StartUp Corporation has just paid a dividend of $1.15 per share. The firm pays annual dividends. It is expected by analysts that the earnings of StartUp will grow by 8.2% per year over the next six years. After that, the earnings will most likely grow at the current industry average of 5.5% per year. Analysts do not expect any changes in the payout ratio of the firm. The cost of capital is 10.0%. What is StartUp’s share price?Question 11Answera.$30.93b.$32.08c.$29.86d.$52.52
Question
StartUp Corporation has just paid a dividend of 30.93b.29.86d.$52.52
Solution
The price of a share in StartUp Corporation can be calculated using the Gordon Growth Model, which is a version of the Dividend Discount Model. This model is used to determine the intrinsic value of a stock, based on a future series of dividends that grow at a constant rate.
Given that the dividends are expected to grow at a different rate in the short term (6 years) than in the long term, we need to calculate the price in two parts.
First, we calculate the present value of the dividends for the first 6 years. The dividend for each year is calculated by multiplying the previous year's dividend by 1.082 (reflecting the 8.2% growth). Each of these dividends is then discounted back to the present using a discount rate of 10%.
Second, we calculate the present value of the dividends from year 7 onwards. This is a perpetuity that grows at a rate of 5.5% per year. The value of this perpetuity at the start of year 7 is calculated as D7 / (r - g) where D7 is the dividend in year 7, r is the discount rate and g is the growth rate. This value is then discounted back to the present.
Adding these two parts together gives the total share price. Without specific numbers, I can't provide the exact answer, but the process would be as described.
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