A European put option will mature in ##T## years with a strike price of ##K## dollars. The underlying asset has a price of ##S## dollars.
What is an expression for the payoff at maturity ##(f_T)## in dollars from owning (being long) the put option?
Acquirer firm plans to launch a takeover of Target firm. The deal is expected to create a present value of synergies totaling $105 million. A cash offer will be made that pays the fair price for the target's shares plus 75% of the total synergy value. The cash will be paid out of the firm's cash holdings, no new debt or equity will be raised.
| Firms Involved in the Takeover | ||
| Acquirer | Target | |
| Assets ($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.
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.
Acquirer firm plans to launch a takeover of Target firm. The deal is expected to create a present value of synergies totaling $2 million. A scrip offer will be made that pays the fair price for the target's shares plus 70% of the total synergy value.
| Firms Involved in the Takeover | ||
| Acquirer | Target | |
| Assets ($m) | 60 | 10 |
| Debt ($m) | 20 | 2 |
| Share price ($) | 10 | 8 |
| Number of shares (m) | 4 | 1 |
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.
Acquirer firm plans to launch a takeover of Target firm. The deal is expected to create a present value of synergies totaling $0.5 million, but investment bank fees and integration costs with a present value of $1.5 million is expected. A 10% cash and 90% scrip offer will be made that pays the fair price for the target's shares only. Assume that the Target and Acquirer agree to the deal. The cash will be paid out of the firms' cash holdings, no new debt or equity will be raised.
| Firms Involved in the Takeover | ||
| Acquirer | Target | |
| Assets ($m) | 60 | 10 |
| Debt ($m) | 20 | 2 |
| Share price ($) | 10 | 8 |
| Number of shares (m) | 4 | 1 |
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 one year European-style call option has a strike price of $4. The option's underlying stock pays no dividends and currently trades at $5. The risk-free interest rate is 10% pa continuously compounded. Use a single step binomial tree to calculate the option price, assuming that the price could rise to $8 ##(u = 1.6)## or fall to $3.125 ##(d = 1/1.6)## in one year. The call option price now is:
A one year European-style put option has a strike price of $4. The option's underlying stock pays no dividends and currently trades at $5. The risk-free interest rate is 10% pa continuously compounded. Use a single step binomial tree to calculate the option price, assuming that the price could rise to $8 ##(u = 1.6)## or fall to $3.125 ##(d = 1/1.6)## in one year. The put option price now is:
Question 381 Merton model of corporate debt, option, real option
In the Merton model of corporate debt, buying a levered company's debt is equivalent to buying risk free government bonds and:
Question 382 Merton model of corporate debt, real option, option
In the Merton model of corporate debt, buying a levered company's shares is equivalent to:
Which of the following is the least useful method or model to calculate the value of a real option in a project?
Question 385 Merton model of corporate debt, real option, option
A risky firm will last for one period only (t=0 to 1), then it will be liquidated. So it's assets will be sold and the debt holders and equity holders will be paid out in that order. The firm has the following quantities:
##V## = Market value of assets.
##E## = Market value of (levered) equity.
##D## = Market value of zero coupon bonds.
##F_1## = Total face value of zero coupon bonds which is promised to be paid in one year.
The levered equity graph above contains bold labels a to e. Which of the following statements about those labels is NOT correct?
One of the reasons why firms may not begin projects with relatively small positive net present values (NPV's) is because they wish to maximise the value of their:
A moped is a bicycle with pedals and a little motor that can be switched on to assist the rider. Mopeds are useful for quick transport using the motor, and for physical exercise when using the pedals unassisted. This offers the rider:
You're thinking of starting a new cafe business, but you're not sure if it will be profitable.
You have to decide what type of cups, mugs and glasses you wish to buy. You can pay to have your cafe's name printed on them, or just buy the plain un-marked ones. For marketing reasons it's better to have the cafe name printed. But the plain un-marked cups, mugs and glasses maximise your:
Some financially minded people insist on a prenuptial agreement before committing to marry their partner. This agreement states how the couple's assets should be divided in case they divorce. Prenuptial agreements are designed to give the richer partner more of the couples' assets if they divorce, thus maximising the richer partner's:
The cheapest mobile phones available tend to be those that are 'locked' into a cell phone operator's network. Locked phones can not be used with other cell phone operators' networks.
Locked mobile phones are cheaper than unlocked phones because the locked-in network operator helps create a monopoly by:
Your firm's research scientists can begin an exciting new project at a cost of $10m now, after which there’s a:
- 70% chance that cash flows will be $1m per year forever, starting in 5 years (t=5). This is the A state of the world.
- 20% chance that cash flows will be $3m per year forever, starting in 5 years (t=5). This is the B state of the world.
- 10% chance of a major break through in which case the cash flows will be $20m per year forever starting in 5 years (t=5), or instead, the project can be expanded by investing another $10m (at t=5) which is expected to give cash flows of $60m per year forever, starting at year 9 (t=9). Note that the perpetual cash flows are either the $20m from year 4 onwards, or the $60m from year 9 onwards after the additional $10m year 5 investment, but not both. This is the C state of the world.
