Fight Finance

Question 60  pay back period

The required return of a project is 10%, given as an effective annual rate.

What is the payback period of the project in years?

Assume that the cash flows shown in the table are received smoothly over the year. So the $121 at time 2 is actually earned smoothly from t=1 to t=2.

Project Cash Flows
Time (yrs)	Cash flow ($)
0	-100
1	11
2	121

(a) 2.7355

(b) 2.3596

(c) 1.7355

(d) 1.2645

(e) 0.2645

Question 116  capital structure, CAPM

A firm changes its capital structure by issuing a large amount of equity and using the funds to repay debt. Its assets are unchanged. Ignore interest tax shields.

According to the Capital Asset Pricing Model (CAPM), which statement is correct?

(a) The beta of the firm's assets will increase.

(b) The beta of the firm's assets will decrease.

(c) The beta of the firm's equity will increase.

(d) The beta of the firm's equity will decrease.

(e) The beta of the firm's equity will be unchanged.

Question 179  bond pricing, capital raising

A firm wishes to raise $20 million now. They will issue 8% pa semi-annual coupon bonds that will mature in 5 years and have a face value of $100 each. Bond yields are 6% pa, given as an APR compounding every 6 months, and the yield curve is flat.

How many bonds should the firm issue?

(a) 140,202

(b) 184,280

(c) 184,460

(d) 186,881

(e) 200,000

Question 229  bond pricing

An investor bought two fixed-coupon bonds issued by the same company, a zero-coupon bond and a 7% pa semi-annual coupon bond. Both bonds have a face value of $1,000, mature in 10 years, and had a yield at the time of purchase of 8% pa.

A few years later, yields fell to 6% pa. Which of the following statements is correct? Note that a capital gain is an increase in price.

(a) The zero-coupon bond and the 7% semi-annual coupon bond were both discount bonds but now they are both premium bonds.

(b) The zero-coupon bond and the 7% semi-annual coupon bond were both premium bonds but now they are both discount bonds.

(c) When yields fell, the investor made a capital loss on both bonds.

(d) When yields fell, the investor made a capital gain on both bonds.

(e) When yields fell, the investor made a capital gain on the zero coupon bond but a loss on the 7% semi-annual coupon bond.

Question 282  expected and historical returns, income and capital returns

You're the boss of an investment bank's equities research team. Your five analysts are each trying to find the expected total return over the next year of shares in a mining company. The mining firm:

• Is regarded as a mature company since it's quite stable in size and was floated around 30 years ago. It is not a high-growth company;
• Share price is very sensitive to changes in the price of the market portfolio, economic growth, the exchange rate and commodities prices. Due to this, its standard deviation of total returns is much higher than that of the market index;
• Experienced tough times in the last 10 years due to unexpected falls in commodity prices.
• Shares are traded in an active liquid market.

Your team of analysts present their findings, and everyone has different views. While there's no definitive true answer, whose calculation of the expected total return is the most plausible? Assume that:

• The analysts' source data is correct and true, but their inferences might be wrong;
• All returns and yields are given as effective annual nominal rates.

(a) Alice says 5% pa since she calculated that this was the average total yield on government bonds over the last 10 years. She says that this is also the expected total yield implied by current prices on one year government bonds.

(b) Bob says 4% pa since he calculated that this was the average total return on the mining stock over the last 10 years.

(c) Cate says 3% pa since she calculated that this was the average growth rate of the share price over the last 10 years.

(d) Dave says 6% pa since he calculated that this was the average growth rate of the share market price index (not the accumulation index) over the last 10 years.

(e) Eve says 15% pa since she calculated that this was the discount rate implied by the dividend discount model using the current share price, forecast dividend in one year and a 3% growth rate in dividends thereafter, which is the expected long term inflation rate.

Question 292  standard deviation, risk

Find the sample standard deviation of returns using the data in the table:

Stock Returns
Year	Return pa
2008	0.3
2009	0.02
2010	-0.2
2011	0.4

The returns above and standard deviations below are given in decimal form.

(a) 0.277075

(b) 0.272519

(c) 0.239954

(d) 0.236008

(e) 0.162070

Question 362  income and capital returns, DDM, real estate

Three years ago Frederika bought a house for $400,000.

Now it's worth $600,000, based on recent similar sales in the area.

Frederika's residential property has an expected total return of 7% pa.

She rents her house out for $2,500 per month, paid in advance. Every 12 months she plans to increase the rental payments.

The present value of 12 months of rental payments is $29,089.48.

The future value of 12 months of rental payments one year ahead is $31,125.74.

What is the expected annual capital yield of the property?

(a) -0.7814%

(b) -0.2724%

(c) 1.8124%

(d) 2%

(e) 2.1518%

Question 452  limited liability, expected and historical returns

What is the lowest and highest expected share price and expected return from owning shares in a company over a finite period of time?

Let the current share price be ##p_0##, the expected future share price be ##p_1##, the expected future dividend be ##d_1## and the expected return be ##r##. Define the expected return as:

##r=\dfrac{p_1-p_0+d_1}{p_0} ##

The answer choices are stated using inequalities. As an example, the first answer choice "(a) ##0≤p<∞## and ##0≤r< 1##", states that the share price must be larger than or equal to zero and less than positive infinity, and that the return must be larger than or equal to zero and less than one.

(a) ##0≤p<∞## and ##0≤r< 1##

(b) ##0≤p<∞## and ##-1≤r< ∞##

(c) ##0≤p<∞## and ##0≤r< ∞##

(d) ##0≤p<∞## and ##-∞≤r< ∞##

(e) ##-∞<p<∞## and ##-∞<r< ∞##

Question 877  arithmetic and geometric averages, utility, utility function

Gross discrete returns in different states of the world are presented in the table below. A gross discrete return is defined as ##P_1/P_0##, where ##P_0## is the price now and ##P_1## is the expected price in the future. An investor can purchase only a single asset, A, B, C or D. Assume that a portfolio of assets is not possible.

Gross Discrete Returns
In Different States of the World
Investment	World states (probability)
asset	Good (50%)	Bad (50%)
A	2	0.5
B	1.1	0.9
C	1.1	0.95
D	1.01	1.01

 

Which of the following statements about the different assets is NOT correct? Asset:

(a) A's Arithmetic Average Gross Discrete Return (AAGDR) is the highest.

(b) B's Geometric Average Gross Discrete Return (GAGDR) is the lowest.

(c) C's GAGDR is higher than its AAGDR.

(d) D's AAGDR and GAGDR are equal since it's volatility is zero.

(e) C's expected utility of wealth would be the highest for an investor with a log utility function.

Question 938  CAPM, SML

The market's expected total return is 10% pa and the risk free rate is 5% pa, both given as effective annual rates.

A stock has a beta of 0.7.

In the last 5 minutes, bad economic news was released showing a higher chance of recession. Over this time the share market fell by 2%. The risk free rate was unchanged. What do you think was the stock's historical return over the last 5 minutes, given as an effective 5 minute rate?

(a) -8.5%

(b) -2.7%

(c) -2%

(d) -1.4%

(e) 0.1%