Final answer:
To determine the price you'd pay for a share of Premier, Inc. today, calculate the present value of the future dividend payments discounted at the required return of 15 percent. The dividends for the next four years are determined by the initial $9.50 payment and the $7.50 annual increase.
Step-by-step explanation:
The question involves calculating the present value of a company's stock based on its dividend policy, which is a concept central to finance and business. Premier, Incorporated has announced it will pay increasing dividends for the next four years and then cease payments. To find the present value of the stock given a required return of 15 percent, we must discount the future dividends back to their present value.
The dividends are projected to increase by $7.50 each year, starting with a $9.50 dividend already paid. The expected dividends over the next four years will be: Year 1: $17 (= $9.50 + $7.50), Year 2: $24.50, Year 3: $32, and Year 4: $39.50. With the required return of 15 percent, we discount these dividends back to their present value.
Calculation
PV = D1 / (1 + r)^1 + D2 / (1 + r)^2 + D3 / (1 + r)^3 + D4 / (1 + r)^4
Where PV is the present value of the stock, D1, D2, D3, and D4 are the dividends for years 1, 2, 3, and 4 respectively, and r is the required rate of return, which is 0.15 in this case.
The sum of these present values will give us the price an investor would be willing to pay for a share today considering the odd dividend policy of the company.