I need a formula for:
A share of common stock of xyz ltd is expected to pay no dividends until next 2 years but at the end of year 2 it will pay $2 as dividends. Dividends are expected to grow at 20% per annum in yrs 3 and 4 and thereafter they are expected to grow at 4% per annum into indefinite future. Assume that the required expected ROR on xyz's common stock is 14%.
Find the current price per share of the stock.
To calculate the current price per share of the stock, we can use the Gordon Growth Model, which is used to value stocks that pay dividends and have a constant growth rate. The formula for the Gordon Growth Model is:
P0 = D1 / (r - g)
Where:
P0 = Current price per share of the stock
D1 = Dividends expected to be paid at the end of year 2
r = Required expected rate of return on the stock
g = Dividend growth rate
In this case, we are given the following information:
D1 = $2 (dividends expected to be paid at the end of year 2)
r = 14% (required expected rate of return on the stock)
g = 20% (dividend growth rate in years 3 and 4), 4% (dividend growth rate after year 4)
Let's plug the values into the formula and calculate the current price per share:
P0 = $2 / (0.14 - 0.20)
First, we need to calculate the present value of the dividends expected to be paid in years 3 and 4:
D2 = D1 * (1 + g) = $2 * (1 + 0.20) = $2.40
D3 = D2 * (1 + g) = $2.40 * (1 + 0.20) = $2.88
Next, we'll calculate the present value of the dividends expected to be paid after year 4, using the perpetual growth rate:
D4 = D3 * (1 + g) = $2.88 * (1 + 0.04) = $2.99
Now we can plug the values into the formula:
P0 = $2 + $2.40 / (0.14 - 0.20) + $2.88 / (0.14 - 0.20) + $2.99 / (0.14 - 0.04)
P0 = $2 + $2.40 / (-0.06) + $2.88 / (-0.06) + $2.99 / (0.10)
P0 = $2 - $40 + $48 + $29.90
P0 = $39.90
Therefore, the current price per share of the stock is $39.90.