Fight Finance

Question 146  APR, effective rate

A three year corporate bond yields 12% pa with a coupon rate of 10% pa, paid semi-annually.

Find the effective six month yield, effective annual yield and the effective daily yield. Assume that each month has 30 days and that there are 360 days in a year.

All answers are given in the same order:

##r_\text{eff semi-annual}##, ##r_\text{eff yearly}##, ##r_\text{eff daily}##.

(a) 0.06, 0.1236, 0.000324.

(b) 0.058301, 0.12, 0.000315.

(c) 0.05, 0.1025, 0.000271.

(d) 0.05, 0.1, 0.000278.

(e) 0.048809, 0.1, 0.000265.

Question 255  bond pricing

In these tough economic times, central banks around the world have cut interest rates so low that they are practically zero. In some countries, government bond yields are also very close to zero.

A three year government bond with a face value of $100 and a coupon rate of 2% pa paid semi-annually was just issued at a yield of 0%. What is the price of the bond?

(a) 94.20452353

(b) 100

(c) 106

(d) 112

(e) The bond is priceless.

Question 282  expected and historical returns, income and capital returns

You're the boss of an investment bank's equities research team. Your five analysts are each trying to find the expected total return over the next year of shares in a mining company. The mining firm:

• Is regarded as a mature company since it's quite stable in size and was floated around 30 years ago. It is not a high-growth company;
• Share price is very sensitive to changes in the price of the market portfolio, economic growth, the exchange rate and commodities prices. Due to this, its standard deviation of total returns is much higher than that of the market index;
• Experienced tough times in the last 10 years due to unexpected falls in commodity prices.
• Shares are traded in an active liquid market.

Your team of analysts present their findings, and everyone has different views. While there's no definitive true answer, whose calculation of the expected total return is the most plausible? Assume that:

• The analysts' source data is correct and true, but their inferences might be wrong;
• All returns and yields are given as effective annual nominal rates.

(a) Alice says 5% pa since she calculated that this was the average total yield on government bonds over the last 10 years. She says that this is also the expected total yield implied by current prices on one year government bonds.

(b) Bob says 4% pa since he calculated that this was the average total return on the mining stock over the last 10 years.

(c) Cate says 3% pa since she calculated that this was the average growth rate of the share price over the last 10 years.

(d) Dave says 6% pa since he calculated that this was the average growth rate of the share market price index (not the accumulation index) over the last 10 years.

(e) Eve says 15% pa since she calculated that this was the discount rate implied by the dividend discount model using the current share price, forecast dividend in one year and a 3% growth rate in dividends thereafter, which is the expected long term inflation rate.

Question 294  short selling, portfolio weights

Which of the following statements about short-selling is NOT true?

(a) Short sellers benefit from price falls.

(b) To short sell, you must borrow the asset from person A and sell it to person B, then later on buy an identical asset from person C and return it to person A.

(c) Short selling only works for assets that are 'fungible' which means that there are many that are identical and substitutable, such as shares and bonds and unlike real estate.

(d) An investor who short-sells an asset has a negative weight in that asset.

(e) An investor who short-sells an asset is said to be 'long' that asset.

Question 327  bill pricing, simple interest rate, no explanation

On 27/09/13, three month Swiss government bills traded at a yield of -0.2%, given as a simple annual yield. That is, interest rates were negative.

If the face value of one of these 90 day bills is CHF1,000,000 (CHF represents Swiss Francs, the Swiss currency), what is the price of one of these bills?

(a) CHF 999,507.09

(b) CHF 1,000,000.00

(c) CHF 1,000,493.39

(d) CHF 1,002,004.01

(e) CHF 1,002,498.39

Question 370  capital budgeting, NPV, interest tax shield, WACC, CFFA

Project Data
Project life	2 yrs
Initial investment in equipment	$600k
Depreciation of equipment per year	$250k
Expected sale price of equipment at end of project	$200k
Revenue per job	$12k
Variable cost per job	$4k
Quantity of jobs per year	120
Fixed costs per year, paid at the end of each year	$100k
Interest expense in first year (at t=1)	$16.091k
Interest expense in second year (at t=2)	$9.711k
Tax rate	30%
Government treasury bond yield	5%
Bank loan debt yield	6%
Levered cost of equity	12.5%
Market portfolio return	10%
Beta of assets	1.24
Beta of levered equity	1.5
Firm's and project's debt-to-equity ratio	25%

Notes

1. The project will require an immediate purchase of $50k of inventory, which will all be sold at cost when the project ends. Current liabilities are negligible so they can be ignored.

Assumptions

• The debt-to-equity ratio will be kept constant throughout the life of the project. The amount of interest expense at the end of each period has been correctly calculated to maintain this constant debt-to-equity ratio. Note that interest expense is different in each year.
• Thousands are represented by 'k' (kilo).
• 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 nominal. The inflation rate is 2% pa.
• All rates are given as effective annual rates.
• The 50% capital gains tax discount is not available since the project is undertaken by a firm, not an individual.

What is the net present value (NPV) of the project?

(a) $684.222k

(b) $690.919k

(c) $697.616k

(d) $698.713k

(e) $710.601k

Question 487  capital budgeting, opportunity cost, sunk cost

A young lady is trying to decide if she should attend university or begin working straight away in her home town.

The young lady's grandma says that she should not go to university because she is less likely to marry the local village boy whom she likes because she will spend less time with him if she attends university.

What's the correct way to classify this item from a capital budgeting perspective when trying to decide whether to attend university?

The cost of not marrying the local village boy should be classified as:

(a) A sunk cost.

(b) An opportunity cost.

(c) A non-pecuniary cost that should be disregarded.

(d) A positive side effect.

(e) A depreciation expense.

Question 701  utility, risk aversion, utility function, gamble

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

Each person has $50 of initial wealth. A coin toss game is offered to each person at a casino where the player can win or lose $50. Each player can flip a coin and if they flip heads, they receive $50. If they flip tails then they will lose $50. Which of the following statements is NOT correct?

(a) Mr Blue's expected utility of wealth from gambling is 7.5 while refusing is 6.25. So the gamble makes him more happy.

(b) Miss Red's expected utility of wealth from gambling is 7.5 and refusing is also 7.5. This is why she is indifferent.

(c) Mr Blue's certainty equivalent of the risky gamble is $70.71. So he would pay to take part in the gamble.

(d) Miss Red's certainty equivalent of the risky gamble is $50.

(e) Mrs Green's certainty equivalent of the risky gamble is $70.71. She would enjoy taking part in the gamble.

Question 811  log-normal distribution, mean and median returns, return distribution, arithmetic and geometric averages

Which of the following statements about probability distributions is NOT correct?

(a) A normally distributed variable’s mean, median and mode are all expected to be equal.

(b) A log-normally distributed variable’s mean, median and mode are all expected to be different. Mean > median > mode.

(c) Future stock prices ##(P_t )## are often assumed to be log-normally distributed.

(d) Stocks’ annual net discrete returns ##(P_t/P_0-1)## must be normally distributed when stock prices ##(P_t)## are log-normally distributed.

(e) The total area under a probability density function (pdf) is always one.

Question 828  future, future valuation, no explanation

You bought a 1.5 year (18 month) futures contract on oil. Oil storage costs are 4% pa continuously compounded and oil pays no dividends. The futures contract is entered into when the oil price is $40 per barrel and the risk-free rate of interest is 10% per annum with continuous compounding.

Which of the following statements is NOT correct?

(a) The initial futures price is $49.3471.

(b) The initial value of the futures contract is zero.

(c) If the oil price falls to $35 per barrel in one year then the value of the futures contract at that time would be -$11.2334.

(d) If the oil price is still at $40 per barrel in one year then the value of the futures contract at that time would be zero.

(e) If the oil price rises to $45 per barrel in one year then the value of the futures contract at that time would be -$1.0314.