A person is thinking about borrowing $100 from the bank at 7% pa and investing it in shares with an expected return of 10% pa. One year later the person intends to sell the shares and pay back the loan in full. Both the loan and the shares are fairly priced.
What is the Net Present Value (NPV) of this one year investment? Note that you are asked to find the present value (##V_0##), not the value in one year (##V_1##).
You just signed up for a 30 year fully amortising mortgage with monthly payments of $1,000 per month. The interest rate is 6% pa which is not expected to change.
How much did you borrow? After 20 years, how much will be owing on the mortgage? The interest rate is still 6% and is not expected to change.
Question 278 inflation, real and nominal returns and cash flows
Imagine that the interest rate on your savings account was 1% per year and inflation was 2% per year.
Let the variance of returns for a share per month be ##\sigma_\text{monthly}^2##.
What is the formula for the variance of the share's returns per year ##(\sigma_\text{yearly}^2)##?
Assume that returns are independently and identically distributed (iid) so they have zero auto correlation, meaning that if the return was higher than average today, it does not indicate that the return tomorrow will be higher or lower than average.
Question 338 market efficiency, CAPM, opportunity cost, technical analysis
A man inherits $500,000 worth of shares.
He believes that by learning the secrets of trading, keeping up with the financial news and doing complex trend analysis with charts that he can quit his job and become a self-employed day trader in the equities markets.
What is the expected gain from doing this over the first year? Measure the net gain in wealth received at the end of this first year due to the decision to become a day trader. Assume the following:
- He earns $60,000 pa in his current job, paid in a lump sum at the end of each year.
- He enjoys examining share price graphs and day trading just as much as he enjoys his current job.
- Stock markets are weak form and semi-strong form efficient.
- He has no inside information.
- He makes 1 trade every day and there are 250 trading days in the year. Trading costs are $20 per trade. His broker invoices him for the trading costs at the end of the year.
- The shares that he currently owns and the shares that he intends to trade have the same level of systematic risk as the market portfolio.
- The market portfolio's expected return is 10% pa.
Measure the net gain over the first year as an expected wealth increase at the end of the year.
Question 449 personal tax on dividends, classical tax system
A small private company has a single shareholder. This year the firm earned a $100 profit before tax. All of the firm's after tax profits will be paid out as dividends to the owner.
The corporate tax rate is 30% and the sole shareholder's personal marginal tax rate is 45%.
The United States' classical tax system applies because the company generates all of its income in the US and pays corporate tax to the Internal Revenue Service. The shareholder is also an American for tax purposes.
What will be the personal tax payable by the shareholder and the corporate tax payable by the company?
The accounting identity states that the book value of a company's assets (A) equals its liabilities (L) plus owners equity (OE), so A = L + OE.
The finance version states that the market value of a company's assets (V) equals the market value of its debt (D) plus equity (E), so V = D + E.
Therefore a business's assets can be seen as a portfolio of the debt and equity that fund the assets.
Let ##\sigma_\text{V total}^2## be the total variance of returns on assets, ##\sigma_\text{V syst}^2## be the systematic variance of returns on assets, and ##\sigma_\text{V idio}^2## be the idiosyncratic variance of returns on assets, and ##\rho_\text{D idio, E idio}## be the correlation between the idiosyncratic returns on debt and equity.
Which of the following equations is NOT correct?
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 929 standard error, mean and median returns, mode return, return distribution, arithmetic and geometric averages, continuously compounding rate
The arithmetic average continuously compounded or log gross discrete return (AALGDR) on the ASX200 accumulation index over the 24 years from 31 Dec 1992 to 31 Dec 2016 is 9.49% pa.
The arithmetic standard deviation (SDLGDR) is 16.92 percentage points pa.
Assume that the data are sample statistics, not population statistics. Assume that the log gross discrete returns are normally distributed.
What is the standard error of your estimate of the sample ASX200 accumulation index arithmetic average log gross discrete return (AALGDR) over the 24 years from 1992 to 2016?
Question 989 PE ratio, Multiples valuation, leverage, accounting ratio
A firm has 20 million stocks, earnings (or net income) of $100 million per annum and a 60% debt-to-equity ratio where both the debt and asset values are market values rather than book values. Similar firms have a PE ratio of 12.
Which of the below statements is NOT correct based on a PE multiples valuation?