Fight Finance

Question 5  DDM

For a price of $6, Carlos will sell you a share which will pay a dividend of $1 in one year and every year after that forever. The required return of the stock is 10% pa.

Would you like to his share or politely ?

Question 201  DDM, income and capital returns

The following is the Dividend Discount Model (DDM) used to price stocks:

###P_0=\dfrac{C_1}{r-g}###

If the assumptions of the DDM hold and the stock is fairly priced, which one of the following statements is NOT correct? The long term expected:

(a) Dividend growth rate is equal to the long term expected growth rate of the stock price.

(b) Dividend growth rate is equal to the long term expected capital return of the stock.

(c) Dividend growth rate is equal to the long term expected dividend yield.

(d) Total return of the stock is equal to its long term required return.

(e) Total return of the stock is equal to the company's long term cost of equity.

Question 204  time calculation, fully amortising loan, APR

You just signed up for a 30 year fully amortising mortgage loan with monthly payments of $1,500 per month. The interest rate is 9% pa which is not expected to change.

To your surprise, you can actually afford to pay $2,000 per month and your mortgage allows early repayments without fees. If you maintain these higher monthly payments, how long will it take to pay off your mortgage?

(a) 38.87 months, which is 3.24 yrs.

(b) 47.91 months, which is 3.99 yrs.

(c) 160.72 months, which is 13.39 yrs.

(d) 164.65 months, which is 13.72 yrs.

(e) None of the above.

Question 358  PE ratio, Multiples valuation

Estimate the Chinese bank ICBC's share price using a backward-looking price earnings (PE) multiples approach with the following assumptions and figures only. Note that the renminbi (RMB) is the Chinese currency, also known as the yuan (CNY).

• The 4 major Chinese banks ICBC, China Construction Bank (CCB), Bank of China (BOC) and Agricultural Bank of China (ABC) are comparable companies;
• ICBC 's historical earnings per share (EPS) is RMB 0.74;
• CCB's backward-looking PE ratio is 4.59;
• BOC 's backward-looking PE ratio is 4.78;
• ABC's backward-looking PE ratio is also 4.78;

Note: Figures sourced from Google Finance on 25 March 2014. Share prices are from the Shanghai stock exchange.

(a) RMB 6.4595

(b) RMB 6.3739

(c) RMB 6.3311

(d) RMB 3.4903

(e) RMB 3.3966

Question 581  APR, effective rate, effective rate conversion

A home loan company advertises an interest rate of 6% pa, payable monthly. Which of the following statements about the interest rate is NOT correct? All rates are given to four decimal places.

(a) The APR compounding monthly is 6.0000% per annum.

(b) The effective monthly rate is 0.5000% per month.

(c) The effective annual rate is 6.1678% per annum.

(d) The effective 6 month rate is 3.0000% per six months.

(e) The APR compounding semi-annually is 6.0755% per annum.

Question 700  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 8.54. So the gamble makes him less happy.

(b) Miss Red's expected utility of wealth from gambling is 5 and refusing is also 5. So the gamble doesn't affect her happiness at all.

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

(d) Miss Red's certainty equivalent of the risky gamble is any wealth. She's indifferent since she always has the same level of happiness.

(e) Mrs Green's certainty equivalent of the risky gamble is $25. This is less than her current wealth which is why she would refuse.

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 774  leverage, WACC, real estate

One year ago you bought a $1,000,000 house partly funded using a mortgage loan. The loan size was $800,000 and the other $200,000 was your wealth or 'equity' in the house asset.

The interest rate on the home loan was 4% pa.

Over the year, the house produced a net rental yield of 2% pa and a capital gain of 2.5% pa.

Assuming that all cash flows (interest payments and net rental payments) were paid and received at the end of the year, and all rates are given as effective annual rates, what was the total return on your wealth over the past year?

(a) 0.4808% pa

(b) 2% pa

(c) 4.5% pa

(d) 6.5% pa

(e) 8.5% pa

Hint: Remember that wealth in this context is your equity (E) in the house asset (V = D+E) which is funded by the loan (D) and your deposit or equity (E).

Question 805  short selling

Short selling is a way to make money from falling prices. In what order must the following steps be completed to short-sell an asset? Let Tom, Dick and Harry be traders in the share market.

• Step P: Purchase the asset from Harry.
• Step G: Give the asset to Tom.
• Step W: Wait and hope that the asset price falls.
• Step B: Borrow the asset from Tom.
• Step S: Sell the asset to Dick.

Select the statement with the correct order of steps.

(a) P, G, W, B, S.

(b) B, G, W, P, S.

(c) B, W, G, P, S.

(d) P, W, S, B, G.

(e) B, S, W, P, G.

Question 858  indirect security, intermediated finance, no explanation

Which of the following transactions involves an ‘indirect security’ using a ‘financial intermediary’?

(a) Alice buys Alan’s shares using their share brokers and the securities exchange.

(b) Bell buys Bob’s house using his real estate agent.

(c) Carla lends Carlos money at an interest rate of 10% pa for 3 years.

(d) Dora lends money to her bank at 2% pa and the bank lends the funds to David at 5% pa.

(e) Eve buys Ernie’s government bond using their brokers and the securities exchange.