To determine the current price of Premier, Incorporated's stock, we need to calculate the present value of the dividends that the company will pay in the future. Given that the dividends will be paid for only four years and the return required is 13%, we can use the Dividend Discount Model (DDM) for a limited time horizon.

Step 1: Outline the Dividend Stream

The dividends will increase by $10.50 each year from the current dividend, which is $6.75. Thus, the dividends for the next four years are:

• Dividend in year 1: $D_1 = 6.75 + 10.50 = 17.25$
• Dividend in year 2: $D_2 = 17.25 + 10.50 = 27.75$
• Dividend in year 3: $D_3 = 27.75 + 10.50 = 38.25$
• Dividend in year 4: $D_4 = 38.25 + 10.50 = 48.75$

After year 4, there will be no more dividends.

Step 2: Present Value of Each Dividend

Now, we need to calculate the present value of each dividend, discounted at the required return of 13%. The present value formula is:

$PV = \frac{D_t}{(1 + r)^t}$

where:

• $D_t$ = dividend in year $t$,
• $r = 0.13$ (13% required return),
• $t$ = the year in which the dividend is paid.

Present Value of Each Dividend:

• $PV_1 = \frac{17.25}{(1 + 0.13)^1} = \frac{17.25}{1.13} = 15.27$
• $PV_2 = \frac{27.75}{(1 + 0.13)^2} = \frac{27.75}{1.2769} = 21.73$
• $PV_3 = \frac{38.25}{(1 + 0.13)^3} = \frac{38.25}{1.4435} = 26.50$
• $PV_4 = \frac{48.75}{(1 + 0.13)^4} = \frac{48.75}{1.6319} = 29.88$

Step 3: Total Present Value (Stock Price)

The total price of the stock today is the sum of the present values of the dividends:

$\text{Price} = PV_1 + PV_2 + PV_3 + PV_4$ $\text{Price} = 15.27 + 21.73 + 26.50 + 29.88 = 93.38$

Thus, the price you would be willing to pay for a share today is $93.38.

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Do you want more details or have any questions about this solution?

Here are 5 related questions that expand on this topic:

1. What happens to the stock price if the required return changes to 10%?
2. How would the stock price change if the dividend increased by $12 per year instead of $10.50?
3. What is the stock's intrinsic value if the company decides to continue paying the final dividend indefinitely?
4. How would inflation affect the stock's value if we consider a long-term scenario?
5. What are the risks involved with companies that have a limited dividend payout policy?

Tip: In finance, understanding the time value of money is crucial when valuing assets like stocks or bonds, as future cash flows are worth less today due to the discounting effect of interest rates.