You deposit money into a bank. Which of the following statements is NOT correct? You:
You bought a house, primarily funded using a home loan from a bank. Which of the following statements is NOT correct?
Question 737 financial statement, balance sheet, income statement
Where can a publicly listed firm's book value of equity be found? It can be sourced from the company's:
Question 738 financial statement, balance sheet, income statement
Where can a private firm's market value of equity be found? It can be sourced from the company's:
Question 739 real and nominal returns and cash flows, inflation
There are a number of different formulas involving real and nominal returns and cash flows. Which one of the following formulas is NOT correct? All returns are effective annual rates. Note that the symbol ##\approx## means 'approximately equal to'.
Question 740 real and nominal returns and cash flows, DDM, inflation
Taking inflation into account when using the DDM can be hard. Which of the following formulas will NOT give a company's current stock price ##(P_0)##? Assume that the annual dividend was just paid ##(C_0)##, and the next dividend will be paid in one year ##(C_1)##.
A home loan company advertises an interest rate of 4.5% pa, payable monthly. Which of the following statements about the interest rate is NOT correct?
Question 742 price gains and returns over time, no explanation
For an asset's price to quintuple (be five times as big, say from $1 to $5) every 5 years, what must be its effective annual capital return?
Question 743 price gains and returns over time, no explanation
How many years will it take for an asset's price to triple (increase from say $1 to $3) if it grows by 5% pa?
Question 744 income and capital returns, real and nominal returns and cash flows, inflation
If someone says "my shares rose by 10% last year", what do you assume that they mean? The effective annual:
Question 745 real and nominal returns and cash flows, inflation, income and capital returns
If the nominal gold price is expected to increase at the same rate as inflation which is 3% pa, which of the following statements is NOT correct?
A stock is expected to pay a dividend of $1 in one year. Its future annual dividends are expected to grow by 10% pa. So the first dividend of $1 is in one year, and the year after that the dividend will be $1.1 (=1*(1+0.1)^1), and a year later $1.21 (=1*(1+0.1)^2) and so on forever.
Its required total return is 30% pa. The total required return and growth rate of dividends are given as effective annual rates. The stock is fairly priced.
Calculate the pay back period of buying the stock and holding onto it forever, assuming that the dividends are received as at each time, not smoothly over each year.
A share will pay its next dividend of ##C_1## in one year, and will continue to pay a dividend every year after that forever, growing at a rate of ##g##. So the next dividend will be ##C_2=C_1 (1+g)^1##, then ##C_3=C_2 (1+g)^1##, and so on forever.
The current price of the share is ##P_0## and its required return is ##r##
Which of the following is NOT equal to the expected share price in 2 years ##(P_2)## just after the dividend at that time ##(C_2)## has been paid?
Question 748 income and capital returns, DDM, ex dividend date
A stock will pay you a dividend of $2 tonight if you buy it today.
Thereafter the annual dividend is expected to grow by 3% pa, so the next dividend after the $2 one tonight will be $2.06 in one year, then in two years it will be $2.1218 and so on. The stock's required return is 8% pa.
What is the stock price today and what do you expect the stock price to be tomorrow, approximately?
Question 749 Multiples valuation, PE ratio, price to revenue ratio, price to book ratio, NPV
A real estate agent says that the price of a house in Sydney Australia is approximately equal to the gross weekly rent times 1000.
What type of valuation method is the real estate agent using?
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.
Telsa Motors advertises that its Model S electric car saves $570 per month in fuel costs. Assume that Tesla cars last for 10 years, fuel and electricity costs remain the same, and savings are made at the end of each month with the first saving of $570 in one month from now.
The effective annual interest rate is 15.8%, and the effective monthly interest rate is 1.23%. What is the present value of the savings?
The following cash flows are expected:
- A perpetuity of yearly payments of $30, with the first payment in 5 years (first payment at t=5, which continues every year after that forever).
- One payment of $100 in 6 years and 3 months (t=6.25).
What is the NPV of the cash flows if the discount rate is 10% given as an effective annual rate?
How much more can you borrow using an interest-only loan compared to a 25-year fully amortising loan if interest rates are 4% pa compounding per month and are not expected to change? If it makes it easier, assume that you can afford to pay $2,000 per month on either loan. Express your answer as a proportional increase using the following formula:
###\text{Proportional Increase} = \dfrac{V_\text{0,interest only}}{V_\text{0,fully amortising}} - 1###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 $50 million now. They will issue 5% pa semi-annual coupon bonds that will mature in 3 years and have a face value of $100 each. Bond yields are 6% pa, given as an APR compounding every 6 months, and the yield curve is flat.
How many bonds should the firm issue?
A firm wishes to raise $50 million now. They will issue 5% pa semi-annual coupon bonds that will mature in 10 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?
Question 758 time calculation, fully amortising loan, no explanation
Two years ago you entered into a fully amortising home loan with a principal of $1,000,000, an interest rate of 6% pa compounding monthly with a term of 25 years.
Then interest rates suddenly fall to 4.5% pa (t=0), but you continue to pay the same monthly home loan payments as you did before. How long will it now take to pay off your home loan? Measure the time taken to pay off the home loan from the current time which is 2 years after the home loan was first entered into.
Assume that the lower interest rate was given to you immediately after the loan repayment at the end of year 2, which was the 24th payment since the loan was granted. Also assume that rates were and are expected to remain constant.
Question 759 time calculation, fully amortising loan, no explanation
Five years ago you entered into a fully amortising home loan with a principal of $500,000, an interest rate of 4.5% pa compounding monthly with a term of 25 years.
Then interest rates suddenly fall to 3% pa (t=0), but you continue to pay the same monthly home loan payments as you did before. How long will it now take to pay off your home loan? Measure the time taken to pay off the home loan from the current time which is 5 years after the home loan was first entered into.
Assume that the lower interest rate was given to you immediately after the loan repayment at the end of year 5, which was the 60th payment since the loan was granted. Also assume that rates were and are expected to remain constant.
Question 760 time calculation, interest only loan, no explanation
Five years ago (##t=-5## years) you entered into an interest-only home loan with a principal of $500,000, an interest rate of 4.5% pa compounding monthly with a term of 25 years.
