Fight Finance

Question 28  DDM, income and capital returns

The following equation is the Dividend Discount Model, also known as the 'Gordon Growth Model' or the 'Perpetuity with growth' equation.

### P_{0} = \frac{C_1}{r_{\text{eff}} - g_{\text{eff}}} ###

What would you call the expression ## C_1/P_0 ##?

(a) The expected total return of the stock.

(b) The expected income return of the stock.

(c) The expected capital return of the stock.

(d) The expected growth rate of the dividend.

(e) The expected growth rate of the stock price.

Question 44  NPV

The required return of a project is 10%, given as an effective annual rate. Assume that the cash flows shown in the table are paid all at once at the given point in time.

What is the Net Present Value (NPV) of the project?

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

(a) -100

(b) 0

(c) 10

(d) 21

(e) 121

Question 353  income and capital returns, inflation, real and nominal returns and cash flows, real estate

A residential investment property has an expected nominal total return of 6% pa and nominal capital return of 3% pa.

Inflation is expected to be 2% pa. All rates are given as effective annual rates.

What are the property's expected real total, capital and income returns? The answer choices below are given in the same order.

(a) 3.9216%, 2.9412%, 0.9804%.

(b) 3.9216%, 0.9804%, 2.9412%.

(c) 3.9216%, 0.9804%, 0.9804%.

(d) 1.9804%, 1.0000%, 0.9804%.

(e) 1.9608%, 0.9804%, 0.9804%.

Question 525  income and capital returns, real and nominal returns and cash flows, inflation

Which of the following statements about cash in the form of notes and coins is NOT correct? Assume that inflation is positive.

Notes and coins:

(a) Pay no income cash flow.

(b) Have a nominal total return of zero.

(c) Have a nominal capital return of zero.

(d) Have a nominal income return of zero.

(e) Have a real total return of zero.

Question 221  credit risk

You're considering making an investment in a particular company. They have preference shares, ordinary shares, senior debt and junior debt.

Which is the safest investment? Which has the highest expected returns?

(a) Junior debt is the safest. Preference shares have the highest expected returns.

(b) Preference shares are the safest. Ordinary shares have the highest expected returns.

(c) Senior debt is the safest. Ordinary shares have the highest expected returns.

(d) Junior debt is the safest. Ordinary shares have the highest expected returns.

(e) Senior debt is the safest. Junior debt have the highest expected returns.

Question 575  inflation, real and nominal returns and cash flows

You expect a nominal payment of $100 in 5 years. The real discount rate is 10% pa and the inflation rate is 3% pa. Which of the following statements is NOT correct?

(a) The nominal cash flow of $100 in 5 years is equivalent to a real cash flow of $86.2609 in 5 years. This means that $86.2609 will buy the same amount of goods and services now as $100 will buy in 5 years.

(b) The real discount rate of 10% pa is equivalent to a nominal discount rate of 13.3333% pa.

(c) The nominal price of goods and services will increase by 3% every year.

(d) The real price of goods and services will increase by 3% every year.

(e) The present value of your payment will increase by the nominal discount rate every year.

Question 126  IRR

What is the Internal Rate of Return (IRR) of the project detailed in the table below?

Assume that the cash flows shown in the table are paid all at once at the given point in time. All answers are given as effective annual rates.

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

(a) 0.21

(b) 0.105

(c) 0.1111

(d) 0.1

(e) 0

Question 49  inflation, real and nominal returns and cash flows, APR, effective rate

In Australia, nominal yields on semi-annual coupon paying Government Bonds with 2 years until maturity are currently 2.83% pa.

The inflation rate is currently 2.2% pa, given as an APR compounding per quarter. The inflation rate is not expected to change over the next 2 years.

What is the real yield on these bonds, given as an APR compounding every 6 months?

(a) 0.3086%

(b) 0.6171%

(c) 0.6181%

(d) 0.6239%

(e) 0.6300%

Question 64  inflation, real and nominal returns and cash flows, APR, effective rate

In Germany, nominal yields on semi-annual coupon paying Government Bonds with 2 years until maturity are currently 0.04% pa.

The inflation rate is currently 1.4% pa, given as an APR compounding per quarter. The inflation rate is not expected to change over the next 2 years.

What is the real yield on these bonds, given as an APR compounding every 6 months?

(a) -1.3529627%

(b) -0.4977348%

(c) 0.4977348%

(d) 1.3529627%

(e) 1.3621776%

Question 565  correlation

What is the correlation of a variable X with a constant C?

