This annuity formula ##\dfrac{C_1}{r}\left(1-\dfrac{1}{(1+r)^3} \right)## is equivalent to which of the following formulas? Note the 3.
In the below formulas, ##C_t## is a cash flow at time t. All of the cash flows are equal, but paid at different times.
The 'time value of money' is most closely related to which of the following concepts?
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.
Question 48 IRR, NPV, bond pricing, premium par and discount bonds, market efficiency
The theory of fixed interest bond pricing is an application of the theory of Net Present Value (NPV). Also, a 'fairly priced' asset is not over- or under-priced. Buying or selling a fairly priced asset has an NPV of zero.
Considering this, which of the following statements is NOT correct?
"Buy low, sell high" is a phrase commonly heard in financial markets. It states that traders should try to buy assets at low prices and sell at high prices.
Traders in the fixed-coupon bond markets often quote promised bond yields rather than prices. Fixed-coupon bond traders should try to:
To value a business's assets, the free cash flow of the firm (FCFF, also called CFFA) needs to be calculated. This requires figures from the firm's income statement and balance sheet. For what figures is the balance sheet needed? Note that the balance sheet is sometimes also called the statement of financial position.
Let the 'income return' of a bond be the coupon at the end of the period divided by the market price now at the start of the period ##(C_1/P_0)##. The expected income return of a premium fixed coupon bond is:
An economy has only two investable assets: stocks and cash.
Stocks had a historical nominal average total return of negative two percent per annum (-2% pa) over the last 20 years. Stocks are liquid and actively traded. Stock returns are variable, they have risk.
Cash is riskless and has a nominal constant return of zero percent per annum (0% pa), which it had in the past and will have in the future. Cash can be kept safely at zero cost. Cash can be converted into shares and vice versa at zero cost.
The nominal total return of the shares over the next year is expected to be:
Which of the following statements about yield curves is NOT correct?
A company advertises an investment costing $1,000 which they say is underpriced. They say that it has an expected total return of 15% pa, but a required return of only 10% pa. Of the 15% pa total expected return, the dividend yield is expected to always be 7% pa and rest is the capital yield.
Assuming that the company's statements are correct, what is the NPV of buying the investment if the 15% total return lasts for the next 100 years (t=0 to 100), then reverts to 10% after that time? Also, what is the NPV of the investment if the 15% return lasts forever?
In both cases, assume that the required return of 10% remains constant, the dividends can only be re-invested at 10% pa and all returns are given as effective annual rates.
The answer choices below are given in the same order (15% for 100 years, and 15% forever):
Question 657 systematic and idiosyncratic risk, CAPM, no explanation
A stock's required total return will decrease when its:
Question 659 APR, effective rate, effective rate conversion, no explanation
A home loan company advertises an interest rate of 9% pa, payable monthly. Which of the following statements about the interest rate is NOT correct? All rates are given with an accuracy of 4 decimal places.
How much more can you borrow using an interest-only loan compared to a 25-year fully amortising loan if interest rates are 6% pa compounding per month and are not expected to change? If it makes it easier, assume that you can afford to pay $2,000 per month on either loan. Express your answer as a proportional increase using the following formula:
###\text{Proportional Increase} = \dfrac{V_\text{0,interest only}}{V_\text{0,fully amortising}} - 1###Question 662 APR, effective rate, effective rate conversion, no explanation
Which of the following interest rate labels does NOT make sense?
A firm has a debt-to-assets ratio of 20%. What is its debt-to-equity ratio?
A company conducts a 10 for 3 stock split. What is the percentage increase in the stock price and the number of shares outstanding? The answers are given in the same order.
A company conducts a 2 for 3 rights issue at a subscription price of $8 when the pre-announcement stock price was $9. Assume that all investors use their rights to buy those extra shares.
What is the percentage increase in the stock price and the number of shares outstanding? The answers are given in the same order.
Question 668 buy and hold, market efficiency, idiom
A quote from the famous investor Warren Buffet: "Much success can be attributed to inactivity. Most investors cannot resist the temptation to constantly buy and sell."
Buffet is referring to the buy-and-hold strategy which is to buy and never sell shares. Which of the following is a disadvantage of a buy-and-hold strategy? Assume that share markets are semi-strong form efficient. Which of the following is NOT an advantage of the strict buy-and-hold strategy? A disadvantage of the buy-and-hold strategy is that it reduces:
Which of the following is NOT a valid method for estimating the beta of a company's stock? Assume that markets are efficient, a long history of past data is available, the stock possesses idiosyncratic and market risk. The variances and standard deviations below denote total risks.
In 2014 the median starting salaries of male and female Australian bachelor degree accounting graduates aged less than 25 years in their first full-time industry job was $50,000 before tax, according to Graduate Careers Australia. See page 9 of this report. Personal income tax rates published by the Australian Tax Office are reproduced for the 2014-2015 financial year in the table below.
| Taxable income | Tax on this income |
|---|---|
| 0 – $18,200 | Nil |
| $18,201 – $37,000 | 19c for each $1 over $18,200 |
| $37,001 – $80,000 | $3,572 plus 32.5c for each $1 over $37,000 |
| $80,001 – $180,000 | $17,547 plus 37c for each $1 over $80,000 |
| $180,001 and over | $54,547 plus 45c for each $1 over $180,000 |
The above rates do not include the Medicare levy of 2%. Exclude the Medicare levy from your calculations
How much personal income tax would you have to pay per year if you earned $50,000 per annum before-tax?
