new millenium company's stock sells at a P/E ratio of 21 times earnings. it is expected to pay dividends of $2 per share in each of the next 5 years and to generate an EPS of $5 i year 5. using the dividends-and-earnings model and a 12% discount rate, compute the stock's justified price.
To compute the stock's justified price using the dividends-and-earnings model, we need to calculate the present value of the future dividends and the present value of the future earnings.
Step 1: Calculate the present value of dividends:
The dividends are expected to be $2 per share for each of the next 5 years. To calculate the present value of these future dividends, we use the formula:
PV(dividends) = D1 / (1 + r) + D2 / (1 + r)^2 + ... + Dn / (1 + r)^n
Where:
PV(dividends) = Present value of dividends
D1, D2, ..., Dn = Dividends in years 1, 2, ..., n
r = Discount rate
In this case, the dividends are the same ($2 per share) for each of the next 5 years, so the formula becomes:
PV(dividends) = $2 / (1 + r) + $2 / (1 + r)^2 + $2 / (1 + r)^3 + $2 / (1 + r)^4 + $2 / (1 + r)^5
Step 2: Calculate the present value of future earnings:
The EPS (earnings per share) in year 5 is expected to be $5. To calculate the present value of this future earnings, we use the formula:
PV(earnings) = E / (1 + r)^n
Where:
PV(earnings) = Present value of earnings
E = Earnings in the future year
r = Discount rate
n = Number of years until we receive the earnings
In this case, the earnings are expected in year 5, so the formula becomes:
PV(earnings) = $5 / (1 + r)^5
Step 3: Compute the stock's justified price:
The justified price of the stock is the present value of dividends plus the present value of earnings. So, the formula becomes:
Justified price = PV(dividends) + PV(earnings)
Now, let's calculate the justified price using the given information:
Given data:
P/E ratio = 21 times earnings
Dividends = $2 per share for each of the next 5 years
EPS in year 5 = $5
Discount rate (r) = 12%
Calculations:
PV(dividends) = $2 / (1 + 0.12) + $2 / (1 + 0.12)^2 + $2 / (1 + 0.12)^3 + $2 / (1 + 0.12)^4 + $2 / (1 + 0.12)^5
PV(earnings) = $5 / (1 + 0.12)^5
Justified price = PV(dividends) + PV(earnings)
By substituting the values into the calculations, we can find the justified price of the stock.