Fight Finance

Question 121  capital structure, leverage, financial distress, interest tax shield

Fill in the missing words in the following sentence:

All things remaining equal, as a firm's amount of debt funding falls, benefits of interest tax shields __________ and the costs of financial distress __________.

(a) Fall, fall.

(b) Fall, rises.

(c) Rise, fall.

(d) Rise, rise.

(e) Remain unchanged, remain unchanged.

Question 290  APR, effective rate, debt terminology

Which of the below statements about effective rates and annualised percentage rates (APR's) is NOT correct?

(a) An effective annual rate could be called: "a yearly rate compounding per year".

(b) An APR compounding monthly could be called: "a yearly rate compounding per month".

(c) An effective monthly rate could be called: "a yearly rate compounding per month".

(d) An APR compounding daily could be called: "a yearly rate compounding per day".

(e) An effective 2-year rate could be called: "a 2-year rate compounding every 2 years".

Question 365  DDM, stock pricing

Stocks in the United States usually pay quarterly dividends. For example, the software giant Microsoft paid a $0.23 dividend every quarter over the 2013 financial year and plans to pay a $0.28 dividend every quarter over the 2014 financial year.

Using the dividend discount model and net present value techniques, calculate the stock price of Microsoft assuming that:

• The time now is the beginning of July 2014. The next dividend of $0.28 will be received in 3 months (end of September 2014), with another 3 quarterly payments of $0.28 after this (end of December 2014, March 2015 and June 2015).
• The quarterly dividend will increase by 2.5% every year, but each quarterly dividend over the year will be equal. So each quarterly dividend paid in the financial year beginning in September 2015 will be $ 0.287 ##(=0.28×(1+0.025)^1)##, with the last at the end of June 2016. In the next financial year beginning in September 2016 each quarterly dividend will be $0.294175 ##(=0.28×(1+0.025)^2)##, with the last at the end of June 2017, and so on forever.
• The total required return on equity is 6% pa.
• The required return and growth rate are given as effective annual rates.
• Dividend payment dates and ex-dividend dates are at the same time.
• Remember that there are 4 quarters in a year and 3 months in a quarter.

What is the current stock price?

(a) $32.71126

(b) $32.298457

(c) $32

(d) $30.859679

(e) $8

Question 512  capital budgeting, CFFA

Find the cash flow from assets (CFFA) of the following project.

Project Data
Project life	2 years
Initial investment in equipment	$6m
Depreciation of equipment per year for tax purposes	$1m
Unit sales per year	4m
Sale price per unit	$8
Variable cost per unit	$3
Fixed costs per year, paid at the end of each year	$1.5m
Tax rate	30%

Note 1: The equipment will have a book value of $4m at the end of the project for tax purposes. However, the equipment is expected to fetch $0.9 million when it is sold at t=2.

Note 2: Due to the project, the firm will have to purchase $0.8m of inventory initially, which it will sell at t=1. The firm will buy another $0.8m at t=1 and sell it all again at t=2 with zero inventory left. The project will have no effect on the firm's current liabilities.

Find the project's CFFA at time zero, one and two. Answers are given in millions of dollars ($m).

(a) -6,   12.25,   16.68

(b) -6.8,   13.25,   14.05

(c) -6.8,   13.25,   15.88

(d) -6.8,   13.25,   18.51

(e) -6.8,   13.25,   17.71

Question 598  future, tailing the hedge, cross hedging

The standard deviation of monthly changes in the spot price of lamb is $0.015 per pound. The standard deviation of monthly changes in the futures price of live cattle is $0.012 per pound. The correlation between the spot price of lamb and the futures price of cattle is 0.4.

It is now January. A lamb producer is committed to selling 1,000,000 pounds of lamb in May. The spot price of live cattle is $0.30 per pound and the June futures price is $0.32 per pound. The spot price of lamb is $0.60 per pound.

The producer wants to use the June live cattle futures contracts to hedge his risk. Each futures contract is for the delivery of 50,000 pounds of cattle.

How many live cattle futures should the lamb farmer sell to hedge his risk? Round your answer to the nearest whole number of contracts.

(a) 9

(b) 10

(c) 19

(d) 23

(e) 47

Question 690  option

A trader just bought a European style put option on CBA stock. The current option premium is $2, the exercise price is $75, the option matures in one year and the spot CBA stock price is $74.

Which of the following statements is NOT correct?

(a) The long trader paid the option premium at the start.

(b) The option is 'out of the money' at the start.

(c) The long trader wishes for the underlying CBA stock price to fall.

(d) The option can only be exercised at maturity.

(e) If the stock price falls to $60 at maturity, then the long trader can buy the underlying stock for $60, exercise his option to sell the underlying stock to his counterparty for $75, making a payoff at maturity of $15 and a profit of $13.

