Chapter 20, Problem 3BP

a)

To determine

Draw a cost-volume-profit graph for M-n-M on an annual basis. Use thousands of mooring- space hours as the measure of volume of activity.

Explanation of Solution

Cost Volume Profit Analysis (CVP Analysis): This analysis is helpful in determining that how any type of change in cost determines company’s income.

Draw a cost-volume-profit graph for M-n-M on an annual basis. Use thousands of mooring- space hours as the measure of volume of activity:

Figure (1)

The above graph is based on the below table:

Mooring space hours	Revenue (sales) ($)	Variable costs ($)	Fixed costs ($)	Total costs ($)
(1)	(2) = (1) $\times$($5)	(3) = (1) $\times$($0.10)	(4)	(5) = (3) + (4)
0	0	0	149.94	149.94
20	100	2	149.94	151.94
30	150	3	149.94	152.94
50	250	5	149.94	154.94
100	500	10	149.94	159.94
200	1000	20	149.94	169.94
240	1200	24	149.94	173.94

Table (1)

Note: all the values in the table (1) are in thousands.

• Mooring space hours per year are 240,000$\left(80\text{spaces}\times \text{3,000 hours per year}\right)$.
• Revenue (sales) at full capacity is $1,200,000 per year $\left(240,000\text{hours}\times \$5\text{per hour}\right)$.
• Annual variable costs are $24,000$\left(240,000\text{hours}\times \$0.10\text{per hour}\right)$

Given,

The mooring charge per boat is $5 per mooring space hour. Variable costs per boat are 10 cents per mooring space hour. Fixed costs per year are as follows:

Fixed costs per year:
General manager’s salary	$32,940
Wages $\left(\$250\text{per}\text{week}\times 52\text{weeks}\times 3\text{workers}\right)$	39,000
Rent on lot $\left(\$5,000\times 12\text{ months}\right)$	60,000
Fixed city taxes $\left(\$1,500\times 12\text{months}\right)$	18,000
Total fixed costs	$149,940

Table (2)

Therefore, Total fixed costs are $149,940.

b)

To determine

Define the contribution margin ratio and compute the annual breakeven point in dollars of mooring revenue.

Explanation of Solution

Contribution Margin Ratio: The contribution margin ratio shows the amount of difference in the actual sales value and the variable expenses in percentage.

$\text{Contribution margin ratio = }\frac{\text{Contribution margin per unit}}{\text{Revenue per unit}}\times 100$

Compute the contribution margin ratio:

Mooring charge per hour	$5.00
Less: Variable costs per hour	($0.10)
Contribution margin per hour	$4.90
Contribution margin ratio $\left(\$4.90÷\$5.00\right)\times 100$	98%

Table (3)

Therefore, contribution margin ratio is 98%.

Break-Even Sales: Sales volume required to cover the fixed and variable costs and left out with neither profit nor loss is called break-even point of sales.

$\text{Break-even sales volume }\left(\text{\$}\right)\text{ =}\frac{\text{ Fixed costs}}{\text{Contribution margin ratio}}$

Fixed costs are $149,940 (refer table 2) and contribution margin ratio is 98%.

Compute the annual break-even point in dollars of mooring revenue:

$\begin{array}{c}\text{Break-even sales volume }\left(\text{\$}\right)\text{ =}\frac{\text{ Fixed costs}}{\text{Contribution margin ratio}}\\ =\frac{\$149,940}{98\%}\\ =\$153,000\end{array}$

Therefore, the annual break-even point in dollars of mooring revenue is $153,000.

c)

To determine

Calculate:

1. 1) Revised contribution margin ratio and total fixed costs.
2. 2) Annual revenue to produce operating income of $112,560 under revised circumstances.

Explanation of Solution

Given,

The three employees were taken off the hourly wage basis and paid 40 cents per boat moored, with the same vacation pay as before. The variable costs per mooring-space hour will now include 20 cents, or one-half of the 40 cents paid to employees per occupied mooring space, because the average boater stays for two hours.

(1). Compute the revised contribution margin ratio:

Mooring charge per hour	$5.00
Less: Variable costs per hour $\left(\$0.10+\$0.20\right)$	(0.30)
Contribution margin per hour	$4.70
Contribution margin ratio $\left(\$4.70÷\$5.00\right)\times 100$	94%

Table (4)

Therefore, revised contribution margin ratio is 94%.

Compute the revised total fixed costs:

Revised fixed costs per year:
General manager’s salary	$32,940
Vacation pay $\left(\$250\text{per}\text{week}\times 2\text{weeks}\times 3\text{workers}\right)$	1,500
Rent $\left(\$5,000\times 12\text{ months}\right)$	60,000
Fixed city taxes $\left(\$1,500\times 12\text{months}\right)$	18,000
Total fixed costs	$112,440

Table (5)

Therefore, revised total fixed costs are $112,440.

(2). Compute the annual revenue to produce operating income of $112,560 under revised circumstances.

$\begin{array}{c}\text{Sales volume }\left(\text{\$}\right)\text{ =}\frac{\text{ Fixed costs}+\text{Target Operting Income}}{\text{Contribution margin ratio}}\\ \text{=}\frac{\$112,440+\$112,560}{94\%}\\ =\frac{225,000}{94\%}\\ =\$239,362\end{array}$

Therefore, $239,362 is the annual revenue to produce operating income of $112,560 under revised circumstances.