Question

Moody Farms just paid a dividend of $3.05 on its stock. The growth rate in dividends is expected to be a constant 5 percent per year indefinitely. Investors require a return of 12 percent for the first three years, a return of 10 percent for the next three years, and a return of 8 percent thereafter. What is the current share price? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

Answer:

The price of the stock today is $96.06

Explanation:

The price of a stock whose earnings are expected to grow at a constant rate forever can be calculated using the dividend discount model which bases the price of a stock on the present value of the expected future dividends from the stock.

As the required rate of return is changing, we will calculate the price in three stages.

The formula for price today under this model is in the given situation is,

P0 =  D1 / (1+r1)  + D2 / (1+r1)^2  + D3 / (1+r1)^3  + D4 / (1+r2)^4  + D5 / (1+r2)^5 +

D6 / (1+r2)^6  + [ D7 / (r3 - g) ] / (1+r2)^6

Where,

• D1, D2, ... D7 represents the dividend in year 1,2, ... 7 (till Year 7)
• r represents the required rate of return
• r1 is 12%
• r2 is 10%
• r3 is 8%

So, price of the stock today is,

P0 = 3.05 * (1+0.05) / (1+0.12)  +  3.05 * (1+0.05)^2 / (1+0.12)^2  +  

3.05 * (1+0.05)^3 / (1+0.12)^3  +  3.05 * (1+0.05)^4 / (1+0.10)^4  +  

3.05 * (1+0.05)^5 / (1+0.10)^5  +  3.05 * (1+0.05)^6 / (1+0.10)^6  +  

[3.05 * (1+0.05)^7 / (0.08 - 0.05)] / (1+0.10)^6

P0 = $96.06