Question 716  return distribution

The below three graphs show probability density functions (PDF) of three different random variables Red, Green and Blue.

Which of the below statements is NOT correct?

(a)##-1 < \text{Red} < \infty## if Red is log-normally distributed.

(b) ##-2 < \text{Green} < 2## if Green is normally distributed.

(c) ##0 < \text{Blue} < \infty## if Blue is log-normally distributed.

(d) If the Green distribution is normal, then the mode = median = mean.

(e) If the Red and Blue distributions are log-normal, then the mode < median < mean.

Question 721  mean and median returns, return distribution, arithmetic and geometric averages, continuously compounding rate

Fred owns some Commonwealth Bank (CBA) shares. He has calculated CBA’s monthly returns for each month in the past 20 years using this formula:

###r_\text{t monthly}=\ln⁡ \left( \dfrac{P_t}{P_{t-1}} \right)###

He then took the arithmetic average and found it to be 1% per month using this formula:

###\bar{r}_\text{monthly}= \dfrac{ \displaystyle\sum\limits_{t=1}^T{\left( r_\text{t monthly} \right)} }{T} =0.01=1\% \text{ per month}###

He also found the standard deviation of these monthly returns which was 5% per month:

###\sigma_\text{monthly} = \dfrac{ \displaystyle\sum\limits_{t=1}^T{\left( \left( r_\text{t monthly} - \bar{r}_\text{monthly} \right)^2 \right)} }{T} =0.05=5\%\text{ per month}###

Which of the below statements about Fred’s CBA shares is NOT correct? Assume that the past historical average return is the true population average of future expected returns.

(a) The returns ##r_\text{t monthly}## are continuously compounded monthly returns and are likely to be normally distributed, so the mean, median and mode of these continuously compounded returns are all equal to 1% per month.

(b) The annualised average continuously compounded return is ##\bar{r}_\text{cc annual}=12×0.01=0.1=12\%\text{ pa}##. The annualised standard deviation is ##\sigma_\text{annual} = \sqrt{12}×0.05=0.173205081=17.32\%\text{ pa}##.

(c) Over the next 10 years the mean, median and mode continuously compounded 10 year returns will all equal ##0.01 \times 12 \times 10 = 120\%##.

(d) Over the next 10 years the expected mean gross discrete 10 year return is ##e^{(0.01 - 0.05^2/2)×12×10} = 2.857651118## and the median gross discrete 10 year return is ##e^{(0.01 + 0.05^2/2)×12×10}=3.857425531##.

(e) If the current price of the CBA shares is $75, then in 10 years they’re expected to have a mean value of ##75×e^{(0.01 + 0.05^2/2)×12×10} = 289.3069148## and a median value of ##75×e^{0.01×12×10}=249.0087692##.

Question 910  money market

Which of the following is NOT a money market security?

(a) Bank accepted bill (BAB).

(b) Certificate of deposit (CD).

(c) Fixed coupon bond.

(d) Promissory note (PN).

(e) Treasury note (TN) or bill.

Question 925  mean and median returns, return distribution, arithmetic and geometric averages, continuously compounding rate, no explanation

The arithmetic average and standard deviation of returns on the ASX200 accumulation index over the 24 years from 31 Dec 1992 to 31 Dec 2016 were calculated as follows:

###\bar{r}_\text{yearly} = \dfrac{ \displaystyle\sum\limits_{t=1992}^{24}{\left( \ln⁡ \left( \dfrac{P_{t+1}}{P_t} \right) \right)} }{T} = \text{AALGDR} =0.0949=9.49\% \text{ pa}###

###\sigma_\text{yearly} = \dfrac{ \displaystyle\sum\limits_{t=1992}^{24}{\left( \left( \ln⁡ \left( \dfrac{P_{t+1}}{P_t} \right) - \bar{r}_\text{yearly} \right)^2 \right)} }{T} = \text{SDLGDR} = 0.1692=16.92\text{ pp pa}###

Assume that the log gross discrete returns are normally distributed and that the above estimates are true population statistics, not sample statistics, so there is no standard error in the sample mean or standard deviation estimates. Also assume that the standardised normal Z-statistic corresponding to a one-tail probability of 2.5% is exactly -1.96.

Which of the following statements is NOT correct? If you invested $1m today in the ASX200, then over the next 4 years:

(a) Continuously compounded mean and median returns are both 37.96% over the 4 year period.

(b) 95% confidence interval of the continuously compounded returns is between -28.3664% and 104.2864% over the 4 year period.

(c) Mean dollar value is $1.547835m while its median dollar value is $1.4617m in 4 years.

(d) 95% confidence interval of the dollar value is between $0.75302m and $2.17038m in 4 years.

(e) 95% confidence interval of the effective annual return is between -24.698% and 183.7332% over the 4 year period.