Then interest rates suddenly fall to 3% pa (##t=0##), but you continue to pay the same monthly home loan payments as you did before. Will your home loan be paid off by the end of its remaining term? If so, in how many years from now? Measure the time taken to pay off the home loan from the current time which is 5 years after the home loan was first entered into.
Assume that the lower interest rate was given to you immediately after the loan repayment at the end of year 5, which was the 60th payment since the loan was granted. Also assume that rates were and are expected to remain constant.
The phone company Optus 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 $80 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 $100 per month. This plan includes the latest smart phone.
Neither plan has any additional payments at the start or end. Assume that the discount rate is 1% per month given as an effective monthly rate.
The only difference between the plans is the phone, so what is the implied cost of the phone as a present value? Given that the latest smart phone actually costs $600 to purchase outright from another retailer, should you commit to the BYO plan or the bundled plan?
Radio-Rentals.com offers the Apple iphone 5S smart phone for rent at $12.95 per week paid in advance on a 2 year contract. After renting the phone, you must return it to Radio-Rentals.
Kogan.com offers the Apple iphone 5S smart phone for sale at $699. You estimate that the phone will last for 3 years before it will break and be worthless.
Currently, the effective annual interest rate is 11.351%, the effective monthly interest rate 0.9% and the effective weekly interest rate is 0.207%. Assume that there are exactly 52 weeks per year and 12 months per year.
Find the equivalent annual cost of renting the phone and also buying the phone. The answers below are listed in the same order.
A stock is expected to pay its first dividend of $20 in 3 years (t=3), which it will continue to pay for the next nine years, so there will be ten $20 payments altogether with the last payment in year 12 (t=12).
From the thirteenth year onward, the dividend is expected to be 4% more than the previous year, forever. So the dividend in the thirteenth year (t=13) will be $20.80, then $21.632 in year 14, and so on forever. The required return of the stock is 10% pa. All rates are effective annual rates. Calculate the current (t=0) stock price.
A 4.5% fixed coupon Australian Government bond was issued at par in mid-April 2009. Coupons are paid semi-annually in arrears in mid-April and mid-October each year. The face value is $1,000. The bond will mature in mid-April 2020, so the bond had an original tenor of 11 years.
Today is mid-September 2015 and similar bonds now yield 1.9% pa.
What is the bond's new price? Note: there are 10 semi-annual coupon payments remaining from now (mid-September 2015) until maturity (mid-April 2020); both yields are given as APR's compounding semi-annually; assume that the yield curve was flat before the change in yields, and remained flat afterwards as well.
An investor bought a 5 year government bond with a 2% pa coupon rate at par. Coupons are paid semi-annually. The face value is $100.
Calculate the bond's new price 8 months later after yields have increased to 3% pa. Note that both yields are given as APR's compounding semi-annually. Assume that the yield curve was flat before the change in yields, and remained flat afterwards as well.
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?
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:
Find Sidebar Corporation's Cash Flow From Assets (CFFA), also known as Free Cash Flow to the Firm (FCFF), over the year ending 30th June 2013.
| Sidebar Corp | ||
| Income Statement for | ||
| year ending 30th June 2013 | ||
| $m | ||
| Sales | 405 | |
| COGS | 100 | |
| Depreciation | 34 | |
| Rent expense | 22 | |
| Interest expense | 39 | |
| Taxable Income | 210 | |
| Taxes at 30% | 63 | |
| Net income | 147 | |
| Sidebar Corp | ||
| Balance Sheet | ||
| as at 30th June | 2013 | 2012 |
| $m | $m | |
| Cash | 0 | 0 |
| Inventory | 70 | 50 |
| Trade debtors | 11 | 16 |
| Rent paid in advance | 4 | 3 |
| PPE | 700 | 680 |
| Total assets | 785 | 749 |
| Trade creditors | 11 | 19 |
| Bond liabilities | 400 | 390 |
| Contributed equity | 220 | 220 |
| Retained profits | 154 | 120 |
| Total L and OE | 785 | 749 |
Note: All figures are given in millions of dollars ($m).
The cash flow from assets was:
Why is Capital Expenditure (CapEx) subtracted in the Cash Flow From Assets (CFFA) formula?
###CFFA=NI+Depr-CapEx - \Delta NWC+IntExp###
A firm has forecast its Cash Flow From Assets (CFFA) for this year and management is worried that it is too low. Which one of the following actions will lead to a higher CFFA for this year (t=0 to 1)? Only consider cash flows this year. Do not consider cash flows after one year, or the change in the NPV of the firm. Consider each action in isolation.
Over the next year, the management of an unlevered company plans to:
- Achieve firm free cash flow (FFCF or CFFA) of $1m.
- Pay dividends of $1.8m
- Complete a $1.3m share buy-back.
- Spend $0.8m on new buildings without buying or selling any other fixed assets. This capital expenditure is included in the CFFA figure quoted above.
Assume that:
- All amounts are received and paid at the end of the year so you can ignore the time value of money.
- The firm has sufficient retained profits to pay the dividend and complete the buy back.
- The firm plans to run a very tight ship, with no excess cash above operating requirements currently or over the next year.
How much new equity financing will the company need? In other words, what is the value of new shares that will need to be issued?
Over the next year, the management of an unlevered company plans to:
- Make $5m in sales, $1.9m in net income and $2m in equity free cash flow (EFCF).
- Pay dividends of $1m.
- Complete a $1.3m share buy-back.
Assume that:
- All amounts are received and paid at the end of the year so you can ignore the time value of money.
- The firm has sufficient retained profits to legally pay the dividend and complete the buy back.
- The firm plans to run a very tight ship, with no excess cash above operating requirements currently or over the next year.
How much new equity financing will the company need? In other words, what is the value of new shares that will need to be issued?
Value the following business project to manufacture a new product.
| Project Data | ||
| Project life | 2 yrs | |
| Initial investment in equipment | $6m | |
| Depreciation of equipment per year | $3m | |
| Expected sale price of equipment at end of project | $0.6m | |
| Unit sales per year | 4m | |
| Sale price per unit | $8 | |
| Variable cost per unit | $5 | |
| Fixed costs per year, paid at the end of each year | $1m | |
| Interest expense per year | 0 | |
| Tax rate | 30% | |
| Weighted average cost of capital after tax per annum | 10% | |
Notes
- The firm's current assets and current liabilities are $3m and $2m respectively right now. This net working capital will not be used in this project, it will be used in other unrelated projects.
Due to the project, current assets (mostly inventory) will grow by $2m initially (at t = 0), and then by $0.2m at the end of the first year (t=1).
Current liabilities (mostly trade creditors) will increase by $0.1m at the end of the first year (t=1).
At the end of the project, the net working capital accumulated due to the project can be sold for the same price that it was bought. - The project cost $0.5m to research which was incurred one year ago.
Assumptions
- 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 3% pa.
- All rates are given as effective annual rates.
- The business considering the project is run as a 'sole tradership' (run by an individual without a company) and is therefore eligible for a 50% capital gains tax discount when the equipment is sold, as permitted by the Australian Tax Office.
What is the expected net present value (NPV) of the project?
Your friend just bought a house for $400,000. He financed it using a $320,000 mortgage loan and a deposit of $80,000.
In the context of residential housing and mortgages, the 'equity' tied up in the value of a person's house is the value of the house less the value of the mortgage. So the initial equity your friend has in his house is $80,000. Let this amount be E, let the value of the mortgage be D and the value of the house be V. So ##V=D+E##.
If house prices suddenly fall by 10%, what would be your friend's percentage change in equity (E)? Assume that the value of the mortgage is unchanged and that no income (rent) was received from the house during the short time over which house prices fell.
Remember:
### r_{0\rightarrow1}=\frac{p_1-p_0+c_1}{p_0} ###
where ##r_{0-1}## is the return (percentage change) of an asset with price ##p_0## initially, ##p_1## one period later, and paying a cash flow of ##c_1## at time ##t=1##.
One year ago you bought $100,000 of shares partly funded using a margin loan. The margin loan size was $70,000 and the other $30,000 was your own wealth or 'equity' in the share assets.
The interest rate on the margin loan was 7.84% pa.
Over the year, the shares produced a dividend yield of 4% pa and a capital gain of 5% pa.
What was the total return on your wealth? Ignore taxes, assume that all cash flows (interest payments and dividends) were paid and received at the end of the year, and all rates above are effective annual rates.
Hint: Remember that wealth in this context is your equity (E) in the house asset (V = D+E) which is funded by the loan (D) and your deposit or equity (E).
Interest expense (IntExp) is an important part of a company's income statement (or 'profit and loss' or 'statement of financial performance').
How does an accountant calculate the annual interest expense of a fixed-coupon bond that has a liquid secondary market? Select the most correct answer:
Annual interest expense is equal to:
A firm has a debt-to-equity ratio of 25%. What is its debt-to-assets ratio?
A manufacturing company is considering a new project in the more risky services industry. The cash flows from assets (CFFA) are estimated for the new project, with interest expense excluded from the calculations. To get the levered value of the project, what should these unlevered cash flows be discounted by?
Assume that the manufacturing firm has a target debt-to-assets ratio that it sticks to.
The US firm Google operates in the online advertising business. In 2011 Google bought Motorola Mobility which manufactures mobile phones.
Assume the following:
- Google had a 10% after-tax weighted average cost of capital (WACC) before it bought Motorola.
- Motorola had a 20% after-tax WACC before it merged with Google.
- Google and Motorola have the same level of gearing.
- Both companies operate in a classical tax system.
You are a manager at Motorola. You must value a project for making mobile phones. Which method(s) will give the correct valuation of the mobile phone manufacturing project? Select the most correct answer.
The mobile phone manufacturing project's:
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}###One formula for calculating a levered firm's free cash flow (FFCF, or CFFA) is to use earnings before interest and tax (EBIT).
###\begin{aligned} FFCF &= (EBIT)(1-t_c) + Depr - CapEx -\Delta NWC + IntExp.t_c \\ &= (Rev - COGS - Depr - FC)(1-t_c) + Depr - CapEx -\Delta NWC + IntExp.t_c \\ \end{aligned} \\###
One formula for calculating a levered firm's free cash flow (FFCF, or CFFA) is to use net operating profit after tax (NOPAT).
###\begin{aligned} FFCF &= NOPAT + Depr - CapEx -\Delta NWC \\ &= (Rev - COGS - Depr - FC)(1-t_c) + Depr - CapEx -\Delta NWC \\ \end{aligned} \\###
A firm has a debt-to-assets ratio of 50%. The firm then issues a large amount of equity to raise money for new projects of similar systematic risk to the company's existing projects. Assume a classical tax system. Which statement is correct?
Question 370 capital budgeting, NPV, interest tax shield, WACC, CFFA
| Project Data | ||
| Project life | 2 yrs | |
| Initial investment in equipment | $600k | |
| Depreciation of equipment per year | $250k | |
| Expected sale price of equipment at end of project | $200k | |
| Revenue per job | $12k | |
| Variable cost per job | $4k | |
| Quantity of jobs per year | 120 | |
| Fixed costs per year, paid at the end of each year | $100k | |
| Interest expense in first year (at t=1) | $16.091k | |
| Interest expense in second year (at t=2) | $9.711k | |
| Tax rate | 30% | |
| Government treasury bond yield | 5% | |
| Bank loan debt yield | 6% | |
| Levered cost of equity | 12.5% | |
| Market portfolio return | 10% | |
| Beta of assets | 1.24 | |
| Beta of levered equity | 1.5 | |
| Firm's and project's debt-to-equity ratio | 25% | |
Notes
- The project will require an immediate purchase of $50k of inventory, which will all be sold at cost when the project ends. Current liabilities are negligible so they can be ignored.
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. Note that interest expense is different in each year.
- Thousands are represented by 'k' (kilo).
- 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 nominal. The inflation rate is 2% pa.
- All rates are given as effective annual rates.
- The 50% capital gains tax discount is not available since the project is undertaken by a firm, not an individual.
What is the net present value (NPV) of the project?
A company issues a large amount of bonds to raise money for new projects of similar risk to the company's existing projects. The net present value (NPV) of the new projects is positive but small. Assume a classical tax system. Which statement is NOT correct?
A firm has a debt-to-assets ratio of 50%. The firm then issues a large amount of debt to raise money for new projects of similar market risk to the company's existing projects. Assume a classical tax system. Which statement is correct?
Question 337 capital structure, interest tax shield, leverage, real and nominal returns and cash flows, multi stage growth model
A fast-growing firm is suitable for valuation using a multi-stage growth model.
It's nominal unlevered cash flow from assets (##CFFA_U##) at the end of this year (t=1) is expected to be $1 million. After that it is expected to grow at a rate of:
- 12% pa for the next two years (from t=1 to 3),
- 5% over the fourth year (from t=3 to 4), and
- -1% forever after that (from t=4 onwards). Note that this is a negative one percent growth rate.
Assume that:
- The nominal WACC after tax is 9.5% pa and is not expected to change.
- The nominal WACC before tax is 10% pa and is not expected to change.
- The firm has a target debt-to-equity ratio that it plans to maintain.
- The inflation rate is 3% pa.
- All rates are given as nominal effective annual rates.
What is the levered value of this fast growing firm's assets?
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?
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}## | $48.5m | Operating free cash flow |
| ##\text{FFCF or CFFA}## | $50m | Firm free cash flow or cash flow from assets |
| ##g## | 0% pa | Growth rate of OFCF and FFCF |
| ##\text{WACC}_\text{BeforeTax}## | 10% pa | Weighted average cost of capital before tax |
| ##\text{WACC}_\text{AfterTax}## | 9.7% pa | Weighted average cost of capital after tax |
| ##r_\text{D}## | 5% pa | Cost of debt |
| ##r_\text{EL}## | 11.25% pa | Cost of levered equity |
| ##D/V_L## | 20% 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?
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?
Find the cash flow from assets (CFFA) of the following project.
| Project Data | ||
| Project life | 2 years | |
| Initial investment in equipment | $6m | |
| Depreciation of equipment per year for tax purposes | $1m | |
| Unit sales per year | 4m | |
| Sale price per unit | $8 | |
| Variable cost per unit | $3 | |
| Fixed costs per year, paid at the end of each year | $1.5m | |
| Tax rate | 30% | |
Note 1: The equipment will have a book value of $4m at the end of the project for tax purposes. However, the equipment is expected to fetch $0.9 million when it is sold at t=2.
Note 2: Due to the project, the firm will have to purchase $0.8m of inventory initially, which it will sell at t=1. The firm will buy another $0.8m at t=1 and sell it all again at t=2 with zero inventory left. The project will have no effect on the firm's current liabilities.
Find the project's CFFA at time zero, one and two. Answers are given in millions of dollars ($m).
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.
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?
You want to buy an apartment worth $300,000. You have saved a deposit of $60,000.
The bank has agreed to lend you $240,000 as an interest only 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?
Question 239 income and capital returns, inflation, real and nominal returns and cash flows, interest only loan
A bank grants a borrower an interest-only residential mortgage loan with a very large 50% deposit and a nominal interest rate of 6% that is not expected to change. Assume that inflation is expected to be a constant 2% pa over the life of the loan. Ignore credit risk.
From the bank's point of view, what is the long term expected nominal capital return of the loan asset?
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 559 variance, standard deviation, covariance, correlation
Which of the following statements about standard statistical mathematics notation is NOT correct?
Diversification in a portfolio of two assets works best when the correlation between their returns is:
All things remaining equal, the variance of a portfolio of two positively-weighted stocks rises as:
| Portfolio Details | ||||||
| Stock | Expected return |
Standard deviation |
Correlation ##(\rho_{A,B})## | Dollars invested |
||
| A | 0.1 | 0.4 | 0.5 | 60 | ||
| B | 0.2 | 0.6 | 140 | |||
What is the standard deviation (not variance) of returns of the above portfolio?
Two risky stocks A and B comprise an equal-weighted portfolio. The correlation between the stocks' returns is 70%.
If the variance of stock A's returns increases but the:
- Prices and expected returns of each stock stays the same,
- Variance of stock B's returns stays the same,
- Correlation of returns between the stocks stays the same.
Which of the following statements is NOT correct?
All things remaining equal, the higher the correlation of returns between two stocks:
An investor wants to make a portfolio of two stocks A and B with a target expected portfolio return of 6% pa.
- Stock A has an expected return of 5% pa.
- Stock B has an expected return of 10% pa.
What portfolio weights should the investor have in stocks A and B respectively?
What is the correlation of a variable X with itself?
The corr(X, X) or ##\rho_{X,X}## equals:
What is the correlation of a variable X with a constant C?
The corr(X, C) or ##\rho_{X,C}## equals:
Question 556 portfolio risk, portfolio return, standard deviation
An investor wants to make a portfolio of two stocks A and B with a target expected portfolio return of 12% pa.
- Stock A has an expected return of 10% pa and a standard deviation of 20% pa.
- Stock B has an expected return of 15% pa and a standard deviation of 30% pa.
The correlation coefficient between stock A and B's expected returns is 70%.
What will be the annual standard deviation of the portfolio with this 12% pa target return?
Let the standard deviation of returns for a share per month be ##\sigma_\text{monthly}##.
What is the formula for the standard deviation of the share's returns per year ##(\sigma_\text{yearly})##?
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.
The covariance and correlation of two stocks X and Y's annual returns are calculated over a number of years. The units of the returns are in percent per annum ##(\% pa)##.
What are the units of the covariance ##(\sigma_{X,Y})## and correlation ##(\rho_{X,Y})## of returns respectively?
Hint: Visit Wikipedia to understand the difference between percentage points ##(\text{pp})## and percent ##(\%)##.
Diversification is achieved by investing in a large amount of stocks. What type of risk is reduced by diversification?
According to the theory of the Capital Asset Pricing Model (CAPM), total risk can be broken into two components, systematic risk and idiosyncratic risk. Which of the following events would be considered a systematic, undiversifiable event according to the theory of the CAPM?
A fairly priced stock has an expected return equal to the market's. Treasury bonds yield 5% pa and the market portfolio's expected return is 10% pa. What is the stock's beta?
The security market line (SML) shows the relationship between beta and expected return.
Buying investment projects that plot above the SML would lead to:
Stock A has a beta of 0.5 and stock B has a beta of 1. Which statement is NOT correct?
A stock's correlation with the market portfolio increases while its total risk is unchanged. What will happen to the stock's expected return and systematic risk?
Assets A, B, M and ##r_f## are shown on the graphs above. Asset M is the market portfolio and ##r_f## is the risk free yield on government bonds. Which of the below statements is NOT correct?
