Question

An all-equity company A has 10 shares outstanding. Its equity Beta is 1.25 and its perpetual annual operating cashflow is expected to be $92. This company is considering acquisition of company B which has 5 shares outstanding, an equity Beta of 2/3 and its perpetual annual operating cashflow is expected to be $16. The expected market return is 10% and the risk-free interest rate is 4%.

1. What would the price per share of company A shares if it acquires Company B with $240 cash payment?
2. What would be the price per share of Company A shares if instead of $240 cash payment, it issues its shares currently worth $240 to company B?
3. Explain with calculations the difference, if any, in Company A share prices in parts b and c.

Answer 1

a). CAPM of Company A (Ke) = Rf + (Rm-Rf)

= 4% + 1.25 (10%-4%)

Ke  = 11.5%

Market Value of shares of company A = Annual Operating Cashflow / Ke

= 92/11.5%

= 800

Market price per share = Market Value / No. of Shares

= 800 / 10

= 80 per share

CAPM of Company B (Ke) = Rf + (Rm-Rf)

= 4% + 2/3(10-4)

= 8%

Market Value of shares of company A = Annual Operating Cashflow / Ke

= 16/8%

= 200

Market price per share = Market Value / No. of Shares

= 200/5

= 40 per share.

Price per share of company A shares if it acquires Company B with $240 cash payment

  Market price per share(A+B) = (Market Value of A +Market Value of B) / No of Shares

= (800+240) / 10

= 104 per share

b) Price per share of Company A shares if instead of $240 cash payment, it issues its shares currently worth $240 to company B

Market price per share(A+B) = (Market Value of A +Market Value of B) / No of Shares

= (800 + 200) / 16(Note 1)

= 62.5 per share

Note 1: Calculation of no. of shares issued to company B

= 240 / 40

= 6

c) 1) When the cost of merger is calculated on the cash consideration and when cost of merger is unaffected by the merger gains.

(2) But when merger is based on the exchange of shares then the cost of merger depends on the gains which has to be shared with the shareholder of B Ltd