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 | 11 |
| 2 | 121 |
A project's NPV is positive. Select the most correct statement:
Question 542 price gains and returns over time, IRR, NPV, income and capital returns, effective return
For an asset price to double every 10 years, what must be the expected future capital return, given as an effective annual rate?
Question 543 price gains and returns over time, IRR, NPV, income and capital returns, effective return
For an asset price to triple every 5 years, what must be the expected future capital return, given as an effective annual rate?
You have $100,000 in the bank. The bank pays interest at 10% pa, given as an effective annual rate.
You wish to consume twice as much now (t=0) as in one year (t=1) and have nothing left in the bank at the end.
How much can you consume at time zero and one? The answer choices are given in the same order.
You have $100,000 in the bank. The bank pays interest at 10% pa, given as an effective annual rate.
You wish to consume half as much now (t=0) as in one year (t=1) and have nothing left in the bank at the end.
How much can you consume at time zero and one? The answer choices are given in the same order.
A project to build a toll road will take 3 years to complete, costing three payments of $50 million, paid at the start of each year (at times 0, 1, and 2).
After completion, the toll road will yield a constant $10 million at the end of each year forever with no costs. So the first payment will be at t=4.
The required return of the project is 10% pa given as an effective nominal rate. All cash flows are nominal.
What is the payback period?
A firm is considering a business project which costs $10m now and is expected to pay a single cash flow of $12.1m in two years.
Assume that the initial $10m cost is funded using the firm's existing cash so no new equity or debt will be raised. The cost of capital is 10% pa.
Which of the following statements about net present value (NPV), internal rate of return (IRR) and payback period is NOT correct?
Question 580 price gains and returns over time, time calculation, effective rate
How many years will it take for an asset's price to quadruple (be four times as big, say from $1 to $4) if the price grows by 15% pa?
Question 579 price gains and returns over time, time calculation, effective rate
How many years will it take for an asset's price to double if the price grows by 10% pa?
An investor owns a whole level of an old office building which is currently worth $1 million. There are three mutually exclusive projects that can be started by the investor. The office building level can be:
- Rented out to a tenant for one year at $0.1m paid immediately, and then sold for $0.99m in one year.
- Refurbished into more modern commercial office rooms at a cost of $1m now, and then sold for $2.4m when the refurbishment is finished in one year.
- Converted into residential apartments at a cost of $2m now, and then sold for $3.4m when the conversion is finished in one year.
All of the development projects have the same risk so the required return of each is 10% pa. The table below shows the estimated cash flows and internal rates of returns (IRR's).
| Mutually Exclusive Projects | |||
| Project | Cash flow now ($) |
Cash flow in one year ($) |
IRR (% pa) |
| Rent then sell as is | -900,000 | 990,000 | 10 |
| Refurbishment into modern offices | -2,000,000 | 2,400,000 | 20 |
| Conversion into residential apartments | -3,000,000 | 3,400,000 | 13.33 |
Which project should the investor accept?
An investor owns an empty block of land that has local government approval to be developed into a petrol station, car wash or car park. The council will only allow a single development so the projects are mutually exclusive.
All of the development projects have the same risk and the required return of each is 10% pa. Each project has an immediate cost and once construction is finished in one year the land and development will be sold. The table below shows the estimated costs payable now, expected sale prices in one year and the internal rates of returns (IRR's).
| Mutually Exclusive Projects | |||
| Project | Cost now ($) |
Sale price in one year ($) |
IRR (% pa) |
| Petrol station | 9,000,000 | 11,000,000 | 22.22 |
| Car wash | 800,000 | 1,100,000 | 37.50 |
| Car park | 70,000 | 110,000 | 57.14 |
Which project should the investor accept?
Your neighbour asks you for a loan of $100 and offers to pay you back $120 in one year.
You don't actually have any money right now, but you can borrow and lend from the bank at a rate of 10% pa. Rates are given as effective annual rates.
Assume that your neighbour will definitely pay you back. Ignore interest tax shields and transaction costs.
The Net Present Value (NPV) of lending to your neighbour is $9.09. Describe what you would do to actually receive a $9.09 cash flow right now with zero net cash flows in the future.
You have $100,000 in the bank. The bank pays interest at 10% pa, given as an effective annual rate.
You wish to consume an equal amount now (t=0), in one year (t=1) and in two years (t=2), and still have $50,000 in the bank after that (t=2).
How much can you consume at each time?
You have $100,000 in the bank. The bank pays interest at 10% pa, given as an effective annual rate.
You wish to consume an equal amount now (t=0) and in one year (t=1) and have nothing left in the bank at the end (t=1).
How much can you consume at each time?
A firm is considering a business project which costs $11m now and is expected to pay a constant $1m at the end of every year forever.
Assume that the initial $11m cost is funded using the firm's existing cash so no new equity or debt will be raised. The cost of capital is 10% pa.
Which of the following statements about net present value (NPV), internal rate of return (IRR) and payback period is NOT correct?
The below graph shows a project's net present value (NPV) against its annual discount rate.
Which of the following statements is NOT correct?
The below graph shows a project's net present value (NPV) against its annual discount rate.
For what discount rate or range of discount rates would you accept and commence the project?
All answer choices are given as approximations from reading off the graph.
A project has the following cash flows:
| Project Cash Flows | |
| Time (yrs) | Cash flow ($) |
| 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.
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 |
If a project's net present value (NPV) is zero, then its internal rate of return (IRR) will be:
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 ($) |
| 0 | -100 |
| 1 | 0 |
| 2 | 121 |
The required return of a project is 10%, given as an effective annual rate. Assume that the cash flows shown in the table are paid all at once at the given point in time.
What is the Net Present Value (NPV) of the project?
| Project Cash Flows | |
| Time (yrs) | Cash flow ($) |
| 0 | -100 |
| 1 | 0 |
| 2 | 121 |
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 295 inflation, real and nominal returns and cash flows, NPV
When valuing assets using discounted cash flow (net present value) methods, it is important to consider inflation. To properly deal with inflation:
(I) Discount nominal cash flows by nominal discount rates.
(II) Discount nominal cash flows by real discount rates.
(III) Discount real cash flows by nominal discount rates.
(IV) Discount real cash flows by real discount rates.
Which of the above statements is or are correct?
There are many ways to write the ordinary annuity formula.
Which of the following is NOT equal to the ordinary annuity formula?
The following cash flows are expected:
- 10 yearly payments of $60, with the first payment in 3 years from now (first payment at t=3 and last at t=12).
- 1 payment of $400 in 5 years and 6 months (t=5.5) from now.
What is the NPV of the cash flows if the discount rate is 10% given as an effective annual rate?
Question 58 NPV, inflation, real and nominal returns and cash flows, Annuity
A project to build a toll bridge will take two years to complete, costing three payments of $100 million at the start of each year for the next three years, that is at t=0, 1 and 2.
After completion, the toll bridge will yield a constant $50 million at the end of each year for the next 10 years. So the first payment will be at t=3 and the last at t=12. After the last payment at t=12, the bridge will be given to the government.
The required return of the project is 21% pa given as an effective annual nominal rate.
All cash flows are real and the expected inflation rate is 10% pa given as an effective annual rate. Ignore taxes.
The Net Present Value is:
The first payment of a constant perpetual annual cash flow is received at time 5. Let this cash flow be ##C_5## and the required return be ##r##.
