For a price of $13, Carla will sell you a share paying a dividend of $1 in one year and every year after that forever. The required return of the stock is 10% pa.
A share was bought for $10 (at t=0) and paid its annual dividend of $0.50 one year later (at t=1). Just after the dividend was paid, the share price was $11 (at t=1).
What was the total return, capital return and income return? Calculate your answers as effective annual rates. The choices are given in the same order:
##r_\text{total}##, ##r_\text{capital}##, ##r_\text{dividend}##.
You have $100,000 in the bank. The bank pays interest at 10% pa, given as an effective annual rate.
You wish to consume an equal amount now (t=0) and in one year (t=1) and have nothing left in the bank at the end (t=1).
How much can you consume at each time?
You want to buy a house priced at $400,000. You have saved a deposit of $40,000. The bank has agreed to lend you $360,000 as a fully amortising loan with a term of 30 years. The interest rate is 8% pa payable monthly and is not expected to change.
What will be your monthly payments?
Question 397 financial distress, leverage, capital structure, NPV
A levered firm has a market value of assets of $10m. Its debt is all comprised of zero-coupon bonds which mature in one year and have a combined face value of $9.9m.
Investors are risk-neutral and therefore all debt and equity holders demand the same required return of 10% pa.
Therefore the current market capitalisation of debt ##(D_0)## is $9m and equity ##(E_0)## is $1m.
A new project presents itself which requires an investment of $2m and will provide a:
- $6.6m cash flow with probability 0.5 in the good state of the world, and a
- -$4.4m (notice the negative sign) cash flow with probability 0.5 in the bad state of the world.
The project can be funded using the company's excess cash, no debt or equity raisings are required.
What would be the new market capitalisation of equity ##(E_\text{0, with project})## if shareholders vote to proceed with the project, and therefore should shareholders proceed with the project?
In Australia in the 1980's, inflation was around 8% pa, and residential mortgage loan interest rates were around 14%.
In 2013, inflation was around 2.5% pa, and residential mortgage loan interest rates were around 4.5%.
If a person can afford constant mortgage loan payments of $2,000 per month, how much more can they borrow when interest rates are 4.5% pa compared with 14.0% pa?
Give your answer as a proportional increase over the amount you could borrow when interest rates were high ##(V_\text{high rates})##, so:
###\text{Proportional increase} = \dfrac{V_\text{low rates}-V_\text{high rates}}{V_\text{high rates}} ###
Assume that:
- Interest rates are expected to be constant over the life of the loan.
- Loans are interest-only and have a life of 30 years.
- Mortgage loan payments are made every month in arrears and all interest rates are given as annualised percentage rates (APR's) compounding per month.
An Apple iPhone 6 smart phone can be bought now for $999. An Android Samsung Galaxy 5 smart phone can be bought now for $599.
If the Samsung phone lasts for four years, approximately how long must the Apple phone last for to have the same equivalent annual cost?
Assume that both phones have equivalent features besides their lifetimes, that both are worthless once they've outlasted their life, the discount rate is 10% pa given as an effective annual rate, and there are no extra costs or benefits from either phone.
Question 759 time calculation, fully amortising loan, no explanation
Five years ago you entered into a fully amortising home loan with a principal of $500,000, an interest rate of 4.5% pa compounding monthly with a term of 25 years.
Then interest rates suddenly fall to 3% 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 5 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 5, which was the 60th payment since the loan was granted. Also assume that rates were and are expected to remain constant.
The phone company Optus have 2 mobile service plans on offer which both have the same amount of phone call, text message and internet data credit. Both plans have a contract length of 24 months and the monthly cost is payable in advance. The only difference between the two plans is that one is a:
- 'Bring Your Own' (BYO) mobile service plan, costing $80 per month. There is no phone included in this plan. The other plan is a:
- 'Bundled' mobile service plan that comes with the latest smart phone, costing $100 per month. This plan includes the latest smart phone.
Neither plan has any additional payments at the start or end. Assume that the discount rate is 1% per month given as an effective monthly rate.
The only difference between the plans is the phone, so what is the implied cost of the phone as a present value? Given that the latest smart phone actually costs $600 to purchase outright from another retailer, should you commit to the BYO plan or the bundled plan?
A stock's returns are normally distributed with a mean of 10% pa and a standard deviation of 20 percentage points pa. What is the 95% confidence interval of returns over the next year? Note that the Z-statistic corresponding to a one-tail:
- 90% normal probability density function is 1.282.
- 95% normal probability density function is 1.645.
- 97.5% normal probability density function is 1.960.
The 95% confidence interval of annual returns is between: