Question
In: Finance
Firm AAA's earnings and dividends are expected to grow by a rate of 0.04 a year....
Firm AAA's earnings and dividends are expected to grow by a rate of 0.04 a year. This growth will stop after year 4. In year 5 and later, it will pay out all earnings as dividends. Assume next year's dividend is 2, the cost of capital is 0.08, and next year's EPS is 12. What is AAA's stock price today? Round your answer to 2 decimal places.
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Expert Solution
| Calculation of Earning per share and dividend | |||||||||
| Dividend (EPS * Dividend payout ratio) | |||||||||
| Earnings first year | $12.0000 | D1 | $2.0000 | ||||||
| Earnings 2 year ( 12. 00 + growth 4 %) | $12.4800 | D2 | $2.0800 | ||||||
| Earnings 3 year (12.48 + growth 4%) | $12.9792 | D3 | $2.1632 | ||||||
| Earnings 4 year (12.9792 + growth 4%) | $13.4984 | D4 | $2.2497 | ||||||
| Earnings 5 year (13.4984 + growth 0) | $13.4984 | D5 | $13.4984 | (100% paid) | |||||
| Calculation of Present value of Equity at end of 5th Year | |||||||||
| Thereafter growth is 0 and Dividend is paid $13.4984 forever. | |||||||||
| So Present Value of Stock at end of year 4 (P4)) immediately after paying dividend shall be calculated by formula. | |||||||||
| Cost of Capital (Ke) = | 0.08 | ||||||||
| Growth rate = | 0% | ||||||||
| P4 = D5 /Ke-g | |||||||||
| . = 13.4984/ (0.08-0) | |||||||||
| $168.73 | |||||||||
| Calculation of Present Value of Stock by Dividend Discount model | |||||||||
| Now, present value of stock shall be calculated by Dividend discount model | |||||||||
| Dividend received upto 4 years and present value of stock received on 4h year end shall be discounted with cost of capital (ke) for relevant period. | |||||||||
| Ke for 1-2 period = | 13% or 0.13 | ||||||||
| ke for 3 to perpetuity = 10% or 0.10 | |||||||||
| Year | Cash flows | P.V.F.= 1/((1+i)^n) | Present value of cash flows | ||||||
| 1 | D1 | $2.0000 | 1/((1+0.08)^1) | 0.9259 | $1.8519 | ||||
| 2 | D2 | $2.0800 | 1/((1+0.08)^2) | 0.8573 | $1.7833 | ||||
| 3 | D3 | $2.1632 | 1/((1+0.08)^3) | 0.7938 | $1.7172 | ||||
| 4 | D4 | $2.2497 | 1/((1+0.08)^4) | 0.7350 | $1.6536 | ||||
| 4 | P4 | $168.7296 | 1/((1+0.08)^4) | 0.6806 | $114.8345 | ||||
| P0 (share price today) | $121.8405 | ||||||||
| So, AAA's stock price today is $121.84 | |||||||||
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