Teddy Company paid a $3.50 dividend this year (D0 = $3.50). Next year the company expects to pay a $4.00 dividend (D1 = $4.00). The stock's dividend is expected to grow at a rate of 15 percent a year until three years from now (t = 3). After this time, the stock's dividend is expected to grow at a constant rate of 4 percent a year. Currently, the risk-free rate is 5 percent, market risk premium (rM - rRF) is 8 percent, and the stock's beta is 1.3. What should be the price of the stock today?
To calculate the price of the stock today, we can use the dividend discount model (DDM) which values a stock based on the present value of its expected future dividends. The formula for the DDM is:
P0 = D0 * (1 + g) / (r - g)
Where:
P0 = Price of the stock today
D0 = Dividend this year = $3.50
g = Growth rate of the dividend = 15% until t = 3, then 4% thereafter
r = Required rate of return = risk-free rate + (beta times market risk premium)
First, let's calculate the required rate of return:
r = 0.05 + (1.3 * 0.08)
r = 0.05 + 0.104
r = 0.154 or 15.4%
Now, let's calculate the price of the stock today:
For the first three years:
P0 = D0 * (1 + g) / (r - g)
P0 = $3.50 * (1 + 0.15) / (0.154 - 0.15)
P0 = $3.50 * (1.15) / (0.004)
P0 = $3.50 * 287.5
For the subsequent years:
P0 = D3 * (1 + g) / (r - g)
P0 = $4.00 * (1 + 0.04) / (0.154 - 0.04)
P0 = $4.00 * (1.04) / 0.114
Finally, add the values for the first three years and the subsequent years to get the total price:
P0 = ($3.50 * 287.5) + ($4.00 * 1.04) / 0.114
P0 ≈ $1,006.25 + $34.39 / 0.114
P0 ≈ $1,040.64 / 0.114
P0 ≈ $9,134.74
Therefore, the price of the stock today should be approximately $9,134.74.
To find the price of the stock today, we can use the Dividend Discount Model (DDM) approach, also known as the Gordon Growth Model. This model calculates the present value of all future expected dividends.
The formula for the Gordon Growth Model is:
P0 = D1 / (r - g)
Where:
P0 = Current price of the stock
D1 = Dividend expected to be paid next year
r = Required rate of return
g = Growth rate of dividends
Let's break down the information given:
D0 = $3.50 (dividend paid this year)
D1 = $4.00 (dividend expected to be paid next year)
Growth rate until t=3 = 15%
Growth rate beyond t=3 = 4%
Risk-free rate (rf) = 5%
Market risk premium (rm - rf) = 8%
Beta (β) = 1.3
First, we need to calculate the required rate of return (r) using the Capital Asset Pricing Model (CAPM):
r = rf + β * (rm - rf)
Substituting the values:
r = 0.05 + 1.3 * 0.08
r = 0.05 + 0.104
r = 0.154 or 15.4%
Now, let's calculate the price of the stock today using the DDM formula:
P0 = $4.00 / (0.154 - 0.15) + $4.00 * (1 + 0.04) / (0.154 - 0.04)^2
P0 = $4.00 / 0.004 + $4.00 * 1.04 / 0.1144
P0 = $1000 + $36.60 ≈ $1036.60
Therefore, the price of the stock today is approximately $1036.60.