Discussion Questions
1. Discuss the various uses for break-even analysis.
2. What factors would cause a difference in the use of financial leverage for a utility company and an automobile company?
3. Explain how the break-even point and operating leverage are affected by the choice of manufacturing facilities (labor intensive versus capital intensive).
4. What role does depreciation play in break-even analysis based on accounting flows? Based on cash flows? Which perspective is longer term in nature?
5. What does risk taking have to do with the use of operating and financial leverage?
6. Discuss the limitations of financial leverage.
7. How does the interest rate on new debt influence the use of financial leverage?
8. Explain how combined leverage brings together operating income and earnings per share.
9. Explain why operating leverage decreases as a company increases sales and shifts away from the break-even point.
10. When you are considering two different financing plans, does being at the
level where earnings per share are equal between the two plans always mean you are indifferent as to which plan is selected?
Problems
1. Gateway Appliance toasters sell for $20 per unit, and the variable cost to produce them is $15. Gateway estimates that the fixed costs are $80,000.
a. Compute the break-even point in units.
b. Fill in the table below (in dollars) to illustrate the break-even point has been achieved.
Sales ...............................
- Fixed costs...................
- Total variable costs .....
Net profit (loss) ..............
2. Hazardous Toys Company produces boomerangs that sell for $8 each and have a variable cost of $7.50. Fixed costs are $15,000.
a. Compute the break-even point in units.
b. Find the sales (in units) needed to earn a profit of $25,000.
3. Ensco Lighting Company has fixed costs of $100,000, sells its units for $28, and has variable costs of $15.50 per unit.
a. Compute the break-even point.
b. Ms. Watts comes up with a new plan to cut fixed costs to $75,000. However, more labor will now be required, which will increase variable costs per unit to $17. The sales price will remain at $28. What is the new break-even point?
c. Under the new plan, what is likely to happen to profitability at very high volume levels (compared to the old plan)?
4. Air Filter, Inc., sells its products for $6 per unit. It has the following costs:
Rent ................................. $100,000
Factory labor ................... $1.20 per unit
Executive salaries under contract ............................
$89,000
Raw material ................... $.60 per unit
Separate the expenses between fixed and variable cost per unit. Using this information and the sales price per unit of $6, compute the break-even point.
5. Eaton Tool Company has fixed costs of $200,000, sells its units for $56, and has variable costs of $31 per unit.
a. Compute the break-even point.
b. Ms. Eaton comes up with a new plan to cut fixed costs to $150,000. However, more labor will now be required, which will increase variable costs per unit to $34.
The sales price will remain at $56. What is the new break-even point?
c. Under the new plan, what is likely to happen to profitability at very high volume levels (compared to the old plan)?
6. Shawn Penn & Pencil Sets, Inc., has fixed costs of $80,000. Its product currently sells for $5 per unit and has variable costs of $2.50 per unit. Mr. Bic, the head of manufacturing, proposes to buy new equipment that will cost $400,000 and drive up fixed costs to $120,000. Although the price will remain at $5 per unit, the increased automation will reduce costs per unit to $2.00.
As a result of Bic's suggestion, will the break-even point go up or down? Compute the necessary numbers.
7. Jay Linoleum Company has fixed costs of $70,000. Its product currently sells for $4 per unit and has variable costs per unit of $2.60. Mr. Thomas, the head of manufacturing, proposes to buy new equipment that will cost $300,000 and drive up fixed costs to $105,000. Although the price will remain at $4 per unit, the increased automation will reduce variable costs per unit to $2.25.
As a result of Thomas's suggestion, will the break-even point go up or down? Compute the necessary numbers.
8. Gibson & Sons, an appliance manufacturer, computes its break-even point strictly on the basis of cash expenditures related to fixed costs. Its total fixed costs are $1,200,000, but 25 percent of this value is represented by depreciation. Its contribution margin (price minus variable cost) for each unit is $2.40. How many units does the firm need to sell to reach the cash break-even point?
9. Air Purifier, Inc., computes its break-even point strictly on the basis of cash expenditures related to fixed costs. Its total fixed costs are $2,400,000, but 15 percent of this value is represented by depreciation. Its contribution margin (price minus variable cost) for each unit is $30. How many units does the firm need to sell to reach the cash break-even point?
10. Draw two break-even graphs-one for a conservative firm using labor-intensive production and another for a capital-intensive firm. Assuming these companies compete within the same industry and have identical sales, explain the impact of changes in sales volume on both firms' profits.
11. The Sterling Tire Company's income statement for 2008 is as follows:
STERLING TIRE COMPANY
Income Statement
For the Year Ended December 31, 2008
Sales (20,000 tires at $60 each)................................... $1,200,000
Less: Variable costs (20,000 tires at $30) .............. 600,000
Fixed costs.................................................... 400,000
Earnings before interest and taxes (EBIT) .................. 200,000
Interest expense........................................................... 50,000
Earnings before taxes (EBT)....................................... 150,000
Income tax expense (30%) .......................................... 45,000
Earnings after taxes (EAT).......................................... $ 105,000
Given this income statement, compute the following:
a. Degree of operating leverage.
b. Degree of financial leverage.
c. Degree of combined leverage.
d. Break-even point in units.
12. The Harmon Company manufactures skates. The company's income statement for 2008 is as follows:
HARMON COMPANY
Income Statement
For the Year Ended December 31, 2008
Sales (30,000 skates @ $25) ......................................................... $750,000
Less: Variable costs (30,000 skates at $7) ................................. 210,000
Fixed costs........................................................................ 270,000
Earnings before interest and taxes (EBIT) .................................... 270,000
Interest expense............................................................................. 170,000
Earnings before taxes (EBT)......................................................... 100,000
Income tax expense (35%) ............................................................ 35,000
Earnings after taxes (EAT)............................................................ $ 65,000
Given this income statement, compute the following:
a. Degree of operating leverage.
b. Degree of financial leverage.
c. Degree of combined leverage.
d. Break-even point in units.
13. Healthy Foods, Inc. sells 50-pound bags of grapes to the military for $10 a bag. The fixed costs of this operation are $80,000, while the variable costs of the popcorn are $.10 per pound.
a. What is the break-even point in bags?
b. Calculate the profit or loss on 12,000 bags and on 25,000 bags.
c. What is the degree of operating leverage at 20,000 bags and at 25,000 bags? Why does the degree of operating leverage change as the quantity sold increases?
d. If Healthy Foods has an annual interest expense of $10,000, calculate the degree of financial leverage at both 20,000 and 25,000 bags.
e. What is the degree of combined leverage at both sales levels?
14. U.S. Steal has the following income statement data:
|
Units Sold
|
Total Variable Costs
|
Fixed Costs
|
Total Costs
|
Total Revenue
|
Operating Income (Loss)
|
|
40,000
|
$ 80,000
|
$50,000
|
$130,000
|
$160,000
|
$30,000
|
|
60,000
|
120,000
|
50,000
|
170,000
|
240,000
|
70,000
|
a. Compute DOL based on the formula below (see page 128 for an example):
DOL = Percent change in operating income Percent change in units sold
b. Confirm that your answer to part a is correct by recomputing DOL using formula 5-3 on page . There may be a slight difference due to rounding.
DOL = Q (P - VC)/Q.(P - VC) - FC
Q represents beginning units sold (all calculations should be done at this level). P can be found by dividing total revenue by units sold. VC can be found by dividing total variable costs by units sold.
15. Leno's Drug Stores and Hall's Pharmaceuticals are competitors in the discount drug chain store business. The separate capital structures for Leno and Hall are presented below.
|
Leno
|
|
Hall
|
|
|
Debt @ 10% .........................
|
$100,000
|
Debt @ 10% ..........................
|
$200,000
|
|
Common stock, $10 par .......
|
200,000
|
Common stock, $10 par ........
|
100,000
|
|
Total .....................................
|
$300,000
|
Total ......................................
|
$300,000
|
|
Shares ...................................
|
20,000
|
Common shares .....................
|
10,000
|
a. Compute earnings per share if earnings before interest and taxes are $20,000, $30,000, and $120,000 (assume a 30 percent tax rate).
b. Explain the relationship between earnings per share and the level of EBIT.
c. If the cost of debt went up to 12 percent and all other factors remained equal, what would be the break-even level for EBIT?
16. In Problem 15, compute the stock price for Hall Pharmaceuticals if it sells at 13 times earnings per share and EBIT is $80,000.
