Hewtex Electronics Manufactures Two Tape Recorder Products
Hewtex Electronics Manufactures Two Products Tape Recorders And Elec
Cleaned assignment instructions
Hewtex Electronics manufactures two products - tape recorders and electronic calculators - and sells them nationally to wholesalers and retailers. The company projects sales of 70,000 tape recorders and 140,000 electronic calculators for the fiscal year ending December 31, 20x7. The projected earnings statement includes sales revenue, production costs, fixed overhead, gross margin, and net income before income taxes. Management plans to reduce the calculator wholesale price from $22.50 to $20.00 starting January 1, 20x8, and will spend an additional $57,000 on advertising in 20x8. They also anticipate changes in material and labor costs, with material costs expected to decrease by 10% for tape recorders and 20% for calculators, while direct labor costs increase by 10%. Sales volume and mix are assumed to remain proportionate, and fixed overhead costs will stay constant. The assignment requires calculations for the break-even units for 20x7, required sales volume for targeted profit in 20x8, and break-even units for 20x8.
Paper For Above instruction
Introduction
Hewtex Electronics is a manufacturing company producing two distinct products: tape recorders and electronic calculators. As a business operating in a competitive environment, Hewtex aims to analyze its historical performance and project future sales, costs, and profitability. This paper focuses on conducting detailed cost-volume-profit (CVP) analysis to determine the break-even sales in units for 20x7, the sales necessary to achieve a target profit margin in 20x8 after modifications in pricing and costs, and the break-even units for 20x8. These calculations are critical for strategic planning, pricing decisions, and evaluating the company's financial health.
Part A: Break-even Analysis for 20x7
To compute the break-even point in units for 20x7, we need to understand the fixed and variable costs per product, as well as the sales prices. Break-even point occurs when total revenues equal total costs, resulting in zero profit.
Sales and Cost Structure:
From the projection:
- Tape Recorders:
- Selling Price per unit: $15.00
- Variable Costs:
- Direct materials: $4.50
- Direct labor: $2.00
- Variable overhead: $2.00
- Fixed Overhead: $1.50 per unit (calculated based on total fixed overhead and units sold)
- Electronic Calculators:
- Selling Price per unit: $22.50
- Variable Costs:
- Direct materials: $910, corresponding to per unit $6.50 (derived from total material cost and units)
- Direct labor: $560, per unit $4.00
- Variable overhead: $420, per unit $3.00
To find the total fixed costs:
- Fixed Overheads are already provided as:
- Tape Recorders: $70,000 (total fixed overhead)
- Calculators: $280,000
Total fixed costs are: $(70,000 + 280,000) = $350,000.
Calculating contribution margin per unit:
Tape Recorders:
- Contribution Margin = Sale Price - Variable Costs
- = $15.00 - ($4.50 + $2.00 + $2.00) = $15.00 - $8.50 = $6.50
Calculators:
- Contribution Margin = $22.50 - ($6.50 + $4.00 + $3.00) = $22.50 - $13.50 = $9.00
Number of units needed to break even:
- Total fixed costs / Contribution margin per unit
Units for Tape Recorders:
- $70,000 / $6.50 ≈ 10,769 units
Units for Calculators:
- $280,000 / $9.00 ≈ 31,111 units
Total units:
- 10,769 (Tape) + 31,111 (Calculators) ≈ 41,880 units
Thus, Hewtex must sell approximately 10,769 tape recorders and 31,111 calculators in 20x7 to break even.
Part B: Target Profit in 20x8 at 9% After Taxes
The goal is to find the sales volume needed in 20x8 to attain 9% profit after income taxes. This involves adjustments to sales prices, costs, and accounting for tax effects.
Changes and assumptions for 20x8:
- Sale price for calculators reduced from $22.50 to $20.00.
- Advertising expenses increase by $57,000.
- Sales mix shifts so that calculators now account for 80% of total revenue, up from 75%.
- Cost reductions:
- Material costs decrease:
- Tape recorders by 10%
- Calculators by 20%
- Labor costs increase by 10% for both products.
- Fixed overhead costs remain unchanged.
Calculations:
Sales revenue targets:
Let total sales be \( S \).
Since 80% of revenue derives from calculators:
- Revenue from calculators = 0.80S
- Revenue from tape recorders = 0.20S
The selling prices are:
- Tape recorder: $15.00 (unchanged)
- Calculator: $20.00 (reduced from $22.50)
Number of calculators sold \( Q_c \):
- \( Q_c = \frac{0.80S}{20} \)
Number of tape recorders sold \( Q_t \):
- \( Q_t = \frac{0.20S}{15} \)
Cost calculations:
Initial costs:
- Material costs:
- Tape recorder: original $4.50 per unit, decreases by 10% to $4.05.
- Calculator: original $6.50 per unit, decreases by 20% to $5.20.
- Direct labor:
- Increases by 10%, so:
- Tape recorder: $2.00 x 1.10 = $2.20
- Calculator: $4.00 x 1.10 = $4.40
- Variable overhead:
- Assume similar proportional increase as labor:
- Tape recorder: $2.00 x 1.10 = $2.20
- Calculator: $3.00 x 1.10 = $3.30
Contribution margin per unit:
- Tape recorder:
- Price: $15.00
- Variable costs: $4.05 + $2.20 + $2.20 = $8.45
- Contribution margin: $15.00 - $8.45 = $6.55
- Calculator:
- Price: $20.00
- Variable costs: $5.20 + $4.40 + $3.30 = $12.90
- Contribution margin: $20.00 - $12.90 = $7.10
Total fixed costs:
- Fixed overhead remains at $350,000.
- Additional advertising expense in 20x8: $57,000.
