Question

National Investor Group is opening an office in Portland, Oregon. Fixed monthly costs are office rent (\(8,100), depreciation on office furniture (\)1,700), utilities (\(2,000), special telephone lines (\)1,500), a connection with an online brokerage service (\(2,500), and the salary of a financial planner (\)5,200). Variable costs include payments to the financial planner (9% of revenue), advertising (11% of revenue), supplies and postage (4% of revenue), and usage fees for the telephone lines and computerized brokerage service (6% of revenue).

Requirements

1. Use the contribution margin ratio approach to compute National’s breakeven revenue in dollars. If the average trade leads to \(1,000 in revenue for National, how many trades must be made to break even?
2. Use the equation approach to compute the dollar revenues needed to earn a monthly target profit of \)12,600.
3. Graph National’s CVP relationships. Assume that an average trade leads to \(1,000 in revenue for National. Show the breakeven point, the sales revenue line, the fixed cost line, the total cost line, the operating loss area, the operating income area, and the sales in units (trades) and dollars when monthly operating income of \)12,600 is earned.
4. Suppose that the average revenue National earns increases to $1,500 per trade. Compute the new breakeven point in trades. How does this affect the breakeven point?

Short answer

1. Diversified’s breakeven revenue in dollars is $30,000
2. Number of trades is 48 trades
3. Breakeven point at $30,000 30 trades.
4. New break-even trade is 25 trades.

Step-by-step solution

Meaning of Break-Even Point

It is a stage of operation during which a business experiences revenues generated in balance with costs incurred. As a result, when a business hits its break-even point, it does not declare any profit or loss from the operation.

(1) Compute National’s breakeven revenue in dollars

Calculate the total percentage of variable costs and contribution margin.

Variable cost	Percentage revenue
Financial planner	9%
Advertising	11%
Supplies and postage	4%
Usage fees	6%
Total	30%

The variable cost is 30% of sales revenue. Hence, the contribution margin would be 70% of sales revenue.

Calculate total fixed costs.

Office rent	$8,100
Depreciation	$1,700
Utilities	$2,000
Telephone lines	$1,500
Brokerage services	$2,500
Salary of a financial planner	$5,200
Total fixed cost	$21,000

Calculate required sales in dollars

$\begin{array}{c}\text{Required\hspace{0.17em}sales\hspace{0.17em}in\hspace{0.17em}dollars}=\frac{\text{Fixedcosts}+\text{Target\hspace{0.17em}profit}}{\text{Contribution\hspace{0.17em}margin\hspace{0.17em}ratio}}\\ =\frac{\mathrm{\$}21,000+\mathrm{\$}0}{70\mathrm{\%}}\\ =\mathrm{\$}30,000\end{array}$

Calculate the required sales in units at break-even when the sales price per trade is $1,000

$\begin{array}{c}\text{Required\hspace{0.17em}sales\hspace{0.17em}in\hspace{0.17em}unit}=\frac{\text{Required\hspace{0.17em}sales\hspace{0.17em}in\hspace{0.17em}dollar}}{\text{Sales\hspace{0.17em}price\hspace{0.17em}per\hspace{0.17em}trade}}\\ =\frac{\mathrm{\$}30,000}{\mathrm{\$}1,000}\\ =30\text{\hspace{0.17em}traders}\end{array}$

(2) Compute the dollar revenues

Calculating the required sales in unit

$\begin{array}{c}\text{Target\hspace{0.17em}profit}=[\text{Net\hspace{0.17em}sales\hspace{0.17em}revenue}-\text{Variable\hspace{0.17em}\hspace{0.17em}costs}]-\text{Fixed\hspace{0.17em}cost}\\ \mathrm{\$}12,600=[(\mathrm{\$}1,000\times \text{Number\hspace{0.17em}of\hspace{0.17em}trade})-(\mathrm{\$}1,000\times 30\mathrm{\%}\times \text{Number\hspace{0.17em}of\hspace{0.17em}trades})]-\mathrm{\$}21,000\\ \mathrm{\$}33,600=[(\mathrm{\$}1,000\times \mathrm{\$}300)\times \text{Number\hspace{0.17em}of\hspace{0.17em}trades}]\\ \mathrm{\$}39,200=\mathrm{\$}700\times \text{Number\hspace{0.17em}of\hspace{0.17em}trades}\end{array}$

$\begin{array}{c}\text{Number\hspace{0.17em}of\hspace{0.17em}trades}=\frac{\mathrm{\$}33,600}{\mathrm{\$}700}\\ =48\text{\hspace{0.17em}trades}\end{array}$

Compute required sales in dollars

$\begin{array}{c}\text{Required\hspace{0.17em}sales\hspace{0.17em}in\hspace{0.17em}dollars}=\text{Required\hspace{0.17em}sales\hspace{0.17em}in\hspace{0.17em}units}\times \text{Sales\hspace{0.17em}price\hspace{0.17em}per\hspace{0.17em}unit}\\ =48\text{\hspace{0.17em}trades}\times \mathrm{\$}1,000\text{\hspace{0.17em}trade}\\ =\mathrm{\$}48,000\end{array}$

(3) Graph National’s CVP relationships

(4) Compute the new breakeven point in trades

Calculate the new break-even point in the unit if sales per trade increase to $1,200.

$\begin{array}{c}\text{New\hspace{0.17em}break-even\hspace{0.17em}trade}=\frac{\text{Required\hspace{0.17em}sales\hspace{0.17em}in\hspace{0.17em}dollars}}{\text{Sales\hspace{0.17em}price\hspace{0.17em}per\hspace{0.17em}trade}}\\ =\frac{\mathrm{\$}30,000}{\mathrm{\$}1,200}\\ =25\text{\hspace{0.17em}trades}\end{array}$

The Break-even point is decreased to 5 trades (30 trades – 25 trades) when the average revenue is increased to $2,000.

Hence, the break-even point is reduced by 33% as follows:$\left(\frac{30\text{\hspace{0.17em}trades}-25\text{\hspace{0.17em}trades}}{30\text{\hspace{0.17em}trades}}\right)$