A $100 stock has a continuously compounded expected total return of 10% pa. Its dividend yield is 2% pa with continuous compounding. What do you expect its price to be in one year?
A $100 stock has a continuously compounded expected total return of 10% pa. Its dividend yield is 2% pa with continuous compounding. What do you expect its price to be in 2.5 years?
Question 637 option, option payoff at maturity, no explanation
Which of the below formulas gives the payoff ##(f)## at maturity ##(T)## from being short a call option? Let the underlying asset price at maturity be ##S_T## and the exercise price be ##X_T##.
Question 638 option, option payoff at maturity, no explanation
Which of the below formulas gives the payoff ##(f)## at maturity ##(T)## from being long a put option? Let the underlying asset price at maturity be ##S_T## and the exercise price be ##X_T##.
Question 639 option, option payoff at maturity, no explanation
Which of the below formulas gives the payoff ##(f)## at maturity ##(T)## from being short a put option? Let the underlying asset price at maturity be ##S_T## and the exercise price be ##X_T##.
Which of the below formulas gives the payoff at maturity ##(f_T)## from being long a future? Let the underlying asset price at maturity be ##S_T## and the locked-in futures price be ##K_T##.
Which of the below formulas gives the payoff at maturity ##(f_T)## from being short a future? Let the underlying asset price at maturity be ##S_T## and the locked-in futures price be ##K_T##.
A trader sells one crude oil futures contract on the CME expiring in one year with a locked-in futures price of $38.94 per barrel. The crude oil spot price is $40.33. If the trader doesn’t close out her contract before expiry then in one year she will have the:
A trader buys one crude oil European style call option contract on the CME expiring in one year with an exercise price of $44 per barrel for a price of $6.64. The crude oil spot price is $40.33. If the trader doesn’t close out her contract before maturity, then at maturity she will have the:
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?
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 Bob.
These were the only trades made in this equity index future. What was the trading volume and what is the open interest?
A trader buys 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 buyer?
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?
In February a company sold one December 40,000 pound (about 18 metric tons) lean hog futures contract. It closed out its position in May.
The spot price was $0.68 per pound in February. The December futures price was $0.70 per pound when the trader entered into the contract in February, $0.60 when he closed out his position in May, and $0.55 when the contract matured in December.
What was the total profit?
An equity index is currently at 5,200 points. The 6 month futures price is 5,300 points and the total required return is 6% pa with continuous compounding. Each index point is worth $25.
What is the implied dividend yield as a continuously compounded rate per annum?
An equity index is currently at 4,800 points. The 1.5 year futures price is 5,100 points and the total required return is 6% pa with continuous compounding. Each index point is worth $25.
What is the implied dividend yield as a continuously compounded rate per annum?
Which of the following statements about futures and forward contracts is NOT correct?
A company can invest funds in a five year project at LIBOR plus 50 basis points pa. The five-year swap rate is 4% pa. What fixed rate of interest can the company earn over the next five years by using the swap?
Which of the below formulas gives the profit ##(\pi)## from being long a call option? Let the underlying asset price at maturity be ##S_T##, the exercise price be ##X_T## and the option price be ##f_{LC,0}##. Note that ##S_T##, ##X_T## and ##f_{LC,0}## are all positive numbers.
Which of the below formulas gives the profit ##(\pi)## from being short a call option? Let the underlying asset price at maturity be ##S_T##, the exercise price be ##X_T## and the option price be ##f_{LC,0}##. Note that ##S_T##, ##X_T## and ##f_{LC,0}## are all positive numbers.
Which of the below formulas gives the profit ##(\pi)## from being long a put option? Let the underlying asset price at maturity be ##S_T##, the exercise price be ##X_T## and the option price be ##f_{LP,0}##. Note that ##S_T##, ##X_T## and ##f_{LP,0}## are all positive numbers.
Which of the below formulas gives the profit ##(\pi)## from being short a put option? Let the underlying asset price at maturity be ##S_T##, the exercise price be ##X_T## and the option price be ##f_{LP,0}##. Note that ##S_T##, ##X_T## and ##f_{LP,0}## are all positive numbers.
A trader sells one crude oil European style call option contract on the CME expiring in one year with an exercise price of $44 per barrel for a price of $6.64. The crude oil spot price is $40.33. If the trader doesn’t close out her contract before maturity, then at maturity she will have the:
A trader buys one crude oil European style put option contract on the CME expiring in one year with an exercise price of $44 per barrel for a price of $6.64. The crude oil spot price is $40.33. If the trader doesn’t close out her contract before maturity, then at maturity she will have the:
A trader sells one crude oil European style put option contract on the CME expiring in one year with an exercise price of $44 per barrel for a price of $6.64. The crude oil spot price is $40.33. If the trader doesn’t close out her contract before maturity, then at maturity she will have the:
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. Bob buys a future from Chris.
