Premiet, Incorporated, has an odd dividend policy. The company has just paid a dividend of \( \$ 7.65 \) per share and has announced that will increase the dividend by \( \$ 10.25 \) per share for each of the next four years, and then never pay another dividend. If you require a return of 16 percent on the company's stock, how much will you pay for a share today?

To determine how much you would pay for a share of Premiet, Incorporated today, we need to calculate the present value of the expected future dividends. Here’s how we do it: 1. **Dividends Over the Next Four Years:** - Year 0: \( \$ 7.65 \) - Year 1: \( \$ 7.65 + \$ 10.25 = \$ 17.90 \) - Year 2: \( \$ 17.90 + \$ 10.25 = \$ 28.15 \) - Year 3: \( \$ 28.15 + \$ 10.25 = \$ 38.40 \) - Year 4: \( \$ 38.40 + \$ 10.25 = \$ 48.65 \) 2. **Present Value Calculation:** The present value (PV) of each dividend is calculated using the formula: \[ PV = \frac{D}{(1 + r)^n} \] where \( D \) is the dividend, \( r \) is the required return (16% or 0.16), and \( n \) is the year. - PV of Year 0: \( \frac{7.65}{(1 + 0.16)^0} = 7.65 \) - PV of Year 1: \( \frac{17.90}{(1 + 0.16)^1} = \frac{17.90}{1.16} \approx 15.43 \) - PV of Year 2: \( \frac{28.15}{(1 + 0.16)^2} = \frac{28.15}{1.3456} \approx 20.92 \) - PV of Year 3: \( \frac{38.40}{(1 + 0.16)^3} = \frac{38.40}{1.560896} \approx 24.59 \) - PV of Year 4: \( \frac{48.65}{(1 + 0.16)^4} = \frac{48.65}{1.811580} \approx 26.85 \) 3. **Total Present Value:** Add the present values of the dividends: \[ Total PV \approx 7.65 + 15.43 + 20.92 + 24.59 + 26.85 \approx 95.44 \] So, the price you would be willing to pay for a share today is approximately **$95.44**.