# Simone's Sweets: Break-Even EBIT and EPS Let's break down the problem step by step. ## Given Data - **Shares Outstanding:** 10,300 - **Market Price per Share:** $24 - **Debt to be Issued:** $104,000 - **Interest Rate:** 6% - **Use of Debt:** Repurchase shares ## Step 1: Shares Repurchased Amount of shares repurchased: \[ \text{Shares Repurchased} = \frac{\$104,000}{\$24} = 4,333.33 \] New shares outstanding after repurchase: \[ \text{New Shares Outstanding} = 10,300 - 4,333.33 = 5,966.67 \] ## Step 2: Interest Expense \[ \text{Interest Expense} = \$104,000 \times .06 = \$6,240 \] ## Step 3: Break-Even EBIT Calculation At break-even EBIT, the **Earnings Per Share (EPS)** is the same whether the firm is all-equity or levered. ### EPS (All-Equity) \[ \text{EPS}_{\text{all-equity}} = \frac{\text{EBIT}}{10,300} \] ### EPS (With Debt) \[ \text{EPS}_{\text{levered}} = \frac{\text{EBIT} - \text{Interest}}{5,966.67} \] Set them equal to solve for break-even EBIT: \[ \frac{\text{EBIT}}{10,300} = \frac{\text{EBIT} - 6,240}{5,966.67} \] Solving for EBIT: \[ \text{EBIT} \times 5,966.67 = (\text{EBIT} - 6,240) \times 10,300 \] \[ 5,966.67 \text{EBIT} = 10,300\text{EBIT} - 64,272,000 \] \[ 64,272,000 = 10,300\text{EBIT} - 5,966.67\text{EBIT} \] \[ 64,272,000 = 4,333.33\text{EBIT} \] \[ \text{EBIT} = \frac{64,272,000}{4,333.33} = \$14,833.98 \] ## Step 4: Break-Even EPS Plug EBIT back into either EPS formula (let's use levered): \[ \text{EPS}_{\text{break-even}} = \frac{14,833.98 - 6,240}{5,966.67} \] \[ = \frac{8,593.98}{5,966.67} \] \[ = \$1.44 \] ## Answer **Break-even EPS:** \[ \boxed{\$1.44} \] **Correct choice:** - $1.44 --- ## Summary Table | Scenario | Shares Outstanding | Interest Expense | Break-Even EPS | |---------------|-------------------|------------------|----------------| | All-Equity | 10,300 | $ | $1.44 | | With Debt | 5,966.67 | $6,240 | $1.44 |

# Break-Even EPS Calculation for Simone's Sweets ## Objective Calculate the earnings per share (EPS) at the break-even EBIT (Earnings Before Interest and Taxes) for Simone's Sweets after issuing debt to repurchase shares. ## Given Data - **Shares Outstanding:** 10,300 - **Market Price per Share:** $24 - **Debt Issued:** $104,000 - **Interest Rate:** 6% ## Step 1: Determine Shares Repurchased Calculate the number of shares repurchased with the debt issued. \[ \text{Shares Repurchased} = \frac{\$104,000}{\$24} = 4,333.33 \] Calculate the new number of shares outstanding after the repurchase. \[ \text{New Shares Outstanding} = 10,300 - 4,333.33 = 5,966.67 \] ## Step 2: Calculate Interest Expense Calculate the annual interest expense from the debt. \[ \text{Interest Expense} = \$104,000 \times 0.06 = \$6,240 \] ## Step 3: Break-Even EBIT Calculation Set the EPS for both the all-equity firm and the levered firm equal to each other. ### EPS Formulas - For the all-equity firm: \[ \text{EPS}_{\text{all-equity}} = \frac{\text{EBIT}}{10,300} \] - For the levered firm: \[ \text{EPS}_{\text{levered}} = \frac{\text{EBIT} - \text{Interest}}{5,966.67} \] ### Set EPS