Assets A, B, M and ##r_f## are shown on the graphs above. Asset M is the market portfolio and ##r_f## is the risk free yield on government bonds. Assume that investors can borrow and lend at the risk free rate. Which of the below 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?
A firm changes its capital structure by issuing a large amount of equity and using the funds to repay debt. Its assets are unchanged. Ignore interest tax shields.
According to the Capital Asset Pricing Model (CAPM), which statement is correct?
The CAPM can be used to find a business's expected opportunity cost of capital:
###r_i=r_f+β_i (r_m-r_f)###
What should be used as the risk free rate ##r_f##?
Which of the following statements about the weighted average cost of capital (WACC) is NOT 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?
Mr Blue, Miss Red and Mrs Green are people with different utility functions.
Note that a fair gamble is a bet that has an expected value of zero, such as paying $0.50 to win $1 in a coin flip with heads or nothing if it lands tails. Fairly priced insurance is when the expected present value of the insurance premiums is equal to the expected loss from the disaster that the insurance protects against, such as the cost of rebuilding a home after a catastrophic fire.
Which of the following statements is NOT correct?
Mr Blue, Miss Red and Mrs Green are people with different utility functions.
Which of the following statements is NOT correct?
Question 703 utility, risk aversion, utility function, gamble
Mr Blue, Miss Red and Mrs Green are people with different utility functions.
Each person has $500 of initial wealth. A coin toss game is offered to each person at a casino where the player can win or lose $500. Each player can flip a coin and if they flip heads, they receive $500. If they flip tails then they will lose $500. Which of the following statements is NOT correct?
Question 704 utility, risk aversion, utility function, gamble
Mr Blue, Miss Red and Mrs Green are people with different utility functions.
Each person has $256 of initial wealth. A coin toss game is offered to each person at a casino where the player can win or lose $256. Each player can flip a coin and if they flip heads, they receive $256. If they flip tails then they will lose $256. Which of the following statements is NOT correct?
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?
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?
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 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?
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:
Fundamentalists who analyse company financial reports and news announcements (but who don't have inside information) will make positive abnormal returns if:
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.
The efficient markets hypothesis (EMH) and no-arbitrage pricing theory are most closely related to which of the following concepts?
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.
A company advertises an investment costing $1,000 which they say is underpriced. They say that it has an expected total return of 15% pa, but a required return of only 10% pa. Assume that there are no dividend payments so the entire 15% total return is all capital return.
Assuming that the company's statements are correct, what is the NPV of buying the investment if the 15% return lasts for the next 100 years (t=0 to 100), then reverts to 10% pa after that time? Also, what is the NPV of the investment if the 15% return lasts forever?
In both cases, assume that the required return of 10% remains constant. All returns are given as effective annual rates.
The answer choices below are given in the same order (15% for 100 years, and 15% forever):
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##).
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 780 mispriced asset, NPV, DDM, market efficiency, no explanation
A company advertises an investment costing $1,000 which they say is under priced. They say that it has an expected total return of 15% pa, but a required return of only 10% pa. Of the 15% pa total expected return, the dividend yield is expected to be 4% pa and the capital yield 11% pa. Assume that the company's statements are correct.
What is the NPV of buying the investment if the 15% total return lasts for the next 100 years (t=0 to 100), then reverts to 10% after that time? Also, what is the NPV of the investment if the 15% return lasts forever?
In both cases, assume that the required return of 10% remains constant, the dividends can only be re-invested at 10% pa and all returns are given as effective annual rates. The answer choices below are given in the same order (15% for 100 years, and 15% forever):
A company advertises an investment costing $1,000 which they say is underpriced. They say that it has an expected total return of 15% pa, but a required return of only 10% pa. Of the 15% pa total expected return, the dividend yield is expected to always be 7% pa and rest is the capital yield.
Assuming that the company's statements are correct, what is the NPV of buying the investment if the 15% total return lasts for the next 100 years (t=0 to 100), then reverts to 10% after that time? Also, what is the NPV of the investment if the 15% return lasts forever?
In both cases, assume that the required return of 10% remains constant, the dividends can only be re-invested at 10% pa and all returns are given as effective annual rates.
The answer choices below are given in the same order (15% for 100 years, and 15% forever):
The average weekly earnings of an Australian adult worker before tax was $1,542.40 per week in November 2014 according to the Australian Bureau of Statistics. Therefore average annual earnings before tax were $80,204.80 assuming 52 weeks per year. 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 $80,204.80 per annum before-tax?
Question 449 personal tax on dividends, classical tax system
A small private company has a single shareholder. This year the firm earned a $100 profit before tax. All of the firm's after tax profits will be paid out as dividends to the owner.
The corporate tax rate is 30% and the sole shareholder's personal marginal tax rate is 45%.
The United States' classical tax system applies because the company generates all of its income in the US and pays corporate tax to the Internal Revenue Service. The shareholder is also an American for tax purposes.
What will be the personal tax payable by the shareholder and the corporate tax payable by the company?
Question 624 franking credit, personal tax on dividends, imputation tax system, no explanation
Which of the following statements about Australian franking credits is NOT correct? Franking credits:
Question 448 franking credit, personal tax on dividends, imputation tax system
A small private company has a single shareholder. This year the firm earned a $100 profit before tax. All of the firm's after tax profits will be paid out as dividends to the owner.
The corporate tax rate is 30% and the sole shareholder's personal marginal tax rate is 45%.
The Australian imputation tax system applies because the company generates all of its income in Australia and pays corporate tax to the Australian Tax Office. Therefore all of the company's dividends are fully franked. The sole shareholder is an Australian for tax purposes and can therefore use the franking credits to offset his personal income tax liability.
What will be the personal tax payable by the shareholder and the corporate tax payable by the company?
A company announces that it will pay a dividend, as the market expected. The company's shares trade on the stock exchange which is open from 10am in the morning to 4pm in the afternoon each weekday. When would the share price be expected to fall by the amount of the dividend? Ignore taxes.
The share price is expected to fall during the:
Currently, a mining company has a share price of $6 and pays constant annual dividends of $0.50. The next dividend will be paid in 1 year. Suddenly and unexpectedly the mining company announces that due to higher than expected profits, all of these windfall profits will be paid as a special dividend of $0.30 in 1 year.