17. Pulp Paper Company and Holt Paper Company are each able to generate earnings before interest and taxes of $150,000.
The separate capital structures for Pulp and Holt are shown below:
|
Pulp
|
|
Holt
|
|
|
Debt @ 10% ........................
|
$ 800,000
|
Debt @ 10% ....................
|
$ 400,000
|
|
Common stock, $5 par ........
|
700,000
|
Common stock, $5, par ...
|
1,100,000
|
|
Total ....................................
|
$1,500,000
|
Total ................................
|
$1,500,000
|
|
Common shares...................
|
140,000
|
Common shares ...............
|
220,000
|
a. Compute earnings per share for both firms. Assume a 40 percent tax rate.
b. In part a, you should have the same answer for both companies' earnings per share. Assuming a P/E ratio of 20 for each company, what would each company's stock price be?
c. Now as part of your analysis, assume the P/E ratio would be 15 for the riskier company in terms of heavy debt utilization in the capital structure and 26 for the less risky company. What would the stock prices for the two firms be under these assumptions? (Note: Although interest rates also would likely be different based on risk, we hold them constant for ease of analysis).
d. Based on the evidence in part c, should management only be concerned about the impact of financing plans on earnings per share or should stockholders' wealth maximization (stock price) be considered as well?
18. Firms in Japan often employ both high operating and financial leverage because of the use of modern technology and close borrower-lender relationships. Assume the Susaki Company has a sales volume of 100,000 units at a price of $25 per unit; variable costs are
$5 per unit and fixed costs are $1,500,000. Interest expense is $250,000. What is the degree of combined leverage for this Japanese firm?
19. Glynn Enterprises and Monroe, Inc., both produce fluid control products. Their financial information is as follows:
|
Capital Structure
|
|
|
|
|
Glynn
|
Monroe
|
|
Debt @ 10% .............................................................
|
$ 1,500,000
|
0
|
|
Common stock, $10 per share..................................
|
500,000
|
$2,000,000
|
|
|
$ 2,000,000
|
$2,000,000
|
|
Common shares........................................................
|
50,000
|
200,000
|
|
Operating Plan
|
|
|
|
Sales (200,000 units at $5 each)...............................
|
$ 1,000,000
|
$ 1,000,000
|
|
Less: Variable costs...............................................
|
600,000
|
200,000
|
|
|
($3 per unit)
|
($1 per unit)
|
|
Fixed costs...................................................
|
0
|
400,000
|
|
Earnings before interest and taxes (EBIT) ...............
|
$ 400,000
|
$ 400,000
|
a. If you combine Glynn's capital structure with Monroe's operating plan, what is the degree of combined leverage?
b. If you combine Monroe's capital structure with Glynn's operating plan, what is the degree of combined leverage?
c. Explain why you got the results you did in parts a and b.
d. In part b, if sales double, by what percent will EPS increase?
20. DeSoto Tools, Inc., is planning to expand production. The expansion will cost $300,000, which can be financed either by bonds at an interest rate of 14 percent or by selling 10,000 shares of common stock at $30 per share. The current income statement before expansion is as follows:
DESOTO TOOLS, INC.
Income Statement
200X
Sales ............................................................................... $1,500,000
Less: Variable costs..................................................... $450,000
Fixed costs......................................................... 550,000 1,000,000
Earnings before interest and taxes.................................. 500,000
Less: Interest expense ................................................. 100,000
Earnings before taxes ..................................................... 400,000
Less: Taxes @ 34%..................................................... 136,000
Earnings after taxes ........................................................ $ 264,000
Shares ............................................................................. 100,000
Earnings per share .......................................................... $ 2.64
After the expansion, sales are expected to increase by $1,000,000. Variable costs will remain at 30 percent of sales, and fixed costs will increase to $800,000. The tax rate is 34 percent.
a. Calculate the degree of operating leverage, the degree of financial leverage, and the degree of combined leverage before expansion. (For the degree of operating leverage, use the formula developed in footnote 2; for the degree of combined leverage, use the formula developed in footnote 3. These instructions apply throughout this problem.)
b. Construct the income statement for the two alternative financing plans.
c. Calculate the degree of operating leverage, the degree of financial leverage, and the degree of combined leverage, after expansion.
d. Explain which financing plan you favor and the risks involved with each plan.
21. Using Standard & Poor's data or annual reports, compare the financial and operating leverage of Exxon, Eastman Kodak, and Delta Airlines for the most current year. Explain the relationship between operating and financial leverage for each company and the resultant combined leverage. What accounts for the differences in leverage of these companies?