Equal Set the two EPS equations equal: \[ \frac{\text{EBIT}}{10,300} = \frac{\text{EBIT} - 6,240}{5,966.67} \] Cross-multiply to solve for EBIT: \[ 5,966.67 \cdot \text{EBIT} = 10,300 \cdot (\text{EBIT} - 6,240) \] Expanding gives: \[ 5,966.67 \cdot \text{EBIT} = 10,300 \cdot \text{EBIT} - 64,272,000 \] Rearranging terms: \[ 64,272,000 = 10,300 \cdot \text{EBIT} - 5,966.67 \cdot \text{EBIT} \] Combine like terms: \[ 64,272,000 = 4,333.33 \cdot \text{EBIT} \] Solve for EBIT: \[ \text{EBIT} = \frac{64,272,000}{4,333.33} \approx 14,833.98 \] ## Step 4: Calculate Break-Even EPS Use the EBIT to compute the break-even EPS using the levered firm formula: \[ \text{EPS}_{\text{break-even}} = \frac{14,833.98 - 6,240}{5,966.67} \] Calculating gives: \[ \text{EPS}_{\text{break-even}} = \frac{8,593.98}{5,966.67} \approx 1.44 \] ## Final Answer The break-even earnings per share (EPS) for Simone's Sweets is: \[ \boxed{\$1.44} \]

# Break-Even EPS Calculation for Simone's Sweets ## Objective Calculate the earnings per share (EPS) at the break-even EBIT (Earnings Before Interest and Taxes) for Simone's Sweets after issuing debt to repurchase shares. ## Given Data - **Shares Outstanding:** \( 10,300 \) - **Market Price per Share:** \( \$24 \) - **Debt Issued:** \( \$104,000 \) - **Interest Rate:** \( 6\% \) ## Step 1: Determine Shares Repurchased Calculate the number of shares repurchased with the debt issued. \[ \text{Shares Repurchased} = \frac{\$104,000}{\$24} = 4,333.33 \] Calculate the new number of shares outstanding after the repurchase. \[ \text{New Shares Outstanding} = 10,300 - 4,333.33 = 5,966.67 \] ## Step 2: Calculate Interest Expense Calculate the annual interest expense from the debt. \[ \text{Interest Expense} = \$104,000 \times 0.06 = \$6,240 \] ## Step 3: Break-Even EBIT Calculation Set the EPS for both the all-equity firm and the levered firm equal to each other. ### EPS Formulas - For the all-equity firm: \[ \text{EPS}_{\text{all-equity}} = \frac{\text{EBIT}}{10,300} \] - For the levered firm: \[ \text{EPS}_{\text{levered}} = \frac{\text{EBIT} - \text{Interest}}{5,966.67} \] ### Set EPS Equal Set the two EPS equations equal: \[ \frac{\text{EBIT}}{10,300} = \frac{\text{EBIT} - 6,240}{5,966.67} \] Cross-multiply to solve for EBIT: \[ 5,966.67 \cdot \text{EBIT} = 10,300 \cdot (\text{EBIT} - 6,240) \] Expanding gives: \[ 5,966.67 \cdot \text{EBIT} = 10,300 \cdot \text{EBIT} - 64,272,000 \] Rearranging terms: \[ 64,272,000 = 10,300 \cdot \text{EBIT} - 5,966.67 \cdot \text{EBIT} \] Combine like terms: \[ 64,272,000 = 4,333.33 \cdot \text{EBIT} \] Solve for EBIT: \[ \text{EBIT} = \frac{64,272,000}{4,333.33} \approx 14,833.98 \] ## Step 4: Calculate Break-Even EPS Use the EBIT to compute the break-even EPS using the levered firm formula: \[ \text{EPS}_{\text{break-even}} = \frac{14,833.98 - 6,240}{5,966.67} \] Calculating gives: \[ \text{EPS}_{\text{break-even}} = \frac{8,593.98}{5,966.67} \approx 1.44 \] ## Final Answer The break-even earnings per share (EPS) for Simone's Sweets is: \[ \boxed{\$1.44} \]