So there will be equal annual cash flows at time 5, 6, 7 and so on forever, and all of the cash flows will be equal so ##C_5 = C_6 = C_7 = ...##
When the perpetuity formula is used to value this stream of cash flows, it will give a value (V) at time:
A stock just paid its annual dividend of $9. The share price is $60. The required return of the stock is 10% pa as an effective annual rate.
What is the implied growth rate of the dividend per year?
Two years ago Fred bought a house for $300,000.
Now it's worth $500,000, based on recent similar sales in the area.
Fred's residential property has an expected total return of 8% pa.
He rents his house out for $2,000 per month, paid in advance. Every 12 months he plans to increase the rental payments.
The present value of 12 months of rental payments is $23,173.86.
The future value of 12 months of rental payments one year ahead is $25,027.77.
What is the expected annual growth rate of the rental payments? In other words, by what percentage increase will Fred have to raise the monthly rent by each year to sustain the expected annual total return of 8%?
The following is the Dividend Discount Model (DDM) used to price stocks:
### P_0 = \frac{d_1}{r-g} ###Assume that the assumptions of the DDM hold and that the time period is measured in years.
Which of the following is equal to the expected dividend in 3 years, ## d_3 ##?
The following equation is the Dividend Discount Model, also known as the 'Gordon Growth Model' or the 'Perpetuity with growth' equation.
###p_0=\frac{d_1}{r_\text{eff}-g_\text{eff}}###
Which expression is NOT equal to the expected capital return?
Question 498 NPV, Annuity, perpetuity with growth, multi stage growth model
A business project is expected to cost $100 now (t=0), then pay $10 at the end of the third (t=3), fourth, fifth and sixth years, and then grow by 5% pa every year forever. So the cash flow will be $10.5 at the end of the seventh year (t=7), then $11.025 at the end of the eighth year (t=8) and so on perpetually. The total required return is 10℅ pa.
Which of the following formulas will NOT give the correct net present value of the project?
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.
Private equity firms are known to buy medium sized private companies operating in the same industry, merge them together into a larger company, and then sell it off in a public float (initial public offering, IPO).
If medium-sized private companies trade at PE ratios of 5 and larger listed companies trade at PE ratios of 15, what return can be achieved from this strategy?
Assume that:
- The medium-sized companies can be bought, merged and sold in an IPO instantaneously.
- There are no costs of finding, valuing, merging and restructuring the medium sized companies. Also, there is no competition to buy the medium-sized companies from other private equity firms.
- The large merged firm's earnings are the sum of the medium firms' earnings.
- The only reason for the difference in medium and large firm's PE ratios is due to the illiquidity of the medium firms' shares.
- Return is defined as: ##r_{0→1} = (p_1-p_0+c_1)/p_0## , where time zero is just before the merger and time one is just after.
When using the dividend discount model, care must be taken to avoid using a nominal dividend growth rate that exceeds the country's nominal GDP growth rate. Otherwise the firm is forecast to take over the country since it grows faster than the average business forever.
Suppose a firm's nominal dividend grows at 10% pa forever, and nominal GDP growth is 5% pa forever. The firm's total dividends are currently $1 billion (t=0). The country's GDP is currently $1,000 billion (t=0).
In approximately how many years will the company's total dividends be as large as the country's GDP?
A low-quality second-hand car can be bought now for $1,000 and will last for 1 year before it will be scrapped for nothing.
A high-quality second-hand car can be bought now for $4,900 and it will last for 5 years before it will be scrapped for nothing.
What is the equivalent annual cost of each car? Assume a discount rate of 10% pa, given as an effective annual rate.
The answer choices are given as the equivalent annual cost of the low-quality car and then the high quality car.
You're advising your superstar client 40-cent who is weighing up buying a private jet or a luxury yacht. 40-cent is just as happy with either, but he wants to go with the more cost-effective option. These are the cash flows of the two options:
- The private jet can be bought for $6m now, which will cost $12,000 per month in fuel, piloting and airport costs, payable at the end of each month. The jet will last for 12 years.
- Or the luxury yacht can be bought for $4m now, which will cost $20,000 per month in fuel, crew and berthing costs, payable at the end of each month. The yacht will last for 20 years.
What's unusual about 40-cent is that he is so famous that he will actually be able to sell his jet or yacht for the same price as it was bought since the next generation of superstar musicians will buy it from him as a status symbol.
Bank interest rates are 10% pa, given as an effective annual rate. You can assume that 40-cent will live for another 60 years and that when the jet or yacht's life is at an end, he will buy a new one with the same details as above.
Would you advise 40-cent to buy the or the ?
Note that the effective monthly rate is ##r_\text{eff monthly}=(1+0.1)^{1/12}-1=0.00797414##
Question 548 equivalent annual cash flow, time calculation, no explanation
An Apple iPhone 6 smart phone can be bought now for $999. An Android Kogan Agora 4G+ smart phone can be bought now for $240.
If the Kogan phone lasts for one year, approximately how long must the Apple phone last for to have the same equivalent annual cost?
Assume that both phones have equivalent features besides their lifetimes, that both are worthless once they've outlasted their life, the discount rate is 10% pa given as an effective annual rate, and there are no extra costs or benefits from either phone.
You just bought a nice dress which you plan to wear once per month on nights out. You bought it a moment ago for $600 (at t=0). In your experience, dresses used once per month last for 6 years.
Your younger sister is a student with no money and wants to borrow your dress once a month when she hits the town. With the increased use, your dress will only last for another 3 years rather than 6.
What is the present value of the cost of letting your sister use your current dress for the next 3 years?
Assume: that bank interest rates are 10% pa, given as an effective annual rate; you will buy a new dress when your current one wears out; your sister will only use the current dress, not the next one that you will buy; and the price of a new dress never changes.
The saying "buy low, sell high" suggests that investors should make a:
Question 490 expected and historical returns, accounting ratio
Which of the following is NOT a synonym of 'required return'?
Total cash flows can be broken into income and capital cash flows. What is the name given to the income cash flow from owning shares?
Total cash flows can be broken into income and capital cash flows.
What is the name given to the cash flow generated from selling shares at a higher price than they were bought?
Question 604 inflation, real and nominal returns and cash flows
Apples and oranges currently cost $1 each. Inflation is 5% pa, and apples and oranges are equally affected by this inflation rate. Note that when payments are not specified as real, as in this question, they're conventionally assumed to be nominal.
Which of the following statements is NOT correct?
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 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.
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 newly floated farming company is financed with senior bonds, junior bonds, cumulative non-voting preferred stock and common stock. The new company has no retained profits and due to floods it was unable to record any revenues this year, leading to a loss. The firm is not bankrupt yet since it still has substantial contributed equity (same as paid-up capital).
On which securities must it pay interest or dividend payments in this terrible financial year?
Which business structure or structures have the advantage of limited liability for equity investors?
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.
Question 531 bankruptcy or insolvency, capital structure, risk, limited liability
Who is most in danger of being personally bankrupt? Assume that all of their businesses' assets are highly liquid and can therefore be sold immediately.
The below screenshot of Commonwealth Bank of Australia's (CBA) details were taken from the Google Finance website on 7 Nov 2014. Some information has been deliberately blanked out.
What was CBA's market capitalisation of equity?
The below screenshot of Microsoft's (MSFT) details were taken from the Google Finance website on 28 Nov 2014. Some information has been deliberately blanked out.
What was MSFT's market capitalisation of equity?
Which of the following statements about book and market equity is NOT correct?
Question 461 book and market values, ROE, ROA, market efficiency
One year ago a pharmaceutical firm floated by selling its 1 million shares for $100 each. Its book and market values of equity were both $100m. Its debt totalled $50m. The required return on the firm's assets was 15%, equity 20% and debt 5% pa.
