Cain Auto Supplies and Able Auto Parts are competitors in the
aftermarket for auto supplies. The separate capital structures for
Cain and Able are presented below.
Cain Debt @ 10% $ 50,000              Able  Debt @ 10%   $100,000
Common stock, $10 par 100,000          Common stock @ $10 par  100,000
  
 Total                                   Total      
 $150,000                                 $150,000   
   
Common shares                            Common shares  
 10,000                                   5,000  

a.Compute earnings per share if earnings before interest and taxes are
$10,000, $15,000, and $50,000 (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?

(a) Work the numbers and you'll see that EPS is as follows (to open in
Excel, copy comma-fomatted text into notepad, save as myfile.csv, and
then open with excel.)
Cain
20 cents @ $10k revenue
55 cents @ $15k revenue
3 dollars @ $50k revenue
Able
(60) cents @ $10k revenue
10 cents @ $15k revenue
5 dollars @ $50k revenue

(b)EPS is fairly straightforward. It translates period performance
into a per-share metric. In other words, EPS is essentially a firm's
Net Income divided by its outstanding shares, which is a weighted
average of all share types. Diluted EPS is more complex and is
probably outside the scope of this discussion based on the problem
parameters. That aside, EPS contains is driven by an independent
component, or debt, and a variable component, or tax. Debt is
independent because a firm's debt rate and amount are only loosely
correlated to revenues. Taxes paid are a function of tax rate and
revenues.

A more succinct mathematical explanation: once a firm covers its
interest and other fixed obligations, it can retain [1-tax_rate] of
excess profits.

(c) By Break Even level, I assume you mean that your net earnings are
0. In other words, interest and tax liability add up to revenues.
Because your debt costs is the same in all three scenarios you end up
with one answer for Cain and one answer for Able.

Cain: $8,571.43
Able: $17,142.86

<<Paste below into notepad, rename as myfile.csv, and open the new
file with Excel. Make sure windows doesn't tack txt on the end to make
it myfile.csv.txt. Excel won't open it right.>>

Cain,,,
Revenue,10000,15000,50000
Interest,-5000,-5000,-5000
Taxes,-3000,-4500,-15000
Net,2000,5500,30000

Shares,10000,10000,10000
EPS,0.2,0.55,3


Able,,,
Revenue,10000,15000,50000
Interest,-10000,-10000,-10000
Taxes,-3000,-4500,-15000
Net,-3000,500,25000

Shares,5000,5000,5000
EPS,-0.6,0.1,5


Break Even Level of EBIT,,,
Cain,,,
Revenue,8571.428571,8571.42857,8571.428571
Interest,-6000,-6000,-6000
Taxes,-2571.428571,-2571.428571,-2571.428571
Net,0,-1E-06,0

Shares,10000,10000,10000
EPS,0,-1E-10,0


Able,,,
Revenue,17142.85714,17142.85714,17142.85714
Interest,-12000,-12000,-12000
Taxes,-5142.857143,-5142.857143,-5142.857142
Net,9.99999E-07,9.99999E-07,-9.99997E-07

Shares,5000,5000,5000
EPS,2E-10,2E-10,-1.99999E-10

Could you please show your work on this one because I think I am doing
something wrong?

Sure. The problem wants you to look at situations where revenues are
10k, 15k, and 50k. Let's look at Cain. You want to reach a net income
(or loss) figure because you need that to calculate EPS. Here is an
example of how I arrived at EPS figures.

Cain
====
Revenues --> 10,000
Interest --> -5,000
Taxes    --> -3,000 (30% of revenues)
Net Inc. -->  2,000

With 10,000 shares, a given shareholder potentially could receive
1/10,000th of the profits for each share that they have. In other
words, you divide your income by the number of shares.

EPS = 2,000/10,000 = .2 --> 20 cents per share.

Note: Preferred dividends need to be subracted from your income figure
before dividing by shares also, but you don't have these in your
problem. The reason is because they are pretty close to debt in terms
of liquidity preference.


I used the Solver plugin in Excel to do Part C. As I said in my
comment, I assume that "break even" meant the Net Income totalled to
zero after interest and taxes. You set it up the same way as A to
start with - in fact, I just copied my work from Part A to a new
spreadsheet. From there you open Solver from the Tools menu. (You may
have to use the add-in manager to activate Solver.) When the Solver
applet comes up you tell it that the Target Cell is where your Net
Income is, the Value should be 0, and the "By Changing" cell is your
revenues.

What this does: Excel iterates through a number range gradually
refining the Revenues to a point where the target cell does what you
specified. In this case, you specified that it should be zero.

I reported for Able that Revenue would be 17,142.86 to make Net Income
and EPS 0. Let's check:

Able
====
Revenues --> 17,142.86
Interest --> -12,000
Taxes    --> -5,142.86 (30% of revenues)
Net Inc. -->  0

You don't *need* Solver, but it sure makes things easier.

Does this help?