Consider the example in slide $6,$ lecture $10.$ Find a risk$-$free arbitrage

strategy similar to the one in slide $7$ if the shares of Somedebt are sold at

$$110$ per share. So the share price of Somedebt must be sold at exactly

$$100$ per share, which is the same as the share price of Nodebt stock. This

illustrates the MM theorem on the irrelevance of financial structure. Slides $7$ example: Nodebt Corporation $$10$M EBIT $=$

Dividends, required rate of return on equity k$=10\%,$

V $=$ $$100$M$,$ P $=$ $$100$

Somedebt Corporation: $$40$M debts, $8\%,$ $$3\mathrm{.}2$ M

per year;

$$ MM: $$60$M equity

$$ P$*(1$M$-$x$)=$ $$60$M$,$ P$*$x $=$ $$40$M

$$ P $=$ $$100,$ x $=400,000.600,000$ shares outstanding; $I$f share price of Somedebt is $$90$: Risk$-$free arbitrage

opportunity

$-$ Sell$-$short $1\%$ of the shares of Nodebt stock at $$100$ per share

$-$ Buy $1\%$ of the shares of Somedebt at $$90$ per share and buy $1\%$ of

the bonds of Somedebt

$-$ Riskless profit: $$60,000$

b$)$ Now, as I mentioned in class, this example is not reasonable, because even

if the share price of Somedebt stock is $$100,$ we can still find another risk$-$

free arbitrage strategy, which is to buy either Somedebt shares or Nodebt

shares and short bonds. Detail the arbitrage strategy and its cash flow.

c$)$ A more robust example of the MM theorem is to assume that EBIT has

equal probabilities of being $$15$M or $$5$M per year. Show that the strategy

in part a is still a risk$-$free arbitrage if the share price of Somedebt stock is

$$110$; however, the strategy in part b is no longer a risk$-$free arbitrage.

d$)$ Use the formula in slide $19,$ Lecture $11$Cost of Equity Capital

ke $=$ k $+($k $$ r$)$ D$\frac{?}{E},$ ke $=$ k $+(1-t)($k $$ r$)$ D$\frac{?}{?}$E