$1.$ Sanford can choose either a safe or a risky project. To keep things simple, let each project cost$$100.$ A safe project yields $$110$ with certainty, while a risky project is equally likely to yield $$208$ or zero. Sanford needs financing for $50$ percent of the cost of his project. Lenders cannot observe his

choice of project. Everyone is risk neutral, and the risk$-$free rate is $6\%.$

a$.$ If Sanford were to sell $$50$ worth of bonds with face value equal to $$53,$ in which project would he invest? Justify your answer. How much would bondholders get paid, on average?

b$.$ How much face value would Sanford need to offer lenders in order to sell $$50$ worth ofbonds?

c$.$ Is Sanford willing to offer the face value required to sell bonds? Explain.

d$.$ Is Sanford willing to finance a project by selling shares? Are savers willing to purchase his shares? Does financing with equity yield an efficient equilibrium?

$2.$ Eschara needs to borrow $$300,000,$ and the risk free rate is $4\%.$ She can try to obtain financing by selling either debt or equity. Eschara$$s job pays a salary of $$60,000$ per year. If she works hard, she has a $50$ percent chance of getting a promotion and an increase in her salary to $$84,000.$ If Eschara

devotes minimal effort to her job, her salary will remain at $$60,000.$ Eschara$$s disutility of working hard is $$11,000.$ Everyone is risk neutral, and all the surplus goes to Eschara. Assume asymmetric

information.

a$.$ How much is Eschara$$s annual cost of funds?

b$.$ Hard work generates how much surplus? Explain.

c$.$ In an equity sale, Eschara must try to sell at least a $1/6$ share. Why?

d$.$ If savers were to accept a $1/6$ share, would Eschara work hard? Show your

computations. How big a share do savers require?

e$.$ In equilibrium, does she obtain financing by using debt or by using equity? Show your computations. Is the equilibrium efficient?

f$.$ Would savers accept a $1/6$ share if information were symmetric? Explain.