A common stock pays an annual dividend per share of $2
1. A common stock pays an annual dividend per share of $2.20. The risk-free is 7% and the risk premium for this stock is 4%. If the annual dividend is expected to remain at $2.20, what is the value of the stock?
Value of Stock = $2.20 / (7% + 4%)
Value of Stock = $2.20 / (11%)
Value of Stock = $20.00
2. Suppose the value of the S&P 500 stock index is currently $1,300. If one-year T-bill rate is 4% and the expected dividend yield on the S&P 500 is 1%, what should the one-year maturity futures price be?
One-year maturity futures price = $1,300 x (1+(4% - 1%))
One-year maturity futures price = $1,300 x 1.03
One-year maturity futures price = $1,339
3. One Chicago has just introduced a new single-stock futures contractor on the stock of Brandex, a company that currently pays no dividends. Each contract call for delivery of 1,000 shares of stock in one year. T T-bill rate is 6% per year.
a. If Brandex stock sells at $120 per share, what should the futures price be?
Futures Price = $120 (1.06)
Futures Price = $127.20
b. If the Brandex stock price drops by 3%, what will be the change in the futures price and the change in the investor’s margin account?
New Spot = $120 (1 – 0.03)
New Spot = $120 x 0.97
New Spot = $116.40
New Futures = $116.40 (1.06)
New Futures = $123.384
The long investor loses:
$127.20 - $123.384 = $3.816 per share or $3.816 (1,000) = $3,816 per contract
c. If the margin on the contract is $12,000, what is the percentage return on the investor’s position?
Percentage return = $12,000 / $127,200 = 9.43%
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