You really want to go on a back packing trip to Europe when you finish university. Currently you have $1,500 in the bank. Bank interest rates are 8% pa, given as an APR compounding per month. If the holiday will cost $2,000, how long will it take for your bank account to reach that amount?
A company has:
- 10 million common shares outstanding, each trading at a price of $90.
- 1 million preferred shares which have a face (or par) value of $100 and pay a constant dividend of 9% of par. They currently trade at a price of $120 each.
- Debentures that have a total face value of $60,000,000 and a yield to maturity of 6% per annum. They are publicly traded and their market price is equal to 90% of their face value.
- The risk-free rate is 5% and the market return is 10%.
- Market analysts estimate that the company's common stock has a beta of 1.2. The corporate tax rate is 30%.
What is the company's after-tax Weighted Average Cost of Capital (WACC)? Assume a classical tax system.
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.
- 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.
Private equity firms are known to buy medium sized private companies operating in the same industry, merge them together into a larger company, and then sell it off in a public float (initial public offering, IPO).
If medium-sized private companies trade at PE ratios of 5 and larger listed companies trade at PE ratios of 15, what return can be achieved from this strategy?
Assume that:
- The medium-sized companies can be bought, merged and sold in an IPO instantaneously.
- There are no costs of finding, valuing, merging and restructuring the medium sized companies. Also, there is no competition to buy the medium-sized companies from other private equity firms.
- The large merged firm's earnings are the sum of the medium firms' earnings.
- The only reason for the difference in medium and large firm's PE ratios is due to the illiquidity of the medium firms' shares.
- Return is defined as: ##r_{0→1} = (p_1-p_0+c_1)/p_0## , where time zero is just before the merger and time one is just after.
A young lady is trying to decide if she should attend university or begin working straight away in her home town.
The young lady's grandma says that she should not go to university because she is less likely to marry the local village boy whom she likes because she will spend less time with him if she attends university.
What's the correct way to classify this item from a capital budgeting perspective when trying to decide whether to attend university?
The cost of not marrying the local village boy should be classified as:
"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:
Question 903 option, Black-Scholes-Merton option pricing, option on stock index
A six month European-style call option on the S&P500 stock index has a strike price of 2800 points.
The underlying S&P500 stock index currently trades at 2700 points, has a continuously compounded dividend yield of 2% pa and a standard deviation of continuously compounded returns of 25% pa.
The risk-free interest rate is 5% pa continuously compounded.
Use the Black-Scholes-Merton formula to calculate the option price. The call option price now is:
Question 921 utility, return distribution, log-normal distribution, arithmetic and geometric averages, no explanation
Who was the first theorist to propose the idea of ‘expected utility’?
Question 948 VaR, expected shortfall
Below is a historical sample of returns on the S&P500 capital index.
| S&P500 Capital Index Daily Returns Ranked from Best to Worst |
||
| 10,000 trading days from 4th August 1977 to 24 March 2017 based on closing prices. |
||
| Rank | Date (DD-MM-YY) |
Continuously compounded daily return (% per day) |
| 1 | 21-10-87 | 9.23 |
| 2 | 08-03-83 | 8.97 |
| 3 | 13-11-08 | 8.3 |
| 4 | 30-09-08 | 8.09 |
| 5 | 28-10-08 | 8.01 |
| 6 | 29-10-87 | 7.28 |
| … | … | … |
| 9980 | 11-12-08 | -5.51 |
| 9981 | 22-10-08 | -5.51 |
| 9982 | 08-08-11 | -5.54 |
| 9983 | 22-09-08 | -5.64 |
| 9984 | 11-09-86 | -5.69 |
| 9985 | 30-11-87 | -5.88 |
| 9986 | 14-04-00 | -5.99 |
| 9987 | 07-10-98 | -6.06 |
| 9988 | 08-01-88 | -6.51 |
| 9989 | 27-10-97 | -6.55 |
| 9990 | 13-10-89 | -6.62 |
| 9991 | 15-10-08 | -6.71 |
| 9992 | 29-09-08 | -6.85 |
| 9993 | 07-10-08 | -6.91 |
| 9994 | 14-11-08 | -7.64 |
| 9995 | 01-12-08 | -7.79 |
| 9996 | 29-10-08 | -8.05 |
| 9997 | 26-10-87 | -8.4 |
| 9998 | 31-08-98 | -8.45 |
| 9999 | 09-10-08 | -12.9 |
| 10000 | 19-10-87 | -23.36 |
| Mean of all 10,000: | 0.0354 | |
| Sample standard deviation of all 10,000: | 1.2062 | |
| Sources: Bloomberg and S&P. | ||
Assume that the one-tail Z-statistic corresponding to a probability of 99.9% is exactly 3.09. Which of the following statements is NOT correct? Based on the historical data, the 99.9% daily: