Question

Suppose two companies X and Z have exactly the same operating characteristics and their business risks are perfectly correlated (i.e., exactly the same cashflows). They differ only in the way they finance their operations. Both companies will be liquidated exactly one year from now and shareholders will receive a liquidating dividend at the end of the year. Company X is expected to pay a liquidating dividend of $55 million, but this is uncertain, so shareholders discount this dividend at a rate of 10%. Z has issued bond to finance its operations. Currently Z’s securities are trading as follows:

Bonds	$10 million
Shares	$42 million

The bonds are AAA rated and the expected return is the same as on the risk free asset which is 5%.

1. Suppose company X has 2,500,000 shares outstanding. What is the current share price of X?
2. What is the total valuation of company Z’s assets today
3. Show how you can set up an arbitrage portfolio in order to benefit from any mispricing of companies X and Z relative to each other.

Answer 1

a). Solution :- Expected dividend per share = Dividend amount / Number of shares outstanding.

= 55000000 / 2500000

= $ 22

Current share price = Expected dividend per share / Discount rate.

= 22 / 0.10

= $ 220.

Conclusion :- Current share price of Company X = $ 220.

b). Total value of assets of Company Z = Valuation of bonds + Valuation of shares.

= 10 Million + 42 Million

= $ 52 Million.

Conclusion :- Total value of assets of Company Z = $ 52 Million.