The security market line (SML) shows the relationship between beta and expected return.

Investment projects that plot **above** the SML would have:

You want to buy an apartment worth $400,000. You have saved a deposit of $80,000. The bank has agreed to lend you the $320,000 as a **fully amortising** mortgage loan with a term of 30 years. The interest rate is 6% pa and is not expected to change. What will be your monthly payments?

A student won $**1**m in a lottery. Currently the money is in a bank account which pays interest at **6**% pa, given as an APR compounding per month.

She plans to spend $**20,000** at the **beginning** of every month from now on (so the first withdrawal will be at t=0). After each withdrawal, she will check how much money is left in the account. When there is less than $**500,000** left, she will donate that remaining amount to charity.

In how many months will she make her last withdrawal and donate the remainder to charity?

**Question 282** expected and historical returns, income and capital returns

You're the boss of an investment bank's equities research team. Your five analysts are each trying to find the **expected total return** over the next year of shares in a mining company. The mining firm:

- Is regarded as a mature company since it's quite stable in size and was floated around 30 years ago. It is not a high-growth company;
- Share price is very sensitive to changes in the price of the market portfolio, economic growth, the exchange rate and commodities prices. Due to this, its standard deviation of total returns is much higher than that of the market index;
- Experienced tough times in the last 10 years due to unexpected falls in commodity prices.
- Shares are traded in an active liquid market.

Assume that:

- The analysts' source data is correct and true, but their inferences might be wrong;
- All returns and yields are given as effective annual nominal rates.

An old company's Firm Free Cash Flow (FFCF, same as CFFA) is forecast in the graph below.

To value the firm's assets, the terminal value needs to be calculated using the perpetuity with growth formula:

###V_{\text{terminal, }t-1} = \dfrac{FFCF_{\text{terminal, }t}}{r-g}###

Which point corresponds to the best time to calculate the terminal value?

**Question 381** Merton model of corporate debt, option, real option

In the Merton model of corporate debt, buying a levered company's debt is equivalent to buying risk free government bonds and:

Find the cash flow from assets (CFFA) of the following project.

One Year Mining Project Data | ||

Project life | 1 year | |

Initial investment in building mine and equipment | $9m | |

Depreciation of mine and equipment over the year | $8m | |

Kilograms of gold mined at end of year | 1,000 | |

Sale price per kilogram | $0.05m | |

Variable cost per kilogram | $0.03m | |

Before-tax cost of closing mine at end of year | $4m | |

Tax rate | 30% | |

Note 1: Due to the project, the firm also anticipates finding some rare diamonds which will give before-tax revenues of $1m at the end of the year.

Note 2: The land that will be mined actually has thermal springs and a family of koalas that could be sold to an eco-tourist resort for an after-tax amount of $3m right now. However, if the mine goes ahead then this natural beauty will be destroyed.

Note 3: The mining equipment will have a book value of $1m at the end of the year for tax purposes. However, the equipment is expected to fetch $2.5m when it is sold.

Find the project's CFFA at time zero and one. Answers are given in millions of dollars ($m), with the first cash flow at time zero, and the second at time one.

A stock **just paid** a dividend of $1. Future annual dividends are expected to grow by 2% pa. The next dividend of $1.02 (=1*(1+0.02)^1) will be in one year, and the year after that the dividend will be $1.0404 (=1*(1+0.02)^2), and so on forever.

Its required total return is 10% pa. The total required return and growth rate of dividends are given as effective annual rates.

Calculate the current stock price.

Alice, Bob, Chris and Delta are traders in the futures market. The following trades occur over a single day in a newly-opened equity index future that matures in one year which the exchange just made available.

1. Alice buys a future from Bob.

2. Chris buys a future from Delta.

3. Delta buys a future from Alice.

These were the only trades made in this equity index future. What was the trading volume and what is the open interest?

**Question 795** option, Black-Scholes-Merton option pricing, option delta, no explanation

Which of the following quantities from the Black-Scholes-Merton option pricing formula gives the **Delta** of a European **put** option?