Question

El Taco Tote just paid a dividend of D₀ = $1.75 per share, and that dividend is expected to grow at a constant rate of 5.50% per year in the future. The company's beta is 1.50, the required return on the market is 9.50%, and the risk-free rate is 3.50%. What is the company's current stock price?

Answer 1

Solution:

As per the Capital Asset Pricing Model (CAPM)  the Required rate of return of a stock can be calculated using the following formula:

R_E = R_F + [ β * ( R_M - R_F ) ]

Where

R_E = Required rate of return of a stock   ; R_F = Risk free rate of return   ; β = Beta of the stock ;

R_M = Required Return on the market

As per the information given in the question we have

R_F = 3.50 %   ;     R_M = 9.50 %   ;    β = 1.50

Applying the above values in the formula we have

= 3.50 % + [ 1.50 * ( 9.50 % - 3.50 % ) ]

= 3.50 % + [ 1.50 * 6 % ]

= 3.50 % + 9 %

= 12.50 %

Thus the required rate of return = 12.50 %

The current price of a stock is calculated using the following formula:

P = [ D₀ * ( 1 + g ) ] / ( k_e – g )

Where

P = Current stock price ;      D₀ = Recent dividend paid ; g = growth rate ;

k_e = Required rate of return of a stock

As per the information given in the question we have :

D₀ = $ 1.75 ;       g = 5.50 % = 0.055 ;    k_e = 12.50 % = 0.125

Applying the above values in the formula we have

= [ 1.75 * ( 1 + 0.055 ) ] / ( 0.125 – 0.055 )

= ( 1.75 * 1.055 ) / 0.07

= 1.8463 / 0.07

= $ 26.375

= $ 26.38 ( when rounded off to two decimal places )

Thus the Company’s current stock price = $ 26.38