Premier, Incorporated, has an odd dividend policy. The company has just paid a dividend of \( \$ 9.00 \) per share and has announced that will increase the dividend by \( \$ 7.00 \) per share for each of the next four years, and then never pay another dividend. If you require a return of 12 percent on the company's stock, how much will you pay for a share today? Note: Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16. Current share price

We first note that the company has just paid a dividend of \( \$9.00 \) per share. For each of the next four years the dividend will increase by \( \$7.00 \) per share. This means that the dividend payments will be made at the end of years 1 through 4 and will be as follows: - At the end of Year 1: \[ D_1 = 9.00 + 7.00 = 16.00 \] - At the end of Year 2: \[ D_2 = D_1 + 7.00 = 16.00 + 7.00 = 23.00 \] - At the end of Year 3: \[ D_3 = D_2 + 7.00 = 23.00 + 7.00 = 30.00 \] - At the end of Year 4: \[ D_4 = D_3 + 7.00 = 30.00 + 7.00 = 37.00 \] Since no dividend is paid after Year 4, the value of the stock today is simply the present value of these four future dividend payments discounted at the required rate of \( 12\% \) (or \( 0.12 \)). The present value (PV) of the dividends is calculated as: \[ P_0 = \frac{D_1}{(1+0.12)^1} + \frac{D_2}{(1+0.12)^2} + \frac{D_3}{(1+0.12)^3} + \frac{D_4}{(1+0.12)^4} \] Substitute the dividend amounts: \[ P_0 = \frac{16.00}{1.12} + \frac{23.00}{1.12^2} + \frac{30.00}{1.12^3} + \frac{37.00}{1.12^4} \] We now compute each term: 1. For Year 1: \[ \frac{16.00}{1.12} \approx 14.2857 \] 2. For Year 2: \[ 1.12^2 = 1.2544, \quad \frac{23.00}{1.2544} \approx 18.3441 \] 3. For Year 3: \[ 1.12^3 \approx 1.404928, \quad \frac{30.00}{1.404928} \approx 21.3510 \] 4. For Year 4: \[ 1.12^4 \approx 1.573519, \quad \frac{37.00}{1.573519} \approx 23.5233 \] Now sum all these present values: \[ P_0 \approx 14.2857 + 18.3441 + 21.3510 + 23.5233 = 77.5041 \] Rounded to 2 decimal places, today's price per share is: \[ \$77.50 \]