In the year since then, the firm:
- Earned net income of $29m.
- Paid dividends totaling $10m.
- Discovered a valuable new drug that will lead to a massive 1,000 times increase in the firm's net income in 10 years after the research is commercialised. News of the discovery was publicly announced. The firm's systematic risk remains unchanged.
Which of the following statements is NOT correct? All statements are about current figures, not figures one year ago.
Hint: Book return on assets (ROA) and book return on equity (ROE) are ratios that accountants like to use to measure a business's past performance.
###\text{ROA}= \dfrac{\text{Net income}}{\text{Book value of assets}}###
###\text{ROE}= \dfrac{\text{Net income}}{\text{Book value of equity}}###
The required return on assets ##r_V## is a return that financiers like to use to estimate a business's future required performance which compensates them for the firm's assets' risks. If the business were to achieve realised historical returns equal to its required returns, then investment into the business's assets would have been a zero-NPV decision, which is neither good nor bad but fair.
###r_\text{V, 0 to 1}= \dfrac{\text{Cash flow from assets}_\text{1}}{\text{Market value of assets}_\text{0}} = \dfrac{CFFA_\text{1}}{V_\text{0}}###
Similarly for equity and debt.
Question 444 investment decision, corporate financial decision theory
The investment decision primarily affects which part of a business?
Question 446 working capital decision, corporate financial decision theory
The working capital decision primarily affects which part of a business?
Question 445 financing decision, corporate financial decision theory
The financing decision primarily affects which part of a business?
Question 447 payout policy, corporate financial decision theory
Payout policy is most closely related to which part of a business?
Question 443 corporate financial decision theory, investment decision, financing decision, working capital decision, payout policy
Business people make lots of important decisions. Which of the following is the most important long term decision?
The expression 'cash is king' emphasizes the importance of having enough cash to pay your short term debts to avoid bankruptcy. Which business decision is this expression most closely related to?
The expression 'you have to spend money to make money' relates to which business decision?
Which of the following decisions relates to the current assets and current liabilities of the firm?
The phone company Telstra have 2 mobile service plans on offer which both have the same amount of phone call, text message and internet data credit. Both plans have a contract length of 24 months and the monthly cost is payable in advance. The only difference between the two plans is that one is a:
- 'Bring Your Own' (BYO) mobile service plan, costing $50 per month. There is no phone included in this plan. The other plan is a:
- 'Bundled' mobile service plan that comes with the latest smart phone, costing $71 per month. This plan includes the latest smart phone.
Neither plan has any additional payments at the start or end.
The only difference between the plans is the phone, so what is the implied cost of the phone as a present value?
Assume that the discount rate is 2% per month given as an effective monthly rate, the same high interest rate on credit cards.
A credit card company advertises an interest rate of 18% pa, payable monthly. Which of the following statements about the interest rate is NOT correct? All rates are given to four decimal places.
Question 213 income and capital returns, bond pricing, premium par and discount bonds
The coupon rate of a fixed annual-coupon bond is constant (always the same).
What can you say about the income return (##r_\text{income}##) of a fixed annual coupon bond? Remember that:
###r_\text{total} = r_\text{income} + r_\text{capital}###
###r_\text{total, 0 to 1} = \frac{c_1}{p_0} + \frac{p_1-p_0}{p_0}###
Assume that there is no change in the bond's total annual yield to maturity from when it is issued to when it matures.
Select the most correct statement.
From its date of issue until maturity, the income return of a fixed annual coupon:
Question 25 bond pricing, zero coupon bond, term structure of interest rates, forward interest rate
A European company just issued two bonds, a
- 2 year zero coupon bond at a yield of 8% pa, and a
- 3 year zero coupon bond at a yield of 10% pa.
What is the company's forward rate over the third year (from t=2 to t=3)? Give your answer as an effective annual rate, which is how the above bond yields are quoted.
Bonds X and Y are issued by the same US company. Both bonds yield 6% pa, and they have the same face value ($100), maturity, seniority, and payment frequency.
The only difference is that bond X pays coupons of 8% pa and bond Y pays coupons of 12% pa. Which of the following statements is true?
A firm wishes to raise $10 million now. They will issue 6% pa semi-annual coupon bonds that will mature in 8 years and have a face value of $1,000 each. Bond yields are 10% pa, given as an APR compounding every 6 months, and the yield curve is flat.
How many bonds should the firm issue? All numbers are rounded up.
A 10 year Australian government bond was just issued at par with a yield of 3.9% pa. The fixed coupon payments are semi-annual. The bond has a face value of $1,000.
Six months later, just after the first coupon is paid, the yield of the bond decreases to 3.65% pa. What is the bond's new price?
A two year Government bond has a face value of $100, a yield of 0.5% and a fixed coupon rate of 0.5%, paid semi-annually. What is its price?
Calculate the price of a newly issued ten year bond with a face value of $100, a yield of 8% pa and a fixed coupon rate of 6% pa, paid semi-annually. So there are two coupons per year, paid in arrears every six months.
Calculate the price of a newly issued ten year bond with a face value of $100, a yield of 8% pa and a fixed coupon rate of 6% pa, paid annually. So there's only one coupon per year, paid in arrears every year.
Question 56 income and capital returns, bond pricing, premium par and discount bonds
Which of the following statements about risk free government bonds is NOT correct?
Hint: Total return can be broken into income and capital returns as follows:
###\begin{aligned} r_\text{total} &= \frac{c_1}{p_0} + \frac{p_1-p_0}{p_0} \\ &= r_\text{income} + r_\text{capital} \end{aligned} ###
The capital return is the growth rate of the price.
The income return is the periodic cash flow. For a bond this is the coupon payment.
Which of the following statements about effective rates and annualised percentage rates (APR's) is NOT correct?
A European bond paying annual coupons of 6% offers a yield of 10% pa.
Convert the yield into an effective monthly rate, an effective annual rate and an effective daily rate. Assume that there are 365 days in a year.
All answers are given in the same order:
### r_\text{eff, monthly} , r_\text{eff, yearly} , r_\text{eff, daily} ###
You want to buy an apartment priced at $500,000. You have saved a deposit of $50,000. The bank has agreed to lend you the $450,000 as an interest only loan with a term of 30 years. The interest rate is 6% pa and is not expected to change. What will be your monthly payments?
You want to buy an apartment priced at $500,000. You have saved a deposit of $50,000. The bank has agreed to lend you the $450,000 as a fully amortising loan with a term of 30 years. The interest rate is 6% pa and is not expected to change. What will be your monthly payments?
You just signed up for a 30 year fully amortising mortgage loan with monthly payments of $1,500 per month. The interest rate is 9% pa which is not expected to change.
To your surprise, you can actually afford to pay $2,000 per month and your mortgage allows early repayments without fees. If you maintain these higher monthly payments, how long will it take to pay off your mortgage?
A prospective home buyer can afford to pay $2,000 per month in mortgage loan repayments. The central bank recently lowered its policy rate by 0.25%, and residential home lenders cut their mortgage loan rates from 4.74% to 4.49%.
How much more can the prospective home buyer borrow now that interest rates are 4.49% rather than 4.74%? Give your answer as a proportional increase over the original amount he could borrow (##V_\text{before}##), so:
###\text{Proportional increase} = \frac{V_\text{after}-V_\text{before}}{V_\text{before}} ###Assume that:
- Interest rates are expected to be constant over the life of the loan.
- Loans are interest-only and have a life of 30 years.
