This is a 1-period model, where a firm invests A > 0 to generate risky cash-flows C. There are 2 states of the world C {CL, CH }. Assume the following:

The respective cash flows in these states are CL and CH , with CL < A < CH . TherespectiveprobabilitiesarepL andpH,withpL+pH =1andpHCH+pLCL A(1+rf).

The risk associated to these cash-flows is diversifiable and the risk-free rate is rf > 0. The face value of debt is D, which pays an interest rate r such that the debt is issued at face value. In case of bankruptcy, there is a cost (D(1 + r) C), where [0, 1] is parameter.

1. Consider D(1 + rf ) > CL. What is the condition on CH for the firm to be able to raise D from investors in a competitive market?

2. Solve for the investor break-even interest rate r, as a function of D.

3. For the following benchmark values, does the condition on CH hold? D=105,CH =130,CL =60,rf =0.03,pH =0.65,pL =0.35,=0.1

Now,defineearningsas:1 w=CArD.

The tax system works in the following way: when earnings are negative the firm pays zero taxes and there is no tax credit, if earnings are positive there is a two-bracket tax system

-A tax rate 1 is applied on the first w earnings

-A tax rate 2 > 1 is applied on earnings in excess of w Example: if w = 100 and earnings are equal to 150, then the tax payment is T = 1001 + (150 100)2 .

4. Using the following benchmark values, build a spreadsheet to get value of the tax shield as a function of CH and plot it on a graph. Report you analytical reasoning. Consider only CH such that pHCH +pLCL A(1+rf). A=75,D=70,CL =60,rf =0.03,pH =0.65,pL =0.35,=0.1,1 =0.2,2 =0.3, w = 20. Find r(D) with the formula computed above.

(Hint: the tax shield is the difference in the tax payment between the unlevered and the levered firm)