Problem $1(10\%)$

For an initial investment of $$100$ this year, a project will generate cash flows of equally likely

either $$140$ with $50\%$ chance or $$90$ with also $50\%$ chance next year. Assume you use no

leverage and create an all$-$equity firm. An investor who would prefer to hold "levered equity"

can do so by using leverage in his own portfolio. Assuming the initial cost of unlevered equity is

$$100,$ the initial cost of levered equity is $$50,$ and the risk$-$free interest rate is $5\%.$

Explain how MM $(1958)$ proved Proposition I using "homemade leverage."