Question

Firm Z is the result of a merger between firm X and firm Y. Firm X was paying 2.50% on its debt and had a beta of 2.2. Firm Y was paying 3.50% on its debt and had a beta of 25. Firm X had 800 M$ assets and 30%-70% equity-debt structure while Firm Y had 200 MS assets and 20%-80% equity-debt structure. 1. What is the WACC of firm Z knowing that the size of the new entity allowed it to have a cost of debt of 1.5%and to have a beta of 1.75, and that the market where the three firms evolve has a premium of 6% and a risk free rate of 1.5%? 2. How does the WACC for Z compare to the WACC of X and Y? How do you explain this finding?

Answer 1

WACC=(E/TV​×Re)+(D/TV​×Rd×(1−Tc))

	Firm X	Firm Y	Firm Z
Beta	2.2	2.5	1.75
Rd	2.50%	3.50%	1.50%
Re	7.00%	10.25%	12.00%
Equity	800	200	1000
Debt	1866.669	800	2666.669
E/TV=	0.3	0.2	0.27
D/TV=	0.7	0.8	0.73
WACC	3.85%	4.85%	4.36%

So WACC of Z =

4.36%

WACC actually represents investor's opportunity cost in investing in an organization. so the WACC of Z is in between firm X and firm Y. so merger of two firms has provided synergies.