# You want to buy SuperTech Inc. stock. They pay quarterly dividends, with the next dividend of...

## Question:

You want to buy SuperTech Inc. stock. They pay quarterly dividends, with the next dividend of S0.40 per share being paid later today. You believe that, during the next 6 years, their quarterly dividends will grow by 20% APR, compounded annually. But after 6 years, their quarterly dividends will grow more slowly... only at 4% APR, compounded annually. If the discount rate on this stock is 12% APR, compounded annually, then what would be a fair price for this stock right now?

## Annual Percentage Rate:

The annual percentage rate is the nominal annual interest rate, which is often the rate legally required to be disclosed. When there is annual compounding of interest, the annual percentage rate is the same as the effective annual rate.

## Answer and Explanation:

We can use the dividend discount model to answer this question. According to the model, the price of a stock is the discounted present value of future dividends. Note that the annual dividend is 0.4 * 4 = 1.6 next year. The annual growth rate is 20% for the next 6 years, and 4% afterwards. The discount rate is 12% per year. The present value of the dividends is:

- {eq}\displaystyle \sum_{t=1}^{6}{\dfrac{1.6*(1 + 20\%)^{t-1}}{(1 + 12\%)^t}} + \dfrac{1.6*(1 + 20\%)^5*(1 + 4\%) }{(12\% - 4\%)(1 + 12\%)^5}\\ = 10.25 + 29.37\\ = 39.62 {/eq}

That is, a fair price for the stock today is $39.62.

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