Pi X Corp has an estimated beta of $1\mathrm{.}8.$ The Australian Govt $10-$year bond is yielding $4\mathrm{.}5\%$ p$.$a$.,$ and the estimated market risk premium is $5\%$ p$.$a$.$ The latest annual dividend of $$1\mathrm{.}25$ a share was paid yesterday and maintained its historic $7$ percent annual rate of growth. You plan to purchase the stock today because you believe that the dividend growth rate will increase to $8$ percent p$.$a$.$ for the next two years and the selling price of the stock will be $$40$ per share at the end of that time $($i$.$e$.$ the end of two years$).(3$ marks$).$

Estimate

$($a$)$ Pi X Corp required rate of return. $(1$ mark$).$

$($b$)$ Pi Corp stock value. $(2$ marks$).$

$[$Remember to quote "Formula number #$"$ and show your workings by typing in the variable$/$number that matches the formula$]$

$[1]E(R_i)=RFR+{}_i(E(R_M)-RFR)$

$[2]V=\frac{D}{k_p}$

$[3]k_p=\frac{D}{P}$

$[4]V_j=\frac{D_1}{(1+k)}+\frac{D_2}{(1+k{)}^2}+\frac{D_3}{(1+k{)}^3}+$dots$+\frac{D_{}}{(1+k{)}^{}}={\displaystyle \underset{t=1}{\overset{n}{}}}\frac{D_t}{(1+k{)}^t}$

$\frac{5}{b}ar(g)=\sqrt[\phantom{2}]{\frac{D_n}{D_0}}-1$

$[6]V_o=\frac{D_0(1+g)}{k-g}$

$[7]V_t=\frac{D_{t+1}}{k-g_c}$

$8$

$V_j=\frac{D_1}{(1+k)}+\frac{D_2}{(1+k{)}^2}+\frac{S{P}_{j2}}{(1+k{)}^2}$

$V_j=\frac{D_1}{(1+k)}+\frac{D_2}{(1+k{)}^2}+\frac{S{P}_{j2}}{(1+k{)}^2}$

$[9]$

$[10]$

FCFE$=NI+NCC-$FCI $$nv $-$ WCInv$+$ Net borrowing

Tax rate