Question

Pasqually Mineral Water, Inc., will pay a quarterly dividend per share of $.95 at the end of each of the next 12 quarters. Thereafter, the dividend will grow at a quarterly rate of 1.3 percent, forever. The appropriate rate of return on the stock is 12 percent, compounded quarterly.

Answer 1

Answer:

• $49.16

Explanation:

The final question is What is the current stock price?

The price of the stock is the present value of all the stream of cash flows that the stock will generate.

You have to split the calculations in two parts: 1) the  quarterly dividend per share of $0.95 at the end of each of the next 12 quarters, and 2) the dividend that will grow at a quarterly rate of 1.3 percent, forever.

1) Quaterly dividend per share of $0.95 ant the ench of each of the next 12 quarters.

A quarter is a period of three months. Use the formula for an annuity adjusting the periods to 12 quarters, and the rate of return to the quarterly return: (12%/12) = 3%.

The formula is:

      $PV=DIVIDEND\times \bigg[\dfrac{1}{r}-\dfrac{1}{r\cdot (1+r)^t}\bigg]$

Substitute:

      $PV=\ 0.95\times \bigg[\dfrac{1}{0.03}-\dfrac{1}{0.03\cdot (1+0.03)^{12}}\bigg]$

      $PV=\ 9.46$

2. Dividend from the 13th quarter that will grow at a quarterly rate of 1.3 percent, forever.

The formula for the price the year n of a stock that pays the first dividend the year n + 1, and that is growing at a rate g is:

     $Price_n=\dfrac{DIVIDEND_{n+1}}{r-g}$

Substitue, n = 12, r = 0.03, and g = 1.3% = 0.013

        $Price_{12}=\dfrac{\ 0.95\times 1.013}{0.03-0.013}=\ 56.61$

That is the value in the quarter 12, only of the dividends since year 13.

You need to discount that value to the current year and add it to the value calculated in the first part.

           $Price_0=\dfrac{\ 56.60}{(1+0.03)^{12}}=\ 39.70$

3) Add the two values

The current price of the stock is:

          $Price=\ 9.46+\ 39.70=\ 49.16$