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BLC industries is expected to pay a dividend of $1.50$ and the dividend is expected to grow at a constant rate of $7$%. This stock is $15$% less risky than the market as a whole. The risk-free rate is $6$%, and the equity risk premium for the market is $8$%. Find the estimated price of the stock.

Using the $r_{CAPM}$ to find effective rate of return.

$r=r_f + \beta (r_m-r_f)$

$r= 0.06+0.15(0.08-0.06)=0.63$

$Price=\frac{D_0(1+g)}{r-g}=\frac{1.50(1+0.07)}{0.063-0.07}$

It is here that I do not see the logic since denominator is negative.

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A beta of less than 1 means that the security will be less volatile than the market. A beta of greater than 1 indicates that the security's price will be more volatile than the market. For example, if a stock's beta is 1.2, it's theoretically 20% more volatile than the market.

In a similar reasoning, $15\text{%}$ less volatile (risky) than the market means beta is $0.85$.

Now go ahead do the calculation with $\text{expected return} = 0.06+.85(0.08-0.6) = 0.077$ $Price=\frac{D_1}{r-g}=\frac{1.50}{0.077-0.07} = 214.3$

It is as simple as this.

Goodluck

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  • $\begingroup$ @Sirus Black, I changed the solution a bit to take care of the fact that dividend is "expected to pay" which itself is $D_1$. Only if it is a divident that is just pay shall you use $D_0(1+g)$ else just use $D_1$. Sorry for the error in my solution and correct your understanding. $\endgroup$ May 20, 2016 at 7:17

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