Katya offers to pay you $10 at the end of every year for the next 5 years (t=1,2,3,4,5) if you pay her $50 now (t=0). You can borrow and lend from the bank at an interest rate of 10% pa, given as an effective annual rate. Ignore credit risk.
Government bonds currently have a return of 5%. A stock has a beta of 2 and the market return is 7%. What is the expected return of the stock?
There are a number of ways that assets can be depreciated. Generally the government's tax office stipulates a certain method.
But if it didn't, what would be the ideal way to depreciate an asset from the perspective of a businesses owner?
A student won $1m 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?
One year ago you bought $100,000 of shares partly funded using a margin loan. The margin loan size was $70,000 and the other $30,000 was your own wealth or 'equity' in the share assets.
The interest rate on the margin loan was 7.84% pa.
Over the year, the shares produced a dividend yield of 4% pa and a capital gain of 5% pa.
What was the total return on your wealth? Ignore taxes, assume that all cash flows (interest payments and dividends) were paid and received at the end of the year, and all rates above are effective annual rates.
Hint: Remember that wealth in this context is your equity (E) in the house asset (V = D+E) which is funded by the loan (D) and your deposit or equity (E).
The boss of WorkingForTheManCorp has a wicked (and unethical) idea. He plans to pay his poor workers one week late so that he can get more interest on his cash in the bank.
Every week he is supposed to pay his 1,000 employees $1,000 each. So $1 million is paid to employees every week.
The boss was just about to pay his employees today, until he thought of this idea so he will actually pay them one week (7 days) later for the work they did last week and every week in the future, forever.
Bank interest rates are 10% pa, given as a real effective annual rate. So ##r_\text{eff annual, real} = 0.1## and the real effective weekly rate is therefore ##r_\text{eff weekly, real} = (1+0.1)^{1/52}-1 = 0.001834569##
All rates and cash flows are real, the inflation rate is 3% pa and there are 52 weeks per year. The boss will always pay wages one week late. The business will operate forever with constant real wages and the same number of employees.
What is the net present value (NPV) of the boss's decision to pay later?
A stock is expected to pay a dividend of $5 per share in 1 month and $5 again in 7 months.
The stock price is $100, and the risk-free rate of interest is 10% per annum with continuous compounding. The yield curve is flat. Assume that investors are risk-neutral.
An investor has just taken a short position in a one year forward contract on the stock.
Find the forward price ##(F_1)## and value of the contract ##(V_0)## initially. Also find the value of the short futures contract in 6 months ##(V_\text{0.5, SF})## if the stock price fell to $90.
Question 722 mean and median returns, return distribution, arithmetic and geometric averages, continuously compounding rate
Here is a table of stock prices and returns. Which of the statements below the table is NOT correct?
| Price and Return Population Statistics | ||||
| Time | Prices | LGDR | GDR | NDR |
| 0 | 100 | |||
| 1 | 50 | -0.6931 | 0.5 | -0.5 |
| 2 | 100 | 0.6931 | 2 | 1 |
| Arithmetic average | 0 | 1.25 | 0.25 | |
| Arithmetic standard deviation | 0.9802 | 1.0607 | 1.0607 | |
Which of the following statements is NOT correct? Money market securities are: