Complete Question:
A stock just paid an annual dividend of $7.7. The dividend is expected to grow by 5% per year for the next 6 years. In 6 years, the P/E ratio is expected to be 25 and the payout ratio to be 80%.
The required rate of return is 8%.
What should be the current stock price?
Answer:
$245.10
Step-by-step explanation:
As we know that:
P/E = Market Price of Stock / Earning Per Share
Here
P/E is 25 time
Earning Per Share is $12.9 per share (Step1)
By putting values, we have:
25 Times = Market Price of Stock / $15.6 per share
25 Times * $12.9 per share = Market Price of Stock
Market Price of Stock = $322.5 per share
Present value computation for first 6 years:
Yrs Future Cash flow Discount Factor Present Value
1 $7.7 *(1.05)^1 0.926 7.49
2 $7.7 *(1.05)^2 0.857 7.28
3 $7.7 *(1.05)^3 0.794 7.08
4 $7.7 *(1.05)^4 0.735 6.88
5 $7.7 *(1.05)^5 0.681 6.69
6 $7.7 *(1.05)^6 + $322.5 0.630 209.68
Present value of stock $245.10
Step1: Find Earning Per Share
As we know that:
Earning Per Share = Dividend / Payout Ratio
Here
Dividend after 6 years = $7.7 (1 + 5%)^6 = $10.32 per share
Payout Ratio = 80% = 0.8
By putting values, we have:
EPS = $10.32 / 0.8 = $12.9 per share