What is the value of a stock that grows at a supernormal rate of 18% for the first four years, and then slows down to a constant growth rate of 10%? An annual dividend of $2.00/share was just paid, and the rate of return on common stock is 13%.
Possible Solution:
For a constant growth rate, we have:
V = D1/k-g
V = the value of the stock = ?
D1 = the dividend next period = $2.00
k = the required rate of return = 13%
g = constant growth rate = 10%
I'm confused on how to combine the constant growth rate formula with the supernormal growth rate of 18%.
To determine the value of the stock, we need to calculate the present value of the dividends during the supernormal growth period and the present value of the dividends during the constant growth period. Let's break it down step by step:
1. Calculate the present value of dividends during the supernormal growth period:
During the supernormal growth period, the growth rate is 18%. We need to find the present value of the dividends for the first four years.
a. Calculate the dividend in year 5:
To calculate the dividend in year 5, we need to find the dividend in year 4 and multiply it by (1 + g), where g is the growth rate of 18%. The dividend in year 4 is $2.00 (as mentioned in the question), so the dividend in year 5 will be $2.00 * (1 + 18%) = $2.00 * 1.18 = $2.36.
b. Calculate the present value of the dividends during the supernormal growth period:
To find the present value of the dividends during the supernormal growth period, we need to discount each dividend back to present value using the required rate of return (13%) as the discount rate. The dividends are $2.00, $2.00, $2.00, and $2.36 for years 1, 2, 3, and 4 respectively.
The present value of the dividends during the supernormal growth period can be calculated as follows:
PV = D1 / (1 + k) + D2 / (1 + k)^2 + D3 / (1 + k)^3 + D4 / (1 + k)^4
where PV is the present value, D1 to D4 are the dividends in years 1 to 4, and k is the required rate of return.
Substituting the values, we get:
PV = $2.00 / (1 + 13%) + $2.00 / (1 + 13%)^2 + $2.00 / (1 + 13%)^3 + $2.36 / (1 + 13%)^4
2. Calculate the present value of dividends during the constant growth period:
After the supernormal growth period (starting from year 5), the growth rate becomes a constant 10%. We can use the constant growth formula, V = D1 / (k - g), to find the present value of dividends during the constant growth period.
a. Calculate the constant dividend (D1) in year 5:
The dividend in year 5 has already been calculated as $2.36 during the supernormal growth period.
b. Calculate the present value of the dividends during the constant growth period:
Applying the constant growth formula, we can find the present value:
PV = D1 / (k - g)
where PV is the present value, D1 is the dividend in year 5, k is the required rate of return, and g is the constant growth rate.
Substituting the values, we get:
PV = $2.36 / (13% - 10%)
3. Calculate the total value of the stock:
To find the total value of the stock, we add the present value of the dividends during the supernormal growth period (from step 1) to the present value of the dividends during the constant growth period (from step 2):
Total Value = Present Value of Supernormal Growth Period + Present Value of Constant Growth Period
Substituting the calculated present values from step 1 and step 2, we get:
Total Value = PV of Supernormal Growth Period + PV of Constant Growth Period
Therefore, to find the total value of the stock, plug in the values calculated above into this equation.