Chapter 3, Problem 68P

a.

To determine

Calculate the profit after tax for Company L.

Answer to Problem 68P

Company L earns $19,800 of profit after tax.

Explanation of Solution

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

Contribution margin:

Particulars	Basic	Retest	Vital
Sales price (unit)	$500	$800	$4,000
Less: variable cost (unit)	$120	$400	$2,800
Contribution margin (unit)	$380	$400	$1,200
Units sold per year	850	100	50
Fixed cost	$390,000
Tax rate	40%

Table: (1)

Compute the profit after tax of Company L:

Particulars	Amount
Sales revenue $\left(\text{Sales unit}\times \text{Sales price}\right)$:
Basic $\left(850\times \$500\right)$	$425,000
Retest $\left(100\times \$800\right)$	$80,000
Vital $\left(50\times \$4,000\right)$	$200,000
Total sales revenue (a)	$705,000
Less:
Variable cost $\text{[sales unit}\times \text{variable cost }\left(\text{unit}\right)]$
Basic $\left(850\times \$120\right)$	$102,000
Retest $\left(100\times \$400\right)$	$40,000
Vital $\left(50\times \$2,800\right)$	$140,000
Total variable cost (b)	$282,000
Contribution:$c=\left(a-b\right)$	$423,000
Less:
Fixed cost (d)	$390,000
Profit before tax:$e=\left(c-d\right)$	$33,000
Tax rate	40%
Tax (f)	$13,200
Profit after tax:$g=\left(e-f\right)$	$19,800

Table: (2)

Thus, Company L earns $19,800 of profit after tax.

b.

To determine

Calculate the sales revenue for basic, retest and vital at the break-even point.

Answer to Problem 68P

The sales revenue for basic, retest and vital is $392,000, $74,000 and $184,000 respectively at the break-even point.

Explanation of Solution

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 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 in order to avoid losses.

Sales mix: This refers to the relative proportions in which a company’s products are sold. Sales mix is computed by expressing the sales of each product as a percentage of total sales.

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 total sales revenue of each product:

Particulars	Sales mix	Break-even point $\text{a}\text{=}(92\text{2}\left(1\right)\times salesmix)$	Sales Price (b)	Total sales revenue $c=\left(a\times b\right)$
Basic	85%	784	$500	$392,000
Retest	10%	92	$800	$74,000
Vital	5%	46	$4,000	$184,000

Table: (3)

Thus, the sales revenue for basic, retest and vital is $392,000 $74,000 and $184,000 respectively.

Working note 1:

Compute the break-even point:

$\begin{array}{c}\text{Break-even point = }\frac{\text{Fixed cost}}{\text{Combined weighted average contribution margin (2)}}\\ =\frac{\$390,000}{\$423}\\ =\text{ 922 units}\end{array}$

Working note 2:

Compute the total weighted average contribution margin:

Particulars	Sales price (a)	Variable cost (b)	Contribution margin $c=\left(a\times b\right)$	Sales mix (d)	Weighted average contribution margin $e=\left(c\times d\right)$
Basic	$500	$120	$380	85%	$323
Retest	$800	$400	$400	10%	$40
Vital	$4,000	$2,800	$1,200	5%	$60
Total weighted average contribution margin					$423

Table: (5)

c.

To determine

Calculate the dollar sales required to earn the profit after tax of $180,000.

Answer to Problem 68P

To earn the profit after tax of $180,000, Company L must make the sales revenue of $693,500, $130,500 and $326,000 for basic, retest and vital respectively.

Explanation of Solution

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 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 in order to avoid losses.

Compute the dollar sales required to earn the profit after tax of $180,000:

The total target volume is 1,631, so it will be distributed among the products in their sales mix ratio.

Particulars	Sales mix	Sales units $\text{a}\text{=}(1,631\left(3\right)\times salesmix)$	Sales price (b)	Sales revenue $c=\left(a\times b\right)$
Basic	85%	1387	$500	$693,500
Retest	10%	163	$800	$130,500
Vital	5%	81.5	$4,000	$326,000
Total sales revenue				$1,149,855

Table: (7)

Thus, to earn the profit after tax of $180,000, Company L must make the sales revenue of basic, retest and vital for $693,500, $130,500 and $326,000 respectively.

Working note 3:

Compute the volume of sales required to earn the profit after tax of $180,000:

$\begin{array}{c}\text{Target}\text{volume}\text{=}\frac{\text{Fixed}\text{cost}\text{+}\text{}\text{Target}\text{operating}\text{profit }÷\text{ (1 - t)}}{\text{Contribution}\text{margin}\text{(1)}}\\ =\frac{\$390,000+\$180,000÷\text{ (1 - 0}\text{.4)}}{\$423}\\ =1,631\text{units}\end{array}$

d.

To determine

1. I.                    Calculate the revenue of the Company L if the number of retests increased to 400 per year, the number of vital increased to 200 per year, while the number of basic dropped to 100.
2. II.                 Calculate the effect on the profit after tax if the company increases its fixed cost to $420,000 with the given product mix.
3. III.              Suggest that the given change is a good idea or not.

Answer to Problem 68P

1. I.                    The revenue of Company L would be $1,170,000 if the number of retests increased to 400 per year, the number of vital increased to 200 per year, while the number of basic dropped to 100.
2. II.                 The profit after tax decreases by $9,000 if the company increases its fixed cost to $420,000 with the given product mix.
3. III.              No, the change of sales mix and an increase in fixed cost is not a good idea for Company L.

Explanation of Solution

I.

Compute the revenue of Company L if the number of retests increased to 400 per year, the number of vital increased to 200 per year, while the number of basic dropped to 100:

Particulars	Amount
Sales revenue $\left(\text{Sales unit}\times \text{Sales price}\right)$:
Basic $\left(100\times \$500\right)$	$50,000
Retest $\left(400\times \$800\right)$	$320,000
Vital $\left(200\times \$4,000\right)$	$800,000
Total sales revenue (a)	$1,170,000

Table: (9)

Thus, The revenue of Company L is $1,170,000 if the number of retests increased to 400 per year, the number of vital increased to 200 per year, while the number of basic dropped to 100.

II.

Compute the change in profit after tax of the given change:

$\begin{array}{c}\text{Decrease}\text{in}\text{profit}\text{=}\text{Original}\text{profit}-\text{Current}\text{profit}\text{(4)}\\ \text{=}\text{\$19,800}-\$10,800\\ =\$9,000\end{array}$

Thus, the profit after tax decreases by $9,000 if the company increases its fixed cost to $420,000 with the given product mix.

Working note 4:

Compute the profit after tax of Company L:

Particulars	Amount
Sales revenue $\left(\text{Sales unit}\times \text{Sales price}\right)$:
Basic $\left(100\times \$500\right)$	$50,000
Retest $\left(400\times \$800\right)$	$320,000
Vital $\left(200\times \$4,000\right)$	$800,000
Total sales revenue (a)	$1,170,000
Less:
Variable cost $\text{[sales unit}\times \text{variable cost }\left(\text{unit}\right)]$
Basic $\left(100\times \$120\right)$	$12,000
Retest $\left(400\times \$400\right)$	$160,000
Vital $\left(200\times \$2,800\right)$	$560,000
Total variable cost (b)	$732,000
Contribution:$c=\left(a-b\right)$	$438,000
Less:
Fixed cost (d)	$420,000
Profit before tax:$e=\left(c-d\right)$	$18,000
Tax rate	40%
Tax (f)	$7,200
Profit after tax: $g=\left(e-f\right)$	$10,800

Table: (11)

III.

If the laboratory’s managers seek to maximize the clinic’s after-tax earnings, this is not a good idea as the profit has decreased by 9,000 with the change in sales mix and an increase in fixed cost.

Thus, the change in sales mix and an increase in fixed cost is not a good idea for Company L.