These were the only trades made in this equity index future. What was the trading volume and what is the open interest?
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. Alice buys a future from Chris.
These were the only trades made in this equity index future. What was the trading volume and what is the open interest?
An equity index stands at 100 points and the one year equity futures price is 107.
The equity index is expected to have a dividend yield of 3% pa. Assume that investors are risk-neutral so their total required return on the shares is the same as the risk free Treasury bond yield which is 10% pa. Both are given as discrete effective annual rates.
Assuming that the equity index is fairly priced, an arbitrageur would recognise that the equity futures are:
A pig farmer in the US is worried about the price of hogs falling and wants to lock in a price now. In one year the pig farmer intends to sell 1,000,000 pounds of hogs. Luckily, one year CME lean hog futures expire on the exact day that he wishes to sell his pigs. The futures have a notional principal of 40,000 pounds (about 18 metric tons) and currently trade at a price of 63.85 cents per pound. The underlying lean hogs spot price is 77.15 cents per pound. The correlation between the futures price and the underlying hogs price is one and the standard deviations are both 4 cents per pound. The initial margin is USD1,500 and the maintenance margin is USD1,200 per futures contract.
Which of the below statements is NOT correct?
An equity index fund manager controls a USD1 billion diversified equity portfolio with a beta of 1.3. The equity manager fears that a global recession will begin in the next year, causing equity prices to tumble. The market does not think that this will happen. If the fund manager wishes to reduce her portfolio beta to 0.5, how many S&P500 futures should she sell?
The US market equity index is the S&P500. One year CME futures on the S&P500 currently trade at 2,062 points and the spot price is 2,091 points. Each point is worth $250. How many one year S&P500 futures contracts should the fund manager sell?
A trader just bought a European style put option on CBA stock. The current option premium is $2, the exercise price is $75, the option matures in one year and the spot CBA stock price is $74.
Which of the following statements is NOT correct?
Question 691 continuously compounding rate, effective rate, continuously compounding rate conversion, no explanation
A bank quotes an interest rate of 6% pa with quarterly compounding. Note that another way of stating this rate is that it is an annual percentage rate (APR) compounding discretely every 3 months.
Which of the following statements about this rate is NOT correct? All percentages are given to 6 decimal places. The equivalent:
The standard deviation of monthly changes in the spot price of corn is 50 cents per bushel. The standard deviation of monthly changes in the futures price of corn is 40 cents per bushel. The correlation between the spot price of corn and the futures price of corn is 0.9.
It is now March. A corn chip manufacturer is committed to buying 250,000 bushels of corn in May. The spot price of corn is 381 cents per bushel and the June futures price is 399 cents per bushel.
The corn chip manufacturer wants to use the June corn futures contracts to hedge his risk. Each futures contract is for the delivery of 5,000 bushels of corn. One bushel is about 127 metric tons.
How many corn futures should the corn chip manufacturer buy to hedge his risk? Round your answer to the nearest whole number of contracts. Remember to tail the hedge.
Question 693 boot strapping zero coupon yield, forward interest rate, term structure of interest rates
Information about three risk free Government bonds is given in the table below.
| Federal Treasury Bond Data | ||||
| Maturity | Yield to maturity | Coupon rate | Face value | Price |
| (years) | (pa, compounding semi-annually) | (pa, paid semi-annually) | ($) | ($) |
| 0.5 | 3% | 4% | 100 | 100.4926 |
| 1 | 4% | 4% | 100 | 100.0000 |
| 1.5 | 5% | 4% | 100 | 98.5720 |
Based on the above government bonds' yields to maturity, which of the below statements about the spot zero rates and forward zero rates is NOT correct?
Which of the below statements about utility is NOT generally accepted by economists? Most people are thought to:
Mr Blue, Miss Red and Mrs Green are people with different utility functions. Which of the statements about the 3 utility functions is NOT correct?
Question 558 portfolio weights, portfolio return, short selling
An investor wants to make a portfolio of two stocks A and B with a target expected portfolio return of 16% pa.
- Stock A has an expected return of 8% pa.
- Stock B has an expected return of 12% pa.
What portfolio weights should the investor have in stocks A and B respectively?
The standard deviation and variance of a stock's annual returns are calculated over a number of years. The units of the returns are percent per annum ##(\% pa)##.
What are the units of the standard deviation ##(\sigma)## and variance ##(\sigma^2)## of returns respectively?
Hint: Visit Wikipedia to understand the difference between percentage points ##(\text{pp})## and percent ##(\%)##.
What is the covariance of a variable X with a constant C?
The cov(X, C) or ##\sigma_{X,C}## equals:
Question 566 capital structure, capital raising, rights issue, on market repurchase, dividend, stock split, bonus issue
A company's share price fell by 20% and its number of shares rose by 25%. Assume that there are no taxes, no signalling effects and no transaction costs.
Which one of the following corporate events may have happened?
A company conducts a 4 for 3 stock split. What is the percentage change in the stock price and the number of shares outstanding? The answers are given in the same order.