Question

Simpson Inc. is considering a vertical merger with The Lachey Company. Simpson currently has a required return of 11%, while Lachey's required return is 15%. The market risk premium is 5% and the risk-free rate is 5%. Assume the market is in equilibrium. If Simpson is going to make up 67% of the new firm (and Lachey will comprise the remaining 33%), what will be the beta of the new merged firm? There will be no additional infusion of debt in the merger.

Answer 1

Required return=	Risk free rate + Beta * Risk premium
Simpson Inc.
11%=	5% + Beta * 5%
Beta=	(11%-5%)/5%
Beta=	1.2
Lachey Company
15%=	5% + Beta * 5%
Beta=	(15%-5%)/5%
Beta=	2
New structure	Weight	Beta	Weighted Beta
Simpson Inc.	67%	1.2	0.80
Lachey Company	33%	2	0.66
		Total	1.46
So combined beta should be 1.46