If investors believe that the windfall profits and dividend is a one-off event, what will be the new share price? If investors believe that the additional dividend is actually permanent and will continue to be paid, what will be the new share price? Assume that the required return on equity is unchanged. Choose from the following, where the first share price includes the one-off increase in earnings and dividends for the first year only ##(P_\text{0 one-off})## , and the second assumes that the increase is permanent ##(P_\text{0 permanent})##:
Note: When a firm makes excess profits they sometimes pay them out as special dividends. Special dividends are just like ordinary dividends but they are one-off and investors do not expect them to continue, unlike ordinary dividends which are expected to persist.
A mining firm has just discovered a new mine. So far the news has been kept a secret.
The net present value of digging the mine and selling the minerals is $250 million, but $500 million of new equity and $300 million of new 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 equity and bond raising to shareholders simultaneously in the same announcement. The shares and bonds will be issued shortly after.
Once the announcement is made and the new shares and bonds are issued, what is the expected increase in the value of the firm's assets ##(\Delta V)##, market capitalisation of debt ##(\Delta D)## and market cap of equity ##(\Delta E)##? Assume that markets are semi-strong form efficient.
The triangle symbol ##\Delta## 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: ##\Delta V = \Delta D+ \Delta E##
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?
In late 2003 the listed bank ANZ announced a 2-for-11 rights issue to fund the takeover of New Zealand bank NBNZ. Below is the chronology of events:
- 23/10/2003. Share price closes at $18.30.
- 24/10/2003. 2-for-11 rights issue announced at a subscription price of $13. The proceeds of the rights issue will be used to acquire New Zealand bank NBNZ. Trading halt announced in morning before market opens.
- 28/10/2003. Trading halt lifted. Last (and only) day that shares trade cum-rights. Share price opens at $18.00 and closes at $18.14.
- 29/10/2003. Shares trade ex-rights.
All things remaining equal, what would you expect ANZ's stock price to open at on the first day that it trades ex-rights (29/10/2003)? Ignore the time value of money since time is negligibly short. Also ignore taxes.
Question 708 continuously compounding rate, continuously compounding rate conversion
Convert a 10% continuously compounded annual rate ##(r_\text{cc annual})## into an effective annual rate ##(r_\text{eff annual})##. The equivalent effective annual rate is:
Which of the following interest rate quotes is NOT equivalent to a 10% effective annual rate of return? Assume that each year has 12 months, each month has 30 days, each day has 24 hours, each hour has 60 minutes and each minute has 60 seconds. APR stands for Annualised Percentage Rate.
Question 710 continuously compounding rate, continuously compounding rate conversion
A continuously compounded monthly return of 1% ##(r_\text{cc monthly})## is equivalent to a continuously compounded annual return ##(r_\text{cc annual})## of:
An effective monthly return of 1% ##(r_\text{eff monthly})## is equivalent to an effective annual return ##(r_\text{eff annual})## of:
Which of the following quantities is commonly assumed to be normally distributed?
The below three graphs show probability density functions (PDF) of three different random variables Red, Green and Blue.
Which of the below statements is NOT correct?
The symbol ##\text{GDR}_{0\rightarrow 1}## represents a stock's gross discrete return per annum over the first year. ##\text{GDR}_{0\rightarrow 1} = P_1/P_0##. The subscript indicates the time period that the return is mentioned over. So for example, ##\text{AAGDR}_{1 \rightarrow 3}## is the arithmetic average GDR measured over the two year period from years 1 to 3, but it is expressed as a per annum rate.
Which of the below statements about the arithmetic and geometric average GDR is NOT correct?
Question 721 mean and median returns, return distribution, arithmetic and geometric averages, continuously compounding rate
Fred owns some Commonwealth Bank (CBA) shares. He has calculated CBA’s monthly returns for each month in the past 20 years using this formula:
###r_\text{t monthly}=\ln \left( \dfrac{P_t}{P_{t-1}} \right)###He then took the arithmetic average and found it to be 1% per month using this formula:
###\bar{r}_\text{monthly}= \dfrac{ \displaystyle\sum\limits_{t=1}^T{\left( r_\text{t monthly} \right)} }{T} =0.01=1\% \text{ per month}###He also found the standard deviation of these monthly returns which was 5% per month:
###\sigma_\text{monthly} = \dfrac{ \displaystyle\sum\limits_{t=1}^T{\left( \left( r_\text{t monthly} - \bar{r}_\text{monthly} \right)^2 \right)} }{T} =0.05=5\%\text{ per month}###Which of the below statements about Fred’s CBA shares is NOT correct? Assume that the past historical average return is the true population average of future expected returns.
Question 722 mean and median returns, return distribution, arithmetic and geometric averages, continuously compounding rate
Here is a table of stock prices and returns. Which of the statements below the table is NOT correct?
| Price and Return Population Statistics | ||||
| Time | Prices | LGDR | GDR | NDR |
| 0 | 100 | |||
| 1 | 50 | -0.6931 | 0.5 | -0.5 |
| 2 | 100 | 0.6931 | 2 | 1 |
| Arithmetic average | 0 | 1.25 | 0.25 | |
| Arithmetic standard deviation | 0.9802 | 1.0607 | 1.0607 | |
Find the cash flow from assets (CFFA) of the following project.
| Project Data | |
| Project life | 2 years |
| Initial investment in equipment | $8m |
| Depreciation of equipment per year for tax purposes | $3m |
| Unit sales per year | 10m |
| Sale price per unit | $9 |
| Variable cost per unit | $4 |
| Fixed costs per year, paid at the end of each year | $2m |
| Tax rate | 30% |
Note 1: Due to the project, the firm will have to purchase $40m of inventory initially (at t=0). Half of this inventory will be sold at t=1 and the other half at t=2.
Note 2: The equipment will have a book value of $2m at the end of the project for tax purposes. However, the equipment is expected to fetch $1m when it is sold. Assume that the full capital loss is tax-deductible and taxed at the full corporate tax rate.
Note 3: The project will be fully funded by equity which investors will expect to pay dividends totaling $10m at the end of each year.
Find the project's CFFA at time zero, one and two. Answers are given in millions of dollars ($m).
The 'time value of money' is most closely related to which of the following concepts?
Question 657 systematic and idiosyncratic risk, CAPM, no explanation
A stock's required total return will decrease when its:
Question 658 CFFA, income statement, balance sheet, no explanation
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 income statement needed? Note that the income statement is sometimes also called the profit and loss, P&L, or statement of financial performance.
