whited inc. stock sells for $35.25 constant rate 4.50% per year required rate return is 11.50% what is stock expected price 5 years from now
To calculate the expected price of the Whited Inc. stock 5 years from now, we can use the formula for the present value of a stock given a constant growth rate:
P0 = D1 / (r - g)
Where:
P0 = Current price of the stock
D1 = Dividend expected to be received in the first year
r = Required rate of return
g = Constant growth rate
Given:
P0 = $35.25 (current stock price)
r = 11.50% (required rate of return)
g = 4.50% (constant growth rate)
To find D1 (dividend expected to be received in the first year), we can use the formula for dividend growth:
D1 = D0 * (1 + g)
Where D0 is the current dividend.
Since we are given the current stock price (P0) and the constant growth rate (g), we need to first calculate the current dividend (D0).
To calculate D0, we can rearrange the formula for stock price:
P0 = D0 / (r - g)
Rearranging the formula:
D0 = P0 * (r - g)
Plugging in the given values:
D0 = $35.25 * (0.1150 - 0.0450)
D0 = $35.25 * 0.0700
D0 = $2.4675
Now, we can calculate D1:
D1 = $2.4675 * (1 + 0.0450)
D1 = $2.4675 * 1.0450
D1 = $2.5793
Finally, we can calculate the expected stock price 5 years from now (P5):
P5 = D6 / (r - g)
Where D6 is the dividend expected to be received in the 6th year.
To calculate D6, we can use the formula for dividend growth:
D6 = D1 * (1 + g)^5
Plugging in the values:
D6 = $2.5793 * (1 + 0.0450)^5
D6 = $2.5793 * 1.2296
D6 = $3.1680
Now, we can calculate P5:
P5 = $3.1680 / (0.1150 - 0.0450)
P5 = $3.1680 / 0.0700
P5 = $45.2571
Therefore, the expected price of the Whited Inc. stock 5 years from now is approximately $45.26.