Consider three companies X Y and Z that are in the same line

Consider three companies X, Y, and Z that are in the same line of business and have the same market capitalization of $20,000,000 and the same share prices of $20. Company A has no debt. Company B has $4,000,000 of debt, and Company C has $12,000,000 of debt. Interest rate is 8%. Determine the number of shares of each company. Determine ROA. ROE and Warnings Per Share (EPS) for each company if EBIT is $2,000,000 and there are no taxes Determine EBIT for which ROE and Earnings Per Share of Company X and Company Z will be the same. What is ROE and framings Per Share of Company Y in this case? Suppose we have invested $1000 in company X but would like to have a return as if we have invested in company Z. What should we do to achieve this goal? (assume EBIT will be as before) Suppose we have 500 shares of company Z but would like to have a return as if we have invested in company Y. What should we do to achieve this goal? (assume EBIT will be as before).

Solution

(a) Number of shares = Capitalization / Share price = $20,000,000 / $20 = 1,000,000 for each company

(b)

(1) ROA = [EBIT - (Debt x Interest rate)] / (Market capitalization + Debt)

Company A: [2,000,000 - 0] / [20,000,000 + 0] = 0.1 = 10%

Company B: [2,000,000 - (4,000,000 x 8%)] / [20,000,000 + 4,000,000]

= [2,000,000 - 320,000] / 24,000,000 = 1,680,000 / 24,000,000 = 0.07 = 7%

Company C: [2,000,000 - (12,000,000 x 8%)] / [20,000,000 + 12,000,000]

= [2,000,000 - 960,000] / 32,000,000 = 1,040,000 / 32,000,000 = 0.0325 = 3.25%

(2) ROE = [EBIT - (Debt x Interest rate)] / Market capitalization

Company A: [2,000,000 - 0] / [20,000,000 + 0] = 0.1 = 10%

Company B: [2,000,000 - (4,000,000 x 8%)] / 20,000,000

= [2,000,000 - 320,000] / 20,000,000 = 1,680,000 / 20,000,000 = 0.084 = 8.4%

Company C: [2,000,000 - (12,000,000 x 8%)] / 20,000,000

= [2,000,000 - 960,000] / 20,000,000 = 1,040,000 / 20,000,000 = 0.052 = 5.2%

(3) EPS ($) = [EBIT - (Debt x Interest rate)] / Number of shares

Company A: [$2,000,000 - 0] / 10,000,000 = $0.20 per share

Company B: $[2,000,000 - (4,000,000 x 8%)] / 10,000,000

= $[2,000,000 - 320,000] / 10,000,000 = $1,680,000 / 10,000,000 = $0.168 per share

Company C: $[2,000,000 - (12,000,000 x 8%)] / 10,000,000

= $[2,000,000 - 960,000] / 10,000,000 = $1,040,000 / 10,000,000 = $0.104 per share

Note: First two multi-part sub-questions are answered.