Question

You are investigating the expansion of your business and have sought out two avenues for the sourcing of funds for the expansion.

The first (Plan A) is an all-ordinary-share capital structure. $10 million would be raised by selling 100,000 shares at $100 each.

Plan B would involve the use of financial leverage. $1 million would be raised issuing bonds with an effective interest rate of 10% (per annum). Under this second plan, the remaining $9 million would be raised by selling 90,000 shares at $100 price per share. The use of financial leverage is considered to be a permanent part of the firm’s capitalisation, so no fixed maturity date is needed for the analysis.

A 25% tax rate is appropriate for the analysis.

REQUIRED:

1. Find the EBIT indifference level associated with the two financing plans using an EBIT–EPS graph. Provide a check of your calculation to prove the EBIT indifference level.   
2. A detailed financial analysis of the firm’s prospects suggests that the long-term earnings before interest and taxes (EBIT) will be $1,500,000 annually. Taking this into consideration, which plan will generate the higher earnings per share (EPS)?

Rather than EBIT, you are interested in other measures of risk associated with a project.

The basic values for your company is as follows:

Total Fixed Costs:                                   $500,000

Price per unit:                                           $18

Costs per unit:                                          $14

What is the accounting break-even point? What does this number represent?         

Answer 1

a. Find the EBIT indifference level associated with the two financing plans using an EBIT–EPS graph. Provide a check of your calculation to prove the EBIT indifference level.

Lets compute the EPS for both options starting with EBIT of $800,000 and increasing by $100,000 till $1,800,000 to plot the EBIT-EPS graph.

Thus, as can be seen, the EBIT indifference level associated with the two financing plans using an EBIT–EPS graph is $1,000,000 where the EPS is same for both plans at $7.50.

To prove :

EBIT = $1,000,000

Plan A = all ordinary share

Net Income= $1,000,000*(1-25%) = $750,000

Number of ordinary shares = 100,000

Earning Per share =  Net Income / Number of ordinary shares = $750,000/100,000 = $7.50

Plan B = Debt + ordinary share

Interest on debt = $1,000,000*10% = $100,000

Net Income= ($1,000,000-$100,000)*(1-25%) = $675,000

Number of ordinary shares = 90,000

Earning Per share =  Net Income / Number of ordinary shares = $675,000/90,000 = $7.50

Indifferent EBIT can also be found using the equation as follows:

Let EBIT be X

EBIT under Plan A = X *(1-25%) / 100,000

EBIT under Plan B = ((X-100,000) *(1-25%)) / 90,000

(X *(1-25%)) / 100,000 = ((X-100,000) *(1-25%)) / 90,000

.75X/100,000 = (0.75X-75000)/90000

.75X/100,000*90,000 = (0.75X-75000)

0.675X = 0.75X-75000

75000 = 0.75X-0.675X

75000 = 0.075X

X = $1,000,000

Workings:

Note:

I had put Bar Graph instead of Line Graph for EBIT-EPS analysis as the difference in EPS between both plans are very less, line graph doesn't visibly reflect the difference.

b. A detailed financial analysis of the firm’s prospects suggests that the long-term earnings before interest and taxes (EBIT) will be $1,500,000 annually. Taking this into consideration, which plan will generate the higher earnings per share (EPS)?

EBIT = $1,500,000

Plan A = all ordinary share

Net Income= $1,500,000*(1-25%) = $1,125,000

Number of ordinary shares = 100,000

Earning Per share =  Net Income / Number of ordinary shares = $1,125,000/100,000 = $11.25

Plan B = Debt + ordinary share

Interest on debt = $1,000,000*10% = $100,000

Net Income= ($1,500,000-$100,000)*(1-25%) = $1,050,000

Number of ordinary shares = 90,000

Earning Per share =  Net Income / Number of ordinary shares = $1,050,000/90,000 = $11.67

Plan B with both debt and ordinary share generates high EPS of $11.67 if the EBIT is $1,500,000.

c. The basic values for your company is as follows:

Total Fixed Costs:                                   $500,000

Price per unit:                                           $18

Costs per unit:                                          $14

The accounting breakeven point represent the sales volume at which the company makes no profit and no loss -- profit being zero.

Plan A:

We have the following equation:

Sales Volume * (Price per unit - Cost per unit) = Fixed Costs + Profit

Let Sales Volume be X

X*($18-$14) = $500,000+0

4X=$500,000

X = $500,000/4 = 125,000

Accounting break-even point = 125,000 sales units for Plan A

Plan B:

We have the following equation:

Sales Volume * (Price per unit - Cost per unit) = Fixed Costs +Interest + Profit

Let Sales Volume be X

X*($18-$14) = $500,000+$100,000+0

4X=$600,000

X = $600,000/4 = 150,000

Accounting break-even point = 150,000 sales units for Plan B

The accounting break-even point for Plan B is higher by 25,000 units (150,000-125,000) to also finance the incremental interest expense due to financial leverage.

(Note: It is assumed that there will be no tax consequence if the company has no profit / loss).