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Sir please I want an explanation of how the answer was arrived at
Four companies are identical in all respect,except for their capital structures, which are as follows
A plc B plc C plc D plc
%. %. %. %.
Equity as proportion
Of total market
capitalization 70. 20. 65. 40
Debt as a portion
Of total market
capitalization 30. 80. 35. 60The equity beta of A plc is 0.89 and the equity beta of D plc is 1.22
Within which ranges will the equity betas of B plc and C plc lie?
A. The beta of B plc and the beta C plc are both higher than 1.22
B. A. The beta of B plc is below the beta of C plc in a range 0.89 to 1.22
C. A. The beta of B plc is above 1.22 and the beta of C plc in the range 0.89 to 1.22
D. A. The beta of B plc is in the range 0.89 to 1.22 and the beta C plc higher than 1.22The answer is C
if i try this question
we just need to find asset beta by degeering the equity beta of A plc or D plc. since they are identical their Asset beta will be same. so for instance we will use A.plc
At fist find asset beta= 0.89x(70/100)=0.623
second regear the asset beta to find B plc equity beta by using the capital structure of B plc = 0.623 x (100/20) =3.115
same step with C plc. degear asset beta using capital structure of C plc = 0.623 x (100/65) = 0.958.
then option c will only match the findings.
As I explain in my free lectures, higher gearing creates more risk for shareholders and therefore a higher equity beta.
B plc has higher gearing than D plc and therefore the equity beta will be higher than D’s equity beta of 1.22.
C plc has gearing in between that of A and D and therefore the equity beta will be between that of A and D.
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