22. Dickinson Company has $12 million in assets. Currently half of these assets are financed with long-term debt at 10 percent and half with common stock having a par value of $8. Ms. Smith, vice-president of finance, wishes to analyze two refinancing plans, one with more debt (D) and one with more equity (E). The company earns a return on assets before interest and taxes of 10 percent. The tax rate is 45 percent.
Under Plan D, a $3 million long-term bond would be sold at an interest rate of 12 percent and 375,000 shares of stock would be purchased in the market at $8 per share and retired.
Under Plan E, 375,000 shares of stock would be sold at $8 per share and the $3,000,000 in proceeds would be used to reduce long-term debt.
a. How would each of these plans affect earnings per share? Consider the current plan and the two new plans.
b. Which plan would be most favorable if return on assets fell to 5 percent? Increased to 15 percent? Consider the current plan and the two new plans.
c. If the market price for common stock rose to $12 before the restructuring, which plan would then be most attractive? Continue to assume that $3 million in debt will be used to retire stock in Plan D and $3 million of new equity will be sold to retire debt in Plan E. Also assume for calculations in part c that return on assets is 10 percent.
23. Johnson Grass and Garden Centers has $20 million in assets, 75 percent financed by debt and 25 percent financed by common stock. The interest rate on the debt is 12 percent and the par value of the stock is $10 per share. President Johnson is considering two financing plans for an expansion to $30 million in assets.
Under Plan A, the debt-to-total-assets ratio will be maintained, but new debt will cost a whopping 15 percent! New stock will be sold at $10 per share. Under Plan B, only new common stock at $10 per share will be issued. The tax rate is 40 percent.
a. If EBIT is 12 percent on total assets, compute earnings per share (EPS) before the expansion and under the two alternatives.
b. What is the degree of financial leverage under each of the three plans?
c. If stock could be sold at $20 per share due to increased expectations for the firm's sales and earnings, what impact would this have on earnings per share for the two expansion alternatives? Compute earnings per share for each.
d. Explain why corporate financial officers are concerned about their stock values!
24. Mr. Katz is in the widget business. He currently sells 2 million widgets a year at $4 each. His variable cost to produce the widgets is $3 per unit, and he has $1,500,000 in fixed costs. His sales-to-assets ratio is four times, and 40 percent of his assets are financed with 9 percent debt, with the balance financed by common stock at $10 per share. The tax rate is 30 percent.
His brother-in-law, Mr. Doberman, says Mr. Katz is doing it all wrong. By reducing his price to $3.75 a widget, he could increase his volume of units sold by 40 percent. Fixed costs would remain constant, and variable costs would remain $3 per unit. His sales-to- assets ratio would be 5 times. Furthermore, he could increase his debt-to-assets ratio to 50 percent, with the balance in common stock. It is assumed that the interest rate would go up by 1 percent and the price of stock would remain constant.
a. Compute earnings per share under the Katz plan.
b. Compute earnings per share under the Doberman plan.
c. Mr. Katz's wife does not think that fixed costs would remain constant under the Doberman plan but that they would go up by 20 percent. If this is the case, should Mr. Katz shift to the Doberman plan, based on earnings per share?
25. Highland Cable Company is considering an expansion of its facilities. Its current income statement is as follows:
Sales .............................................................................................. $4,000,000
Less: Variable expense (50% of sales)....................................... 2,000,000
Fixed expense................................................................... 1,500,000
Earnings before interest and taxes (EBIT) .................................... 500,000
Interest (10% cost) ........................................................................ 140,000
Earnings before taxes (EBT)......................................................... 360,000
Tax (30%)...................................................................................... 108,000
Earnings after taxes (EAT)............................................................ $ 252,000
Shares of common stock ............................................................... 200,000
Earnings per share ......................................................................... $ 1.26
Highland Cable Company is currently financed with 50 percent debt and 50 percent equity (common stock, par value of $10). To expand the facilities, Mr. Highland estimates a need for $2 million in additional financing. His investment banker has laid out three plans for him to consider:
1. Sell $2 million of debt at 13 percent.
2. Sell $2 million of common stock at $20 per share.
3. Sell $1 million of debt at 12 percent and $1 million of common stock at $25 per share.
Variable costs are expected to stay at 50 percent of sales, while fixed expenses will increase to $1,900,000 per year. Mr. Highland is not sure how much this expansion will add to sales, but he estimates that sales will rise by $1 million per year for the next five years.
