Question

Consider the following information: BB BBB AA AAA Rating 12.2% 5.5% 2.2% 0.45% 0.2% 0.1% 0.0% Average Default Rate 48.0% 16.0% 8.0% 3.0% 3.0% 1.0% Recession Default Rate 0.0% 0.31 0.26 0.17 0.05 0.10 0.05 0.05 Average Beta Debt Rating Total Enterprise Value ($mm) Equity Beta Market Company Capitalization (Smm) Taggart Transcontinental 4500 8000 1.1 BBB Rearden Metal 3800 7200 1.3 AAA Wyatt Oil 2400 3800 0.9 Nielson Motors 1500 4400 1.75 BB What is your estimate of the debt beta for Taggart Transcontinental? What is your estimate of the asset beta for Nielson Motors? Suppose that because of the large need for steel in building railroad infrastructure, Taggart Transcontinental and Rearden Metal decide to form into one large conglomerate. Your estimate of the asset beta for this new conglomerate is closest to: A) 0.42. B) 0.59. C) 0.66. D) 0.68.

Answer 1

Answer(1):

We are given with a rating of BBB for Taggart Transcontinental. The corresponding debt beta for BBB from the rating table would be 0.10

Answer(2):

We are given with a rating of BB for Nielson motors. The corresponding debt beta for BB from the rating table is 0.17

Now to calculate the asset beta we use the formula

u = (E/V)*E + (1 - (E/V))*D

where V is the Enterprise value and E is the market capitalization.

=>  u = (1500/4400)*1.75 + ((4400-1500)/4400) * 0.17 ( Since E = 1.75)

=> Asset beta = 0.71

Answer(3):

We are given with a rating of BBB for Taggart Transcontinental. The corresponding debt beta for BBB from the rating table would be 0.10

=> Asset beta for Taggart would be  

= (4500/8000)*1.1 + ((8000-4500)/8000)*0.10 = 0.663 (Using the equation from above)

Simlarly, We are given witha rating of AAA for Raerden . The corresponding debt beta for AAA from the rating table would be 0.05

=> Asset beta for Raerden would be

= (3800/7200)*1.3 + ((7200-3800)/3800)*0.05 = 0.710

Now Asset beta of the conglomerate would be the weighted average of the individual asset betas w.r.t to their Enterprise Value.

=> $\beta$ _combined = (8000/(8000+7200))*0.663 + (72000/(7200+8000))*0.710 = 0.685

Option D is the correct answer

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