I need help figuring out the solution to this problem.  Any help would
be appreciated.  Answers, formulas, etc.


A project has fixed costs of $1,000 per year, depreciation charges of
$500 a year, revenue of $6,000 a year, and variable costs equal to
two-thirds of revenues.
						
a. If sales increase by 5 percent, what will be the increase in pretax
profits?

b. What is the degree of operating leverage of this project?

c. Confirm that the percentage change in profits equals DOL times the
percentage change in sales.
						
Instructions						
						
Enter formulas to solve this problem.									
a. If sales increase by 5 percent, what will be the increase in pretax
profits?	Before	          After
Revenue		  ??              FORMULA				
Variable costs	  0 	            0 				
Fixed costs	1,000 		    ??		
Depreciation	500 		    ??		
Pretax profit	($1,500)	    $0 				
						

b. What is the degree of operating leverage of this project?		

Degree Operating Leverage		FORMULA				
						
c. Confirm that the percentage change in profits equals DOL times the
percentage change in sales.
						
Percentage change in profits		?				
DOL x % change in sales		        ?

Hi trickortreat!!

Before start to solve this problem, we need to define some terms:

EBIT: 
EBIT stands for "earnings before interest and taxes" which is used as
a measure of earnings performance of firms that is not clouded by
changes in debt or equity types, or tax rules.
From "Definition of EBIT at About.com:
http://economics.about.com/cs/economicsglossary/g/ebit.htm

EBIT  = Revenues - Fixed costs - Depreciation - Variable costs


DOL:
Operating leverage measures the effect of fixed costs on the firm.
There are two formulas to calculate the DOL:

1st DOL formula :

       % change in EBIT        
DOL = --------------------     
      % change in Revenues      
 
where:
% change in EBIT = (change in EBIT / EBIT_0)*100 


2nd DOL formula:
DOL = (Revenues - Variable costs) / EBIT

--------------------------------------------------

Now we can solve the problem:

a. If sales increase by 5 percent, what will be the increase in pretax
profits?

Recall the EBIT formula:
EBIT  = Revenues - Fixed costs - Depreciation - Variable costs

If you see the definition of EBIT you can see that EBIT and pretax
profits are the same thing, then the increase in pretax profits is the
variation of the EBIT, that is the difference between the final EBIT
and the initial EBIT:

Increase in pretax profit = EBIT_1 - EBIT_0

We have that:
EBIT_0 = $6000 - $1000 - $500 - (2/3*$6000) = $500
EBIT_1 = 1.05*$6000 - $1000 - $500 - (2/3*1.05*$6000) = $600

Then:
Increase in pretax profit = EBIT_1 - EBIT_0 =
                          = $600 - $500 =
                          = $100

The increase in pretax profits is $100.

----------------------------------------------------------

b. What is the degree of operating leverage of this project?

We can use the 2nd DOL formula:
 
DOL = (Revenues - Variable costs) / EBIT =
    = ($6,000 - 2/3*$6,000) / $500 =
    = ($6,000 - $4,000) / 500 =
    = $2,000 / $500 =
    = 4

The degree of operating leverage of this project (DOL) is 4.

-------------------------------------------------------

c. Confirm that the percentage change in profits equals DOL times the
percentage change in sales.


% change in profits = 100 * Increase in pretax profit / EBIT_0 =
                    = 100 * $100/$500 =
                    = 100 * 0.20 =
                    = 20%

The problem also states that the % change in revenues is 5%, so we have that:
(remember that the DOL is equal to 4 in this problem).

% change in profits  / % change in revenues = 20/5 = 4 = DOL

Then:
% change in profits = 4 * % change in revenues =
                    = DOL * % change in revenues  


This confirm the statement that the percentage change in profits
equals DOL times the percentage change in sales.

We can generalize this conclusion using the 1ST DOL formula:

       % change in EBIT        
DOL = --------------------     
      % change in Revenues      

Then:

% change in EBIT  = DOL * % change in Revenues      

---------------------------------------------------------

I hope that this helps. If you find something unclear or need further
assistance on this, feel free to request for a clarification before
rate this answer. I will be glad to respond to your requests.

Best regards.
livioflores-ga