Question

Tony’s Gelati has the following capital structure: $100 Million in debt with a beta of 0; $40 Million of Preferred Stock with beta 0.2; and $200 Million of common stock with beta 1.2.

a) What is the firm’s asset beta?

b) How would the asset beta change if Tony issued an additional $140 Million of common stock and used the cash to repurchase all the debt and preferred stock?

c) Assuming CAPM, what discount rate should we use for investments that expand the scale of operations without changing the asset beta? Assume a risk premium of 8.6 and a treasury rate of 5.

Answer 1

A. Asset beta is 0.7294

B. Asset beta will increase to 1.2

C. Discount Rate as per CAPM is 11.27%

A)

Here

Debt = $100 Million

Debt beta = 0

Preferred Stock = $40 Million

Preferred Stock beta = 0.2

Common Stock = $200 Million

Common Stock beta = 1.2

Asset beta = ((Weight Of Debt * Debt beta) + (Weight Of Preferred * Preferred Stock beta) + (Weight of Common Stock * Common Stock beta)) / Total Weight

                 = ((100 * 0) +(40 * 0.2) + (200 * 1.2)) / (100+40+200)

                 = (0 + 8 + 240) / 340

                 = 248/340

= 0.7294117647

So the Asset Beta is 0.7294

B)

Now if all Debt and Preferred Stocks are paid off for $140 Million. So only the common stocks of value $340 Million will exist that has beta of 1.2

Here

Debt = 0 Million

Debt beta = 0

Preferred Stock = 0 Million

Preferred Stock beta = 0.2

Common Stock = $340 Million

Common Stock beta = 1.2

So Asset Beta = ((Weight Of Debt * Debt beta) + (Weight Of Preferred * Preferred Stock beta) + (Weight of Common Stock * Common Stock beta)) / Total Weight

= ((0 * 0) + (0 * 0.2) + (340 * 1.2)) / (0+0+340)

= (0 + 0 + 480) / 340

= 480/340

=1.2

So now Asset beta will increase to 1.2

C)

Original Asset beta = 0.7294

Treasury Rate = Risk Free rate = 5% = 0.05

Risk Premium = 8.6% = 0.086

Discount Rate or Cost of Capital = Risk Free rate + (Beta * market Risk Premium)

   = 0.05 + (0.7294 * 0.086)

   = 0.05 + 0.0627284

   = 0.1127284

    =11.27%

So Discount Rate as per CAPM is 11.27%