times 20\%\right)\\ =\$300,000-\left(\$300,000\times 20\%\right)\\ =\$240,000\end{array}$

Working note 14:

Compute the revised variable cost:

$\begin{array}{c}\text{Revised}\text{variable}\text{cost}\text{=}\text{Variable}\text{cost}+\left(120\times 1\text{0\%}\right)\\ \text{=}\text{\$120}+1\text{0\%}\\ \text{=}\$132\end{array}$

Working note 15:

Compute the total revenue:

$\begin{array}{c}\text{Total}\text{revenue}\text{=}\text{Sales}\text{price}\times \text{Units}\text{sold}\\ \text{=}\text{\$270}\times \text{5,000}\\ \text{=}\text{\$1,350,000}\end{array}$

Working note 16:

Compute the total costs:

$\begin{array}{c}\text{Total}\text{costs}\text{=}\text{Variable}\text{cost}\text{+}\text{Fixed}\text{cost}\\ \text{=}(\text{Units}\text{sold}\times \text{Variable}\text{cost)}+\text{Fixed}\text{cost}\\ \text{=}(5,000\times \$132)+\$240,000\\ =\$900,000\end{array}$