# XYZ Inc. just paid out a dividend (D0) of $2.25. The firm anticipates that its annual dividends will grow at 20% a year over the next 6 years (from August 2012 to July 2018). From August 2018...

** **XYZ Inc. just paid out a dividend (*D*0) of $2.25. The firm anticipates that its annual dividends will grow at 20% a year over the next 6 years (from August 2012 to July 2018). From August 2018 onwards, the management expects that the firm’s dividends will grow in perpetuity at 4% per year. Work out the price of the stock assuming that the risk of its future cash flows justifies a discount rate of 16%.

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### 1 Answer

The price of a stock is the sum of the future cash flows discounted at a rate equal to the expected returns.

The present dividend paid out by XYZ Inc. is $2.25. It is anticipated that the dividends grow at 20% for 6 years, followed by a growth of 4% for perpetuity.

The discount rate to be used to calculate the present value of the future dividends is 16%.

For the first 6 years, the total discounted cash flow is 2.25*( (1.2/1.16)^6 - 1)/(1.2/1.16 - 1) = 14.72 The dividend at the end of six years is 2.25*1.2^5 = 5.59872. The discounted cash flow for perpetuity following the 6 year is 5.59872/(1 - 1.04/1.16) = 54.12. The present price of the stock is the sum of the discounted value of all the dividends received. This is 14.72 + 54.12 = 68.83

This gives the present price of the stock as $68.83