Question

United Birdseed is expected to pay the following dividends over the next three years: After year 3, dividends are expected to grow by 5% per year forever. The expected/required return on United Birdseed stock is 10%. What is the stock price?

Answer 1

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