For a price of $95, Nicole will sell you a 10 year bond paying semi-annual coupons of 8% pa. The face value of the bond is $100. Other bonds with the same risk, maturity and coupon characteristics trade at a yield of 8% pa.
All things remaining equal, the variance of a portfolio of two positively-weighted stocks rises as:
Question 408 leverage, portfolio beta, portfolio risk, real estate, CAPM
You just bought a house worth $1,000,000. You financed it with an $800,000 mortgage loan and a deposit of $200,000.
You estimate that:
- The house has a beta of 1;
- The mortgage loan has a beta of 0.2.
What is the beta of the equity (the $200,000 deposit) that you have in your house?
Also, if the risk free rate is 5% pa and the market portfolio's return is 10% pa, what is the expected return on equity in your house? Ignore taxes, assume that all cash flows (interest payments and rent) were paid and received at the end of the year, and all rates are effective annual rates.
A stock has a beta of 1.5. The market's expected total return is 10% pa and the risk free rate is 5% pa, both given as effective annual rates.
Over the last year, bad economic news was released showing a higher chance of recession. Over this time the share market fell by 1%. So ##r_{m} = (P_{0} - P_{-1})/P_{-1} = -0.01##, where the current time is zero and one year ago is time -1. The risk free rate was unchanged.
What do you think was the stock's historical return over the last year, given as an effective annual rate?
The following cash flows are expected:
- A perpetuity of yearly payments of $30, with the first payment in 5 years (first payment at t=5, which continues every year after that forever).
- One payment of $100 in 6 years and 3 months (t=6.25).
What is the NPV of the cash flows if the discount rate is 10% given as an effective annual rate?
Question 758 time calculation, fully amortising loan, no explanation
Two years ago you entered into a fully amortising home loan with a principal of $1,000,000, an interest rate of 6% pa compounding monthly with a term of 25 years.
Then interest rates suddenly fall to 4.5% pa (t=0), but you continue to pay the same monthly home loan payments as you did before. How long will it now take to pay off your home loan? Measure the time taken to pay off the home loan from the current time which is 2 years after the home loan was first entered into.
Assume that the lower interest rate was given to you immediately after the loan repayment at the end of year 2, which was the 24th payment since the loan was granted. Also assume that rates were and are expected to remain constant.
Question 780 mispriced asset, NPV, DDM, market efficiency, no explanation
A company advertises an investment costing $1,000 which they say is under priced. 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 be 4% pa and the capital yield 11% pa. Assume 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):
A one year European-style call option has a strike price of $4.
The option's underlying stock currently trades at $5, pays no dividends and its standard deviation of continuously compounded returns is 47% pa.
The risk-free interest rate is 10% pa continuously compounded.
Use the Black-Scholes-Merton formula to calculate the option price. The call option price now is:
Question 882 Asian currency crisis, foreign exchange rate, original sin, no explanation
In the 1997 Asian currency crisis, the businesses most vulnerable to bankruptcy were those that:
A stock has a beta of 1.2. Its next dividend is expected to be $20, paid one year from now.
Dividends are expected to be paid annually and grow by 1.5% pa forever.
Treasury bonds yield 3% pa and the market portfolio's expected return is 7% pa. All returns are effective annual rates.
What is the price of the stock now?