# 1. Compute Weighted-Average Shares To calculate weighted-average shares,each share issuance or repurchase is weighted by the fraction of the year it was outstanding**. ## Step 1: Timeline and Share Movements - **Jan 1:** Issued 10,000 shares (outstanding all year) - **Mar 1:** Issued 20,000 shares (outstanding Mar 1–Dec 31, 10 months) - **Jul 1:** Issued 30,000 shares (outstanding Jul 1–Dec 31, 6 months) - **Dec 1:** Repurchased 5,000 shares (repurchased for 1 month) ## Step 2: Calculate Weighted Shares For each transaction, multiply the number of shares by the portion of the year outstanding: 1. **Jan 1 Issuance:** \( 10,000 \times 12/12 = 10,000 \) 2. **Mar 1 Issuance:** Shares outstanding from Mar 1–Dec 31 (10 months): \( 20,000 \times 10/12 = 16,666.67 \) 3. **Jul 1 Issuance:** Shares outstanding from Jul 1–Dec 31 (6 months): \( 30,000 \times 6/12 = 15,000 \) 4. **Dec 1 Repurchase:** 5,000 shares repurchased and thus not outstanding for 1 month: \( 5,000 \times 1/12 = 416.67 \) This amount is subtracted since these shares were not outstanding for the last month. ## Step 3: Add/Subtract the Weighted Shares \[ \begin{align*} \text{Weighted-average shares} &= 10,000 \\ &+ 16,666.67 \\ &+ 15,000 \\ &- 416.67 \\ &= 41,250 \end{align*} \] **Final Answer:** > **Weighted-average shares outstanding = 41,250** --- # 2. Compute Basic EPS The formula for basic earnings per share (EPS) is: \[ \text{Basic EPS} = \frac{\text{Net Income}}{\text{Weighted-Average Shares Outstanding}} \] Given: - Net income = $60,000 - Weighted-average shares = 41,250 (from above) \[ \text{Basic EPS} = \frac{60,000}{41,250} = \$1.45 \] **Final Answer:** > **Beta’s basic EPS for the year = \$1.45 per share**