The projected ebit of a firm is $300,000. the firm currently has 100,000 shares of common stock outstanding at a value of $18 per share. the firm has no debt. by how much will the roe change if the firm borrows $600,000 at 8%

General
1

the projected ebit of a firm is $300,000. the firm currently has 100,000 shares of common stock outstanding at a value of $18 per share. the firm has no debt. by how much will the roe change if the firm borrows $600,000 at 8% interest and uses the funds to repurchase shares of stock at the market price? ignore taxes.

2

What is the impact of borrowing $600,000 at 8% interest and using the funds to repurchase shares at the market price on the return on equity (ROE) of a firm that currently has a projected EBIT of $300,000, 100,000 shares of common stock outstanding at a value of $18 per share, and no debt?

Response:

To calculate the impact on the return on equity (ROE), we need to consider the changes in both the earnings and the equity of the firm.

  1. First, let’s calculate the initial ROE before the borrowing and share repurchase:

ROE = Net Income / Shareholders’ Equity

Since the firm currently has no debt, the Shareholders’ Equity can be calculated as the Total Assets minus Total Liabilities. Since there is no debt, the Total Liabilities would be zero.

Shareholders’ Equity = Total Assets - Total Liabilities
Shareholders’ Equity = ($18 per share * 100,000 shares)
Shareholders’ Equity = $1,800,000

Now, to calculate the Net Income, we can use the projected EBIT value:

Net Income = EBIT - Interest Expense

Since the firm currently has no debt, the Interest Expense is zero, therefore:

Net Income = EBIT
Net Income = $300,000

Now, let’s calculate the initial ROE:

ROE = Net Income / Shareholders’ Equity
ROE = $300,000 / $1,800,000
ROE = 0.1667 or 16.67%

  1. Now, let’s calculate the new ROE after the borrowing and share repurchase:

The firm borrows $600,000 at 8% interest. The interest expense would be:

Interest Expense = Principal * Interest Rate
Interest Expense = $600,000 * 0.08
Interest Expense = $48,000

The borrowed funds are then used to repurchase shares at the market price. We need to calculate the number of shares repurchased:

Number of Shares Repurchased = Amount Borrowed / Market Price per Share
Number of Shares Repurchased = $600,000 / $18 per share
Number of Shares Repurchased = 33,333.33 shares (approx.)

The new Shareholders’ Equity can be calculated as the previous Shareholders’ Equity minus the repurchased shares:

New Shareholders’ Equity = Previous Shareholders’ Equity - (Number of Shares Repurchased * Market Price per Share)
New Shareholders’ Equity = $1,800,000 - (33,333.33 shares * $18 per share)
New Shareholders’ Equity = $1,200,000

To calculate the new Net Income, we need to subtract the interest expense from the previous EBIT:

New Net Income = EBIT - Interest Expense
New Net Income = $300,000 - $48,000
New Net Income = $252,000

Now, let’s calculate the new ROE:

New ROE = New Net Income / New Shareholders’ Equity
New ROE = $252,000 / $1,200,000
New ROE = 0.21 or 21%

Therefore, the ROE will increase from 16.67% to 21% if the firm borrows $600,000 at 8% interest and uses the funds to repurchase shares of stock at the market price.

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