PROBLEM TWO $(6$ marks$)$

DCM Corp. has annual cost of debt and common equity of $R_B=8\mathrm{.}0\%$ and $R_S=18\mathrm{.}0\%$ It has $45,000$ corporate bonds outstanding, valued at $$987\mathrm{.}62$ each, and $36,500,000$ common shares with a market value of $1\mathrm{.}55$ each. DCM$\text{'}$s corporate tax rate is $35\%.$ DCM Corp. exists in a Modigliani and Miller with corporate taxes.

a$)$ What is the cost of capital for DCM Cop. $(1\frac{1}{2}$ marks$)$

b$)$ Draw and label a diagram $($label both axes$)$ showing the relationship of the cost of equity for the unlevered firm, the after$-$tax cost of debt, the cost of equity for the levered firm and the WACC in this M&M world. $(\frac{11}{2}$ marks$)$

c$)$ Suppose that in the M&M world describe, DCM Corp. decides to decrease financial leverage to zero, by moving to all$-$equity financing. Calculate DCM$\text{'}$s new cost of capital? $($Assume debt is essentially risk$-$free.$)(\frac{11}{2}$ marks$)$

d$)$ If the value of the firm is determined by the following equation:

$V_L=V_U+TcB-B^2$

where $P{V}_{\text{f}\text{i}\text{n}\text{a}\text{n}\text{a}\text{c}\text{i}\text{a}\text{l}\text{d}\text{i}\text{s}\text{t}\text{r}\text{e}\text{s}\text{s}costs}=B^2,$ and $B$ is in millions of dollars, what would the optimal level of debt be $($in millions of dollars, to $2$ decimal places$)?$ Verify that you have found the optimal level of debt $($for full marks$).(\frac{11}{2}$ marks$)$

Hint:

The first derivative is:

The second derivative is:

$V_L^{\text{'}}=Tc-2B$

$V_L^{\text{'}\text{'}}=-2$Ok