The firm's cost of capital is 10% pa.
What's the present value (at t=0) of the option to expand in year 5?
Question 433 Merton model of corporate debt, real option, option, no explanation
A risky firm will last for one period only (t=0 to 1), then it will be liquidated. So it's assets will be sold and the debt holders and equity holders will be paid out in that order. The firm has the following quantities:
##V## = Market value of assets.
##E## = Market value of (levered) equity.
##D## = Market value of zero coupon bonds.
##F_1## = Total face value of zero coupon bonds which is promised to be paid in one year.
What is the payoff to equity holders at maturity, assuming that they keep their shares until maturity?
Question 397 financial distress, leverage, capital structure, NPV
A levered firm has a market value of assets of $10m. Its debt is all comprised of zero-coupon bonds which mature in one year and have a combined face value of $9.9m.
Investors are risk-neutral and therefore all debt and equity holders demand the same required return of 10% pa.
Therefore the current market capitalisation of debt ##(D_0)## is $9m and equity ##(E_0)## is $1m.
A new project presents itself which requires an investment of $2m and will provide a:
- $6.6m cash flow with probability 0.5 in the good state of the world, and a
- -$4.4m (notice the negative sign) cash flow with probability 0.5 in the bad state of the world.
The project can be funded using the company's excess cash, no debt or equity raisings are required.
What would be the new market capitalisation of equity ##(E_\text{0, with project})## if shareholders vote to proceed with the project, and therefore should shareholders proceed with the project?
Question 398 financial distress, capital raising, leverage, capital structure, NPV
A levered firm has zero-coupon bonds which mature in one year and have a combined face value of $9.9m.
Investors are risk-neutral and therefore all debt and equity holders demand the same required return of 10% pa.
In one year the firm's assets will be worth:
- $13.2m with probability 0.5 in the good state of the world, or
- $6.6m with probability 0.5 in the bad state of the world.
A new project presents itself which requires an investment of $2m and will provide a certain cash flow of $3.3m in one year.
The firm doesn't have any excess cash to make the initial $2m investment, but the funds can be raised from shareholders through a fairly priced rights issue. Ignore all transaction costs.
Should shareholders vote to proceed with the project and equity raising? What will be the gain in shareholder wealth if they decide to proceed?
You believe that the price of a share will fall significantly very soon, but the rest of the market does not. The market thinks that the share price will remain the same. Assuming that your prediction will soon be true, which of the following trades is a bad idea? In other words, which trade will NOT make money or prevent losses?
A man just sold a call option to his counterparty, a lady. The man has just now:
A European put option will mature in ##T## years with a strike price of ##K## dollars. The underlying asset has a price of ##S## dollars.
What is an expression for the payoff at maturity ##(f_T)## in dollars from having written (being short) the put option?
Question 432 option, option intrinsic value, no explanation
An American style call option with a strike price of ##K## dollars will mature in ##T## years. The underlying asset has a price of ##S## dollars.
What is an expression for the current intrinsic value in dollars from owning (being long) the American style call option? Note that the intrinsic value of an option does not subtract the premium paid to buy the option.
Which of the following statements about option contracts is NOT correct? For every:
If trader A has sold the right that allows counterparty B to buy the underlying asset from him at maturity if counterparty B wants then trader A is:
After doing extensive fundamental analysis of a company, you believe that their shares are overpriced and will soon fall significantly. The market believes that there will be no such fall.
Which of the following strategies is NOT a good idea, assuming that your prediction is true?
Question 636 option, option payoff at maturity, no explanation
Which of the below formulas gives the payoff ##(f)## at maturity ##(T)## from being long a call option? Let the underlying asset price at maturity be ##S_T## and the exercise price be ##X_T##.
Question 637 option, option payoff at maturity, no explanation
Which of the below formulas gives the payoff ##(f)## at maturity ##(T)## from being short a call option? Let the underlying asset price at maturity be ##S_T## and the exercise price be ##X_T##.
Question 638 option, option payoff at maturity, no explanation
Which of the below formulas gives the payoff ##(f)## at maturity ##(T)## from being long a put option? Let the underlying asset price at maturity be ##S_T## and the exercise price be ##X_T##.
Which one of the below option and futures contracts gives the possibility of potentially unlimited gains?
A trader buys one crude oil European style call option contract on the CME expiring in one year with an exercise price of $44 per barrel for a price of $6.64. The crude oil spot price is $40.33. If the trader doesn’t close out her contract before maturity, then at maturity she will have the:
Which of the below formulas gives the profit ##(\pi)## from being long a call option? Let the underlying asset price at maturity be ##S_T##, the exercise price be ##X_T## and the option price be ##f_{LC,0}##. Note that ##S_T##, ##X_T## and ##f_{LC,0}## are all positive numbers.
Which of the below formulas gives the profit ##(\pi)## from being short a call option? Let the underlying asset price at maturity be ##S_T##, the exercise price be ##X_T## and the option price be ##f_{LC,0}##. Note that ##S_T##, ##X_T## and ##f_{LC,0}## are all positive numbers.
