A stock was bought for $8 and paid a dividend of $0.50 one year later (at t=1 year). Just after the dividend was paid, the stock price was $7 (at t=1 year).

What were the total, capital and dividend returns given as effective annual rates? The choices are given in the same order:

##r_\text{total}##, ##r_\text{capital}##, ##r_\text{dividend}##.

A stock is expected to pay the following dividends:

Cash Flows of a Stock | ||||||

Time (yrs) | 0 | 1 | 2 | 3 | 4 | ... |

Dividend ($) | 8 | 8 | 8 | 20 | 8 | ... |

After year 4, the dividend will grow in perpetuity at 4% pa. The required return on the stock is 10% pa. Both the growth rate and required return are given as effective annual rates.

What is the current price of the stock?

A stock is expected to pay the following dividends:

Cash Flows of a Stock | ||||||

Time (yrs) | 0 | 1 | 2 | 3 | 4 | ... |

Dividend ($) | 0 | 6 | 12 | 18 | 20 | ... |

After year 4, the dividend will grow in perpetuity at 5% pa. The required return of the stock is 10% pa. Both the growth rate and required return are given as effective annual rates.

If all of the dividends since time period zero were deposited into a bank account yielding **8%** pa as an effective annual rate, how much money will be in the bank account in 2.5 years (in other words, at t=2.5)?

**Question 408** leverage, portfolio beta, portfolio risk, real estate, CAPM

You just bought a house worth $**1,000,000**. You financed it with an $**800,000** mortgage loan and a deposit of $**200,000**.

You estimate that:

- The house has a beta of
**1**; - The mortgage loan has a beta of
**0.2**.

What is the beta of the equity (the $200,000 deposit) that you have in your house?

Also, if the risk free rate is **5**% pa and the market portfolio's return is **10**% pa, what is the expected return on equity in your house? Ignore taxes, assume that all cash flows (interest payments and rent) were paid and received at the end of the year, and all rates are effective annual rates.

The expression 'you have to spend money to make money' relates to which business decision?

A trader **buys** one crude oil **futures** contract on the CME expiring in one year with a locked-in futures price of $38.94 per barrel. If the trader doesn’t close out her contract before expiry then in one year she will have the:

A trader **sells** a one year futures contract on crude oil. The contract is for the delivery of 1,000 barrels. The current futures price is $38.94 per barrel. The initial margin is $3,410 per contract, and the maintenance margin is $3,100 per contract.

What is the smallest price change that would lead to a margin call for the seller?

**Question 760** time calculation, interest only loan, no explanation

**Five** years ago (##t=-5## years) you entered into an **interest-only** home loan with a principal of $**500,000**, an interest rate of **4.5**% pa compounding monthly with a term of **25** years.

Then interest rates suddenly fall to **3**% pa (##t=0##), but you continue to pay the same monthly home loan payments as you did before. Will your home loan be paid off by the end of its remaining term? If so, in how many years from now? Measure the time taken to pay off the home loan from the current time which is 5 years after the home loan was first entered into.

Assume that the lower interest rate was given to you immediately after the loan repayment at the end of year 5, which was the 60th payment since the loan was granted. Also assume that rates were and are expected to remain constant.

A **one** year European-style **call** option has a strike price of $**4**. The option's underlying stock pays no dividends and currently trades at $**5**. The risk-free interest rate is **10**% pa continuously compounded. Use a **single** step binomial tree to calculate the option price, assuming that the price could rise to $**8** ##(u = 1.6)## or fall to $**3.125** ##(d = 1/1.6)## in one year. The call option price now is: