Fight Finance

Question 247  cross currency interest rate parity, no explanation

In the so called 'Swiss Loans Affair' of the 1980's, Australian banks offered loans denominated in Swiss Francs to Australian farmers at interest rates as low as 4% pa. This was far lower than interest rates on Australian Dollar loans which were above 10% due to very high inflation in Australia at the time.

In the late-1980's there was a large depreciation in the Australian Dollar. The Australian Dollar nearly halved in value against the Swiss Franc. Many Australian farmers went bankrupt since they couldn't afford the interest payments on the Swiss Franc loans because the Australian Dollar value of those payments nearly doubled. The farmers accused the banks of promoting Swiss Franc loans without making them aware of the risks.

What fundamental principal of finance did the Australian farmers (and the bankers) fail to understand?

(a) Home-made leverage.

(b) Diversification.

(c) Cross-currency interest rate parity.

(d) Time value of money.

(e) The undiversifiable nature of systematic risk.

Question 421  takeover

Acquirer firm plans to launch a takeover of Target firm. The deal is expected to create a present value of synergies totaling $105 million. A scrip offer will be made that pays the fair price for the target's shares plus 75% of the total synergy value.

Firms Involved in the Takeover
	Acquirer	Target
Assets ($m)	6,000	700
Debt ($m)	4,800	400
Share price ($)	40	20
Number of shares (m)	30	15

Ignore transaction costs and fees. Assume that the firms' debt and equity are fairly priced, and that each firms' debts' risk, yield and values remain constant. The acquisition is planned to occur immediately, so ignore the time value of money.

Calculate the merged firm's share price and total number of shares after the takeover has been completed.

(a) $26.7778 share price and 45m shares on issue.

(b) $40.875 share price and 39.266055m shares on issue.

(c) $42.0639 share price and 38.15625m shares on issue.

(d) $42.8 share price and 37.5m shares on issue.

(e) $50.875 share price and 30m shares on issue.

Question 423  takeover

Acquirer firm plans to launch a takeover of Target firm. The deal is expected to create a present value of synergies totaling $105 million. A 40% scrip and 60% cash offer will be made that pays the fair price for the target's shares plus 75% of the total synergy value. The cash will be paid out of the firm's cash holdings, no new debt or equity will be raised.

Firms Involved in the Takeover
	Acquirer	Target
Assets ($m)	6,000	700
Debt ($m)	4,800	400
Share price ($)	40	20
Number of shares (m)	30	15

Ignore transaction costs and fees. Assume that the firms' debt and equity are fairly priced, and that each firms' debts' risk, yield and values remain constant. The acquisition is planned to occur immediately, so ignore the time value of money.

Calculate the merged firm's share price and total number of shares after the takeover has been completed.

(a) $36.74 share price and 37.5m shares on issue.

(b) $37.925 share price and 30m shares on issue.

(c) $40.875 share price and 33.706422m shares on issue.

(d) $40.875 share price and 35.559633m shares on issue.

(e) $47.5556 share price and 33.75m shares on issue.

Question 517  DDM

A stock is expected to pay its next dividend of $1 in one year. Future annual dividends are expected to grow by 2% pa. So the first dividend of $1 will be in one year, the year after that $1.02 (=1*(1+0.02)^1), and a year later $1.0404 (=1*(1+0.02)^2) and so on forever.

Its required total return is 10% pa. The total required return and growth rate of dividends are given as effective annual rates.

Calculate the current stock price.

(a) $10

(b) $12.254902

(c) $12.5

(d) $12.75

(e) $13.75

Question 722  mean and median returns, return distribution, arithmetic and geometric averages, continuously compounding rate

Here is a table of stock prices and returns. Which of the statements below the table is NOT correct?

Price and Return Population Statistics
Time	Prices	LGDR	GDR	NDR
0	100
1	50	-0.6931	0.5	-0.5
2	100	0.6931	2	1
Arithmetic average		0	1.25	0.25
Arithmetic standard deviation		0.9802	1.0607	1.0607

 

(a) The geometric average of the gross discrete returns (GAGDR) equals 1 which is 100%.

(b) ##\text{GAGDR} = \exp \left( \text{AALGDR} \right)##. The GAGDR is equal to the natural exponent of the arithmetic average of the logarithms of the gross discrete returns (AALGDR).

(c) ##\text{GAGDR} = \left( P_T/P_0 \right)^{1/T}##. The GAGDR equals the ratio of the last and first prices raised to the power of the inverse of the number of time periods between them.

(d) ##\text{LGAGDR} = \text{AALGDR}##. This is always true, regardless of the distribution of the prices or returns and the number of return observations. The logarithm of the geometric average of the gross discrete returns (LGAGDR) is always equal to the arithmetic average of the logarithms of the gross discrete returns (AALGDR).

(e) ##\text{LAAGDR} = \text{AALGDR} + \text{SDLGDR}^2/2##. This is always true, regardless of the distribution of the prices or returns and the number of return observations. The logarithm of the arithmetic average of the gross discrete returns (LAAGDR) equals the arithmetic average of the logarithms of the gross discrete returns (AALGDR) plus half the variance of the LGDR's.

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 736  debt terminology

You bought a house, primarily funded using a home loan from a bank. Which of the following statements is NOT correct?

(a) The home loan is a debt liability to the bank.

(b) The bank invested in your debt.

(c) You are indebted to the bank.

(d) You owe the bank principal and interest payments.

(e) You sold your promise to the bank to pay the principal and interest.

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 794  option, Black-Scholes-Merton option pricing, option delta, no explanation

Which of the following quantities from the Black-Scholes-Merton option pricing formula gives the Delta of a European call option?

(a) ##N[d_1]##

(b) ##N[d_2]##

(c) ##−N[−d_1]##

(d) ##−N[−d_2]##

(e) ##N[−d_2]##

Where:

###d_1=\dfrac{\ln⁡[S_0/K]+(r+\sigma^2/2).T)}{\sigma.\sqrt{T}}### ###d_2=d_1-\sigma.\sqrt{T}=\dfrac{\ln⁡[S_0/K]+(r-\sigma^2/2).T)}{\sigma.\sqrt{T}}###

Question 856  credit terms, no explanation

Your supplier’s credit terms are "1/10 net 30". Which of the following statements about these credit terms is NOT correct?

If you intend to buy an item from your supplier for a tag price of $100 and you:

(a) Pay straightaway then you only have to pay $99.

(b) Pay on the 10th day then you’ll be asked to pay the full $100.

(c) Pay on the 11th day then you’ll be asked to pay the full $100.

(d) Pay on the 30th day then you’ll be asked to pay the full $100.

(e) Pay on the 40th day then you’ll be asked to pay the full $100 and the business owner may be upset with you and might not give you credit next time.