Question 659 APR, effective rate, effective rate conversion, no explanation
A home loan company advertises an interest rate of 9% pa, payable monthly. Which of the following statements about the interest rate is NOT correct? All rates are given with an accuracy of 4 decimal places.
How much more can you borrow using an interest-only loan compared to a 25-year fully amortising loan if interest rates are 6% pa compounding per month and are not expected to change? If it makes it easier, assume that you can afford to pay $2,000 per month on either loan. Express your answer as a proportional increase using the following formula:
###\text{Proportional Increase} = \dfrac{V_\text{0,interest only}}{V_\text{0,fully amortising}} - 1###A stock's total standard deviation of returns is 20% pa. The market portfolio's total standard deviation of returns is 15% pa. The beta of the stock is 0.8.
What is the stock's diversifiable standard deviation?
Question 662 APR, effective rate, effective rate conversion, no explanation
Which of the following interest rate labels does NOT make sense?
A firm has a debt-to-assets ratio of 20%. What is its debt-to-equity ratio?
Question 664 real and nominal returns and cash flows, inflation
What is the present value of real payments of $100 every year forever, with the first payment in one year? The nominal discount rate is 7% pa and the inflation rate is 4% pa.
A company conducts a 10 for 3 stock split. What is the percentage increase in the stock price and the number of shares outstanding? The answers are given in the same order.
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.
Question 667 forward foreign exchange rate, foreign exchange rate, cross currency interest rate parity, no explanation
The Australian cash rate is expected to be 2% pa over the next one year, while the US cash rate is expected to be 0% pa, both given as nominal effective annual rates. The current exchange rate is 0.73 USD per AUD.
What is the implied 1 year USD per AUD forward foreign exchange rate?
Question 668 buy and hold, market efficiency, idiom
A quote from the famous investor Warren Buffet: "Much success can be attributed to inactivity. Most investors cannot resist the temptation to constantly buy and sell."
Buffet is referring to the buy-and-hold strategy which is to buy and never sell shares. Which of the following is a disadvantage of a buy-and-hold strategy? Assume that share markets are semi-strong form efficient. Which of the following is NOT an advantage of the strict buy-and-hold strategy? A disadvantage of the buy-and-hold strategy is that it reduces:
Which of the following is NOT a valid method for estimating the beta of a company's stock? Assume that markets are efficient, a long history of past data is available, the stock possesses idiosyncratic and market risk. The variances and standard deviations below denote total risks.
"Buy low, sell high" is a phrase commonly heard in financial markets. It states that traders should try to buy assets at low prices and sell at high prices.
Traders in the fixed-coupon bond markets often quote promised bond yields rather than prices. Fixed-coupon bond traders should try to:
A stock's required total return will increase when its:
Let the 'income return' of a bond be the coupon at the end of the period divided by the market price now at the start of the period ##(C_1/P_0)##. The expected income return of a premium fixed coupon bond is:
Question 626 cross currency interest rate parity, foreign exchange rate, forward foreign exchange rate
The Australian cash rate is expected to be 2% pa over the next one year, while the Japanese cash rate is expected to be 0% pa, both given as nominal effective annual rates. The current exchange rate is 100 JPY per AUD.
What is the implied 1 year forward foreign exchange rate?
Which of the following statements about yield curves is NOT correct?
Question 767 idiom, corporate financial decision theory, no explanation
The sayings "Don't cry over spilt milk", "Don't regret the things that you can't change" and "What's done is done" are most closely related to which financial concept?
Question 768 accounting terminology, book and market values, no explanation
Accountants and finance professionals have lots of names for the same things which can be quite confusing.
Which of the following groups of items are NOT synonyms?
"Buy low, sell high" is a well-known saying. It suggests that investors should buy low then sell high, in that order.
How would you re-phrase that saying to describe short selling?
Question 770 expected and historical returns, income and capital returns, coupon rate, bond pricing
Which of the following statements is NOT correct? Assume that all events are a surprise and that all other things remain equal. So for example, don't assume that just because a company's dividends and profit rise that its required return will also rise, assume the required return stays the same.
Question 771 debt terminology, interest expense, interest tax shield, credit risk, no explanation
You deposit money into a bank account. Which of the following statements about this deposit is NOT correct?
Question 772 interest tax shield, capital structure, leverage
A firm issues debt and uses the funds to buy back equity. Assume that there are no costs of financial distress or transactions costs. Which of the following statements about interest tax shields is NOT correct?
One year ago you bought a $1,000,000 house partly funded using a mortgage loan. The loan size was $800,000 and the other $200,000 was your wealth or 'equity' in the house asset.
The interest rate on the home loan was 4% pa.
Over the year, the house produced a net rental yield of 2% pa and a capital gain of 2.5% pa.
Assuming that all cash flows (interest payments and net rental payments) were paid and received at the end of the year, and all rates are given as effective annual rates, what was the total return on your wealth over the past year?
Hint: Remember that wealth in this context is your equity (E) in the house asset (V = D+E) which is funded by the loan (D) and your deposit or equity (E).
Below is a graph of 3 peoples’ utility functions, Mr Blue (U=W^(1/2) ), Miss Red (U=W/10) and Mrs Green (U=W^2/1000). Assume that each of them currently have $50 of wealth.
Which of the following statements about them is NOT correct?
(a) Mr Blue would prefer to invest his wealth in a well diversified portfolio of stocks rather than a single stock, assuming that all stocks had the same total risk and return.
Question 776 market efficiency, systematic and idiosyncratic risk, beta, income and capital returns
Which of the following statements about returns is NOT correct? A stock's:
The market's expected total return is 10% pa and the risk free rate is 5% pa, both given as effective annual rates.
A stock has a beta of 0.5.
In the last 5 minutes, the federal government unexpectedly raised taxes. Over this time the share market fell by 3%. 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?
Question 778 CML, systematic and idiosyncratic risk, portfolio risk, CAPM
The capital market line (CML) is shown in the graph below. The total standard deviation is denoted by σ and the expected return is μ. Assume that markets are efficient so all assets are fairly priced.
Which of the below statements is NOT correct?
