Question

Suppose the portfolio of a large institutional investor “Parthenon” has an expected return of 13 percent and its beta relative to the market portfolio is 2, while its return’s standard deviation is 8 percent. Suppose there is a firm called “Atlantis”, whose equity beta is 2. The equity value of “Atlantis” is £1 million and its debt is worth £1.5 million. Its debt is a consol bond (i.e. perpetual bond) with an annual coupon of £45,000. The present value of the tax shield for “Atlantis” is £0.45 million. The risk free rate is 1 percent. Assuming that CAPM (Capital Asset Pricing Model) holds, answer the following questions.

a) What should be the expected return on the market portfolio?

b) What should be the standard deviation of the market portfolio's return?

c) What is the interest rate at which “Atlantis” is borrowing (before tax)?

d) Assuming the Modigliani-Miller theorem with corporate taxes, what should be the cost of equity for “Atlantis” when it is unlevered?

e) Suppose that the increase in the costs of financial distress for “Atlantis” is £0.2 for a marginal increase (i.e. £1) in its debt from the current capital structure. Assuming that the predictions of the trade-off theory hold, what can we say about the optimal capital structure for “Atlantis”? Explain.

Answer 1

A) CAPM model:

E(R)=Risk Free Rate + B(R_m-R_f)

=13=1+ 2(R_m-1)

=12=2R_m-2

=14=2R_m

=R_m=7

Hence, the expected return on the market portfolio is 7%.

B) Standard Deviation of Market Portfolio :

2=8/SD of Market Portfolio

SD of Market Portfolio =4 %

  

C) The cost of borrowing is:

45,000/1,500,000= 3%

D) First we will calculate the unlevered Beta (B_u)

B_u=B_L/(1+(1-T)*(D/E)

     =2/(1+(1-0.10)*(1.5/1)

     =2/(1+1.35)

      =0.85

Therefore, unlevered cost of capital:

1+0.85*(7-1)

=6.1%