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 trader sells one crude oil European style call option contract on the CME expiring in one year with an exercise price of $44 per barrel for a price of $6.64. The crude oil spot price is $40.33. If the trader doesn’t close out her contract before maturity, then at maturity she will have the:
A trader buys one crude oil European style put option contract on the CME expiring in one year with an exercise price of $44 per barrel for a price of $6.64. The crude oil spot price is $40.33. If the trader doesn’t close out her contract before maturity, then at maturity she will have the:
A trader just bought a European style put option on CBA stock. The current option premium is $2, the exercise price is $75, the option matures in one year and the spot CBA stock price is $74.
Which of the following statements is NOT correct?
A company runs a number of slaughterhouses which supply hamburger meat to McDonalds. The company is afraid that live cattle prices will increase over the next year, even though there is widespread belief in the market that they will be stable. What can the company do to hedge against the risk of increasing live cattle prices? Which statement(s) are correct?
(i) buy call options on live cattle.
(ii) buy put options on live cattle.
(iii) sell call options on live cattle.
Select the most correct response:
Below are 4 option graphs. Note that the y-axis is payoff at maturity (T). What options do they depict? List them in the order that they are numbered.
You have just sold an 'in the money' 6 month European put option on the mining company BHP at an exercise price of $40 for a premium of $3.
Which of the following statements best describes your situation?
You operate a cattle farm that supplies hamburger meat to the big fast food chains. You buy a lot of grain to feed your cattle, and you sell the fully grown cattle on the livestock market.
You're afraid of adverse movements in grain and livestock prices. What options should you buy to hedge your exposures in the grain and cattle livestock markets?
Select the most correct response:
Question 271 CAPM, option, risk, systematic risk, systematic and idiosyncratic risk
All things remaining equal, according to the capital asset pricing model, if the systematic variance of an asset increases, its required return will increase and its price will decrease.
If the idiosyncratic variance of an asset increases, its price will be unchanged.
What is the relationship between the price of a call or put option and the total, systematic and idiosyncratic variance of the underlying asset that the option is based on? Select the most correct answer.
Call and put option prices increase when the:
A stock, a call, a put and a bond are available to trade. The call and put options' underlying asset is the stock they and have the same strike prices, ##K_T##.
You are currently long the stock. You want to hedge your long stock position without actually trading the stock. How would you do this?
A 12 month European-style call option with a strike price of $11 is written on a dividend paying stock currently trading at $10. The dividend is paid annually and the next dividend is expected to be $0.40, paid in 9 months. The risk-free interest rate is 5% pa continuously compounded and the standard deviation of the stock’s continuously compounded returns is 30 percentage points pa. The stock's continuously compounded returns are normally distributed. Using the Black-Scholes-Merton option valuation model, determine which of the following statements is NOT correct.
A one year European-style call option has a strike price of $4.
The option's underlying stock currently trades at $5, pays no dividends and its standard deviation of continuously compounded returns is 47% pa.
The risk-free interest rate is 10% pa continuously compounded.
Use the Black-Scholes-Merton formula to calculate the option price. The call option price now is:
A one year European-style put option has a strike price of $4.
The option's underlying stock currently trades at $5, pays no dividends and its standard deviation of continuously compounded returns is 47% pa.
The risk-free interest rate is 10% pa continuously compounded.
Use the Black-Scholes-Merton formula to calculate the option price. The put option price now is:
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?
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 278 inflation, real and nominal returns and cash flows
Imagine that the interest rate on your savings account was 1% per year and inflation was 2% per year.
Question 992 inflation, real and nominal returns and cash flows
You currently have $100 in the bank which pays a 10% pa interest rate.
Oranges currently cost $1 each at the shop and inflation is 5% pa which is the expected growth rate in the orange price.
This information is summarised in the table below, with some parts missing that correspond to the answer options. All rates are given as effective annual rates. Note that when payments are not specified as real, as in this question, they're conventionally assumed to be nominal.
| Wealth in Dollars and Oranges | ||||
| Time (year) | Bank account wealth ($) | Orange price ($) | Wealth in oranges | |
| 0 | 100 | 1 | 100 | |
| 1 | 110 | 1.05 | (a) | |
| 2 | (b) | (c) | (d) | |
Which of the following statements is NOT correct? Your:
Question 993 inflation, real and nominal returns and cash flows
In February 2020, the RBA cash rate was 0.75% pa and the Australian CPI inflation rate was 1.8% pa.
You currently have $100 in the bank which pays a 0.75% pa interest rate.
Apples currently cost $1 each at the shop and inflation is 1.8% pa which is the expected growth rate in the apple price.