- Mortgage loan payments are made every month in arrears and all interest rates are given as annualised percentage rates compounding per month.
A home loan company advertises an interest rate of 6% pa, payable monthly. Which of the following statements about the interest rate is NOT correct? All rates are given to four decimal places.
A semi-annual coupon bond has a yield of 3% pa. Which of the following statements about the yield is NOT correct? All rates are given to four decimal places.
Which of the below statements about effective rates and annualised percentage rates (APR's) is NOT correct?
A credit card offers an interest rate of 18% pa, compounding monthly.
Find the effective monthly rate, effective annual rate and the effective daily rate. Assume that there are 365 days in a year.
All answers are given in the same order:
### r_\text{eff monthly} , r_\text{eff yearly} , r_\text{eff daily} ###
Calculate the effective annual rates of the following three APR's:
- A credit card offering an interest rate of 18% pa, compounding monthly.
- A bond offering a yield of 6% pa, compounding semi-annually.
- An annual dividend-paying stock offering a return of 10% pa compounding annually.
All answers are given in the same order:
##r_\text{credit card, eff yrly}##, ##r_\text{bond, eff yrly}##, ##r_\text{stock, eff yrly}##
On his 20th birthday, a man makes a resolution. He will deposit $30 into a bank account at the end of every month starting from now, which is the start of the month. So the first payment will be in one month. He will write in his will that when he dies the money in the account should be given to charity.
The bank account pays interest at 6% pa compounding monthly, which is not expected to change.
If the man lives for another 60 years, how much money will be in the bank account if he dies just after making his last (720th) payment?
You want to buy an apartment priced at $300,000. You have saved a deposit of $30,000. The bank has agreed to lend you the $270,000 as a fully amortising loan with a term of 25 years. The interest rate is 12% pa and is not expected to change.
What will be your monthly payments? Remember that mortgage loan payments are paid in arrears (at the end of the month).
You want to buy an apartment worth $400,000. You have saved a deposit of $80,000. The bank has agreed to lend you the $320,000 as a fully amortising mortgage loan with a term of 30 years. The interest rate is 6% pa and is not expected to change. What will be your monthly payments?
You just signed up for a 30 year fully amortising mortgage loan with monthly payments of $2,000 per month. The interest rate is 9% pa which is not expected to change.
How much did you borrow? After 5 years, how much will be owing on the mortgage? The interest rate is still 9% and is not expected to change.
You just signed up for a 30 year fully amortising mortgage loan with monthly payments of $1,500 per month. The interest rate is 9% pa which is not expected to change.
How much did you borrow? After 10 years, how much will be owing on the mortgage? The interest rate is still 9% and is not expected to change.
You just agreed to a 30 year fully amortising mortgage loan with monthly payments of $2,500. The interest rate is 9% pa which is not expected to change.
How much did you borrow? After 10 years, how much will be owing on the mortgage? The interest rate is still 9% and is not expected to change. The below choices are given in the same order.
You want to buy an apartment priced at $300,000. You have saved a deposit of $30,000. The bank has agreed to lend you the $270,000 as an interest only loan with a term of 25 years. The interest rate is 12% pa and is not expected to change.
What will be your monthly payments? Remember that mortgage payments are paid in arrears (at the end of the month).
You just borrowed $400,000 in the form of a 25 year interest-only mortgage with monthly payments of $3,000 per month. The interest rate is 9% pa which is not expected to change.
You actually plan to pay more than the required interest payment. You plan to pay $3,300 in mortgage payments every month, which your mortgage lender allows. These extra payments will reduce the principal and the minimum interest payment required each month.
At the maturity of the mortgage, what will be the principal? That is, after the last (300th) interest payment of $3,300 in 25 years, how much will be owing on the mortgage?
A young lady is trying to decide if she should attend university or not.
The young lady's parents say that she must attend university because otherwise all of her hard work studying and attending school during her childhood was a waste.
What's the correct way to classify this item from a capital budgeting perspective when trying to decide whether to attend university?
The hard work studying at school in her childhood should be classified as:
What is the net present value (NPV) of undertaking a full-time Australian undergraduate business degree as an Australian citizen? Only include the cash flows over the duration of the degree, ignore any benefits or costs of the degree after it's completed.
Assume the following:
- The degree takes 3 years to complete and all students pass all subjects.
- There are 2 semesters per year and 4 subjects per semester.
- University fees per subject per semester are $1,277, paid at the start of each semester. Fees are expected to remain constant in real terms for the next 3 years.
- There are 52 weeks per year.
- The first semester is just about to start (t=0). The first semester lasts for 19 weeks (t=0 to 19).
- The second semester starts immediately afterwards (t=19) and lasts for another 19 weeks (t=19 to 38).
- The summer holidays begin after the second semester ends and last for 14 weeks (t=38 to 52). Then the first semester begins the next year, and so on.
- Working full time at the grocery store instead of studying full-time pays $20/hr and you can work 35 hours per week. Wages are paid at the end of each week and are expected to remain constant in real terms.
- Full-time students can work full-time during the summer holiday at the grocery store for the same rate of $20/hr for 35 hours per week.
- The discount rate is 9.8% pa. All rates and cash flows are real. Inflation is expected to be 3% pa. All rates are effective annual.
The NPV of costs from undertaking the university degree is:
A young lady is trying to decide if she should attend university. Her friends say that she should go to university because she is more likely to meet a clever young man than if she begins full time work straight away.
What's the correct way to classify this item from a capital budgeting perspective when trying to find the Net Present Value of going to university rather than working?
The opportunity to meet a desirable future spouse should be classified as:
A man is thinking about taking a day off from his casual painting job to relax.
He just woke up early in the morning and he's about to call his boss to say that he won't be coming in to work.
But he's thinking about the hours that he could work today (in the future) which are:
A man has taken a day off from his casual painting job to relax.
It's the end of the day and he's thinking about the hours that he could have spent working (in the past) which are now:
Find Candys Corporation's Cash Flow From Assets (CFFA), also known as Free Cash Flow to the Firm (FCFF), over the year ending 30th June 2013.
| Candys Corp | ||
| Income Statement for | ||
| year ending 30th June 2013 | ||
| $m | ||
| Sales | 200 | |
| COGS | 50 | |
| Operating expense | 10 | |
| Depreciation | 20 | |
| Interest expense | 10 | |
| Income before tax | 110 | |
| Tax at 30% | 33 | |
| Net income | 77 | |
| Candys Corp | ||
| Balance Sheet | ||
| as at 30th June | 2013 | 2012 |
| $m | $m | |
| Assets | ||
| Current assets | 220 | 180 |
| PPE | ||
| Cost | 300 | 340 |
| Accumul. depr. | 60 | 40 |
| Carrying amount | 240 | 300 |
| Total assets | 460 | 480 |
| Liabilities | ||
| Current liabilities | 175 | 190 |
| Non-current liabilities | 135 | 130 |
| Owners' equity | ||
| Retained earnings | 50 | 60 |
| Contributed equity | 100 | 100 |
| Total L and OE | 460 | 480 |
Note: all figures are given in millions of dollars ($m).
Find Ching-A-Lings Corporation's Cash Flow From Assets (CFFA), also known as Free Cash Flow to the Firm (FCFF), over the year ending 30th June 2013.
| Ching-A-Lings Corp | ||
| Income Statement for | ||
| year ending 30th June 2013 | ||
| $m | ||
| Sales | 100 | |
| COGS | 20 | |
| Depreciation | 20 | |
| Rent expense | 11 | |
| Interest expense | 19 | |
| Taxable Income | 30 | |
| Taxes at 30% | 9 | |
| Net income | 21 | |
| Ching-A-Lings Corp | ||
| Balance Sheet | ||
| as at 30th June | 2013 | 2012 |
| $m | $m | |
| Inventory | 49 | 38 |
| Trade debtors | 14 | 2 |
| Rent paid in advance | 5 | 5 |
| PPE | 400 | 400 |
| Total assets | 468 | 445 |
| Trade creditors | 4 | 10 |
| Bond liabilities | 200 | 190 |
| Contributed equity | 145 | 145 |
| Retained profits | 119 | 100 |
| Total L and OE | 468 | 445 |
Note: All figures are given in millions of dollars ($m).
The cash flow from assets was:
To value a business's assets, the free cash flow of the firm (FCFF, also called CFFA) needs to be calculated. This requires figures from the firm's income statement and balance sheet. For what figures is the balance sheet needed? Note that the balance sheet is sometimes also called the statement of financial position.
Which one of the following will decrease net income (NI) but increase cash flow from assets (CFFA) in this year for a tax-paying firm, all else remaining constant?
Remember:
###NI = (Rev-COGS-FC-Depr-IntExp).(1-t_c )### ###CFFA=NI+Depr-CapEx - \Delta NWC+IntExp###Which one of the following will have no effect on net income (NI) but decrease cash flow from assets (CFFA or FFCF) in this year for a tax-paying firm, all else remaining constant?
Remember:
###NI=(Rev-COGS-FC-Depr-IntExp).(1-t_c )### ###CFFA=NI+Depr-CapEx - ΔNWC+IntExp###Find the cash flow from assets (CFFA) of the following project.
| One Year Mining Project Data | ||
| Project life | 1 year | |
| Initial investment in building mine and equipment | $9m | |
| Depreciation of mine and equipment over the year | $8m | |
| Kilograms of gold mined at end of year | 1,000 | |
| Sale price per kilogram | $0.05m | |
| Variable cost per kilogram | $0.03m | |
| Before-tax cost of closing mine at end of year | $4m | |
| Tax rate | 30% | |
Note 1: Due to the project, the firm also anticipates finding some rare diamonds which will give before-tax revenues of $1m at the end of the year.
Note 2: The land that will be mined actually has thermal springs and a family of koalas that could be sold to an eco-tourist resort for an after-tax amount of $3m right now. However, if the mine goes ahead then this natural beauty will be destroyed.
Note 3: The mining equipment will have a book value of $1m at the end of the year for tax purposes. However, the equipment is expected to fetch $2.5m when it is sold.
Find the project's CFFA at time zero and one. Answers are given in millions of dollars ($m), with the first cash flow at time zero, and the second at time one.
You want to buy an apartment worth $500,000. You have saved a deposit of $50,000. The bank has agreed to lend you the $450,000 as a fully amortising mortgage loan with a term of 25 years. The interest rate is 6% pa and is not expected to change.
What will be your monthly payments?
You just signed up for a 30 year fully amortising mortgage with monthly payments of $1,000 per month. The interest rate is 6% pa which is not expected to change.
How much did you borrow? After 20 years, how much will be owing on the mortgage? The interest rate is still 6% and is not expected to change.
You want to buy a house priced at $400,000. You have saved a deposit of $40,000. The bank has agreed to lend you $360,000 as a fully amortising loan with a term of 30 years. The interest rate is 8% pa payable monthly and is not expected to change.
What will be your monthly payments?
Your friend just bought a house for $1,000,000. He financed it using a $900,000 mortgage loan and a deposit of $100,000.
In the context of residential housing and mortgages, the 'equity' or 'net wealth' tied up in a house is the value of the house less the value of the mortgage loan. Assuming that your friend's only asset is his house, his net wealth is $100,000.
If house prices suddenly fall by 15%, what would be your friend's percentage change in net wealth?
Assume that:
- No income (rent) was received from the house during the short time over which house prices fell.
- Your friend will not declare bankruptcy, he will always pay off his debts.
Here are the Net Income (NI) and Cash Flow From Assets (CFFA) equations:
###NI=(Rev-COGS-FC-Depr-IntExp).(1-t_c)###
###CFFA=NI+Depr-CapEx - \varDelta NWC+IntExp###
What is the formula for calculating annual interest expense (IntExp) which is used in the equations above?
Select one of the following answers. Note that D is the value of debt which is constant through time, and ##r_D## is the cost of debt.
Which one of the following will decrease net income (NI) but increase cash flow from assets (CFFA) in this year for a tax-paying firm, all else remaining constant?
Remember:
###NI=(Rev-COGS-FC-Depr-IntExp).(1-t_c )### ###CFFA=NI+Depr-CapEx - ΔNWC+IntExp###A firm has a debt-to-equity ratio of 60%. What is its debt-to-assets ratio?
A retail furniture company buys furniture wholesale and distributes it through its retail stores. The owner believes that she has some good ideas for making stylish new furniture. She is considering a project to buy a factory and employ workers to manufacture the new furniture she's designed. Furniture manufacturing has more systematic risk than furniture retailing.
Her furniture retailing firm's after-tax WACC is 20%. Furniture manufacturing firms have an after-tax WACC of 30%. Both firms are optimally geared. Assume a classical tax system.
Which method(s) will give the correct valuation of the new furniture-making project? Select the most correct answer.
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 method commonly seen in textbooks for calculating a levered firm's free cash flow (FFCF, or CFFA) is the following:
###\begin{aligned} FFCF &= (Rev - COGS - Depr - FC - IntExp)(1-t_c) + \\ &\space\space\space+ Depr - CapEx -\Delta NWC + IntExp(1-t_c) \\ \end{aligned}###
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}###
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 69 interest tax shield, capital structure, leverage, WACC
Which statement about risk, required return and capital structure is the most correct?
A firm is considering a new project of similar risk to the current risk of the firm. This project will expand its existing business. The cash flows of the project have been calculated assuming that there is no interest expense. In other words, the cash flows assume that the project is all-equity financed.
In fact the firm has a target debt-to-equity ratio of 1, so the project will be financed with 50% debt and 50% equity. To find the levered value of the firm's assets, what discount rate should be applied to the project's unlevered cash flows? Assume a classical tax system.
Question 99 capital structure, interest tax shield, Miller and Modigliani, trade off theory of capital structure
A firm changes its capital structure by issuing a large amount of debt and using the funds to repurchase shares. Its assets are unchanged.
Assume that:
- The firm and individual investors can borrow at the same rate and have the same tax rates.
- The firm's debt and shares are fairly priced and the shares are repurchased at the market price, not at a premium.
- There are no market frictions relating to debt such as asymmetric information or transaction costs.
- Shareholders wealth is measured in terms of utiliity. Shareholders are wealth-maximising and risk-averse. They have a preferred level of overall leverage. Before the firm's capital restructure all shareholders were optimally levered.
According to Miller and Modigliani's theory, which statement is correct?
Question 121 capital structure, leverage, financial distress, interest tax shield
Fill in the missing words in the following sentence:
All things remaining equal, as a firm's amount of debt funding falls, benefits of interest tax shields __________ and the costs of financial distress __________.
A firm plans to issue equity and use the cash raised to pay off its debt. No assets will be bought or sold. Ignore the costs of financial distress.
Which of the following statements is NOT correct, all things remaining equal?
