Question

Firm A plans to acquire Firm B. The acquisition would result in incremental cash flows for Firm A of $10 million in each of the first five years. Firm A expects to divest Firm B at the end of the fifth year for $100 million. The beta for Firm A is 1.1, which is expected to remain unchanged after the acquisition. The risk-free rate, Rf, is 7%, and the expected market rate of return, Rm is 15%. Firm A is financed by 80% equity and 20% debt, and this leverage will remain unchanged after the acquisition. Firm A pays interest of 10% on its debt, which will also remain unchanged after the acquisition.
i) Disregarding taxes, what is the maximum price that Firm A should pay for Firm B?



ii) Firm A has a stock price of $30 per share and 10 million shares outstanding. If Firm B shareholders are to be paid the maximum price determined in part (a) via a new stock issue, then how many new shares will be issued and what will be the postmerger stock price?

Answer 1

according to capm expected return=R_f+beta(R_m-R_f)

given that Rf=7% Rm=15% Beta=1.1

Expected return=7+1.1(15-7)=7+8.8=15.8

Re=15.8% return on equity equity %=80

Rd=10%     return on debt     debt %=20

Average cost of capital=15.8(0.8)+10(0.2)=14.64

firm recieves $10million for five years so

present value=c(1-(1+i)^-5)/(i)

P1=present value=10(1-(1+0.1464)^-5)/(0.1464)=10(1-0.505)/0.1464=10x3.38=33.8$million

After 5 years 100$ million would be recieved

P2=Present value=100/(1+0.1464)⁵=100/1.98=50.50

Total value=P1+P2=33.8+50.50=84.30

Total present value=84.3$million

That is maximum price should A for Firm B at present=84.3$million         Answer(1)

As said same capital structure will be maintained so

Equity capital=0.8x84.3=67.44$ million

Price of one equity share=30

So shares to issued=67.44/30=2.248 million shares would issued

So 2.248 million shares would be issued                Answer(2)

Total shares after merger=10+2.248=12.248 million shares

Initial equity capital=30x10 million

New Equity value=300/12.248=24.49=24.5$

Post merger value of share=24.5$                        Answer(3)