This information is summarised in the table below, with some parts missing that correspond to the answer options. All rates are given as effective annual rates. Note that when payments are not specified as real, as in this question, they're conventionally assumed to be nominal.
| Wealth in Dollars and Apples | ||||
| Time (year) | Bank account wealth ($) | Apple price ($) | Wealth in apples | |
| 0 | 100 | 1 | 100 | |
| 1 | 100.75 | 1.018 | (a) | |
| 2 | (b) | (c) | (d) | |
Which of the following statements is NOT correct? Your:
Question 407 income and capital returns, inflation, real and nominal returns and cash flows
A stock has a real expected total return of 7% pa and a real expected capital return of 2% pa.
Inflation is expected to be 2% pa. All rates are given as effective annual rates.
What is the nominal expected total return, capital return and dividend yield? The answers below are given in the same order.
In the 'Austin Powers' series of movies, the character Dr. Evil threatens to destroy the world unless the United Nations pays him a ransom (video 1, video 2). Dr. Evil makes the threat on two separate occasions:
- In 1969 he demands a ransom of $1 million (=10^6), and again;
- In 1997 he demands a ransom of $100 billion (=10^11).
If Dr. Evil's demands are equivalent in real terms, in other words $1 million will buy the same basket of goods in 1969 as $100 billion would in 1997, what was the implied inflation rate over the 28 years from 1969 to 1997?
The answer choices below are given as effective annual rates:
Question 522 income and capital returns, real and nominal returns and cash flows, inflation, real estate
A residential investment property has an expected nominal total return of 6% pa and nominal capital return of 2.5% pa. Inflation is expected to be 2.5% pa.
All of the above are effective nominal rates and investors believe that they will stay the same in perpetuity.
What are the property's expected real total, capital and income returns?
The answer choices below are given in the same order.
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:
Question 526 real and nominal returns and cash flows, inflation, no explanation
How can a nominal cash flow be precisely converted into a real cash flow?
Question 574 inflation, real and nominal returns and cash flows, NPV
What is the present value of a nominal payment of $100 in 5 years? The real discount rate is 10% pa and the inflation rate is 3% pa.
Question 576 inflation, real and nominal returns and cash flows
What is the present value of a nominal payment of $1,000 in 4 years? The nominal discount rate is 8% pa and the inflation rate is 2% pa.
Question 1022 inflation linked bond, breakeven inflation rate, inflation, real and nominal returns and cash flows
Below is a graph of 10-year US treasury fixed coupon bond yields (red), inflation-indexed bond yields (green) and the 'breakeven' inflation rate (blue). Note that inflation-indexed bonds are also called treasury inflation protected securities (TIPS) in the US. In other countries they're called inflation-linked bonds (ILB's). For more information, see PIMCO's great article about inflation linked bonds here.
The 10 year breakeven inflation rate (blue) equals the:
PIMCO gives the following example of an Inflation Linked Bond (ILB), called Treasury Inflation Protected Securities (TIPS) in the US.
How do ILBs work?
An ILB’s explicit link to a nationally-recognized inflation measure means that any increase in price levels directly translates into higher principal values. As a hypothetical example, consider a $1,000 20-year U.S. TIPS with a 2.5% coupon (1.25% on semiannual basis), and an inflation rate of 4%. The principal on the TIPS note will adjust upward on a daily basis to account for the 4% inflation rate. At maturity, the principal value will be $2,208 (4% per year, compounded semiannually). Additionally, while the coupon rate remains fixed at 2.5%, the dollar value of each interest payment will rise, as the coupon will be paid on the inflation-adjusted principal value. The first semiannual coupon of 1.25% paid on the inflation-adjusted principal of $1,020 is $12.75, while the final semiannual interest payment will be 1.25% of $2,208, which is $27.60.
Forecast the semi-annual coupon paid in 10 years based on the bond details given above. The 20th semi-annual coupon, paid in 10 years, is expected to be:
Question 1023 monetary policy, inflation, breakeven inflation rate
If the breakeven inflation rate was far above the US Fed's long term 2% average inflation target, the Fed would be expected to:
Former RBA Governor Phil Lowe says that if the economy is growing very strongly, then prices might be growing too:
Former RBA Governor Phil Lowe says that when the RBA raise interest rates, homeowners' mortgage loan interest expense will be:
Question 1018 RBA cash rate, monetary policy, foreign exchange rate
RBA Governor Phil Lowe says that when the RBA raises the cash rate (by surprise), the Australian dollar (AUD) tends to:
Question 1019 RBA cash rate, monetary policy, wealth effect
Former RBA Governor Phil Lowe says that when the RBA raise the cash rate, asset prices tend to:
Question 1020 Federal funds rate, monetary policy, dot plot
US Federal Reserve Chair Jerome Powell showed the 'dot plot' of Federal Open Market Committee (FOMC) members' estimated future Fed fund rates following their quarterly summary of economic projections on 15 Dec 2021. The dot plot shows that committee members intended to make monetary policy more:
Question 1021 Federal funds rate, monetary policy, quantitative easing, tapering
US Fed Chair Jerome Powell held a news conference following the 25-26 January 2022 FOMC meeting.
