Question

What is the value of a common stock if: 

a. the firm's earnings and dividends are growing annually at 4 percent, the current dividend is $1.32, and investors require a 8 percent return on investments in common stock?

b. What is the value of this stock if you add risk to the analysis and the firm's beta coefficient is 0.8, the risk-free rate is 1.5 percent, and the return on the market is 8.5 percent?

c. If the price of the stock is $35, what is the rate of return offered by the stock? Should the investor acquire this stock?

Answer 1

The value of the stock can be calculated with help of constant dividend growth model. According to this model,

where, Po is the current market price.
D0= Dividend just paid by company.
g = Growth rate
Ke = cost of equity

Here,

A)

D0 = 1.32$

g = 4 %

Ke = 8 %

Po = 34.32 $

Value of the stock = 34.32 $

B)

According to capital asset pricing model -

E(Ri) = Rf + ( E(Rm) - Rf ) * beta of security

where,
E(Ri) = Expected return on security i
rf = risk free return
E(Rm) = Expected market return

Expected return on security = 1.5 + ( 8.5 - 1.5) * 0.8

= 1.5 + 7 * 0.8

= 1.5 + 5.6

= 7.1 %

Required rate = 7.1 %

The value of the stock can be calculated with help of constant dividend growth model. According to this model,

Po = 44.284 $ (approx)

Value of the stock = 44.284 $

c) Here, price of the stock is given as $ 35, rate of return (ke) can be calculated as -

35 ( Ke - 0.04) = 1.3728

35Ke - 1.4 = 1.3728

35Ke = 1.3728 + 1.4

35Ke = 2.7728

Ke = 2.7728 / 35

= 0.0792 (approx)

= 7.92 %

rate of return = 7.92 %

Based on CAPM equation, Required rate is 7.1 %.

As the stock is providing more return (7.92 %) than the required return, investor should acquire the stock.