The corr(X, C) or ##\rho_{X,C}## equals:

(a) var(X) or ##\sigma_X^2##

(b) sd(X) or ##\sigma_X##

(c) 1

(d) 0

(e) Mathematically undefined

Question 94  leverage, capital structure, real estate

Your friend just bought a house for $400,000. He financed it using a $320,000 mortgage loan and a deposit of $80,000.

In the context of residential housing and mortgages, the 'equity' tied up in the value of a person's house is the value of the house less the value of the mortgage. So the initial equity your friend has in his house is $80,000. Let this amount be E, let the value of the mortgage be D and the value of the house be V. So ##V=D+E##.

If house prices suddenly fall by 10%, what would be your friend's percentage change in equity (E)? Assume that the value of the mortgage is unchanged and that no income (rent) was received from the house during the short time over which house prices fell.

Remember:

### r_{0\rightarrow1}=\frac{p_1-p_0+c_1}{p_0} ###

where ##r_{0-1}## is the return (percentage change) of an asset with price ##p_0## initially, ##p_1## one period later, and paying a cash flow of ##c_1## at time ##t=1##.

(a) -100%

(b) -50%

(c) -12.5%

(d) -10%

(e) -8%

Question 238  CFFA, leverage, interest tax shield

A company increases the proportion of debt funding it uses to finance its assets by issuing bonds and using the cash to repurchase stock, leaving assets unchanged.

Ignoring the costs of financial distress, which of the following statements is NOT correct:

(a) The company is increasing its debt-to-assets and debt-to-equity ratios. These are types of 'leverage' or 'gearing' ratios.

(b) The company will pay less tax to the government due to the benefit of interest tax shields.

(c) The company's net income, also known as earnings or net profit after tax, will fall.

(d) The company's expected levered firm free cash flow (FFCF or CFFA) will be higher due to tax shields.

(e) The company's expected levered equity free cash flow (EFCF) will not change.

Question 366  opportunity cost, NPV, CFFA

Your friend is trying to find the net present value of an investment which:

• Costs $1 million initially (t=0); and
• Pays a single positive cash flow of $1.1 million in one year (t=1).

The investment has a total required return of 10% pa due to its moderate level of undiversifiable risk.

Your friend is aware of the importance of opportunity costs and the time value of money, but he is unsure of how to find the NPV of the project.

He knows that the opportunity cost of investing the $1m in the project is the expected gain from investing the money in shares instead. Like the project, shares also have an expected return of 10% since they have moderate undiversifiable risk. This opportunity cost is $0.1m ##(=1m \times 10\%)## which occurs in one year (t=1).

He knows that the time value of money should be accounted for, and this can be done by finding the present value of the cash flows in one year.

Your friend has listed a few different ways to find the NPV which are written down below.

Method 1: ##-1m + \dfrac{1.1m}{(1+0.1)^1} ##

Method 2: ##-1m + 1.1m - 1m \times 0.1 ##

Method 3: ##-1m + \dfrac{1.1m}{(1+0.1)^1} - 1m \times 0.1 ##

Which of the above calculations give the correct NPV? Select the most correct answer.

(a) Method 1 only.

(b) Method 2 only.

(c) Method 3 only.

(d) Methods 1 and 2 only.

(e) Methods 1 and 3 only.

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 371  interest tax shield, CFFA

One method for calculating a firm's free cash flow (FFCF, or CFFA) is to ignore interest expense. That is, pretend that interest expense ##(IntExp)## is zero:

###\begin{aligned} FFCF &= (Rev - COGS - Depr - FC - IntExp)(1-t_c) + Depr - CapEx -\Delta NWC + IntExp \\ &= (Rev - COGS - Depr - FC - 0)(1-t_c) + Depr - CapEx -\Delta NWC - 0\\ \end{aligned}###

Does this annual FFCF with zero interest expense or the annual interest tax shield?

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 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 617  systematic and idiosyncratic risk, risk, CAPM

A stock's required total return will increase when its:

(a) Systematic risk increases.

(b) Idiosyncratic risk increases.

(c) Total risk increases.

(d) Systematic risk decreases.

(e) Idiosyncratic risk decreases.

Question 669  beta, CAPM, risk

Which of the following is NOT a valid method for estimating the beta of a company's stock? Assume that markets are efficient, a long history of past data is available, the stock possesses idiosyncratic and market risk. The variances and standard deviations below denote total risks.