Nick Timiraos reporting for The Wall Street Journal asked: "Raising rates and reducing the balance sheet both restrain the economy, both tighten monetary policy. How should we think about the relationship between the two? For example, how much passive runoff is equal to every quarter percentage point increase in your benchmark rate?"
Jerome Powell replied: "So, again, we think of the balance sheet as moving in a predictable manner, sort of in the background, and that the active tool meeting to meeting is not -- both of them, it's the federal funds rate. There are rules of thumbs. I'm reluctant to land on one of them that equate this. And there's also an element of uncertainty around the balance sheet. I think we have a much better sense, frankly, of how rate increases affect financial conditions and, hence, economic conditions. Balance sheet is still a relatively new thing for the markets and for us, so we're less certain about that." (US Fed, 2022)
When Nick Timiraos mentioned 'reducing the balance sheet', he's referring to:
Estimate the US bank JP Morgan's share price using a price earnings (PE) multiples approach with the following assumptions and figures only:
- The major US banks JP Morgan Chase (JPM), Citi Group (C) and Wells Fargo (WFC) are comparable companies;
- JP Morgan Chase's historical earnings per share (EPS) is $4.37;
- Citi Group's share price is $50.05 and historical EPS is $4.26;
- Wells Fargo's share price is $48.98 and historical EPS is $3.89.
Note: Figures sourced from Google Finance on 24 March 2014.
Estimate the Chinese bank ICBC's share price using a backward-looking price earnings (PE) multiples approach with the following assumptions and figures only. Note that the renminbi (RMB) is the Chinese currency, also known as the yuan (CNY).
- The 4 major Chinese banks ICBC, China Construction Bank (CCB), Bank of China (BOC) and Agricultural Bank of China (ABC) are comparable companies;
- ICBC 's historical earnings per share (EPS) is RMB 0.74;
- CCB's backward-looking PE ratio is 4.59;
- BOC 's backward-looking PE ratio is 4.78;
- ABC's backward-looking PE ratio is also 4.78;
Note: Figures sourced from Google Finance on 25 March 2014. Share prices are from the Shanghai stock exchange.
Which firms tend to have low forward-looking price-earnings (PE) ratios? Only consider firms with positive PE ratios.
Itau Unibanco is a major listed bank in Brazil with a market capitalisation of equity equal to BRL 85.744 billion, EPS of BRL 3.96 and 2.97 billion shares on issue.
Banco Bradesco is another major bank with total earnings of BRL 8.77 billion and 2.52 billion shares on issue.
Estimate Banco Bradesco's current share price using a price-earnings multiples approach assuming that Itau Unibanco is a comparable firm.
Note that BRL is the Brazilian Real, their currency. Figures sourced from Google Finance on the market close of the BVMF on 24 July 2015.
A stock has a beta of 1.2. Its next dividend is expected to be $20, paid one year from now.
Dividends are expected to be paid annually and grow by 1.5% pa forever.
Treasury bonds yield 3% pa and the market portfolio's expected return is 7% pa. All returns are effective annual rates.
What is the price of the stock now?
Question 935 real estate, NPV, perpetuity with growth, multi stage growth model, DDM
You're thinking of buying an investment property that costs $1,000,000. The property's rent revenue over the next year is expected to be $50,000 pa and rent expenses are $20,000 pa, so net rent cash flow is $30,000. Assume that net rent is paid annually in arrears, so this next expected net rent cash flow of $30,000 is paid one year from now.
The year after, net rent is expected to fall by 2% pa. So net rent at year 2 is expected to be $29,400 (=30,000*(1-0.02)^1).
The year after that, net rent is expected to rise by 1% pa. So net rent at year 3 is expected to be $29,694 (=30,000*(1-0.02)^1*(1+0.01)^1).
From year 3 onwards, net rent is expected to rise at 2.5% pa forever. So net rent at year 4 is expected to be $30,436.35 (=30,000*(1-0.02)^1*(1+0.01)^1*(1+0.025)^1).
Assume that the total required return on your investment property is 6% pa. Ignore taxes. All returns are given as effective annual rates.
What is the net present value (NPV) of buying the investment property?
Question 989 PE ratio, Multiples valuation, leverage, accounting ratio
A firm has 20 million stocks, earnings (or net income) of $100 million per annum and a 60% debt-to-equity ratio where both the debt and asset values are market values rather than book values. Similar firms have a PE ratio of 12.
Which of the below statements is NOT correct based on a PE multiples valuation?
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 new company's Firm Free Cash Flow (FFCF, same as CFFA) is forecast in the graph below.
To value the firm's assets, the terminal value needs to be calculated using the perpetuity with growth formula:
###V_{\text{terminal, }t-1} = \dfrac{FFCF_{\text{terminal, }t}}{r-g}###
Which point corresponds to the best time to calculate the terminal value?
Use the below information to value a levered company with constant annual perpetual cash flows from assets. The next cash flow will be generated in one year from now, so a perpetuity can be used to value this firm. Both the operating and firm free cash flows are constant (but not equal to each other).
| Data on a Levered Firm with Perpetual Cash Flows | ||
| Item abbreviation | Value | Item full name |
| ##\text{OFCF}## | $100m | Operating free cash flow |
| ##\text{FFCF or CFFA}## | $112m | Firm free cash flow or cash flow from assets (includes interest tax shields) |
| ##g## | 0% pa | Growth rate of OFCF and FFCF |
| ##\text{WACC}_\text{BeforeTax}## | 7% pa | Weighted average cost of capital before tax |
| ##\text{WACC}_\text{AfterTax}## | 6.25% pa | Weighted average cost of capital after tax |
| ##r_\text{D}## | 5% pa | Cost of debt |
| ##r_\text{EL}## | 9% pa | Cost of levered equity |
| ##D/V_L## | 50% pa | Debt to assets ratio, where the asset value includes tax shields |
| ##t_c## | 30% | Corporate tax rate |
What is the value of the levered firm including interest tax shields?
Use the below information to value a levered company with annual perpetual cash flows from assets that grow. The next cash flow will be generated in one year from now. Note that ‘k’ means kilo or 1,000. So the $30k is $30,000.
| Data on a Levered Firm with Perpetual Cash Flows | ||
| Item abbreviation | Value | Item full name |
| ##\text{OFCF}## | $30k | Operating free cash flow |
| ##g## | 1.5% pa | Growth rate of OFCF |
| ##r_\text{D}## | 4% pa | Cost of debt |
| ##r_\text{EL}## | 16.3% pa | Cost of levered equity |
| ##D/V_L## | 80% pa | Debt to assets ratio, where the asset value includes tax shields |
| ##t_c## | 30% | Corporate tax rate |
| ##n_\text{shares}## | 100k | Number of shares |
Which of the following statements is NOT correct?
Use the below information to value a mature levered company with growing annual perpetual cash flows and a constant debt-to-assets ratio. The next cash flow will be generated in one year from now, so a perpetuity can be used to value this firm. The firm's debt funding comprises annual fixed coupon bonds that all have the same seniority and coupon rate. When these bonds mature, new bonds will be re-issued, and so on in perpetuity. The yield curve is flat.
| Data on a Levered Firm with Perpetual Cash Flows | ||
| Item abbreviation | Value | Item full name |
| ##\text{OFCF}_1## | $12.5m | Operating free cash flow at time 1 |
| ##\text{FFCF}_1 \text{ or }\text{CFFA}_1## | $14m | Firm free cash flow or cash flow from assets at time 1 |
| ##\text{EFCF}_1## | $11m | Equity free cash flow at time 1 |
| ##\text{BondCoupons}_1## | $1.2m | Bond coupons paid to debt holders at time 1 |
| ##g## | 2% pa | Growth rate of OFCF, FFCF, EFCF and Debt cash flow |
| ##\text{WACC}_\text{BeforeTax}## | 9% pa | Weighted average cost of capital before tax |
| ##\text{WACC}_\text{AfterTax}## | 8.25% pa | Weighted average cost of capital after tax |
| ##r_\text{D}## | 5% pa | Bond yield |
| ##r_\text{EL}## | 13% pa | Cost or required return of levered equity |
| ##D/V_L## | 50% pa | Debt to assets ratio, where the asset value includes tax shields |
| ##n_\text{shares}## | 1m | Number of shares |
| ##t_c## | 30% | Corporate tax rate |
Which of the following statements is NOT correct?
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}###Question 413 CFFA, interest tax shield, depreciation tax shield
There are many ways to calculate a firm's free cash flow (FFCF), also called cash flow from assets (CFFA).
One method is to use the following formulas to transform net income (NI) into FFCF including interest and depreciation tax shields:
###FFCF=NI + Depr - CapEx -ΔNWC + IntExp###
###NI=(Rev - COGS - Depr - FC - IntExp).(1-t_c )###
Another popular method is to use EBITDA rather than net income. EBITDA is defined as:
###EBITDA=Rev - COGS - FC###
One of the below formulas correctly calculates FFCF from EBITDA, including interest and depreciation tax shields, giving an identical answer to that above. Which formula is correct?
Question 418 capital budgeting, NPV, interest tax shield, WACC, CFFA, CAPM
| Project Data | ||
| Project life | 1 year | |
| Initial investment in equipment | $8m | |
| Depreciation of equipment per year | $8m | |
| Expected sale price of equipment at end of project | 0 | |
| Unit sales per year | 4m | |
| Sale price per unit | $10 | |
| Variable cost per unit | $5 | |
| Fixed costs per year, paid at the end of each year | $2m | |
| Interest expense in first year (at t=1) | $0.562m | |
| Corporate tax rate | 30% | |
| Government treasury bond yield | 5% | |
| Bank loan debt yield | 9% | |
| Market portfolio return | 10% | |
| Covariance of levered equity returns with market | 0.32 | |
| Variance of market portfolio returns | 0.16 | |
| Firm's and project's debt-to-equity ratio | 50% | |
Notes
- Due to the project, current assets will increase by $6m now (t=0) and fall by $6m at the end (t=1). Current liabilities will not be affected.
