In Australia, domestic university students are allowed to buy concession tickets for the bus, train and ferry which sell at a discount of 50% to full-price tickets.
The Australian Government do not allow international university students to buy concession tickets, they have to pay the full price.
Some international students see this as unfair and they are willing to pay for fake university identification cards which have the concession sticker.
What is the most that an international student would be willing to pay for a fake identification card?
Assume that international students:
- consider buying their fake card on the morning of the first day of university from their neighbour, just before they leave to take the train into university.
- buy their weekly train tickets on the morning of the first day of each week.
- ride the train to university and back home again every day seven days per week until summer holidays 40 weeks from now. The concession card only lasts for those 40 weeks. Assume that there are 52 weeks in the year for the purpose of interest rate conversion.
- a single full-priced one-way train ride costs $5.
- have a discount rate of 11% pa, given as an effective annual rate.
Approach this question from a purely financial view point, ignoring the illegality, embarrassment and the morality of committing fraud.
A company has:
- 50 million shares outstanding.
- The market price of one share is currently $6.
- The risk-free rate is 5% and the market return is 10%.
- Market analysts believe that the company's ordinary shares have a beta of 2.
- The company has 1 million preferred stock which have a face (or par) value of $100 and pay a constant dividend of 10% of par. They currently trade for $80 each.
- The company's debentures are publicly traded and their market price is equal to 90% of their face value.
- The debentures have a total face value of $60,000,000 and the current yield to maturity of corporate debentures is 10% per annum. The corporate tax rate is 30%.
What is the company's after-tax weighted average cost of capital (WACC)? Assume a classical tax system.
A five year bond has a face value of $100, a yield of 12% and a fixed coupon rate of 6%, paid semi-annually.
What is the bond's price?
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 stock has a beta of 0.5. Its next dividend is expected to be $3, paid one year from now. Dividends are expected to be paid annually and grow by 2% pa forever. Treasury bonds yield 5% pa and the market portfolio's expected return is 10% pa. All returns are effective annual rates.
What is the price of the stock now?
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?
Question 398 financial distress, capital raising, leverage, capital structure, NPV
A levered firm has 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.
In one year the firm's assets will be worth:
- $13.2m with probability 0.5 in the good state of the world, or
- $6.6m with probability 0.5 in the bad state of the world.
A new project presents itself which requires an investment of $2m and will provide a certain cash flow of $3.3m in one year.
The firm doesn't have any excess cash to make the initial $2m investment, but the funds can be raised from shareholders through a fairly priced rights issue. Ignore all transaction costs.
Should shareholders vote to proceed with the project and equity raising? What will be the gain in shareholder wealth if they decide to proceed?
You just entered into a fully amortising home loan with a principal of $600,000, a variable interest rate of 4.25% pa and a term of 25 years.
Immediately after settling the loan, the variable interest rate suddenly falls to 4% pa! You can't believe your luck. Despite this, you plan to continue paying the same home loan payments as you did before. How long will it now take to pay off your home loan?
Assume that the lower interest rate was granted immediately and that rates were and are now again expected to remain constant. Round your answer up to the nearest whole month.
The average weekly earnings of an Australian adult worker before tax was $1,542.40 per week in November 2014 according to the Australian Bureau of Statistics. Therefore average annual earnings before tax were $80,204.80 assuming 52 weeks per year. Personal income tax rates published by the Australian Tax Office are reproduced for the 2014-2015 financial year in the table below:
| Taxable income | Tax on this income |
|---|---|
| 0 – $18,200 | Nil |
| $18,201 – $37,000 | 19c for each $1 over $18,200 |
| $37,001 – $80,000 | $3,572 plus 32.5c for each $1 over $37,000 |
| $80,001 – $180,000 | $17,547 plus 37c for each $1 over $80,000 |
| $180,001 and over | $54,547 plus 45c for each $1 over $180,000 |
The above rates do not include the Medicare levy of 2%. Exclude the Medicare levy from your calculations
How much personal income tax would you have to pay per year if you earned $80,204.80 per annum before-tax?
Question 785 fixed for floating interest rate swap, non-intermediated swap
The below table summarises the borrowing costs confronting two companies A and B.
| Bond Market Yields | ||||
| Fixed Yield to Maturity (%pa) | Floating Yield (%pa) | |||
| Firm A | 3 | L - 0.4 | ||
| Firm B | 5 | L + 1 | ||
Firm A wishes to borrow at a floating rate and Firm B wishes to borrow at a fixed rate. Design a non-intermediated swap that benefits firm A only. What will be the swap rate?