Question

Medallion Cooling​ Systems, Inc., has total assets of $9,800,000​, EBIT of $2,050,000​, and preferred dividends of $201,000 and is taxed at a rate of 40%. In an effort to determine the optimal capital​ structure, the firm has assembled data on the cost of​ debt, the number of shares of common stock for various levels of​ indebtedness, and the overall required return on​ investment:
Capital structure/debt Cost of​ debt Number of stock shares Rate of​ return
0% 0% 200,000 12.3%
15 7.8 175,000 13.1
30 9.1 140,000 14.2
45 12.1 111,000 16.3
60 15.2 75,000 20.1

Calculate earnings per share for each level of indebtedness.

Answer 1

Answer:

Earnings per share:

0% debt = $5.145 per share

15% debt = $5.487 per share

30% debt = $6.203 per share

45% debt =  $6.386 per share

60% debt = $6.570 per share

Explanation:

The earnings per share is the monetary value of how much each share of common stock outstanding has earned. The earnings per share can be calculated by dividing the Net Income attributable to common stockholders by the number of common stock shares outstanding.

Net Income attributable to Common stockholders = Net Income - Preferred stock dividends

Thus, Earnings per share = (Net Income - Preferred stock dividends) / Number of common stock shares outstanding

To calculate Earnings per share at each level of indebtedness, we first need to calculate the net income at each debt level. The net income will change as interest is deducted before calculating net income.

Net Income = EBIT - interest - tax

Total debt = Total assets * weightage of debt in capital structure

Tax = EBT * tax rate

a. 0% debt

Net Income = 2,050,000 - 0 - (2050000 * 0.4) = $1,230,000

Earnings per share = (1230000 - 201000) / 200000   =  $5.145 per share

b. 15% debt

Total debt = 9,800,000 * 0.15 = 1470000

EBT = 2,050,000 - (1470000 * 0.078)  =  $1935340

Net Income = 1935340 - ( 1935340 * 0.4) = $1161204

Earnings per share = (1161204 - 201000) / 175000   =  $5.487 per share

c. 30% debt

Total debt = 9,800,000 * 0.30 = 2940000

EBT = 2050000 - (2940000 * 0.091)   =  $1782460

Net Income = 1782460 - (1782460 * 0.4) = $1069476

Earnings per share = (1069476 - 201000) / 140000   =  $6.203 per share

d. 45% debt

Total debt = 9,800,000 * 0.45 = 4410000

EBT = 2050000 - (4410000 * 0.121)   =  $1516390

Net Income = 1516390 - (1516390 * 0.4) = $909834

Earnings per share = (909834 - 201000) / 111000   =  $6.386 per share

e. 60% debt

Total debt = 9,800,000 * 0.60 = 5880000

EBT = 2050000 - (5880000 * 0.152)  =  $1156240

Net Income = 1156240 - (1156240 * 0.4) = $693744

Earnings per share = (693744 - 201000) / 75000   =  $6.570 per share