Fight Finance

Question 36  DDM, perpetuity with growth

A stock pays annual dividends which are expected to continue forever. It just paid a dividend of $10. The growth rate in the dividend is 2% pa. You estimate that the stock's required return is 10% pa. Both the discount rate and growth rate are given as effective annual rates. Using the dividend discount model, what will be the share price?

(a) $127.5

(b) $125

(c) $102

(d) $101.98

(e) $100

Question 345  capital budgeting, break even, NPV

Project Data
Project life	10 yrs
Initial investment in factory	$10m
Depreciation of factory per year	$1m
Expected scrap value of factory at end of project	$0
Sale price per unit	$10
Variable cost per unit	$6
Fixed costs per year, paid at the end of each year	$2m
Interest expense per year	0
Tax rate	30%
Cost of capital per annum	10%

Notes

1. The firm's current liabilities are forecast to stay at $0.5m. The firm's current assets (mostly inventory) is currently $1m, but is forecast to grow by $0.1m at the end of each year due to the project.
   At the end of the project, the current assets accumulated due to the project can be sold for the same price that they were bought.
2. A marketing survey was used to forecast sales. It cost $1.4m which was just paid. The cost has been capitalised by the accountants and is tax-deductible over the life of the project, regardless of whether the project goes ahead or not. This amortisation expense is not included in the depreciation expense listed in the table above.

Assumptions

• All cash flows occur at the start or end of the year as appropriate, not in the middle or throughout the year.
• All rates and cash flows are real. The inflation rate is 3% pa.
• All rates are given as effective annual rates.

Find the break even unit production (Q) per year to achieve a zero Net Income (NI) and Net Present Value (NPV), respectively. The answers below are listed in the same order.

(a) 750,000 and 750,000.

(b) 750,000 and 951,682.

(c) 750,000 and 987,396.

(d) 750,000 and 1,009,805.

(e) 750,000 and 1,024,807.

Question 399  option, no explanation

A European call option will mature in ##T## years with a strike price of ##K## dollars. The underlying asset has a price of ##S## dollars.

What is an expression for the payoff at maturity ##(f_T)## in dollars from owning (being long) the call option?

(a) ##\max(S_T - K, 0)##.

(b) ##\max(S_T - K, K)##.

(c) ##\max(K-S_T, 0)##.

(d) ##\max(K-S_T, K)##.

(e) ##\min(K-S_T, 0)##.

Question 449  personal tax on dividends, classical tax system

A small private company has a single shareholder. This year the firm earned a $100 profit before tax. All of the firm's after tax profits will be paid out as dividends to the owner.

The corporate tax rate is 30% and the sole shareholder's personal marginal tax rate is 45%.

The United States' classical tax system applies because the company generates all of its income in the US and pays corporate tax to the Internal Revenue Service. The shareholder is also an American for tax purposes.

What will be the personal tax payable by the shareholder and the corporate tax payable by the company?

(a) Personal tax of $6.43 and corporate tax of $45.

(b) Personal tax of $15 and corporate tax of $30.

(c) Personal tax of $16.5 and corporate tax of $45.

(d) Personal tax of $31.5 and corporate tax of $30.

(e) Personal tax of $45 and corporate tax of $0.

Question 660  fully amortising loan, interest only loan, APR

How much more can you borrow using an interest-only loan compared to a 25-year fully amortising loan if interest rates are 6% pa compounding per month and are not expected to change? If it makes it easier, assume that you can afford to pay $2,000 per month on either loan. Express your answer as a proportional increase using the following formula:

###\text{Proportional Increase} = \dfrac{V_\text{0,interest only}}{V_\text{0,fully amortising}} - 1###

(a) 77.6034%

(b) 30.3779%

(c) 28.8603%

(d) 22.3966%

(e) 7.5304%

Question 705  utility, risk aversion, utility function

Mr Blue, Miss Red and Mrs Green are people with different utility functions.

Which of the following statements is NOT correct?

(a) Mr Blue is as happy with zero wealth as he is with $1,000. Similarly for Miss Red and Mrs Green.

(b) All of the people would appear irrational to an economist. Though Mr Blue appears to be rational when he has more than $192 in wealth.

(c) Mr Blue is risk averse. Miss Red is risk neutral. Mrs Green is risk loving.

(d) Miss Red is totally indifferent to how much wealth she has. She doesn't care about gaining or losing money.

(e) Mr Blue prefers more to less up to a wealth of around $192. At about $192 he is the happiest he can be. This is his bliss point. With more than $192 he becomes less happy.

Question 727  inflation, real and nominal returns and cash flows

The Australian Federal Government lends money to domestic students to pay for their university education. This is known as the Higher Education Contribution Scheme (HECS). The nominal interest rate on the HECS loan is set equal to the consumer price index (CPI) inflation rate. The interest is capitalised every year, which means that the interest is added to the principal. The interest and principal does not need to be repaid by students until they finish study and begin working.

Which of the following statements about HECS loans is NOT correct?

(a) The real interest rate is zero.

(b) The nominal amount owing on the loan will increase at the inflation rate over time, if there are no extra payments or borrowings.

(c) The real amount owing on the loan in today's money will remain the same over time, if there are no extra payments or borrowings.

(d) The interest rate on the HECS loan advantages rich domestic students because they are able to pay off their debt sooner and avoid paying as much HECS interest.

(e) The interest rate on the HECS loan advantages all domestic students because the alternative of borrowing from the bank to pay for education would usually attract a higher interest rate.

Question 743  price gains and returns over time, no explanation

How many years will it take for an asset's price to triple (increase from say $1 to $3) if it grows by 5% pa?

(a) 17.7643 years

(b) 22.5171 years

(c) 29.2722 years

(d) 40 years

(e) 60 years

Question 814  expected and historical returns

If future required returns rise, and future expected cash flows remain the same, then prices will , or remain the ?

Question 895  comparative advantage in trade, production possibilities curve

Adam and Bella are the only people on a remote island.

Luckily there are Coconut and Date palm trees on the island that grow delicious fruit. The problem is that harvesting the fruit takes a lot of work.

Adam can pick 7 coconuts per hour, 6 dates per hour or any linear combination of coconuts and dates. For example, he could pick 3.5 coconuts and 3 dates per hour.

Bella can pick 3 coconuts per hour, 5 dates per hour or any linear combination. For example, she could pick 1.5 coconuts and 2.5 dates per hour.

This information is summarised in the table and graph:

Harvest Rates Per Hour
	Coconuts	Dates
Adam	7	6
Bella	3	5

 

Which of the following statements is NOT correct?

(a) Adam’s opportunity cost of picking one date per hour is 7/6 coconuts, so he picks around 1.1667 coconuts per one date per one hour.

(b) Bella’s opportunity cost of picking one date per hour is 3/5 coconuts, so she picks around 0.6 coconuts per one date per one hour.

(c) Adam’s opportunity cost of picking one coconut per hour is 6/7 dates, so he picks around 0.8571 dates per one coconut per one hour.

(d) Bella’s opportunity cost of picking one coconut per hour is 5/3 dates, so she picks around 1.6667 dates per one coconut per one hour.

(e) The gradients (rise over run) of the lines in the graph are measured in dates per one coconut per hour.