Assumptions
- The debt-to-equity ratio will be kept constant throughout the life of the project. The amount of interest expense at the end of each period has been correctly calculated to maintain this constant debt-to-equity ratio.
- Millions are represented by 'm'.
- All cash flows occur at the start or end of the year as appropriate, not in the middle or throughout the year.
- All rates and cash flows are real. The inflation rate is 2% pa. All rates are given as effective annual rates.
- The project is undertaken by a firm, not an individual.
What is the net present value (NPV) of the project?
Question 1039 gross domestic product, inflation, business cycle
In this business cycle graph shown in the RBA's article explaining recessions, how might 'output' on the y-axis be measured?
The ‘output’ y-axis amount in the business cycle chart can be measured by:
Question 852 gross domestic product, inflation, employment, no explanation
When the economy is booming (in an upswing), you tend to see:
Calculate Australia’s GDP over the 2016 calendar year using the below table:
| Australian Gross Domestic Product Components | ||||
| A$ billion, 2016 Calendar Year from 1 Jan 2016 to 31 Dec 2016 inclusive | ||||
| Consumption | Investment | Government spending | Exports | Imports |
| 971 | 421 | 320 | 328 | 344 |
Source: ABS 5206.0 Australian National Accounts: National Income, Expenditure and Product. Table 3. Expenditure on Gross Domestic Product (GDP), Current prices.
Over the 2016 calendar year, Australia’s GDP was:
Question 841 gross domestic product, government spending
The government spends money on:
- Goods and services such as defence, police, schools, hospitals and roads; and
- Transfer payments (also called welfare) such as the pension, dole, disability support and student support.
When calculating GDP (=C+I+G+X-M), the ‘government spending’ component (G) is supposed to include:
Question 850 gross domestic product, gross domestic product per capita
Below is a table showing some countries’ GDP, population and GDP per capita.
| Countries' GDP and Population | |||
| GDP | Population | GDP per capita | |
| USD million | millions of people | USD | |
| United States | 18,036,648 | 325 | 55,492 |
| China | 11,158,457 | 1,383 | 8,066 |
| Japan | 4,383,076 | 127 | 34,586 |
| Germany | 3,363,600 | 83 | 40,623 |
| Norway | 500,519 | 5 | 95,027 |
Source: "GDP and its breakdown at current prices in US Dollars" United Nations Statistics Division. December 2016.
Using this data only, which one of these countries’ citizens have the highest living standards?
Which form of production is included in the Gross Domestic Product (GDP) reported by the government statistics agency?
Question 1036 Minsky financial instability hypothesis, leverage
Hyman Minsky, author of 'The Financial Instability Hypothesis' (1992), wrote:
In particular, over a protracted period of good times, capitalist economies tend to move from a financial structure dominated by hedge finance units to a structure in which there is large weight to units engaged in speculative and Ponzi finance. Furthermore, if an economy with a sizeable body of speculative financial units is in an inflationary state, and the authorities attempt to exorcise inflation by monetary constraint, then speculative units will become Ponzi units and the net worth of previously Ponzi units will quickly evaporate. Consequently, units with cash flow shortfalls will be forced to try to make position by selling out position. This is likely to lead to a collapse of asset values.
Which of the below statements explaining this quote is NOT correct?
Question 1038 fire sale, leverage, no explanation
Listen to 'Lessons and Questions from the GFC' on 6 December 2018 by RBA Deputy Governor Guy Debelle from 17:58 to 20:08 or read the below transcript:
Guy Debelle talks about the GFC and says that the Australian government’s guarantee of wholesale debt and deposits on 12 October 2008 was "introduced to facilitate the flow of credit to the real economy at a reasonable price and, in some cases, alleviate the need for asset fire sales, which have the capacity to tip markets and the economy into a worse equilibrium... The crisis very much demonstrated the critical importance of keeping the lending flowing. The lesson is that countries that did that fared better than countries that didn't. That lesson is relevant to the situation today in Australia, where there is a risk that a reduced appetite to lend will overly curtail borrowing with consequent effects for the Australian economy." (Debelle, 2019)
When assets are sold in a fire sale, there’s usually a large increase in the:
Here's an excerpt from an interview between Magellan fund co-founder Hamish Douglass and AFR reporter Vesna Poljak, which appeared in the Australian Financial Review article ‘It's all about interest rates: Hamish Douglass’, 19 July 2019:
Take a business growing at 4 per cent a year, with a cost of equity of 10 per cent based off a 5 per cent risk-free rate and a 5 per cent market risk premium: you would value that at around 16.6 times free cashflow.
Now take a business growing at the same rate, with a 4 per cent risk free rate. At a 9 per cent cost of equity that would command a 20 times multiple, he says.
At a 3 per cent risk-free rate, the cost of equity is 8 per cent, and the multiple is 25.
Finally at 2 per cent – 'which is where the world is at the moment' – the same business would be worth around 33 times free cashflow.
