Company Z-prime’s earnings and dividends per share are expected to grow by 4% a year. Its growth will stop after year 4. In year 5 and afterward, it will pay out all earnings as dividends. Assume next year’s dividend is $2, the market capitalization rate is 12% and next year’s EPS is $9. What is Z-prime’s stock price?
We need to follow the below steps to calculate the price:
Particulars | 1 | 2 | 3 | 4 | 5 |
Earnings | $ 9.00 | $ 9.36 | $ 9.73 | $ 10.12 | $ 10.53 |
Dividends | $ 2.00 | $ 2.08 | $ 2.16 | $ 2.25 | $ 10.53 |
So year 5 earnings are 10.53 at 4% growth rate each year.
The entire earnings from year 5 onwards is distributed as dividends so it is a perpetuity as the growth rate is 0
PV of perpetuity at the end of year 4 or beginning of year 5 = Dividend/capitalization rate
PV of perpetuity at the end of year 4 or beginning of year 5 = 10.53/0.12 = $87.74
Now we find the PV of the dividends and terminal value:
Year | CF | Discount Factor | Discounted CF | ||
1 | $ 2.00 | 1/(1+0.12)^1= | 0.892857143 | 0.892857142857143*2= | $ 1.79 |
2 | $ 2.08 | 1/(1+0.12)^2= | 0.797193878 | 0.79719387755102*2.08= | $ 1.66 |
3 | $ 2.16 | 1/(1+0.12)^3= | 0.711780248 | 0.711780247813411*2.1632= | $ 1.54 |
4 | $ 2.25 | 1/(1+0.12)^4= | 0.635518078 | 0.635518078404831*2.249728= | $ 1.43 |
4 | $ 87.74 | 1/(1+0.12)^4= | 0.635518078 | 0.635518078404831*87.739392= | $ 55.76 |
Price = Sum of all Discounted CF | $ 62.17 |
So the price of the stock = $62.17
Company Z-prime’s earnings and dividends per share are expected to grow by 4% a year. Its...
Company Z prime's earnings and dividends per share are expected to grow by 2% a year. Its growth will stop after year 4 In year 5 and afterward it will pay out all eamings as dividends Assume next year's dividend is $6, the market capitalization rate is 12% and next year's EPS is $11. What is Z-prime's stock price? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Stock price
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