For a price of $10.20 each, Renee will sell you 100 shares. Each share is expected to pay dividends in perpetuity, growing at a rate of 5% pa. The next dividend is one year away (t=1) and is expected to be $1 per share.
The required return of the stock is 15% pa.
Question 108 bond pricing, zero coupon bond, term structure of interest rates, forward interest rate
An Australian company just issued two bonds:
- A 1 year zero coupon bond at a yield of 10% pa, and
- A 2 year zero coupon bond at a yield of 8% pa.
What is the forward rate on the company's debt from years 1 to 2? Give your answer as an APR compounding every 6 months, which is how the above bond yields are quoted.
A stock was bought for $8 and paid a dividend of $0.50 one year later (at t=1 year). Just after the dividend was paid, the stock price was $7 (at t=1 year).
What were the total, capital and dividend returns given as effective annual rates? The choices are given in the same order:
##r_\text{total}##, ##r_\text{capital}##, ##r_\text{dividend}##.
Over the next year, the management of an unlevered company plans to:
- Achieve firm free cash flow (FFCF or CFFA) of $1m.
- Pay dividends of $1.8m
- Complete a $1.3m share buy-back.
- Spend $0.8m on new buildings without buying or selling any other fixed assets. This capital expenditure is included in the CFFA figure quoted above.
Assume that:
- All amounts are received and paid at the end of the year so you can ignore the time value of money.
- The firm has sufficient retained profits to pay the dividend and complete the buy back.
- The firm plans to run a very tight ship, with no excess cash above operating requirements currently or over the next year.
How much new equity financing will the company need? In other words, what is the value of new shares that will need to be issued?
Question 415 income and capital returns, real estate, no explanation
You just bought a residential apartment as an investment property for $500,000.
You intend to rent it out to tenants. They are ready to move in, they would just like to know how much the monthly rental payments will be, then they will sign a twelve-month lease.
You require a total return of 8% pa and a rental yield of 5% pa.
What would the monthly paid-in-advance rental payments have to be this year to receive that 5% annual rental yield?
Also, if monthly rental payments can be increased each year when a new lease agreement is signed, by how much must you increase rents per year to realise the 8% pa total return on the property?
Ignore all taxes and the costs of renting such as maintenance costs, real estate agent fees, utilities and so on. Assume that there will be no periods of vacancy and that tenants will promptly pay the rental prices you charge.
Note that the first rental payment will be received at t=0. The first lease agreement specifies the first 12 equal payments from t=0 to 11. The next lease agreement can have a rental increase, so the next twelve equal payments from t=12 to 23 can be higher than previously, and so on forever.
Question 556 portfolio risk, portfolio return, standard deviation
An investor wants to make a portfolio of two stocks A and B with a target expected portfolio return of 12% pa.
- Stock A has an expected return of 10% pa and a standard deviation of 20% pa.
- Stock B has an expected return of 15% pa and a standard deviation of 30% pa.
The correlation coefficient between stock A and B's expected returns is 70%.
What will be the annual standard deviation of the portfolio with this 12% pa target return?
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?
Which of the below formulas gives the profit ##(\pi)## from being short a call option? Let the underlying asset price at maturity be ##S_T##, the exercise price be ##X_T## and the option price be ##f_{LC,0}##. Note that ##S_T##, ##X_T## and ##f_{LC,0}## are all positive numbers.
Question 841 gross domestic product, government spending
The government spends money on:
- Goods and services such as defence, police, schools, hospitals and roads; and
- Transfer payments (also called welfare) such as the pension, dole, disability support and student support.
When calculating GDP (=C+I+G+X-M), the ‘government spending’ component (G) is supposed to include:
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: