Fight Finance

Question 185  NPV, DDM, no explanation

A stock is expected to pay the following dividends:

Cash Flows of a Stock
Time (yrs)	0	1	2	3	4	...
Dividend ($)	2	2	2	10	3	...

After year 4, the dividend will grow in perpetuity at 4% pa. The required return on the stock is 10% pa. Both the growth rate and required return are given as effective annual rates.

What will be the price of the stock in 5 years (t = 5), just after the dividend at that time has been paid?

(a) 61.5018

(b) 56.2432

(c) 54.0800

(d) 52.0000

(e) 48.0769

Question 222  fully amortising loan, APR

You just agreed to a 30 year fully amortising mortgage loan with monthly payments of $2,500. The interest rate is 9% pa which is not expected to change.

How much did you borrow? After 10 years, how much will be owing on the mortgage? The interest rate is still 9% and is not expected to change. The below choices are given in the same order.

(a) $320,725.47,     $284,977.19

(b) $310,704.66,     $277,862.39

(c) $310,704.66,     $197,354.23

(d) $308,209.62,     $273,856.37

(e) $308,209.62,     $192,529.73

Question 309  stock pricing, ex dividend date

A company announces that it will pay a dividend, as the market expected. The company's shares trade on the stock exchange which is open from 10am in the morning to 4pm in the afternoon each weekday. When would the share price be expected to fall by the amount of the dividend? Ignore taxes.

The share price is expected to fall during the:

(a) Day of the payment date, between the payment date's morning opening price and afternoon closing price.

(b) Night before the payment date, between the previous day's afternoon closing price and the payment date's morning opening price.

(c) Day of the ex-dividend date, between the ex-dividend date's morning opening price and afternoon closing price.

(d) Night before the ex-dividend date, between the last with-dividend date's afternoon closing price and the ex-dividend date's morning opening price.

(e) Day of the last with-dividend date, between the with-dividend date's morning opening price and afternoon closing price.

Question 346  NPV, annuity due

Your poor friend asks to borrow some money from you. He would like $1,000 now (t=0) and every year for the next 5 years, so there will be 6 payments of $1,000 from t=0 to t=5 inclusive. In return he will pay you $10,000 in seven years from now (t=7).

What is the net present value (NPV) of lending to your friend?

Assume that your friend will definitely pay you back so the loan is risk-free, and that the yield on risk-free government debt is 10% pa, given as an effective annual rate.

(a) $1,340.7944

(b) $1,172.2533

(c) $776.3205

(d) $705.7459

(e) $340.7944

Question 367  CFFA, interest tax shield

There are many ways to calculate a firm's free cash flow (FFCF), also called cash flow from assets (CFFA). Some include the annual interest tax shield in the cash flow and some do not.

Which of the below FFCF formulas include the interest tax shield in the cash flow?

###(1) \quad FFCF=NI + Depr - CapEx -ΔNWC + IntExp### ###(2) \quad FFCF=NI + Depr - CapEx -ΔNWC + IntExp.(1-t_c)### ###(3) \quad FFCF=EBIT.(1-t_c )+ Depr- CapEx -ΔNWC+IntExp.t_c### ###(4) \quad FFCF=EBIT.(1-t_c) + Depr- CapEx -ΔNWC### ###(5) \quad FFCF=EBITDA.(1-t_c )+Depr.t_c- CapEx -ΔNWC+IntExp.t_c### ###(6) \quad FFCF=EBITDA.(1-t_c )+Depr.t_c- CapEx -ΔNWC### ###(7) \quad FFCF=EBIT-Tax + Depr - CapEx -ΔNWC### ###(8) \quad FFCF=EBIT-Tax + Depr - CapEx -ΔNWC-IntExp.t_c### ###(9) \quad FFCF=EBITDA-Tax - CapEx -ΔNWC### ###(10) \quad FFCF=EBITDA-Tax - CapEx -ΔNWC-IntExp.t_c###

The formulas for net income (NI also called earnings), EBIT and EBITDA are given below. Assume that depreciation and amortisation are both represented by 'Depr' and that 'FC' represents fixed costs such as rent.

###NI=(Rev - COGS - Depr - FC - IntExp).(1-t_c )### ###EBIT=Rev - COGS - FC-Depr### ###EBITDA=Rev - COGS - FC### ###Tax =(Rev - COGS - Depr - FC - IntExp).t_c= \dfrac{NI.t_c}{1-t_c}###

(a) 1, 3, 5, 7, 9.

(b) 2, 4, 6, 8, 10.

(c) 1, 4, 6, 8, 10.

(d) 2, 3, 5, 7, 9.

(e) 1, 3, 5, 8, 10.

Question 440  option, no explanation

Two put options are exactly the same, but one has a low and the other has a high exercise price. Which option would you expect to have the higher price, the option with the or exercise price, or should they have the price?

Question 618  capital structure, no explanation

Who owns a company's shares? The:

(a) Company.

(b) Debt holders.

(c) Equity holders.

(d) Chief Executive Officer (CEO).

(e) Board of directors.

Question 634  continuously compounding rate

A $100 stock has a continuously compounded expected total return of 10% pa. Its dividend yield is 2% pa with continuous compounding. What do you expect its price to be in one year?

(a) $112.749685

(b) $110.517092

(c) $110

(d) $108.328707

(e) $108

Question 758  time calculation, fully amortising loan, no explanation

Two years ago you entered into a fully amortising home loan with a principal of $1,000,000, an interest rate of 6% pa compounding monthly with a term of 25 years.

Then interest rates suddenly fall to 4.5% pa (t=0), but you continue to pay the same monthly home loan payments as you did before. How long will it now take to pay off your home loan? Measure the time taken to pay off the home loan from the current time which is 2 years after the home loan was first entered into.

Assume that the lower interest rate was given to you immediately after the loan repayment at the end of year 2, which was the 24th payment since the loan was granted. Also assume that rates were and are expected to remain constant.

(a) 276 months, which is 23 years.

(b) 234 months, which is 19 years and 6 months.

(c) 220 months, which is 18 years and 4 months.

(d) 184 months, which is 15 years and 4 months.

(e) 156 months, which is 13 years.

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.