The following table shows a sample of historical total returns of shares in two different companies A and B.
| Stock Returns | ||
| Total effective annual returns | ||
| Year | ##r_A## | ##r_B## |
| 2007 | 0.2 | 0.4 |
| 2008 | 0.04 | -0.2 |
| 2009 | -0.1 | -0.3 |
| 2010 | 0.18 | 0.5 |
What is the historical sample covariance (##\hat{\sigma}_{A,B}##) and correlation (##\rho_{A,B}##) of stock A and B's total effective annual returns?
Stock A and B's returns have a correlation of 0.3. Which statement is NOT correct?
| Portfolio Details | ||||||
| Stock | Expected return |
Standard deviation |
Correlation | Dollars invested |
||
| A | 0.1 | 0.4 | 0.5 | 60 | ||
| B | 0.2 | 0.6 | 140 | |||
What is the expected return of the above portfolio?
| Portfolio Details | ||||||
| Stock | Expected return |
Standard deviation |
Covariance ##(\sigma_{A,B})## | Beta | Dollars invested |
|
| A | 0.2 | 0.4 | 0.12 | 0.5 | 40 | |
| B | 0.3 | 0.8 | 1.5 | 80 | ||
What is the standard deviation (not variance) of the above portfolio? Note that the stocks' covariance is given, not correlation.
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.
- 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.
Which of the following statements about short-selling is NOT true?
Question 558 portfolio weights, portfolio return, short selling
An investor wants to make a portfolio of two stocks A and B with a target expected portfolio return of 16% pa.
- Stock A has an expected return of 8% pa.
- Stock B has an expected return of 12% pa.
What portfolio weights should the investor have in stocks A and B respectively?
What is the covariance of a variable X with itself?
The cov(X, X) or ##\sigma_{X,X}## equals:
What is the covariance of a variable X with a constant C?
The cov(X, C) or ##\sigma_{X,C}## equals:
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?
Hint: Visit Wikipedia to understand the difference between percentage points ##(\text{pp})## and percent ##(\%)##.
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.
Which of the below statements about utility is NOT generally accepted by economists? Most people are thought to:
Mr Blue, Miss Red and Mrs Green are people with different utility functions. Which of the statements about the 3 utility functions is NOT correct?
Mr Blue, Miss Red and Mrs Green are people with different utility functions. Which of the statements about the 3 utility functions is NOT correct?
Mr Blue, Miss Red and Mrs Green are people with different utility functions. Which of the statements about the 3 utility functions is NOT correct?
Mr Blue, Miss Red and Mrs Green are people with different utility functions. Which of the statements about the 3 utility functions is NOT correct?
Question 699 utility, risk aversion, utility function, gamble
Mr Blue, Miss Red and Mrs Green are people with different utility functions.
Each person has $50 of initial wealth. A coin toss game is offered to each person at a casino where the player can win or lose $50. Each player can flip a coin and if they flip heads, they receive $50. If they flip tails then they will lose $50. Which of the following statements is NOT correct?
Question 700 utility, risk aversion, utility function, gamble
Mr Blue, Miss Red and Mrs Green are people with different utility functions.
Each person has $50 of initial wealth. A coin toss game is offered to each person at a casino where the player can win or lose $50. Each player can flip a coin and if they flip heads, they receive $50. If they flip tails then they will lose $50. Which of the following statements is NOT correct?
Question 701 utility, risk aversion, utility function, gamble
Mr Blue, Miss Red and Mrs Green are people with different utility functions.
Each person has $50 of initial wealth. A coin toss game is offered to each person at a casino where the player can win or lose $50. Each player can flip a coin and if they flip heads, they receive $50. If they flip tails then they will lose $50. Which of the following statements is NOT correct?
Question 702 utility, risk aversion, utility function, gamble
Mr Blue, Miss Red and Mrs Green are people with different utility functions.
Each person has $50 of initial wealth. A coin toss game is offered to each person at a casino where the player can win or lose $50. Each player can flip a coin and if they flip heads, they receive $50. If they flip tails then they will lose $50. Which of the following statements is NOT correct?
A stock has a beta of 1.5. The market's expected total return is 10% pa and the risk free rate is 5% pa, both given as effective annual rates.
What do you think will be the stock's expected return over the next year, given as an effective annual rate?
A stock has a beta of 1.5. The market's expected total return is 10% pa and the risk free rate is 5% pa, both given as effective annual rates.
In the last 5 minutes, bad economic news was released showing a higher chance of recession. Over this time the share market fell by 1%. 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 stock has a beta of 1.5. The market's expected total return is 10% pa and the risk free rate is 5% pa, both given as effective annual rates.
Over the last year, bad economic news was released showing a higher chance of recession. Over this time the share market fell by 1%. So ##r_{m} = (P_{0} - P_{-1})/P_{-1} = -0.01##, where the current time is zero and one year ago is time -1. The risk free rate was unchanged.
What do you think was the stock's historical return over the last year, given as an effective annual rate?
According to the theory of the Capital Asset Pricing Model (CAPM), total variance can be broken into two components, systematic variance and idiosyncratic variance. Which of the following events would be considered the most diversifiable according to the theory of the CAPM?
A stock's required total return will increase when its:
Treasury bonds currently have a return of 5% pa. A stock has a beta of 0.5 and the market return is 10% pa. What is the expected return of the stock?
A stock has a beta of 0.5. Its next dividend is expected to be $3, paid one year from now. Dividends are expected to be paid annually and grow by 2% pa forever. Treasury bonds yield 5% pa and the market portfolio's expected return is 10% pa. All returns are effective annual rates.
What is the price of the stock now?
Question 235 SML, NPV, CAPM, risk
The security market line (SML) shows the relationship between beta and expected return.
Investment projects that plot on the SML would have:
Question 244 CAPM, SML, NPV, risk
Examine the following graph which shows stocks' betas ##(\beta)## and expected returns ##(\mu)##:
Assume that the CAPM holds and that future expectations of stocks' returns and betas are correctly measured. Which statement is NOT correct?
| Portfolio Details | ||||||
| Stock | Expected return |
Standard deviation |
Correlation | Beta | Dollars invested |
|
| A | 0.2 | 0.4 | 0.12 | 0.5 | 40 | |
| B | 0.3 | 0.8 | 1.5 | 80 | ||
What is the beta of the above portfolio?
Which statement(s) are correct?
(i) All stocks that plot on the Security Market Line (SML) are fairly priced.
(ii) All stocks that plot above the Security Market Line (SML) are overpriced.
(iii) All fairly priced stocks that plot on the Capital Market Line (CML) have zero idiosyncratic risk.
Select the most correct response:
A firm changes its capital structure by issuing a large amount of debt and using the funds to repurchase shares. Its assets are unchanged. Ignore interest tax shields.
According to the Capital Asset Pricing Model (CAPM), which statement is correct?
The total return of any asset can be broken down in different ways. One possible way is to use the dividend discount model (or Gordon growth model):
###p_0 = \frac{c_1}{r_\text{total}-r_\text{capital}}###
Which, since ##c_1/p_0## is the income return (##r_\text{income}##), can be expressed as:
###r_\text{total}=r_\text{income}+r_\text{capital}###
So the total return of an asset is the income component plus the capital or price growth component.
Another way to break up total return is to use the Capital Asset Pricing Model:
###r_\text{total}=r_\text{f}+β(r_\text{m}- r_\text{f})###
###r_\text{total}=r_\text{time value}+r_\text{risk premium}###
So the risk free rate is the time value of money and the term ##β(r_\text{m}- r_\text{f})## is the compensation for taking on systematic risk.
Using the above theory and your general knowledge, which of the below equations, if any, are correct?
