Problems Essay

1. Given the following information:

Total assets $250,000
Debt (12% interest rate) $150,000
Equity $40,000
Variable costs of production $150 per unit
Fixed cost of production $50,000
Units Sold 1,000
Sales price $210 per unit

What happens to operating income and net income if output is increased by 10 percent? Verify your answer. Solution:

The operating income:

Revenues: $210 x (1,000) = $210,000
Expenses: $150 x (1,000) + $50,000 = $200,000
Operating income: $210,000 - 200,000 = $10,000
Net income: $10,000 - (.12 x 150,000) = ($8,000)

With 10% increase in revenue:

Revenues: $210 x (1,100) = 231,000
Expenses: $150 x (1,100) + $50,000 = $215,000
Operating income: $231,000 - $215,000 = $16,000
Net income $16,000 - (.12 x $150,000) = ($2,000)
Operating income rose from $10,000 to $16,000 for a 60% increase.

Net income rose from ($8,000) to ($2,000) which cut losses by $6,000. Losses were cut by 75%.

2. A firm needs $800 to start and has the following expectations:

Sales $1,600
Expenses $1,450
Tax rate 33% of earnings

a. What are earnings if the owners invest (use their own money) for the $800 needed to start?
b. If the firm borrows $400 of the $800 at an interest rate of 10%, what are the firm's net earnings?
c. What is the return on the owners' investment in each case? Why do the returns differ?
d. If expenses rise to $1,500, what will be the returns in each case?
e. In which case did the returns decline more?
f. What generalization can you draw from the above?

Solution:

a. and b.

a. b. No financial leverage With financial leverage
Sales $1,600 $1,600
Expenses 1,450 1,450
EBIT 150 150
Interest 0 40
EBT 150 110
Taxes 50 36.30
Net earnings $100 $73.70

c. Return on equity $100/$800 = 12.5% $73.70/$400 = 18.4%

The return for b is higher because of