Let's break down the problem and solve it step-by-step: ### Given Data: - Current per share:330 - after 5 years: \$465- Growth rate of assets per share: 3% per year - ROA (Return on Assets): 1.6% - ROE (Return on Equity): 11.% - Cost of equity: 11.% ### Step 1: Calculate the projected assets per share after 5 years The assets grow at 3% annually: \[ \text{Assets after 5 years} = 330 \times (1 + .03)^5 \] \[ = 330 \times (1.159274) \] \[ \approx 382.55 \] But the problem states the assets after 5 years will be \$465, so this suggests the growth rate might be used to verify or for other calculations. ### Step 2: Find the book value of equity per share after 5 years Since ROE is 11%, and assets are \$465: \[ \text{Equity} = \frac{\text{Assets} \times \text{ROE}}{\text{ROA}} \] But typically, the valuation model for stocks based on dividends or earnings is used. Since the problem asks for the stock value, it is likely using the Gordon Growth Model, which is: \[ P = \frac{D_1}{k - g} \] Where: - \(P\): Price of stock - \(D_1\): Dividend in year 1 - \(k\): required rate of return (cost of equity) - \(g\): growth rate of dividends (or earnings) ### Step 3: Calculate dividends Dividends are based on ROE and equity: \[ D = \text{ROE} \times \text{Equity} \] In 5 years, the Equity per share: \[ \text{Equity}_5 = \text{Assets}_5 \times \text{Equity/Assets ratio} \] Assuming the entire assets are financed by equity (since no debt info is provided), then: \[ \text{Equity}_5 = 465 \] and the dividend in year 6: \[ D_6 = \text{ROE} \times \text{Equity}_5 = .016 \times 465 \approx 7.44 \] ### Step 4: Calculate the stock price Using the Gordon Growth Model: \[ P = \frac{D_6}{k - g} \] where: - \(D_6 = 7.44\) - \(k = 11\% = .11\) - \(g = 3\% = .03\) \[ P = \frac{7.44}{.11 - .03} = \frac{7.44}{.08} = 93 \] ### **Final Answer:** \[ \boxed{\$93} \] **The value of the bank's stock is approximately \$93.**