Fight Finance

Question 3  DDM, income and capital returns

The following equation is called the Dividend Discount Model (DDM), Gordon Growth Model or the perpetuity with growth formula: ### P_0 = \frac{ C_1 }{ r - g } ###

What is ##g##? The value ##g## is the long term expected:

(a) Income return of the stock.

(b) Capital return of the stock.

(c) Total return of the stock.

(d) Dividend yield of the stock.

(e) Price-earnings ratio of the stock.

Question 435  option, no explanation

Will the price of a call option on equity or if the standard deviation of returns (risk) of the underlying shares becomes higher?

Question 445  financing decision, corporate financial decision theory

The financing decision primarily affects which part of a business?

(a) Assets.

(b) Liabilities and owner's equity.

(c) Current assets and current liabilities.

(d) Dividends and buy backs.

(e) Net income, also known as earnings or net profit after tax.

Question 529  DDM, real and nominal returns and cash flows, inflation, real estate, no explanation

If housing rents are constrained from growing more than the maximum target inflation rate, and houses can be priced as a perpetuity of growing net rental cash flows, then what is the implication for house prices, all things remaining equal? Select the most correct answer.

(a) Real house prices must grow by more than the maximum target inflation rate in perpetuity.

(b) Real house prices must grow by less than or equal to the maximum target inflation rate in perpetuity.

(c) Nominal house prices must grow by more than the maximum target inflation rate in perpetuity.

(d) Nominal house prices must grow by less than or equal to the maximum target inflation rate in perpetuity.

(e) Real house prices must grow by more than nominal house prices in perpetuity.

Background: Since 1990, many central banks across the world have become 'inflation targeters'. They have adopted a policy of trying to keep inflation in a predictable narrow range, with the hope of encouraging long-term lending to fund more investment and maintain higher GDP growth.

Australia's central bank, the Reserve Bank of Australia (RBA), has specifically stated their inflation target range is between 2 and 3% pa.

Some Australian residential property market commentators suggest that because rental costs comprise a large part of the Australian consumer price index (CPI), rent costs across the nation cannot significantly exceed the maximum inflation target range of 3% pa without the prices of other goods growing by less than the target range for long periods, which is unlikely.

Question 548  equivalent annual cash flow, time calculation, no explanation

An Apple iPhone 6 smart phone can be bought now for $999. An Android Kogan Agora 4G+ smart phone can be bought now for $240.

If the Kogan phone lasts for one year, 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.

(a) 11 years

(b) 9 years

(c) 7 years

(d) 5 years

(e) 3 years

Question 553  bond pricing, income and capital returns

An investor bought a 20 year 5% pa fixed coupon government bond priced at par. The face value is $100. Coupons are paid semi-annually and the next one is in 6 months.

Six months later, just after the coupon at that time was paid, yields suddenly and unexpectedly rose to 5.5% pa. Note that all yields above are given as APR's compounding semi-annually.

What was the bond investors' historical total return over that first 6 month period, given as an effective semi-annual rate?

(a) -0.084351

(b) -0.059351

(c) -0.046851

(d) -0.034351

(e) -0.008907

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 699  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 5 while refusing is 7.07. So the gamble makes him less happy.

(b) Mrs Green's expected utility of wealth from gambling is 7.07 while refusing is 5. So the gamble makes her more happy.

(c) Mr Blue's certainty equivalent of the risky gamble is $25. This is less than his current wealth of $50 which is why he would refuse.

(d) Miss Red's certainty equivalent of the risky gamble is $50. This is equal to her current wealth of $50 which is why she is indifferent to gambling or not.

(e) Mrs Green's certainty equivalent of the risky gamble is $70.71. This is more than her current wealth of $50 which is why she would accept.

Question 789  rights issue, capital raising

A firm wishes to raise $30 million now. The firm's current market value of equity is $60m and the market price per share is $20. They estimate that they'll be able to issue shares in a rights issue at a subscription price of $15. Ignore the time value of money and assume that all shareholders exercise their rights. Which of the following statements is NOT correct?

(a) The firm currently has 3m shares on issue and will need to sell 2m new shares in the rights issue.

(b) The company should do a 2-for-3 rights issue.

(c) After the rights issue the market share price will be $17.

(d) The value of one right would be $3.

(e) If you don't take part in the rights issue and it is non-renounceable, you will lose $2 per share.

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.