(I) ##r_\text{income}=r_\text{time value}##
(II) ##r_\text{income}=r_\text{risk premium}##
(III) ##r_\text{capital}=r_\text{time value}##
(IV) ##r_\text{capital}=r_\text{risk premium}##
(V) ##r_\text{income}+r_\text{capital}=r_\text{time value}+r_\text{risk premium}##
Which of the equations are correct?
Question 408 leverage, portfolio beta, portfolio risk, real estate, CAPM
You just bought a house worth $1,000,000. You financed it with an $800,000 mortgage loan and a deposit of $200,000.
You estimate that:
- The house has a beta of 1;
- The mortgage loan has a beta of 0.2.
What is the beta of the equity (the $200,000 deposit) that you have in your house?
Also, if the risk free rate is 5% pa and the market portfolio's return is 10% pa, what is the expected return on equity in your house? Ignore taxes, assume that all cash flows (interest payments and rent) were paid and received at the end of the year, and all rates are effective annual rates.
A firm can issue 5 year annual coupon bonds at a yield of 8% pa and a coupon rate of 12% pa.
The beta of its levered equity is 1. Five year government bonds yield 5% pa with a coupon rate of 6% pa. The market's expected dividend return is 4% pa and its expected capital return is 6% pa.
The firm's debt-to-equity ratio is 2:1. The corporate tax rate is 30%.
What is the firm's after-tax WACC? Assume a classical tax system.
There are many different ways to value a firm's assets. Which of the following will NOT give the correct market value of a levered firm's assets ##(V_L)##? Assume that:
- The firm is financed by listed common stock and vanilla annual fixed coupon bonds, which are both traded in a liquid market.
- The bonds' yield is equal to the coupon rate, so the bonds are issued at par. The yield curve is flat and yields are not expected to change. When bonds mature they will be rolled over by issuing the same number of new bonds with the same expected yield and coupon rate, and so on forever.
- Tax rates on the dividends and capital gains received by investors are equal, and capital gains tax is paid every year, even on unrealised gains regardless of when the asset is sold.
- There is no re-investment of the firm's cash back into the business. All of the firm's excess cash flow is paid out as dividends so real growth is zero.
- The firm operates in a mature industry with zero real growth.
- All cash flows and rates in the below equations are real (not nominal) and are expected to be stable forever. Therefore the perpetuity equation with no growth is suitable for valuation.
Where:
###r_\text{WACC before tax} = r_D.\frac{D}{V_L} + r_{EL}.\frac{E_L}{V_L} = \text{Weighted average cost of capital before tax}### ###r_\text{WACC after tax} = r_D.(1-t_c).\frac{D}{V_L} + r_{EL}.\frac{E_L}{V_L} = \text{Weighted average cost of capital after tax}### ###NI_L=(Rev-COGS-FC-Depr-\mathbf{IntExp}).(1-t_c) = \text{Net Income Levered}### ###CFFA_L=NI_L+Depr-CapEx - \varDelta NWC+\mathbf{IntExp} = \text{Cash Flow From Assets Levered}### ###NI_U=(Rev-COGS-FC-Depr).(1-t_c) = \text{Net Income Unlevered}### ###CFFA_U=NI_U+Depr-CapEx - \varDelta NWC= \text{Cash Flow From Assets Unlevered}###Question 100 market efficiency, technical analysis, joint hypothesis problem
A company selling charting and technical analysis software claims that independent academic studies have shown that its software makes significantly positive abnormal returns. Assuming the claim is true, which statement(s) are correct?
(I) Weak form market efficiency is broken.
(II) Semi-strong form market efficiency is broken.
(III) Strong form market efficiency is broken.
(IV) The asset pricing model used to measure the abnormal returns (such as the CAPM) had mis-specification error so the returns may not be abnormal but rather fair for the level of risk.
Select the most correct response:
Select the most correct statement from the following.
'Chartists', also known as 'technical traders', believe that:
Question 48 IRR, NPV, bond pricing, premium par and discount bonds, market efficiency
The theory of fixed interest bond pricing is an application of the theory of Net Present Value (NPV). Also, a 'fairly priced' asset is not over- or under-priced. Buying or selling a fairly priced asset has an NPV of zero.
Considering this, which of the following statements is NOT correct?
An economy has only two investable assets: stocks and cash.
Stocks had a historical nominal average total return of negative two percent per annum (-2% pa) over the last 20 years. Stocks are liquid and actively traded. Stock returns are variable, they have risk.
Cash is riskless and has a nominal constant return of zero percent per annum (0% pa), which it had in the past and will have in the future. Cash can be kept safely at zero cost. Cash can be converted into shares and vice versa at zero cost.
The nominal total return of the shares over the next year is expected to be:
A person is thinking about borrowing $100 from the bank at 7% pa and investing it in shares with an expected return of 10% pa. One year later the person intends to sell the shares and pay back the loan in full. Both the loan and the shares are fairly priced.
What is the Net Present Value (NPV) of this one year investment? Note that you are asked to find the present value (##V_0##), not the value in one year (##V_1##).
Fundamentalists who analyse company financial reports and news announcements (but who don't have inside information) will make positive abnormal returns if:
Question 119 market efficiency, fundamental analysis, joint hypothesis problem
Your friend claims that by reading 'The Economist' magazine's economic news articles, she can identify shares that will have positive abnormal expected returns over the next 2 years. Assuming that her claim is true, which statement(s) are correct?
(i) Weak form market efficiency is broken.
(ii) Semi-strong form market efficiency is broken.
(iii) Strong form market efficiency is broken.
(iv) The asset pricing model used to measure the abnormal returns (such as the CAPM) is either wrong (mis-specification error) or is measured using the wrong inputs (data errors) so the returns may not be abnormal but rather fair for the level of risk.
Select the most correct response:
Question 338 market efficiency, CAPM, opportunity cost, technical analysis
A man inherits $500,000 worth of shares.
He believes that by learning the secrets of trading, keeping up with the financial news and doing complex trend analysis with charts that he can quit his job and become a self-employed day trader in the equities markets.
What is the expected gain from doing this over the first year? Measure the net gain in wealth received at the end of this first year due to the decision to become a day trader. Assume the following:
- He earns $60,000 pa in his current job, paid in a lump sum at the end of each year.
- He enjoys examining share price graphs and day trading just as much as he enjoys his current job.
- Stock markets are weak form and semi-strong form efficient.
- He has no inside information.
- He makes 1 trade every day and there are 250 trading days in the year. Trading costs are $20 per trade. His broker invoices him for the trading costs at the end of the year.
- The shares that he currently owns and the shares that he intends to trade have the same level of systematic risk as the market portfolio.
- The market portfolio's expected return is 10% pa.
Measure the net gain over the first year as an expected wealth increase at the end of the year.
The theory of fixed interest bond pricing is an application of the theory of Net Present Value (NPV). Also, a 'fairly priced' asset is not over- or under-priced. Buying or selling a fairly priced asset has an NPV of zero.
Considering this, which of the following statements is NOT correct?
Question 339 bond pricing, inflation, market efficiency, income and capital returns
Economic statistics released this morning were a surprise: they show a strong chance of consumer price inflation (CPI) reaching 5% pa over the next 2 years.
This is much higher than the previous forecast of 3% pa.
A vanilla fixed-coupon 2-year risk-free government bond was issued at par this morning, just before the economic news was released.
What is the expected change in bond price after the economic news this morning, and in the next 2 years? Assume that:
- Inflation remains at 5% over the next 2 years.
- Investors demand a constant real bond yield.
