FI $414$ Stock Pricing Problems

Use the following data for questions $1$ through $4.$

Stock A has a systematic risk of ${}_A=1\mathrm{.}5.$ The risk$-$free rate is $r_F=2\%$ and the return on the

market portfolio is $\frac{?}{\text{b}\text{a}\text{r}}(r{)}_M=12\%.$ The last dividend paid was $D_0=$$$2\mathrm{.}25.$ The growth rate of

dividends in the first period is $g_1=3\%,$ and from the second period on is $g_{2+}=2\%.$

The required rate of return for A is

a$.2\%$

b$.12\%$

c$.3\%$

d$.17\%$

e$.1\mathrm{.}5\%$

$\frac{?}{\text{b}\text{a}\text{r}}(R{)}_A=R_F+{}_{A^{}}(\frac{?}{\text{b}\text{a}\text{r}}(R{)}_M-R_F)$

$=\mathrm{.}02+1\mathrm{.}5(\mathrm{.}12-\mathrm{.}02)$

$=17\%$

a$.$ $$16\mathrm{.}55$

b$.$ $$15\mathrm{.}45$

c$.$ $$15\mathrm{.}76$

d$.$ $$19\mathrm{.}31$

$D_1=D_0(1+g_1)$

$D_1=2\mathrm{.}3175=2\mathrm{.}25(1+\mathrm{.}03)$

$D_2=2\mathrm{.}295=2\mathrm{.}25(1+\mathrm{.}02)$

e$.$ $$13\mathrm{.}24$

The price at time $1,P_0,$ is

a$.$ $$16\mathrm{.}55$

b$.$ $$15\mathrm{.}45$

c$.$ $$15\mathrm{.}76$

d$.$ $$19\mathrm{.}31$

e$.$ $$13\mathrm{.}24$

If the actual rate of return is $14\%,$ Stock A$\text{'}$s price is $$19\mathrm{.}31,$ and

I. Stock $A$ is overpriced and should be sold

II$.$ Stock A has a Jensen's Alpha of $-3\%$

III. Stock $A$ is in equilibrium

a$.$ I only

b$.$ II only

c$.$ III only

d$.$ I and II only

e$.$ I, II$,$ and III

A preferred stock has a par value of $$25$ and pays a constant dividend based on a dividend yield

of $6\%.$ If the price is currently $$20,$ the required rate of return is$,$

a$.3\%$

b$.7\mathrm{.}5\%$

c$.3\mathrm{.}75\%$

d$.10\%$

e$.4\%$