Prob1
Bergals School of Economics Spring1998/9 Tel Aviv University
PROBLEM SET1
Yossi Spiegel
Problem1
An all-equity firm expects to have an annual before-tax net operating income of50in perpetuity. The required ROR on the firm’s stock is20%.Assume that the corporate tax rate is40%and that there are no personal taxes.
(a)Compute the market value of the firm.
(b)Compute the market value of the firm under the assumption that the firm issues consol
bonds with face value60that carry an annual interest rate of10%and pays the proceeds to equityholders as a dividend.Explain the intuition for your answer.
(c)Repeat your answer to part(b)assuming that individuals pay a tax rate of30%on their
income from interest.As before,assume that income from equity is tax-exempt. Problem2
A firm has an expected annual cash flow of100in perpetuity,and the appropriate discount rate for these cash flows is10%.The risk-free interest rate is less than10%.The firm has100 shares outstanding.For simplicity assume that there are no taxes.
(a)What is the maximum price that investors would be willing to offer for each of the firm’s
shares?
(b)Compute the expected EPS and the EPS-price ratio for the firm.
(c)An analyst argues that a debt-for equity swap can increase the firm’s value since the new
debt will result in a higher EPS-price ratio.Evaluate this argument.
(d)Suppose that the firm eventually issues debt to increase the EPS-price ratio by2.
Compute the amount of5%perpetual debt that must be issued to achieve this goal.How many shares will be repurchased in the process and at what price?
2
(e)Summarize the post capital restructuring situation of the firm:What are the market
values of debt and equity,the cost of equity and average cost of capital,number of shares outstanding,the expected EPS,price per share,and EPS-price ratio.
(f)Are old shareholders of the firm better off,worse off,or just as well off as before? Problem3
The following question is based on the F.Modigliani’s article"MM-Past,Present,Future,"(J. Of Econ.Perspectives,Fall1988,pp.149-158).
Suppose that the financial policy of a firm is to maintain a debt level which is in a stable proportion to the expected cash flow of the firm.That is,if the expected cash flow of the firm is Xˉ,then the firm issues debt with face value D=dXˉ,where d∈[0,1).The interest rate on D is r.Assume that the corporate tax rate is t
C
and that all interest payments are tax deductible.
(a)Compute the total after-tax payoff to equityholders when d=0(i.e.,the firm is all-
equity).Using your answer,compute the market value of the firm.
(b)Compute the total after-tax payoff to the firm’s equityholders when d>https://www.wendangku.net/doc/3d4491552.html,ing your
answer,compute the market value of the firm.
(c)Using your answers to(a)and(b),express the value of a leveraged firm,V
L ,as a
function of an all-equity firm,V
U
.
(d)Compare your answer in part(c)to M&M’s Proposition1with corporate taxes.Explain
the difference.Which model predicts a larger impact of debt on firm value?What is the intuition for this?
Problem4
Consider the following variant of the Kraus and Litzenberger model we studied in class.The firm is established in period0and operates only in period1.The firm’s earnings are represented by
a random variable X?distributed uniformly over the interval[X
0,X
1
](that is,the probability that
earnings will be below some value z is0if z 0,1if z>X 1 ,and z/(X 1 -X )otherwise,and the mean earnings of the firm are(X 0+X 1 )/2).When the firm is established in period0it issues debt with face value D.Debt is due at the end of period1at which point the firm is liquidated and its equityholders and debtholders are paid according to their respective claims.If the firm cannot pay D in full it goes bankrupt.Bankruptcy imposes extra costs on debtholders,which are equal to C=b(D-X),b>1(assume that b is small enough to ensure that the limited liability constraint of debtholders is never violated).In addition,assume that the firm pays a corporate tax rate t C on its profits,the amount D is fully tax deductible,and the firm pays taxes only if it remains solvent. (a)Assume that D 0.Explain in words the meaning of this https://www.wendangku.net/doc/3d4491552.html,pute the market value of equity,E,and debt,B,and combine them together to compute the market value of the firm,V.How much debt will the firm issue if its objective is to maximize V?Explain the intuition for this result. (b)Assume that X 0 1 .Describe the payoffs of equityholders and debtholders for different values of X(in particular,specify the payoffs for X’s below D and X’s above D). Compute again the market values of equity,E,debt,B,and the market value of the firm,V. (c)Assume that the firm chooses D with the objective of maximizing V.Write the first order condition for the firm’s problem and explain in words the relevant https://www.wendangku.net/doc/3d4491552.html,pute the optimal level of debt,D*.How is D*affected by increases in b and t C ?Explain the intuition. Problem5 The following question is based on Kim"Miller’s Equilibrium,Shareholders Leverage Clienteles, and Optimal Capital Structure"(JF,1982,pp.301-319).A firm is established in period0and operates only in period1.The earnings of the firm are represented by a random variable X? distributed over the interval[X 0,X 1 ]according to a cumulative distribution function F(x).When the firm is established in period0it issues debt with face value D that is due at the end of period 1.If the firm cannot pay D in full it goes bankrupt and its debtholders become the residual claimant.Assume that the firm pays a corporate tax rate t C on its profits,the amount D is fully tax deductible,the firm pays taxes only if it remains solvent,and that investors pay a tax rate t E on income from equity and t D on income from debt. (a)Compute the market value of the firm when D=0(and denote it by V(0)). (b)Compute the market values of equity,E,and debt,B,when D>0. (c)Express the market value of the firm V(D),as a function of V(0)and compare your answer to Miller’s formula(equation(1)in topic2in my notes). (d)Suppose now that if the firm goes bankrupt,its debtholders incur a constant cost C such that C .Express again the market value of the firm,V(D),as a function of V(0). (e)Write the first order condition for D*and carefully explain its components.Then, express the first order condition in terms of the Hazard rate of the distribution of earnings. How is D*affected by the various tax rates?Explain the intuition for your result.