Question

stock that has a current price of $25.00, a beta of 1.25, and a dividend yield of 6%. If the Treasury bill yield is 5% and the market portfolio is expected to return 14%, what should MUSS’s stock sell for at the end of an investor's two year investment horizon?

Answer 1

$30.2067

Step-by-step explanation:

From the given question, using the dividend discount model

`V_0 = (D_1)/(r - g)`

where:

r is the Expected return on stock and be calculated as:

Expected return on stock = Risk free rate + Beta × (Expected Market Return - Risk free rate)

Expected return on stock = 5% + 1.25 × (14% - 5%) = 16.25%

However, the current price in this process will b used as the dividend price for all future expenses.

Dividend Yield = Current Dividend/The Share Price

Current dividend D0 = 6% × $25.00 = $1.50

D₁ = D₀ × (1 + g)

D₁ = 1.5 × (1 + g)

Thus, we can now employ the use of the growth dividend model (constant) to determine the value of g as follows:

`25 = (1.5 * (1 + g))/(0.1625 - g)`

By cross multiply, we have:

4.0625 - 25g = 1.5 + 1.5g

collect like terms, we have:

4.0625 - 1.5 = 1.5g + 25g

2.5625 = 26.5g

Divide both sides by 26.5, we have:

2.5625/26.5 = 26.5g/26.5

g = 9.67%

Similarly, suppose the value for the second year-end to be Y₂;

Then the constant growth dividend model can be computed as:

`Y_2 = (D_3)/(r - g)`

where;

D₃ = D₂ × (1 + g)

D₂ × (1 + g) = D₁ × (1 + g) × (1 + g)

D₁ × (1 + g) × (1 + g) = D₀ × (1 + g) × (1 + g) × (1 + g)

D₁ × (1 + g) × (1 + g) = D₀ × (1 + g) × (1 + g) × (1 + g) = D₀ × (1 + g) × 3

D₃ = 1.5 × (1 + 9.67%) × 3

D₃ = $1.9876

Finally:

`Y_2 = (D_3)/(r - g)`

`Y_2 = (1.9876)/(0.1625 - 0.0967)`

Y₂ = $30.2067