Calculate the risk premium and probabilities , Financial Management

Johnson & Johnson (JNJ) is trading at 68.15 (Sep 12th 2012 close). JNJ is a large health care conglomerate. It has done well so far this year (though not as well as the market) and may continue to do well. You believe that it is less vulnerable to the risks of the "fiscal cliff" and decide to take a closer look at it.

After careful analysis you conclude that in one year the price will be (44, 58, 71, 76, 91) with associated probabilities of (0.1, 0.2, 0.4, 0.2, 0.1). Looking at the company's past record you determine that JNJ will pay a dividend of 2.52 (two quarterly dividends of 0.61 and two quarterly dividends of 0.65). If you invest your funds risk-free in the money market you will receive 1%.

a. What is the expected return of JNJ stock? What is the risk premium of JNJ stock?

b. Calculate the standard deviation of the return of JNJ stock (remember that you are using probabilities to do this, not historical data).

You become convinced that this investment opportunity is a good one. In the current conditions

JNJ seems like a safe investment. You decide to buy JNJ stock on margin. You purchase 200 shares, financing half with your own investment and borrowing half from your broker.

c. How much do you borrow from your broker? What is your initial margin?

Tomorrow bad news reaches the economy and the price of JNJ stock drops to 44 immediately.

d. What is the new margin on the account? Do you receive a margin call? If you do, assume that you close your position immediately.

e. Calculate the return on your investment. What would the return have been if you had not borrowed any funds (Hint: what is the return on JNJ stock)?

 

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