# It is now January 1, 1988. Prosun Engineering is expected to experience a 30 percent annual growth rate for the next two years. After the first two years the growth rate will decline to 8% and stay...

It is now January 1, 1988. Prosun Engineering is expected to experience a 30 percent annual growth rate for the next two years. After the first two years the growth rate will decline to 8% and stay there indefinitey. The required rate of return on Prosun's stock is 12% and the most recent annual dividend which was paid yesterday was \$1.50/share. Calculate the current market price of Prosun's common stock.

justaguide | College Teacher | (Level 2) Distinguished Educator

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The present annual dividend paid by the company is \$1.5 /share. To proceed with the problem the assumption has to be made that the dividend amount increases at the same rate as that at which the corporation is expected to grow.

There is an expected growth of 30% in the next two years and 8% growth in the following years.

The expected dividend return for 1989 is 1.5*1.3 = \$1.95 and that for 1990 is 1.5*1.3*1.3 = \$ 2.535

If the required rate of return is 12%, to find the present stock price the sum of all future dividends discounted at 12% per annum should be estimated.

This is given by: `1.5*1.3/1.12 + 1.5*1.3^2/1.12^2 + 1.5*1.3^2*1.08/1.12^3 + ...`

= `1.95/1.12 + 2.535/1.12^2 + 2.535/1.12^2*(1.08/1.12 + 1.08^2/1.12^2 + ...)`

The infinite geometric series `1.08/1.12 + 1.08^2/1.12^2 + ...` is equal to `1.08/1.12*1/(1 - 1.08/1.12) = 27`

This gives a current market price of approximately \$58.325

The current market price of the stock is \$58.33