12 2
Breakeven Comparisonsalgebraicgiven The Price And Cost Data Show
Given the price and cost data shown in the accompanying table for each of the three firms, F, G, and H, answer the following questions. Firm F G H Sale price per unit $ 18.00 $ 21.00 $ 30.00 Variable operating cost per unit 6.75 13.50 12.00 Fixed operating cost 45,000 30,000 90,000 What is the operating breakeven point in units for each firm? How would you rank these firms in terms of their risk? 12-6 Breakeven point—Changing costs/revenues JWG Company publishes Creative Crosswords Last year the book of puzzles sold for $10 with variable operating cost per book of $8 and fixed operating costs of $40,000.
How many books must JWG sell this year to achieve the breakeven point for the stated operating costs, given the following different circumstances? All figures remain the same as for last year. Fixed operating costs increase to $44,000; all other figures remain the same. The selling price increases to $10.50; all costs remain the same as for last year. Variable operating cost per book increases to $8.50; all other figures remain the same.
What conclusions about the operating breakeven point can be drawn from your answers? 12-8 EBIT sensitivity Stewart Industries sells its finished product for $9 per unit. Its fixed operating costs are $20,000, and the variable operating cost per unit is $5. Calculate the firm’s earnings before interest and taxes (EBIT) for sales of 10,000 units. Calculate the firm’s EBIT for sales of 8,000 and 12,000 units, respectively.
Calculate the percentage changes in sales (from the 10,000-unit base level) and associated percentage changes in EBIT for the shifts in sales indicated in part b. On the basis of your findings in part c, comment on the sensitivity of changes in EBIT in response to changes in sales. P-4 Future values For each of the cases shown in the following table, calculate the future value of the single cash flow deposited today that will be available at the end of the deposit period if the interest is compounded annually at the rate specified over the given period. Case Single cash flow Interest rate Deposit period (years) A $ 200 5% 20 B 4, C 10, D 25, E 37, F 40, P-11 Present values For each of the cases shown in the following table, calculate the present value of the cash flow, discounting at the rate given and assuming that the cash flow is received at the end of the period noted. Case Single cash flow Discount rate End of period (years) A $ 7,000 12% 4 B 28, C 10, D 150, E 45,
Paper For Above instruction
The assessment of breakeven points, sensitivity analysis, and the valuation of future and present cash flows
are fundamental concepts in managerial finance. They help managers make informed decisions about pricing, cost control, investment, and risk management. This paper explores these concepts through detailed calculations and interpretations based on hypothetical data and scenarios, aiming to impart a comprehensive understanding of financial analysis techniques in a business context.
Breakeven Analysis and Risk Assessment
Breakeven analysis is vital for understanding the minimum sales volume necessary to avoid losses. It involves calculating the breakeven point where total revenue equals total costs, considering both fixed and variable costs. For firms F, G, and H, with differing prices and costs, the calculation of the operating breakeven point in units reveals insights into each firm's risk profile. Specifically, the breakeven point is calculated as fixed costs divided by contribution margin per unit, where contribution margin is the difference between selling price and variable cost per unit. A lower breakeven point indicates a lower risk, as the firm needs fewer sales to cover its fixed costs.
For firm F:
Contribution margin = $18.00 - $6.75 = $11.25
Breakeven units = $45,000 / $11.25 = 4,000 units
For firm G:
Contribution margin = $21.00 - $13.50 = $7.50
Breakeven units = $30,000 / $7.50 = 4,000 units
For firm H:
Contribution margin = $30.00 - $12.00 = $18.00
Breakeven units = $90,000 / $18.00 = 5,000 units
Based on these calculations, firms F and G share the same breakeven volume, indicating similar risk levels, which are lower than firm H's higher breakeven point and hence higher risk.
Impact of Changing Costs and Revenues on Breakeven Points
JWG Company's breakeven sales volume can be affected significantly by changes in fixed costs, sales price, and variable costs. When fixed costs increase from $40,000 to $44,000, the breakeven number of
books increases, highlighting higher risk due to higher fixed commitments. Conversely, an increase in the selling price to $10.50 decreases the breakeven volume, indicating a potential reduction in risk, assuming variable costs and fixed costs stay constant. An increase in variable costs to $8.50 per book raises the breakeven point, thus reflecting increased operational risk.
