Final answer:
The current price of the firm's stock (P0) should be $25.32 today.
Step-by-step explanation:
To calculate the current price of the firm's stock (P0), we need to compute the present value of the expected dividends and the terminal value. The present value (PV) is calculated using the formula:
PV = D1/(1+r)^1 + D2/(1+r)^2 + D3/(1+r)^3 + ... + Dn/(1+r)^n
where D1, D2, D3 are the expected dividends for each year, r is the required rate of return, and n is the number of years.
In this case, the expected dividends for the next three years are $1.10, $1.20, and $1.30. The terminal value is calculated using the formula:
Terminal Value = Dn * (1+g)/(r-g)
where Dn is the last expected dividend, g is the expected growth rate of dividends after year n, and r is the required rate of return.
In this case, the expected growth rate is 5%. Using these values and a required rate of return of 12%, we can calculate the present value of the expected dividends and the terminal value. Summing these values will give us the current price of the firm's stock (P0).
Calculating the present value of the expected dividends:
PV = 1.10/(1+0.12)^1 + 1.20/(1+0.12)^2 + 1.30/(1+0.12)^3
PV = $0.9823 + $1.016 + $1.040 = $3.0383 (rounded to $3.04)
Calculating the terminal value:
Terminal Value = 1.30 * (1+0.05)/(0.12-0.05) = $22.28
Finally, summing the present value of the expected dividends and the terminal value will give us the current price of the firm's stock:
P0 = $3.04 + $22.28 = $25.32 (rounded to $25.32)