Suppose an entrepreneur invests in two projects that are identical in all respects

except in terms of their financing. Each of the projects requires an initial investment

of 10 million today (at date 0) and is expected to generate a single cash flow at the

end of the year (at date 1). The cash flow at date 1 is either 20 million or 12 million

with equal probability depending on the state of the economy. The entrepreneur

decides to finance one project (the unlevered project) by selling all the shares in the

unlevered project for 10 million and using the sales proceeds to finance the initial

outlay of 10 million using 100% equity finance. To finance the other project (the

levered project), she issues 5 million worth of debt and by selling all the shares in

the levered project she just manages to raise the remaining 5 million in the form of

levered-equity finance. The debt is assumed to be risk-free and the risk-free interest

rate is 2%. All debt and equity are traded in perfect capital markets.

a) How could an investor replicate the payoffs from an investment in the equity of

the unlevered project by investing in the securities of the levered project? Derive

and show the investors payoffs in each case at dates 0 and 1.

(5 marks)

b) Now suppose the investor prefers levered equity. How could the investor replicate

the payoffs from the equity in the levered project by investing, among other

things, in the unlevered project? Derive and show the investors payoffs in each

case at dates 0 and 1.