Question

Lenow’s Drug Stores and Hall’s Pharmaceuticals are competitors in the discount drug chain store business. The separate capital structures for Lenow and Hall are presented here.

Lenow				Hall
Debt @ 10%	$	100,000		Debt @ 10%	$	200,000
Common stock, $10 par		200,000		Common stock, $10 par		100,000
Total	$	300,000		Total	$	300,000
Common shares		20,000		Common shares		10,000

a. Complete the following table given earnings before interest and taxes of $20,000, $30,000, and $120,000. Assume the tax rate is 30 percent. (Round your answers to 2 decimal places.)
  

b-1. What is the EBIT/TA rate when the firm's have equal EPS?
  

b-2. What is the cost of debt?
  

b-3. State 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?

Answer 1

Before we populate the table, we need to calculate the EPS is a detailed manner for each of the two firms.

All financials below are in $ except nos. of shares.

For Lenow:

Debt = D = 100,000; Interest rate, i = 10%; Hence, interest, I = i x D = 10% x 100,000 = 10,000

Please pay attention to the second row in the table below. That explains how each column has been calculated. That will help you understand the mathematics as well as the output.

Table 1 - EPS calculation for Lenow

EBIT	Interest	EBT	TAX	Net Income	No of Shares	EPS
	I	EBIT - I	30% x EBT	EBT - Taxes	N	Net income / N
20,000	10,000	10,000	3,000	7,000	20,000	0.35
30,000	10,000	20,000	6,000	14,000	20,000	0.70
120,000	10,000	110,000	33,000	77,000	20,000	3.85

For Hall:

Debt = D = 200,000; Interest rate, i = 10%; Hence, interest, I = i x D = 10% x 200,000 = 20,000

Please pay attention to the second row in the table below. That explains how each column has been calculated. That will help you understand the mathematics as well as the output.

Table 2 - EPS calculation for Hall

EBIT	Interest	EBT	TAX	Net Income	No of Shares	EPS
	I	EBIT - I	30% x EBT	EBT - Taxes	N	Net income / N
20,000	20000	-	-	-	10,000	-
30,000	20000	10,000	3,000	7,000	10,000	0.70
120,000	20000	100,000	30,000	70,000	10,000	7.00

We can now get into the questions.

Part (a)

Complete the table below.

TA = Total Assets = Debt + Common stock = 300,000 for each of the two firms.

EBIT	Total Assets	EBIT / TA	Lenow EPS	Hall EPS	Relationship
	TA		Table 1	Table 2
20,000	300,000	6.67%	0.35	-	EPS of Lenow > EPS of Hall
30,000	300,000	10.00%	0.70	0.70	EPS of both the companies are equal
120,000	300,000	40.00%	3.85	7.00	EPS of Lenow < EPS of Hall

Part (b) - 1

What is the EBIT/TA rate when the firm's have equal EPS?

Please refer to the table above. For EBIT / TA = 10%, the firm's have equal EPS

b-2. What is the cost of debt?

Pre tax Cost of debt is 10%

Post tax cost of debt = 10% x (1 - tax rate) = 10% x (1 - 30%) = 7%
  
b-3. State the relationship between earnings per share and the level of EBIT.

Mathematical relationship is given by: EPS = Net income / Nos. of shares outstanding = (EBIT - I - T) / N = (EBIT - I) x (1 - T) / N

By observation when EBIT / TA < Pre tax cost of debt or EBIT < Pre tax cost of debt x Total assets, a firm with a lower leverage will have higher EPS.

By observation when EBIT / TA = Pre tax cost of debt or EBIT = Pre tax cost of debt x Total assets, EPS is independent of capital structure.

By observation when EBIT / TA > Pre tax cost of debt or EBIT > Pre tax cost of debt x Total assets, a firm with higher leverage will have higher EPS.

EBIT = Pre tax cost of debt x total asset is the indifference 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?

If B is the break even EBIT then

EPS of Lenow = EPS of Hall

i.e (B - Interest expense of Lenow) x (1 - T) / Number of shares of Lenow = (B - Interest expense of Hall) x (1 - T) / Number of shares of Hall

Or, (B - Interest expense of Lenow) / Number of shares of Lenow = (B - Interest expense of Hall) / Number of shares of Hall

Interest expenses for Lenow = i x D = 12% x 100,000 = 12,000

Interest expenses for Hall = i x D = 12% x 200,000 = 24,000

Hence, (B - 12,000) / 20,000 = (B - 24,000) / 10,000

Or, B - 12,000 = 2B - 48,000

Or, B = 36,000 = Break even EBIT