[SusanStudies]

A company currently has 1,000 shares of common stock outstanding with zero debt. It has the choice of raising an additional $100,000 by issuing 9% long-term debt, or issuing 500 shares of common stock. The company has a 40% tax rate. What level of earnings before interest and taxes (EBIT) would result in the same earnings per share (EPS) for the two financing options?

A. An EBIT of $27,000 would result in EPS of $10.80 for both.

B. An EBIT of $27,000 would result in EPS of $7.20 for both.

C. An EBIT of ($18,000) would result in EPS of ($7.20) for both.

D. An EBIT of ($10,800) would result in EPS of ($7.92) for both.

OK, Since this question is asking what EBIT is, I’m thinking I would have to try each EBIT amount and work all the way through the calculation of EPS for each alternative to see if Alt 1 EPS = Alt 2 EPS. Is there a quicker way to determine which EBIT works?

The correct answer is (A) but if I’d started with letter (D) first, as Cindy from Yaeger suggests, I would have blown 6-7 mintues or more, trying to figure this out. I’m looking for a better approach if anyone has a suggestion.

Thank you,

AUD: 07/11/11 - Passed
BEC: 08/27/11 - Passed
FAR: 01/17/12 - Passed
REG: 04/30/12; Re-take 7/16/12 - Passed

FINISHED!!!!!!!!

[rknight21]

lol i have been seeing this question in my studies but ignored it because it seem more like an outlier kind of question. this morning i actually spent time trying to understand it since i have only 2 weeks more of studying…..now my approach is to quickly disregard C & D assuming EBIT wouldnt be negative…. now A & B's EBIT is the same so working for EPS shouldnt take more than 20 seconds tops…

[kb24]

EPS (equity) = EBIT * (1-tax rate)/# of shares after sale of equity

EPS (debt) = (EBIT – interest paid on debt) * (1-tax rate)/# of shares

Set up an equation equating the two and solve for EBIT. In this case

EBIT (.6)/1500 = (EBIT-9000)(.6)/1000

Once you have EBIT, you can solve for EPS.

A general hint if you are trying to work backwards from the answers is to look for common factors amongst two or three of the answers. A lot of times where there are multiple parts to the answer two or more will have one part correct. In this case the first two answers have EBIT of $27K so those would be the first two I'd start with.

FAR 4/1/11 - 89
AUD 4/15/11 - 85
REG 4/29/11 - 80
BEC 5/13/11 - 85

[SusanStudies]

kb24, I swear you should go into teaching!!! Your responses and explanations are always so clear and very helpful. This now makes complete sense. The explanation provided in the software did not show how the $27k was determined…you did. THANKS!!

Good luck rknight!

AUD: 07/11/11 - Passed
BEC: 08/27/11 - Passed
FAR: 01/17/12 - Passed
REG: 04/30/12; Re-take 7/16/12 - Passed

FINISHED!!!!!!!!

[Zack Wright]

For those wondering, here is how you solve for the $27,000 EBIT part:

As stated before,

Debt Option = Equity Option
EPS (debt) = ((EBIT – interest paid on debt) * (1-tax rate)) / # of shares outstanding
EPS (equity) = (EBIT * (1-tax rate)) / # of shares outstanding after the sale of equity

Now, let's plug in what we know for the Debt Option and the Equity Option and do algebra!

Debt Option = Equity Option
[(EBIT – (9% x $100,000)) x (1-0.40)] / 1,000 = [EBIT – 0 Interest x (1-0.40)] / 1,500

[(EBIT – $9,000) x 0.6] / 1,000 = [EBIT x 0.6] / 1,500

[0.6 EBIT – $5,400] / 1,000 = 0.6 EBIT / 1,500

0.6 EBIT – $5,400 = 0.4 EBIT

YIKES! How did we get this??? (0.6 EBIT – $5,400 = 0.4 EBIT)
To get rid of the 1,000 denominator on the left, we have to multiply BOTH denominators ONlY by 1,000.

The left side of the equal sign simply just canceled out the 1,000 and removed it (again, the numerator is untouched).

The right side is the fun side!

0.6 EBIT x (1,000 / 1,500).

0.6 EBIT x 0.66666666666….7

0.4 EBIT for the right side. (in a basic calculator, do the math for 1000/1500 first, then multiply by 0.6.)

Now, back to the algebra:

From before:
0.6 EBIT – $5,400 = 0.4 EBIT

0.6 EBIT – 0.4EBIT = $5,400

0.2 EBIT = $5,400

EBIT = $5,400/0.2

EBIT = $27,000

Now, you can solve for EPS.

[Zack Wright]

Here is how you solve for EPS once you know what EBIT is.

Here is the formula to solve for EPS (normally):

(Net Income – the Current Preferred Dividend)
divided by
Weighted Average Common Shares Outstanding

We will not use this formula this time.

To solve for EPS for this problem, you will use the same formula from earlier that we used to solve for EBIT.

The difference this time is that WE KNOW what EBIT is! ($27,000)

Just like with the balance sheet (A = L + E), both sides of the equal sign need to match.
Debt Option = Equity Option

Option 1—issue 9% debt:
EPS (debt) = ((EBIT – interest paid on debt) * (1-tax rate)) / # of shares outstanding

EPS (debt) = [($27,000 – ($100,000 × 9%)) x (1-0.4)] / 1,000 shares

EPS (debt) = [($27,000 – $9,000) x (0.6)] / 1,000 shares

EPS (debt) = [($27,000 – $9,000) x (0.6)] / 1,000 shares

EPS (debt) = $10,800 / 1,000 shares

EPS (debt) = $10.80 Earnings Per Share

Option 2—issue 500 shares of common stock
EPS (more equity) = ((EBIT – interest paid on debt) * (1-tax rate)) / # of shares outstanding after the sale of additional equity

EPS (more equity) = [($27,000 – $0 interest) x (1-0.4)] / 1,500 shares

EPS (more equity) = [$27,000 x 0.6] / 1,500 shares

EPS (more equity) = $16,200 / 1,500

EPS (more equity) = $10.80 Earnings Per Share

Because the $10.80 matches for both, you know that everything is correct.

What level of earnings before interest and taxes (EBIT) would result in the same earnings per share (EPS) for the two financing options?

For EPS for both of the financing options to be the same ($10.80 earnings per share), our EBIT needs to be $27,000.

For analysis, remember that EBIT = (Sales – Variable Costs) – Fixed Costs
aka
the Contribution Margin – Fixed Costs.

This is probably the toughest M/C question in all of BEC folks! If you can solve this one, you can solve ANY of the BEC questions! I PROMISE!!

[Author]

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