(a) ##Β_E=\dfrac{cov(r_E,r_M )}{var(r_M)}##

(b) ##Β_E=\dfrac{correl(r_E,r_M ).sd(r_E)}{sd(r_M)} ##

(c) ##Β_E=\dfrac{sd(r_E)}{sd(r_M)}##,   since ##var(r_E)=β_E^2.var(r_M)##

(d) ##Β_E=\dfrac{r_E-r_f}{r_M-r_f }##,   since ##r_E=r_f+Β_E. (r_M-r_f )##

(e) ##Β_E= \left(B_V - \dfrac{D}{V}.Β_D \right).\dfrac{V}{E}##,   since ##B_V=\dfrac{E}{V}.Β_E+\dfrac{D}{V}.Β_D ##

Question 668  buy and hold, market efficiency, idiom

A quote from the famous investor Warren Buffet: "Much success can be attributed to inactivity. Most investors cannot resist the temptation to constantly buy and sell."

Buffet is referring to the buy-and-hold strategy which is to buy and never sell shares. Which of the following is a disadvantage of a buy-and-hold strategy? Assume that share markets are semi-strong form efficient. Which of the following is NOT an advantage of the strict buy-and-hold strategy? A disadvantage of the buy-and-hold strategy is that it reduces:

(a) Capital gains tax.

(b) Explicit transaction costs such as brokerage fees.

(c) Implicit transaction costs such as bid-ask spreads.

(d) Portfolio rebalancing.

(e) Time wasted on researching whether it's better to buy or sell.

Question 307  risk, variance

Let the variance of returns for a share per month be ##\sigma_\text{monthly}^2##.

What is the formula for the variance of the share's returns per year ##(\sigma_\text{yearly}^2)##?

Assume that returns are independently and identically distributed (iid) so they have zero auto correlation, meaning that if the return was higher than average today, it does not indicate that the return tomorrow will be higher or lower than average.

(a) ##\sigma_\text{yearly}^2 = \sigma_\text{monthly}^2##

(b) ##\sigma_\text{yearly}^2 = \sigma_\text{monthly}^2 \times 12##

(c) ##\sigma_\text{yearly}^2 = \sigma_\text{monthly}^2 \times 12^2##

(d) ##\sigma_\text{yearly}^2 = \sigma_\text{monthly}^2 \times \sqrt{12}##

(e) ##\sigma_\text{yearly}^2 = \sigma_\text{monthly}^2 \times {12}^{1/3}##

Question 560  standard deviation, variance, needs refinement

The standard deviation and variance of a stock's annual returns are calculated over a number of years. The units of the returns are percent per annum ##(\% pa)##.

What are the units of the standard deviation ##(\sigma)## and variance ##(\sigma^2)## of returns respectively?

(a) Percentage points per annum ##(\text{pp pa})## and percentage points per annum ##(\text{pp pa})##.

(b) Percentage points per annum ##(\text{pp pa})## and percentage points per annum all squared ##\left( (\text{pp pa})^2 \right)##.

(c) Percentage points per annum all squared ##\left( (\text{pp pa})^2 \right)## and percentage points per annum ##(\text{pp pa})##.

(d) Percentage points per annum all squared ##\left( (\text{pp pa})^2 \right)## and percentage points per annum all squared ##\left( (\text{pp pa})^2 \right)##.

(e) Percent per annum ##(\% pa)## and percent per annum ##(\% pa)##.

Hint: Visit Wikipedia to understand the difference between percentage points ##(\text{pp})## and percent ##(\%)##.

Question 706  utility, risk aversion, utility function

Mr Blue, Miss Red and Mrs Green are people with different utility functions.

Note that a fair gamble is a bet that has an expected value of zero, such as paying $0.50 to win $1 in a coin flip with heads or nothing if it lands tails. Fairly priced insurance is when the expected present value of the insurance premiums is equal to the expected loss from the disaster that the insurance protects against, such as the cost of rebuilding a home after a catastrophic fire.

Which of the following statements is NOT correct?

(a) Mr Blue, Miss Red and Mrs Green all prefer more wealth to less. This is rational from an economist's point of view.

(b) Mr Blue is risk averse. He will not enjoy a fair gamble and would like to buy fairly priced insurance.

(c) Miss Red is risk-neutral. She will not enjoy a fair gamble but wouldn't oppose it either. Similarly with fairly priced insurance.

(d) Mrs Green is risk-loving. She would enjoy a fair gamble and would dislike fairly priced insurance.

(e) Mr Blue would like to buy insurance, but only if it is fairly or under priced.