In: Finance
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%.
(a) Suppose company X has 2,500,000 shares outstanding. What is the current share price of X?
(b) What is the total valuation of company Z's assets today?
(c) 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.
(a) | |||||||
Company X is expected to pay a liquidating dividend of $55 million | |||||||
Dicount factor is 10% | |||||||
So valuation of Company X = $55Million/(1+10%) | |||||||
= $ 50 Millions | |||||||
(b) | |||||||
Total valuation of company Z's assets today = Bonds Value + Shares | |||||||
= $10 Million + $42 Million | |||||||
= 52 Million. | |||||||
Shares outstanding = 2,500,000 | |||||||
Curent price of X is $52,000,000/2,500,000 = $20.8 per share. | |||||||
('c) | |||||||
Both the company has same operating characteristics and their business risks are perfectly correlated (i.e., exactly the same cashflows) except t in the way they finance their operations. Their financing operation has been discounted adequately. | |||||||
Hence, their present valuation should be same after adjusting for risk involved.. | |||||||
We should enter into long position for company X and short position for Company Z |