Calculations:
Original breakeven volume:
= Fixed costs / (Price - Variable cost) = $40,000 / ($10 - $8) = 20,000 books
With fixed costs at $44,000:
= $44,000 / ($10 - $8) = 22,000 books
With increased price to $10.50:
= $40,000 / ($10.50 - $8) = 16,667 books
With increased variable cost to $8.50:
= $40,000 / ($10 - $8.50) = 26,667 books
These results demonstrate that rising fixed costs escalate breakeven volumes, increasing financial risk, while higher selling prices reduce breakeven points, thereby lowering risk; increased variable costs do the opposite.
EBIT Sensitivity to Sales Volume
Stewart Industries' EBIT analysis shows how changes in sales volume influence profitability. The contribution margin per unit = $9 - $5 = $4. The EBIT at different sales levels can be calculated as follows:
At 10,000 units:
EBIT = (10,000 x $4) - $20,000 = $20,000
At 8,000 units:
EBIT = (8,000 x $4) - $20,000 = $12,000
At 12,000 units:
EBIT = (12,000 x $4) - $20,000 = $28,000
This illustrates the linear relationship between sales volume and EBIT.
Percentage change in sales from 10,000 to 8,000 units:
= [(8,000 - 10,000)/10,000] x 100 = -20%
Corresponding percentage change in EBIT:
= [(12,000 - 20,000)/20,000] x 100 = -40%
Similarly, from 10,000 to 12,000 units:
= +20% in sales = +40% in EBIT
The sensitivity analysis shows that EBIT varies proportionally more than sales, especially for decreases in sales, indicating high operating leverage.
Future and Present Value Calculations
Financial decision-making often involves calculating the future value (FV) of investments or cash flows, and the present value (PV) of future receipts, considering the time value of money. Using compound interest formulas, the FV of a cash flow can be computed as:
FV = PV × (1 + r)^n
where PV is the present value, r is the interest rate, and n is the number of periods.
Similarly, the PV is calculated as:
PV = FV / (1 + r)^n
These calculations enable managers to assess the worth of investments or receipts over time, incorporating interest accrual or discounting.
Examples:
- For a cash flow of $200 over 20 years at 5%:
FV = $200 × (1 + 0.05)^20 ≈ $200 × 2.6533 ≈ $530.66
- For a cash flow of $7,000 over 4 years at 12%:
PV = $7,000 / (1 + 0.12)^4 ≈ $7,000 / 1.5748 ≈ $4,448.31
Applying these formulas across different cases allows for strategic investment planning and valuation.
Conclusion
Analyzing breakeven points, sensitivity to operational changes, and the valuation of future or present cash flows provides critical insights into financial stability and risk management. Firms with lower breakeven points, high contributions margins, and stable cash flows are generally less risky, while those with higher fixed costs or sensitivity to sales fluctuations face greater financial challenges. Accurate calculations and understanding of these concepts enable businesses to make strategic decisions that optimize profitability and mitigate risks effectively.
References
Brigham, E. F., & Ehrhardt, M. C. (2016). Financial Management: Theory & Practice (15th ed.). Cengage Learning.
Ross, S. A., Westerfield, R. W., & Jaffe, J. (2018). Corporate Finance (12th ed.). McGraw-Hill Education.
Hillier, D., Grinblatt, M., & Titman, S. (2014). Financial Markets and Corporate Strategy (3rd ed.). McGraw-Hill Education.
Damodaran, A. (2012). Investment Valuation: Tools and Techniques for Determining the Value of Any Asset (3rd ed.). Wiley Finance.
Penman, S. H. (2013). Financial Statement Analysis and Security Valuation (5th ed.). McGraw-Hill Education.
Gitman, L. J., & Zutter, C. J. (2015). Principles of Managerial Finance (14th ed.). Pearson.
Ross, S. A., & Westerfield, R. W. (2018). Fundamentals of Corporate Finance (12th ed.). McGraw-Hill Education.
Shapiro, A. C. (2013). Multinational Financial Management (10th ed.). Wiley.
Anthony, R. N., & Govindarajan, V. (2014). Management Control Systems (13th ed.). McGraw-Hill Education.
Higgins, R. C. (2012). Analysis for Financial Management (10th ed.). McGraw-Hill Education.
