Nero Violins has the following capital structure: Security Beta Total Market Val

Question

Nero Violins has the following capital structure:

  Security Beta Total Market Value
($ millions)
  Debt 0         $ 119   
  Preferred stock 0.39         59   
  Common stock 1.39         318   

a.What is the firm's asset beta? (Hint: What is the beta of a portfolio of all the firm's securities?) (Do not round intermediate calculations. Round your answer to 3 decimal places.)

Asset beta   

b.Assume that the CAPM is correct. What discount rate should Nero set for investments that expand the scale of its operations without changing its asset beta? Assume a risk-free interest rate of 4% and a market risk premium of 5%. (Do not round intermediate calculations. Round your answer to 3 decimal places.)

  Discount rate %  

Explanation / Answer

Asset beta is the weighted average of all betas:

Asset beta = (Bd x Vd + Bp xVp + Bc x Vc)/ (total assets)

                     = ( 0x119 + 0.39 x59 + 1.39 x318)/(119+59+318)

                      = 465.03/496

                      = 0.938

b)

Cost of capital = Rf + MRP x beta

                                = 4% + 5% x 0.938

                                = 8.69%

Discount rate = 8.69%

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