Quantitative Problems

1. Suppose QuickCharge Corporation manufactures phone chargers. They sell their chargers for $20. Their fixed operating costs are $100,000 and their variable operating costs are $10 per charger. Currently they are selling 30,000 chargers per year. A. What is QuickCharge’s EBIT (earnings before interest and taxes) at current sales of 30,000? B. What is QuickCharge’s breakeven point? C. Calculate the EBIT if QuickCharge’s sales increase 50% to 45,000 chargers. What is the percent of change in EBIT under this increase in sales? Also, calculate the EBIT if the company's sales decrease 50% to 15,000 chargers. What is the percent of change in EBIT under this decrease in sales? D. What is QuickCharge’s degree of operating leverage? Based on your computation, what does its operating leverage say about QuickCharge’s business risk? 2. The StayDry Umbrella Corporation will have an EBIT of $100,000 if there is a normal amount of rain this year. But if there is a drought, they will have an EBIT of only $50,000. The interest rate on debt is 10%, and the tax rate is 35%. The company does not pay any preferred dividends. A. If StayDry has zero debt and 50,000 outstanding shares, what will its EPS (earnings per share) be if there is normal rain? What will its EPS be if there is a drought? What is its DFL (degree of financial leverage)? B. Now suppose StayDry has decided to take on $300,000 in debt and has used these funds to buy back half of the outstanding shares so now there are only 25,000 outstanding shares. What is the new EPS and DFL for both normal rain and drought? C. Based on your answers to a) and b) above, what are the trade-offs management has to make between zero debt or $300,000 in debt? What are the benefits and disadvantages of taking on this debt?

Sample Solution

QuickCharge Corporation Analysis:

A. EBIT:

EBIT = Revenue - (Variable Costs + Fixed Costs) EBIT = (30,000 chargers * $20/charger) - ($10/charger * 30,000 chargers) - $100,000 EBIT = $600,000 - $300,000 - $100,000 = $200,000

B. Breakeven Point:

Breakeven Point = Fixed Costs / (Price - Variable Cost) Breakeven Point = $100,000 / ($20/charger - $10/charger) = 5,000 chargers

C. EBIT with Sales Changes:

50% Sales Increase:

50% Increase = 30,000 chargers * 50% = 15,000 chargers New Sales = 30,000 chargers + 15,000 chargers = 45,000 chargers New EBIT = (45,000 chargers * $20/charger) - ($10/charger * 45,000 chargers) - $100,000 = $350,000 Percent Change in EBIT = (($350,000 - $200,000) / $200,000) * 100% = 75% increase

Full Answer Section

50% Sales Decrease:

50% Decrease = 30,000 chargers * 50% = 15,000 chargers New Sales = 30,000 chargers - 15,000 chargers = 15,000 chargers New EBIT = (15,000 chargers * $20/charger) - ($10/charger * 15,000 chargers) - $100,000 = $50,000 Percent Change in EBIT = (($50,000 - $200,000) / $200,000) * 100% = 75% decrease

D. Degree of Operating Leverage (DOL):

DOL = (Contribution Margin / EBIT) DOL = ((Price - Variable Cost) / EBIT) DOL = (($20/charger - $10/charger) / $200,000) = 1.5

Interpretation: A DOL of 1.5 indicates that a 1% change in sales will lead to a 1.5% change in EBIT. This means QuickCharge Corporation has high operating leverage, making it more sensitive to changes in sales volume. High operating leverage can be risky as small changes in sales can significantly impact profits.

StayDry Umbrella Corporation Analysis:

A. EPS and DFL (Zero Debt):

Normal Rain:

EPS = (EBIT - Interest) / Outstanding Shares EPS = ($100,000 - 0) / 50,000 shares = $2.00 per share

Drought:

EPS = ($50,000 - 0) / 50,000 shares = $1.00 per share

DFL:

DFL = (Change in EBIT) / (Change in Sales) DFL = (($100,000 - $50,000) / ($50,000 - $0)) = 2.0

Interpretation: A DFL of 2.0 indicates that a 1% change in sales will lead to a 2% change in EBIT. This means StayDry has high financial leverage, further amplifying the effect of sales changes on profitability.

B. EPS and DFL (with Debt):

New EBIT (Normal Rain):

Interest Expense = Debt * Interest Rate = $300,000 * 10% = $30,000 New EBIT = $100,000 - $30,000 = $70,000

New EBIT (Drought):

New EBIT = $50,000 - $30,000 = $20,000

New EPS (Normal Rain):

EPS = ($70,000 - 0) / 25,000 shares = **

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