The question is incomplete. See the complete one below:
Dividends per share at time 1: Div 1 1.00
Dividends per share at time 2: Div 2 1.20
Dividends per share at time 3: Div 3 1.44
Growth Rate after time 3 forever: g 0.05
Discount Rate: r 0.10
Find the price per share of United Bird Seed at time 0
Answer:
Stock price = $24.703
Explanation:
The Dividend Valuation Model is a technique used to value the worth of an asset. According to this model, the value of an asset is the sum of the present values of the future cash flows would arise from the asset discounted at the required rate of return.
In this question, the cash flows are the dividends as given in the question and the rate of return (discount rate) is 10%
The Present Value of a future cash flow is the amount that needs to be invested today at a particular rate of return to equal the same cash flow in the future. Present value means the value in year 0 or now
The idea is premised on the concept of the time value of money. The idea that $1 today is not the same as $1 tomorow. The $1 of today is worth more than that of tomorrow; and because of the opportunity to earn interest.
So if an asset (e.g a stock) promises some cash flows in the future, those cash flows need to be brought to their present values and then be added to arrive at the value of the asset
The process of calculating the present value of a future sum is called discounting. So to calculate the stock price in this question, we shall discount the future dividends using the required rate of return and then add them together.
This is done as follows:
PV of Div. in year 1= 1.00/(1.10)= 0.909
PV of Div. year 2= 1.20/(1.10)²= 0.992
PV of Div in year 3= 1.44/(1.10)³=0.082
PV (in year 3) of Div payable in year 4 and beyond = (1.44×1.05)/(0.10-0.05)= 30.24.
PV (in year 0) of Div payable in year 4 and beyond= 30.24/(1.10)³= 22.720
Stock price = Sum of the PV of the future dividends
=0.909+0.992+0.082+22.720= $24.703
