You want to buy an apartment worth $500,000. You have saved a deposit of $50,000. The bank has agreed to lend you the $450,000 as a fully amortising mortgage loan with a term of 25 years. The interest rate is 6% pa and is not expected to change.
What will be your monthly payments?
A stock is expected to pay the following dividends:
| Cash Flows of a Stock | ||||||
| Time (yrs) | 0 | 1 | 2 | 3 | 4 | ... |
| Dividend ($) | 2 | 2 | 2 | 10 | 3 | ... |
After year 4, the dividend will grow in perpetuity at 4% pa. The required return on the stock is 10% pa. Both the growth rate and required return are given as effective annual rates.
What is the current price of the stock?
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.
Acquirer firm plans to launch a takeover of Target firm. The deal is expected to create a present value of synergies totaling $105 million. A scrip offer will be made that pays the fair price for the target's shares plus 75% of the total synergy value.
| Firms Involved in the Takeover | ||
| Acquirer | Target | |
| Assets ($m) | 6,000 | 700 |
| Debt ($m) | 4,800 | 400 |
| Share price ($) | 40 | 20 |
| Number of shares (m) | 30 | 15 |
Ignore transaction costs and fees. Assume that the firms' debt and equity are fairly priced, and that each firms' debts' risk, yield and values remain constant. The acquisition is planned to occur immediately, so ignore the time value of money.
Calculate the merged firm's share price and total number of shares after the takeover has been completed.
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?
Question 719 mean and median returns, return distribution, arithmetic and geometric averages, continuously compounding rate
A stock has an arithmetic average continuously compounded return (AALGDR) of 10% pa, a standard deviation of continuously compounded returns (SDLGDR) of 80% pa and current stock price of $1. Assume that stock prices are log-normally distributed. The graph below summarises this information and provides some helpful formulas.
In one year, what do you expect the median and mean prices to be? The answer options are given in the same order.
Question 748 income and capital returns, DDM, ex dividend date
A stock will pay you a dividend of $2 tonight if you buy it today.
Thereafter the annual dividend is expected to grow by 3% pa, so the next dividend after the $2 one tonight will be $2.06 in one year, then in two years it will be $2.1218 and so on. The stock's required return is 8% pa.
What is the stock price today and what do you expect the stock price to be tomorrow, approximately?
An investor owns a portfolio with:
- 80% invested in stock A; and
- 20% invested in stock B.
Today there was a:
- 10% rise in stock A's price; and
- No change in stock B's price.
No dividends were paid on either stock. What was the total historical portfolio return on this day? All returns above and answer options below are given as effective daily rates.
Question 923 omitted variable bias, CAPM, single factor model, single index model, no explanation
Capital Asset Pricing Model (CAPM) and the Single Index Model (SIM) are single factor models whose only risk factor is the market portfolio’s return. Say a Taxi company and an Umbrella company are influenced by two factors, the market portfolio return and rainfall. When it rains, both the Taxi and Umbrella companies’ stock prices do well. When there’s no rain, both do poorly. Assume that rainfall risk is a systematic risk that cannot be diversified and that rainfall has zero correlation with the market portfolio’s returns.
Which of the following statements about these two stocks is NOT correct?
The CAPM and SIM:
To receive the dividend you must own the stock when the market closes on which date?