Q45PGB - Horngren'S Financial And Managerial Accounting

Question

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?

Step-by-Step Solution

Answer

1. Diversified’s breakeven revenue in dollars is $40,000
2. Number of trades is 70 trades
3. Breakeven point at $40,000 50 trades.
4. New break-even trade is 20 trades.

Step 1: Meaning of Contribution Margin

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.

Step 2: (1) Computing Diversified’s breakeven revenue in dollars.

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

Financial planner % of revenue	9%
Advertising % of revenue	11%
Supplies and postage % of revenue	4%
Usage fees % of revenue	6%
Total % of variable costs and contribution margin	30%

Calculating the total fixed cost

Office rent	$8,000
Depreciation	$1,700
Utilities	$2,400
Telephone lines	$1,500
Brokerage services	$2,500
Salary of a financial planner	$11,900
Total fixed cost	$28,000

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.

Step 3: (2) Computing the dollar revenues

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

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

Step 4: (3) Graph Diversified’s CVP relationships

Step 5: Effect of breakeven point

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: $\left(\frac{50\text{\hspace{0.17em}trades}-20\text{\hspace{0.17em}trades}}{50\text{\hspace{0.17em}trades}}\right)$