Diversified Investor Group is opening an office in Boise, Idaho. Fixed monthly costs are office rent (\(8,000), depreciation on office furniture (\)1,700), utilities (\(2,400), special telephone lines (\)1,500), a connection with an online brokerage service (\(2,500), and the salary of a financial planner (\)11,900). 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 Diversified’s breakeven revenue in dollars. If the average trade leads to \(800 in revenue for Diversified, how many trades must be made to break even?
2. Use the equation approach to compute the dollar revenues needed to earn a monthly target profit of \)11,200.
3. Graph Diversified’s CVP relationships. Assume that an average trade leads to \(800 in revenue for Diversified. Show the breakeven point, the sales revenue line, the fixed cost line, the total cost line, the operating loss area, the operating income area, and the sales in units (trades) and dollars when monthly operating income of \)11,200 is earned.
4. Suppose that the average revenue Diversified earns increases to $2,000 per trade. Compute the new breakeven point in trades. How does this affect the breakeven point?

The contribution margin is the sum of sales revenue left over after covering the business entity's fixed costs. The inconsistency between sales income and variable costs is what determines it.

Calculate the required sales in the unit at break-even when the sales price per trade is $800

Calculating the total % of variable costs and contribution margin

Calculating the total fixed cost

Calculating the required sales in dollar

$\begin{array}{c}\text{Required\hspace{0.17em}sales\hspace{0.17em}in\hspace{0.17em}dollars}=\frac{\text{Fixedcosts}+\text{Target\hspace{0.17em}profit}}{\text{Contribution\hspace{0.17em}margin\hspace{0.17em}ratio}}\\ =\frac{\mathrm{\$}28,000+\mathrm{\$}0}{70\mathrm{\%}}\\ =\mathrm{\$}40,000\end{array}$

Calculate the required sales in units at break-even when the sales price per trade is $800

$\begin{array}{c}\text{Required\hspace{0.17em}sales\hspace{0.17em}in\hspace{0.17em}unit}=\frac{\text{Required\hspace{0.17em}sales\hspace{0.17em}in\hspace{0.17em}dollar}}{\text{Sales\hspace{0.17em}price\hspace{0.17em}per\hspace{0.17em}trade}}\\ =\frac{\mathrm{\$}40,000}{\mathrm{\$}800}\\ =50\text{\hspace{0.17em}traders}\end{array}$

Therefore, the required sales in the unit at break-even when the sales price per trade is $800 are 50 traders.

$\begin{array}{c}\text{Target\hspace{0.17em}profit}=[\text{Net\hspace{0.17em}sales\hspace{0.17em}revenue}-\text{Variable\hspace{0.17em}\hspace{0.17em}costs}]-\text{Fixed\hspace{0.17em}cost}\\ \mathrm{\$}11,200=[(\mathrm{\$}800\times \text{Number\hspace{0.17em}of\hspace{0.17em}trade})-(\mathrm{\$}800\times 30\mathrm{\%}\times \text{Number\hspace{0.17em}of\hspace{0.17em}trades})]-\mathrm{\$}28,000\\ \mathrm{\$}39,200=[(\mathrm{\$}800\times \mathrm{\$}240)\times \text{Number\hspace{0.17em}of\hspace{0.17em}trades}]\\ \mathrm{\$}39,200=\mathrm{\$}560\times \text{Number\hspace{0.17em}of\hspace{0.17em}trades}\end{array}$

$\begin{array}{c}\text{Number\hspace{0.17em}of\hspace{0.17em}trades}=\frac{\mathrm{\$}39,200}{\mathrm{\$}560}\\ =70\text{\hspace{0.17em}trades}\end{array}$

Calculate the new break-even point in the unit if sales per trade increase to $2,000.

$\begin{array}{c}\text{New\hspace{0.17em}break-even\hspace{0.17em}trade}=\frac{\text{Required\hspace{0.17em}sales\hspace{0.17em}in\hspace{0.17em}dollars}}{\text{Sales\hspace{0.17em}price\hspace{0.17em}per\hspace{0.17em}trade}}\\ =\frac{\mathrm{\$}40,000}{\mathrm{\$}2,000}\\ =20\text{\hspace{0.17em}trades}\end{array}$

The Break-even point is decreased to 30 trades (50 trades – 20 trades) when the average revenue is increased to $2,000.

Hence, the break-even point is reduced by 60% as follows: $\left(\frac{50\text{\hspace{0.17em}trades}-20\text{\hspace{0.17em}trades}}{50\text{\hspace{0.17em}trades}}\right)$