Mr. Highland is interested in a thorough analysis of his expansion plans and methods of financing. He would like you to analyze the following:
a. The break-even point for operating expenses before and after expansion (in sales dollars).
b. The degree of operating leverage before and after expansion. Assume sales of
$4 million before expansion and $5 million after expansion. Use the formula in footnote 2.
c. The degree of financial leverage before expansion at sales of $4 million and for all three methods of financing after expansion. Assume sales of $5 million for the second part of this question.
d. Compute EPS under all three methods of financing the expansion at $5 million in sales (first year) and $9 million in sales (last year).
e. What can we learn from the answer to part d about the advisability of the three methods of financing the expansion?
COMPREHENSIVE PROBLEM
|
ASPEN SKI COMPANY
|
|
Balance Sheet
|
|
December 31, 2008
|
|
Assets
|
|
Liabilities and Stockholders' Equity
|
|
Cash..........................................
|
$ 40,000
|
Accounts payable......................
|
$1,800,000
|
|
Marketable securities ...............
|
60,000
|
Accrued expenses .....................
|
100,000
|
|
Accounts receivable .................
|
1,000,000
|
Notes payable (current).............
|
600,000
|
|
Inventory ..................................
|
3,000,000
|
Bonds (10%) .............................
|
2,000,000
|
|
Gross plant
and equipment......................
|
5,000,000
|
Common stock (1.5 million shares, par value $1) ..............
|
1,500,000
|
|
Less: Accumulated depreciation .......................
|
|
Retained earnings...................... Total liabilities and
|
1,100,000
|
|
2,000,000
|
|
|
Total assets ...............................
|
$7,100,000
|
stockholders' equity...............
|
$7,100,000
|
Income Statement-2008
Sales (credit)............................................................. $6,000,000
Fixed costs*.............................................................. 1,800,000
Variable costs (0.60) ................................................ 3,600,000
Earnings before interest and taxes............................ 600,000
Less: Interest ........................................................ 200,000
Earnings before taxes ............................................... 400,000
Less: Taxes @ 40%.............................................. 160,000
Earnings after taxes .................................................. 240,000
Dividends ................................................................. 43,200
Increased retained earnings ...................................... $ 196,800
*Fixed costs include (a) lease expense of $190,000 and (b) depreciation of $400,000.
Note: Aspen Ski also has $100,000 per year in sinking fund obligations associated with its bond issue. The sinking fund represents an annual repayment of the principal amount of the bond. It is not tax-deductible.
Ratios
Aspen Ski (to be filled in)
Industry
Profit margin ............................ 6.1%
Return on assets ....................... 6.5%
Return on equity....................... 8.9%
Receivables turnover................ 4.9x
Inventory turnover.................... 4.4x
Fixed-asset turnover ................. 2.1x
Total-asset turnover.................. 1.06x
Current ratio ............................. 1.4x
Quick ratio................................ 1.1x
Debt to total assets ................... 27%
Interest coverage ...................... 4.2x
Fixed charge coverage.............. 3.0x
a. Analyze Aspen Ski Company, using ratio analysis. Compute the ratios above for Aspen and compare them to the industry data that is given. Discuss the weak points, strong points, and what you think should be done to improve the company's performance.
b. In your analysis, calculate the overall break-even point in sales dollars and the cash break-even point. Also compute the degree of operating leverage, degree of financial leverage, and degree of combined leverage.
c. Use the information in parts a and b to discuss the risk associated with this company. Given the risk, decide whether a bank should loan funds to Aspen Ski.
Aspen Ski Company is trying to plan the funds needed for 2009. The management anticipates an increase in sales of 20 percent, which can be absorbed without increasing fixed assets.
d. What would be Aspen's needs for external funds based on the current balance sheet? Compute RNF (required new funds). Notes payable (current) are not part of the liability calculation.
e. What would be the required new funds if the company brings its ratios into line with the industry average during 2009? Specifically examine receivables turnover, inventory turnover, and the profit margin. Use the new values to recompute the factors in RNF (assume liabilities stay the same).
f. Do not calculate, only comment on these questions. How would required new funds change if the company:
1. Were at full capacity?
2. Raised the dividend payout ratio?
3. Suffered a decreased growth in sales?
4. Faced an accelerated inflation rate?