Fight Finance

Question 190  pay back period

A project has the following cash flows:

Project Cash Flows
Time (yrs)	Cash flow ($)
0	-400
1	0
2	500

What is the payback period of the project in years?

Normally cash flows are assumed to happen at the given time. But here, assume that the cash flows are received smoothly over the year. So the $500 at time 2 is actually earned smoothly from t=1 to t=2.

(a) -0.80

(b) 0.80

(c) 1.20

(d) 1.80

(e) 2.20

Question 246  foreign exchange rate, forward foreign exchange rate, cross currency interest rate parity

Suppose the Australian cash rate is expected to be 8.15% pa and the US federal funds rate is expected to be 3.00% pa over the next 2 years, both given as nominal effective annual rates. The current exchange rate is at parity, so 1 USD = 1 AUD.

What is the implied 2 year forward foreign exchange rate?

(a) 1 USD = 1.1025 AUD

(b) 1.1025 USD = 1 AUD

(c) 1 USD = 1.05 AUD

(d) 1 USD = 1.1 AUD

(e) 1.1 USD = 1 AUD

Question 568  rights issue, capital raising, capital structure

A company conducts a 1 for 5 rights issue at a subscription price of $7 when the pre-announcement stock price was $10. What is the percentage change in the stock price and the number of shares outstanding? The answers are given in the same order. Ignore all taxes, transaction costs and signalling effects.

(a) -16.67%, 20%

(b) -5%, 20%

(c) 0%, 20%

(d) 7.14%, 20%

(e) 11.67%, 0%

Question 678  option, option profit, no explanation

Which of the below formulas gives the profit ##(\pi)## from being short a put option? Let the underlying asset price at maturity be ##S_T##, the exercise price be ##X_T## and the option price be ##f_{LP,0}##. Note that ##S_T##, ##X_T## and ##f_{LP,0}## are all positive numbers.

(a) ##\pi_{SP}=-max⁡(S_T-X_T,0) - f_{LP,0}##

(b) ##\pi_{SP}=-max⁡(X_T-S_T,0) + f_{LP,0}##

(c) ##\pi_{SP}=max⁡(S_T-X_T,0) - f_{LP,0}##

(d) ##\pi_{SP}=max⁡(X_T-S_T,0) + f_{LP,0}##

(e) ##\pi_{SP}=max(X_T-S_T,0) - f_{LP,0}##

Question 688  future, hedging

A pig farmer in the US is worried about the price of hogs falling and wants to lock in a price now. In one year the pig farmer intends to sell 1,000,000 pounds of hogs. Luckily, one year CME lean hog futures expire on the exact day that he wishes to sell his pigs. The futures have a notional principal of 40,000 pounds (about 18 metric tons) and currently trade at a price of 63.85 cents per pound. The underlying lean hogs spot price is 77.15 cents per pound. The correlation between the futures price and the underlying hogs price is one and the standard deviations are both 4 cents per pound. The initial margin is USD1,500 and the maintenance margin is USD1,200 per futures contract.

Which of the below statements is NOT correct?

(a) The pig farmer should sell futures to hedge against the danger of falling hog prices.

(b) The pig farmer should transact 30 lean hogs futures contracts with tailing since futures contracts require margins.

(c) The total initial margin that must be paid to the pig farmer’s futures broker is $45,000.

(d) If the futures price falls by more than 0.01175 cents per pound (rounded to 5 decimal places) then the pig farmer will receive a margin call from their broker.

(e) The future is trading in backwardation since the spot price exceeds the futures price, so the current basis is positive 13.30 cents.

Question 733  DDM, income and capital returns

A share’s current price is $60. It’s expected to pay a dividend of $1.50 in one year. The growth rate of the dividend is 0.5% pa and the stock’s required total return is 3% pa. The stock’s price can be modeled using the dividend discount model (DDM):

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

Which of the following methods is NOT equal to the stock’s expected price in one year and six months (t=1.5 years)? Note that the symbolic formulas shown in each line below do equal the formulas with numbers. The formula is just repeated with symbols and then numbers in case it helps you to identify the incorrect statement more quickly.

(a) ##P_{1.5}=P_0 (1+g)^1 (1+r)^{0.5}=60(1+0.005)^1 (1+0.03)^{0.5}##

(b) ##P_{1.5}=(P_0 (1+r)^1-C_1 ) (1+r)^{0.5}=(60(1+0.03)^1-1.5) (1+0.03)^{0.5}##

(c) ##P_{1.5}=\dfrac{C_1}{r-g} (1+r)^1 (1+g)^{0.5}=\dfrac{1.5}{0.03-0.005} (1+0.03)^1 (1+0.005)^{0.5}##

(d) ##P_{1.5}=\dfrac{C_1 (1+g)^1}{r-g} (1+r)^{0.5}=\dfrac{1.5(1+0.005)^1}{0.03-0.005} (1+0.03)^{0.5}##

(e) ##P_{1.5}=\dfrac{C_1 (1+g)^2}{r-g}/(1+r)^{0.5} +C_1 (1+g)^1/(1+r)^{0.5} =\dfrac{1.5(1+0.005)^2}{0.03-0.005}/(1+0.03)^{0.5} +1.5(1+0.005)^1/(1+0.03)^{0.5} ##

Question 735  debt terminology

You deposit money into a bank. Which of the following statements is NOT correct? You:

(a) Are a lender.

(b) Issued debt.

(c) Bought debt.

(d) Are a debt holder.

(e) Own a debt asset.

Question 754  fully amortising loan, interest only loan

How much more can you borrow using an interest-only loan compared to a 25-year fully amortising loan if interest rates are 4% 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) 63.1508%

(b) 60.0299%

(c) 58.3511%

(d) 36.8492%

(e) 11.5269%

Question 790  mean and median returns, return distribution, arithmetic and geometric averages, continuously compounding rate, log-normal distribution, VaR, confidence interval

A risk manager has identified that their hedge fund’s continuously compounded portfolio returns are normally distributed with a mean of 10% pa and a standard deviation of 30% pa. The hedge fund’s portfolio is currently valued at $100 million. Assume that there is no estimation error in these figures and that the normal cumulative density function at 1.644853627 is 95%.

Which of the following statements is NOT correct? All answers are rounded to the nearest dollar.

(a) Future portfolio values have a log-normal distribution. The mean (expected or arithmetic average) portfolio value in one year is $115,603,957.

(b) The median (50th percentile) portfolio value in one year is $115,603,957.

(c) The 90% confidence interval of continuously compounded portfolio returns over the next year ##(r_{0 \rightarrow 1})## is ##-39.3456088\% < r_{0 \rightarrow 1} < 59.3456088\%##.

(d) The 90% confidence interval of portfolio values in one year ##(V_1)## is ##\$67,472,095 < V_1 < \$181,023,395##.

(e) The annual 95% relative VaR is $48,131,863 and the absolute VaR is $32,527,905.

Question 821  option, option profit, option payoff at maturity, no explanation

You just paid $4 for a 3 month European style call option on a stock currently priced at $47 with a strike price of $50. The stock’s next dividend will be $1 in 4 months’ time. Note that the dividend is paid after the option matures. Which of the below statements is NOT correct?

(a) You have the right to buy the underlying stock in 3 months’ time for a price of $50 if you want.

(b) If the dividend in 4 months were unexpectedly cancelled because the firm decided to re-invest its cash rather than pay it out then the 3 month call option price would be unaffected.

(c) If the stock price is $49 in 3 months then you wouldn’t exercise the ‘out of the money’ option.

(d) If the stock price is $51 in 3 months then you wouldn’t exercise or else you’ll incur a loss of $3.

(e) If the stock price is $57 in 3 months then you would exercise. Your profit would be $3 and payoff at maturity $7.