Let's break down the problem step by step. ## **Step 1: Calculate the price of Consolidated stock** **Given:** - Annual dividend = $10 per share (perpetuity) - Required rate of return = 8% - Shares outstanding = 1.2 million The price of a perpetuity stock is: \[ P = \frac{D}{r} \] Where: - \(P\) = price per share - \(D\) = annual dividend per share = $10 - \(r\) = required rate of return = 8% = 0.08 \[ P = \frac{10}{0.08} = \$125 \] --- ## **Step 2: Calculate the total market value of equity** \[ \text{Total Market Value} = \text{Price per Share} \times \text{Number of Shares} \] \[ = 125 \times 1.2\,\text{million} = \$150\,\text{million} \] --- ## **Step 3: Company increases next year's dividend to $20 per share** ### **a) How much new equity capital will the company need to raise to finance the extra dividend payment?** - Next year's dividend = $20 per share (was $10 per share) - Extra dividend per share = $20 - $10 = $10 - Total extra dividend = $10 \(\times\) 1.2 million = **$12 million** If the company doesn't change its investment or borrowing plans, it must raise this $12 million by issuing new equity. **New equity capital required = $12 million** --- ### **b) What will be the total present value of dividends paid each year on the new shares that the company will need to issue?** - The $12 million in new shares will entitle their holders to future dividends of $10 per share (like the existing shares). - Let \(N\) = number of new shares issued. \[ \text{Amount to raise} = N \times \text{Price per Share} \] \[ 12,000,000 = N \times 125 \implies N = \frac{12,000,000}{125} = 96,000 \text{ shares} \] Each of these 96,000 shares will receive $10 per year in perpetuity. So, total dividends paid each year on the new shares: \[ \text{Dividends per year} = 96,000 \times 10 = \$960,000 \] The present value of these dividends (perpetuity): \[ \text{PV} = \frac{960,000}{0.08} = \$12,000,000 \] So, **total present value of dividends paid each year on the new shares = $12 million**. --- ### **c) What will be the transfer of value from the old shareholders to the new shareholders?** The transfer of value is the present value of the dividends that will now go to new shareholders instead of old shareholders, i.e., $12 million. --- ### **d) Is this figure more than, less than, or the same as the extra dividend that the old shareholders will receive?** - Extra dividend received by old shareholders = $12 million (in year 1) - Transfer of value to new shareholders = $12 million (present value) **The figure is the same as the extra dividend that the old shareholders will receive.** --- ## **Final Answers:** ### 1. **Price of Consolidated stock:** **$125 per share** ### 2. **Total market value of equity:** **$150 million** ### 3. **New equity capital needed to raise:** **$12 million** ### 4. **Total present value of dividends paid each year on the new shares:** **$12 million** ### 5. **Transfer of value from old to new shareholders:** **$12 million** ### 6. **Is this more than, less than, or the same as the extra dividend?** **The same as the extra dividend that the old shareholders will receive.** --- **Explanation:** When a company pays an extra dividend by issuing new equity, existing shareholders get the extra cash up front, but future dividends are now shared with the new shareholders, leaving the old shareholders no better off in present value terms. This is a classic illustration of the "dividend irrelevance" principle in finance.