- Total fixed costs: $350,000 + $57,000 = $407,000.
Target profit before taxes:
- After-tax profit = 9% of sales
- Taxes = 55%
- Profit before taxes \( P_b \):
\[ P_b = \frac{\text{Target net profit}}{1 - \text{tax rate}} = \frac{0.09 S}{0.45} = 0.2 S \]
Total contribution needed:
\[ \text{Contribution margin} \times \text{units} - fixed costs = profit before taxes \]
Expressed as:
\[ (Q_t \times CM_t) + (Q_c \times CM_c) - 407,000 = 0.2 S \]
Where:
\(Q_t = \frac{0.20S}{15}\)
\(Q_c = \frac{0.80S}{20}\)
Calculating total contribution:
\[
Q_t \times 6.55 + Q_c \times 7.10 = \frac{0.20S}{15} \times 6.55 + \frac{0.80S}{20} \times 7.10
\]
Simplify:
\[
\left( \frac{0.20}{15} \times 6.55 + \frac{0.80}{20} \times 7.10 \right) S
\]
Calculate each:
\[
\frac{0.20}{15} = 0.01333,\quad 0.01333 \times 6.55 \approx 0.0874
\]
\[
\frac{0.80}{20} = 0.04,\quad 0.04 \times 7.10 = 0.284
\]
Sum:
\[
0.0874 + 0.284 = 0.3714
\]
Thus:
\[
0.3714 S - 407,000 = 0.2 S
\]
Solve for S:
\[
0.3714 S - 0.2 S = 407,000
\]
\[
0.1714 S = 407,000
\]
\[
S = \frac{407,000}{0.1714} \approx 2,374,985
\]
Therefore, approximate sales revenue needed:
\[
S \approx \$2,375,000
\]
Corresponding units:
- Tape recorders:
\[
Q_t = \frac{0.20 \times 2,375,000}{15} \approx \frac{475,000}{15} \approx 31,667
\]
- Calculators:
\[
Q_c = \frac{0.80 \times 2,375,000}{20} \approx \frac{1,900,000}{20} = 95,000
\]
Hewtex must sell approximately 31,667 tape recorders and 95,000 calculators in 20x8 to achieve a 9% after-tax profit.
Part C: Break-even Units in 20x8
To determine the break-even units for 20x8, we need to find the sales level where total revenues equal total costs, with no profit.
Fixed costs are $407,000, and variable costs per unit are:
- Tape recorders:
- Material: $4.05
- Labor: $2.20
- Overhead: $2.20
- Total variable cost per unit: $8.45
- Calculators:
- Material: $5.20
- Labor: $4.40
- Overhead: $3.30
- Total variable cost per unit: $12.90
Contribution margins:
- Tape recorder: $15.00 - $8.45 = $6.55
- Calculator: $20.00 - $12.90 = $7.10
Set sales quantities \(Q_t\) and \(Q_c\):
Total revenue:
\[
R = 15 Q_t + 20 Q_c
\]
Total variable costs:
\[
VC = 8.45 Q_t + 12.90 Q_c
\]
Total profit:
\[
\text{Contribution Margin Total} - Fixed Costs = 0
\]
Expressed mathematically:
\[
6.55 Q_t + 7.10 Q_c = 407,000
\]
Recall that sales are proportioned by sales mix:
\[
Q_t = \frac{Q}{(Q_t + Q_c)} \times Q_t, \text{ and similarly for } Q_c
\]
Since the sales mix is proportional:
- Let \(Q_t = x\)
- \(Q_c = y\)
The break-even condition:
\[
6.55 x + 7.10 y = 407,000
\]
To find the combined units, and given the sales mix remains the same, express \(Q_c\) in terms of \(Q_t\):
From the 20x7 sales ratio:
- Approximately 1 tape recorder per unit sells 1 calculator (since economic proportions are similar to the original).
Alternatively, considering the proportion of revenue from each product:
\[
\frac{\text{Revenue from tape recorders}}{\text{Total revenue}} = 0.20
\]
\[
\frac{15 Q_t}{15 Q_t + 20 Q_c} = 0.20
\]
Cross-multiplied:
\[
15 Q_t = 0.20 (15 Q_t + 20 Q_c)
\]
\[
15 Q_t = 3 Q_t + 4 Q_c
\]
\[
15 Q_t - 3 Q_t = 4 Q_c
\]
\[
12 Q_t = 4 Q_c
\]
\[
Q_c = 3 Q_t
\]
Using this in the break-even contribution margin equation:
\[
6.55 Q_t + 7.10 \times 3 Q_t = 407,000
\]
\[
6.55 Q_t + 21.30 Q_t = 407,000
\]
\[
27.85 Q_t = 407,000
\]
\[
Q_t = \frac{407,000}{27.85} \approx 14,611
\]
Corresponding calculator units:
\[
Q_c = 3 \times 14,611 \approx 43,833
\]
Final conclusion: Hewtex must sell approximately 14,611 tape recorders and 43,833 calculators in 20x8 to break even, maintaining the same sales mix proportion.
Conclusion
This comprehensive analysis highlights critical points for Hewtex Electronics. To break even in 20x7, approximately 10,769 tape recorders and 31,111 calculators must be sold, with a total of about 41,880 units. To achieve a targeted 9% after-tax profit in 20x8, the company needs to generate approximately $2.375 million in sales, corresponding to about 31,667 tape recorders and 95,000 calculators. Lastly, to break even in 20x8, the sales targets are roughly 14,611 tape recorders and 43,833 calculators, aligned with the sales mix proportion.
By understanding these figures, Hewtex can set realistic sales goals, adjust pricing strategies, and allocate marketing efforts efficiently, ensuring sustainable profitability amid evolving market conditions.
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