- The bond price falls by the (after-tax) value of the coupon the night before the ex-coupon date, as in real life.
A managed fund charges fees based on the amount of money that you keep with them. The fee is 2% of the start-of-year amount, but it is paid at the end of every year.
This fee is charged regardless of whether the fund makes gains or losses on your money.
The fund offers to invest your money in shares which have an expected return of 10% pa before fees.
You are thinking of investing $100,000 in the fund and keeping it there for 40 years when you plan to retire.
What is the Net Present Value (NPV) of investing your money in the fund? Note that the question is not asking how much money you will have in 40 years, it is asking: what is the NPV of investing in the fund? Assume that:
- The fund has no private information.
- Markets are weak and semi-strong form efficient.
- The fund's transaction costs are negligible.
- The cost and trouble of investing your money in shares by yourself, without the managed fund, is negligible.
Question 416 real estate, market efficiency, income and capital returns, DDM, CAPM
A residential real estate investor believes that house prices will grow at a rate of 5% pa and that rents will grow by 2% pa forever.
All rates are given as nominal effective annual returns. Assume that:
- His forecast is true.
- Real estate is and always will be fairly priced and the capital asset pricing model (CAPM) is true.
- Ignore all costs such as taxes, agent fees, maintenance and so on.
- All rental income cash flow is paid out to the owner, so there is no re-investment and therefore no additions or improvements made to the property.
- The non-monetary benefits of owning real estate and renting remain constant.
Which one of the following statements is NOT correct? Over time:
Question 65 annuity with growth, needs refinement
Which of the below formulas gives the present value of an annuity with growth?
Hint: The equation of a perpetuity without growth is: ###V_\text{0, perp without growth} = \frac{C_\text{1}}{r}###
The formula for the present value of an annuity without growth is derived from the formula for a perpetuity without growth.
The idea is than an annuity with T payments from t=1 to T inclusive is equivalent to a perpetuity starting at t=1 with fixed positive cash flows, plus a perpetuity starting T periods later (t=T+1) with fixed negative cash flows. The positive and negative cash flows after time period T cancel each other out, leaving the positive cash flows between t=1 to T, which is the annuity.
###\begin{aligned} V_\text{0, annuity} &= V_\text{0, perp without growth from t=1} - V_\text{0, perp without growth from t=T+1} \\ &= \dfrac{C_\text{1}}{r} - \dfrac{ \left( \dfrac{C_\text{T+1}}{r} \right) }{(1+r)^T} \\ &= \dfrac{C_\text{1}}{r} - \dfrac{ \left( \dfrac{C_\text{1}}{r} \right) }{(1+r)^T} \\ &= \dfrac{C_\text{1}}{r}\left(1 - \dfrac{1}{(1+r)^T}\right) \\ \end{aligned}###
The equation of a perpetuity with growth is:
###V_\text{0, perp with growth} = \dfrac{C_\text{1}}{r-g}###A managed fund charges fees based on the amount of money that you keep with them. The fee is 2% of the end-of-year amount, paid at the end of every year.
This fee is charged regardless of whether the fund makes gains or losses on your money.
The fund offers to invest your money in shares which have an expected return of 10% pa before fees.
You are thinking of investing $100,000 in the fund and keeping it there for 40 years when you plan to retire.
How much money do you expect to have in the fund in 40 years? Also, what is the future value of the fees that the fund expects to earn from you? Give both amounts as future values in 40 years. Assume that:
- The fund has no private information.
- Markets are weak and semi-strong form efficient.
- The fund's transaction costs are negligible.
- The cost and trouble of investing your money in shares by yourself, without the managed fund, is negligible.
- The fund invests its fees in the same companies as it invests your funds in, but with no fees.
The below answer choices list your expected wealth in 40 years and then the fund's expected wealth in 40 years.
In 2014 the median starting salaries of male and female Australian bachelor degree accounting graduates aged less than 25 years in their first full-time industry job was $50,000 before tax, according to Graduate Careers Australia. See page 9 of this report. Personal income tax rates published by the Australian Tax Office are reproduced for the 2014-2015 financial year in the table below.
| Taxable income | Tax on this income |
|---|---|
| 0 – $18,200 | Nil |
| $18,201 – $37,000 | 19c for each $1 over $18,200 |
| $37,001 – $80,000 | $3,572 plus 32.5c for each $1 over $37,000 |
| $80,001 – $180,000 | $17,547 plus 37c for each $1 over $80,000 |
| $180,001 and over | $54,547 plus 45c for each $1 over $180,000 |
The above rates do not include the Medicare levy of 2%. Exclude the Medicare levy from your calculations
How much personal income tax would you have to pay per year if you earned $50,000 per annum before-tax?
Question 494 franking credit, personal tax on dividends, imputation tax system
A firm pays a fully franked cash dividend of $100 to one of its Australian shareholders who has a personal marginal tax rate of 15%. The corporate tax rate is 30%.
What will be the shareholder's personal tax payable due to the dividend payment?
Due to floods overseas, there is a cut in the supply of the mineral iron ore and its price increases dramatically. An Australian iron ore mining company therefore expects a large but temporary increase in its profit and cash flows. The mining company does not have any positive NPV projects to begin, so what should it do? Select the most correct answer.
A pharmaceutical firm has just discovered a valuable new drug. So far the news has been kept a secret.
The net present value of making and commercialising the drug is $200 million, but $600 million of bonds will need to be issued to fund the project and buy the necessary plant and equipment.
The firm will release the news of the discovery and bond raising to shareholders simultaneously in the same announcement. The bonds will be issued shortly after.
Once the announcement is made and the bonds are issued, what is the expected increase in the value of the firm's assets (ΔV), market capitalisation of debt (ΔD) and market cap of equity (ΔE)?
The triangle symbol is the Greek letter capital delta which means change or increase in mathematics.
Ignore the benefit of interest tax shields from having more debt.
Remember: ##ΔV = ΔD+ΔE##
Question 513 stock split, reverse stock split, stock dividend, bonus issue, rights issue
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?
A company conducts a 4 for 3 stock split. What is the percentage change in the stock price and the number of shares outstanding? The answers are given in the same order.
In mid 2009 the listed mining company Rio Tinto announced a 21-for-40 renounceable rights issue. Below is the chronology of events:
- 04/06/2009. Share price opens at $69.00 and closes at $66.90.
- 05/06/2009. 21-for-40 rights issue announced at a subscription price of $28.29.
- 16/06/2009. Last day that shares trade cum-rights. Share price opens at $76.40 and closes at $75.50.
- 17/06/2009. Shares trade ex-rights. Rights trading commences.
All things remaining equal, what would you expect Rio Tinto's stock price to open at on the first day that it trades ex-rights (17/6/2009)? Ignore the time value of money since time is negligibly short. Also ignore taxes.
Question 455 income and capital returns, payout policy, DDM, market efficiency
A fairly priced unlevered firm plans to pay a dividend of $1 next year (t=1) which is expected to grow by 3% pa every year after that. The firm's required return on equity is 8% pa.
The firm is thinking about reducing its future dividend payments by 10% so that it can use the extra cash to invest in more projects which are expected to return 8% pa, and have the same risk as the existing projects. Therefore, next year's dividend will be $0.90. No new equity or debt will be issued to fund the new projects, they'll all be funded by the cut in dividends.
What will be the stock's new annual capital return (proportional increase in price per year) if the change in payout policy goes ahead?
Assume that payout policy is irrelevant to firm value (so there's no signalling effects) and that all rates are effective annual rates.