(Forward Price, Dividend, and Value of Existing Forward Contracts

) The risk-free

interest rate is fixed at 5% per annum with continuous compounding for all maturities. ABC is

a public firm that pays no dividend.

(1 points)

(10.1)

On Feb 1st, the spot price of ABC is $51. Find the one-year forward price of ABCs stock.

(1 points) On Sep 1st, spot price of ABC becomes $53. Find the 5-month futures price of ABC.

(10.2)

(1 points)

(10.3)

Suppose Bill entered into a

short

position of 1 million shares of ABC on Feb 1st using a

one-year forward contract. On Sep 1st, what is the value Bills position?

(1 points)

(10.4)

At 10 am on Oct 1st, spot price of the stock is $55. What is the four-month forward

premium of ABC?

(1 points)

(10.5)

At 10:01 am on Oct 1st, ABC unexpectedly announces that it will issue a one-time dividend

of $5 on Dec 1st. What is the present value of this one-time dividend?

(2 points)

(10.6)

Market reacts positively to the announcement. Spot price of ABC appreciates immediately

to $56 per share. What is the four-month forward premium of ABC right after the

announcement?

(1 points) What is the value of Bills forward contract right after the announcement?

(10.7)

(2 points)

(10.8)

Alternatively, the dividend could be paid out continuously from Oct 1st of this year to Feb

1st of the next year. What is the equivalent continuously compounded dividend rate that

would lead to the same forward premium?

(2 (bonus))