In August 2021, the RBA overnight cash rate and 3 year Australian government treasury bond yield were both 0.1% pa. If this low risk-free yield was expected to persist forever, what approximate equity price-to-cashflow multiple would that imply for a business expected to grow at 4% pa in perpetuity with a 5% equity risk premium?
In the 1997 Asian financial crisis many countries' exchange rates depreciated rapidly against the US dollar (USD). The Thai, Indonesian, Malaysian, Korean and Filipino currencies were severely affected. The below graph shows these Asian countries' currencies in USD per one unit of their currency, indexed to 100 in June 1997.
Of the statements below, which is NOT correct? The Asian countries':
Question 882 Asian currency crisis, foreign exchange rate, original sin, no explanation
In the 1997 Asian currency crisis, the businesses most vulnerable to bankruptcy were those that:
Question 1014 book build, initial public offering, capital raising, demand schedule
A firm is floating its stock in an IPO and its underwriter has received the following bids, listed in order from highest to lowest share price:
| IPO Book Build Bids | ||
| Bidders | Share price | Number of shares |
| $/share | millions | |
| BidderA | 2.5 | 2 |
| BidderB | 2 | 1.5 |
| BidderC | 1.5 | 4 |
| BidderD | 1 | 3 |
| BidderE | 0.5 | 2 |
Suppose that the firm's owner wishes to raise $6 million to expand the business by selling new stock in the initial public offering (IPO). The owner currently holds 8 million stock which are not for sale. Which of the following statements is NOT correct?
Question 566 capital structure, capital raising, rights issue, on market repurchase, dividend, stock split, bonus issue
A company's share price fell by 20% and its number of shares rose by 25%. Assume that there are no taxes, no signalling effects and no transaction costs.
Which one of the following corporate events may have happened?
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.
Question 625 dividend re-investment plan, capital raising
Which of the following statements about dividend re-investment plans (DRP's) is NOT correct?
A company conducts a 2 for 3 rights issue at a subscription price of $8 when the pre-announcement stock price was $9. Assume that all investors use their rights to buy those extra shares.
What is the percentage increase in the stock price and the number of shares outstanding? The answers are given in the same order.
A firm wishes to raise $50 million now. They will issue 7% pa semi-annual coupon bonds that will mature in 6 years and have a face value of $100 each. Bond yields are 5% pa, given as an APR compounding every 6 months, and the yield curve is flat.
How many bonds should the firm issue?
A firm wishes to raise $30 million now. The firm's current market value of equity is $60m and the market price per share is $20. They estimate that they'll be able to issue shares in a rights issue at a subscription price of $15. Ignore the time value of money and assume that all shareholders exercise their rights. Which of the following statements is NOT correct?
Question 803 capital raising, rights issue, initial public offering, on market repurchase, no explanation
Which one of the following capital raisings or payouts involve the sale of shares to existing shareholders only?
Question 1009 lemons problem, asymmetric information, adverse selection
Akerlof’s 1970 paper ‘The Market for "Lemons": Quality Uncertainty and the Market Mechanism’ provides a famous example of asymmetric information leading to market failure. This example is commonly known as the ‘Lemons Problem’. Imagine that half of all second hand cars are:
- Lemons worth $5,000 each. Lemons are bad second-hand cars with hidden faults that only the seller knows about; and the other half are
- Plums worth $10,000 each. Plums are good second-hand cars without faults.
Car buyers can’t tell the difference between lemon and plum cars.
Car sellers know whether their car is a lemon or a plum since they’ve driven the car for a long time. However, plum car owners cannot prove their cars’ higher quality to buyers. Also, lemon car owners are known to dis-honestly claim that their cars are plums.
What will be the market price of second hand cars?
Question 1010 lemons problem, asymmetric information, adverse selection, fungible
The ‘Lemons Problem’ is likely to more adversely affect the desirability of which type of investment?
Question 1011 winners curse
A teacher fills up a large jar with coins. The jar is auctioned among a large class of wealthy accounting students who have never studied economics or finance.
The auction is conducted in the English style, which is as an open-outcry ascending auction. This means that the winning bidder is able to bid, win and pay slightly more than the second highest bidder's private valuation, but less than their own private valuation.
The jar of coins is not allowed to be weighed by students and is filled with different-valued coins so it’s difficult to value. Therefore there is a wide distribution of bidders’ fair value estimates. Students’ bids are purely profit-driven, there is no fame to be gained by being the winner or loser.
Assume that each bidder bids up to their personal estimate of the fair value of the jar of coins without observing the number of other bidders during the auction. The winning bidder is likely to:
A levered firm has only 2 assets on its balance sheet with the below market values and CAPM betas. The risk free rate is 3% pa and the market risk premium is 5% pa. Assume that the CAPM is correct and all assets are fairly priced.
| Balance Sheet Market Values and Betas | ||
| Balance sheet item | Market value ($m) | Beta |
| Cash asset | 0.5 | 0 |
| Truck assets | 0.5 | 2 |
| Loan liabilities | 0.25 | 0.1 |
| Equity funding | ? | ? |
Which of the following statements is NOT correct?