Question 779 mean and median returns, return distribution, arithmetic and geometric averages, continuously compounding rate
Fred owns some BHP shares. He has calculated BHP’s monthly returns for each month in the past 30 years using this formula:
###r_\text{t monthly}=\ln \left( \dfrac{P_t}{P_{t-1}} \right)###He then took the arithmetic average and found it to be 0.8% per month using this formula:
###\bar{r}_\text{monthly}= \dfrac{ \displaystyle\sum\limits_{t=1}^T{\left( r_\text{t monthly} \right)} }{T} =0.008=0.8\% \text{ per month}###He also found the standard deviation of these monthly returns which was 15% per month:
###\sigma_\text{monthly} = \dfrac{ \displaystyle\sum\limits_{t=1}^T{\left( \left( r_\text{t monthly} - \bar{r}_\text{monthly} \right)^2 \right)} }{T} =0.15=15\%\text{ per month}###Assume that the past historical average return is the true population average of future expected returns and the stock's returns calculated above ##(r_\text{t monthly})## are normally distributed. Which of the below statements about Fred’s BHP shares is NOT correct?
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 |
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 |
If a project's net present value (NPV) is zero, then its internal rate of return (IRR) will be:
The required return of a project is 10%, given as an effective annual rate.
What is the payback period of the project in years?
Assume that the cash flows shown in the table are received smoothly over the year. So the $121 at time 2 is actually earned smoothly from t=1 to t=2.
| Project Cash Flows | |
| Time (yrs) | Cash flow ($) |
| 0 | -100 |
| 1 | 11 |
| 2 | 121 |
A 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 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.
The below graph shows a project's net present value (NPV) against its annual discount rate.
Which of the following statements is NOT correct?
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?
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?
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 $9.09 cash flow right now with zero net cash flows in the future.
An investor owns an empty block of land that has local government approval to be developed into a petrol station, car wash or car park. The council will only allow a single development so the projects are mutually exclusive.
All of the development projects have the same risk and the required return of each is 10% pa. Each project has an immediate cost and once construction is finished in one year the land and development will be sold. The table below shows the estimated costs payable now, expected sale prices in one year and the internal rates of returns (IRR's).
| Mutually Exclusive Projects | |||
| Project | Cost now ($) |
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?
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?
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?
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 $4) if the price grows by 15% pa?
The required return of a project is 10%, given as an effective annual rate. Assume that the cash flows shown in the table are paid all at once at the given point in time.
What is the Net Present Value (NPV) of the project?
| Project Cash Flows | |
| Time (yrs) | Cash flow ($) |
| 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're considering a business project which costs $11m now and is expected to pay a single cash flow of $11m in one year. So you pay $11m now, then one year later you receive $11m.
Assume that the initial $11m cost is funded using the your 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 the net present value (NPV), internal rate of return (IRR) and payback period is NOT correct?
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?
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?
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.
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?
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.
Suppose you had $100 in a savings account and the interest rate was 2% per year.
After 5 years, how much do you think you would have in the account if you left the money to grow?
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.
Jan asks you for a loan. He wants $100 now and offers to pay you back $120 in 1 year. You can borrow and lend from the bank at an interest rate of 10% pa, given as an effective annual rate.
Ignore credit risk. Remember:
### V_0 = \frac{V_t}{(1+r_\text{eff})^t} ###
Katya offers to pay you $10 at the end of every year for the next 5 years (t=1,2,3,4,5) if you pay her $50 now (t=0). You can borrow and lend from the bank at an interest rate of 10% pa, given as an effective annual rate. Ignore credit risk.
The following equation is called the Dividend Discount Model (DDM), Gordon Growth Model or the perpetuity with growth formula: ### P_0 = \frac{ C_1 }{ r - g } ###
What is ##g##? The value ##g## is the long term expected:
For a price of $13, Carla will sell you a share paying a dividend of $1 in one year and every year after that forever. The required return of the stock is 10% pa.
For a price of $6, Carlos will sell you a share which will pay a dividend of $1 in one year and every year after that forever. The required return of the stock is 10% pa.
For a price of $102, Andrea will sell you a share which just paid a dividend of $10 yesterday, and is expected to pay dividends every year forever, growing at a rate of 5% pa.
So the next dividend will be ##10(1+0.05)^1=$10.50## in one year from now, and the year after it will be ##10(1+0.05)^2=11.025## and so on.
The required return of the stock is 15% pa.
For a price of $100, Vera will sell you a 2 year bond paying semi-annual coupons of 10% pa. The face value of the bond is $100. Other bonds with similar risk, maturity and coupon characteristics trade at a yield of 8% pa.
For a price of $100, Carol will sell you a 5 year bond paying semi-annual coupons of 16% pa. The face value of the bond is $100. Other bonds with similar risk, maturity and coupon characteristics trade at a yield of 12% pa.
For a price of $100, Rad will sell you a 5 year bond paying semi-annual coupons of 16% pa. The face value of the bond is $100. Other bonds with the same risk, maturity and coupon characteristics trade at a yield of 6% pa.
For a price of $100, Andrea will sell you a 2 year bond paying annual coupons of 10% pa. The face value of the bond is $100. Other bonds with the same risk, maturity and coupon characteristics trade at a yield of 6% pa.
For a price of $95, Nicole will sell you a 10 year bond paying semi-annual coupons of 8% pa. The face value of the bond is $100. Other bonds with the same risk, maturity and coupon characteristics trade at a yield of 8% pa.
Question 419 capital budgeting, NPV, interest tax shield, WACC, CFFA, CAPM, no explanation
| Project Data | ||
| Project life | 1 year | |
| Initial investment in equipment | $6m | |
| Depreciation of equipment per year | $6m | |
| Expected sale price of equipment at end of project | 0 | |
| Unit sales per year | 9m | |
| Sale price per unit | $8 | |
| Variable cost per unit | $6 | |
| Fixed costs per year, paid at the end of each year | $1m | |
| Interest expense in first year (at t=1) | $0.53m | |
| Tax rate | 30% | |
| Government treasury bond yield | 5% | |
| Bank loan debt yield | 6% | |
| Market portfolio return | 10% | |
| Covariance of levered equity returns with market | 0.08 | |
| Variance of market portfolio returns | 0.16 | |
| Firm's and project's debt-to-assets ratio | 50% | |
Notes
- Due to the project, current assets will increase by $5m now (t=0) and fall by $5m at the end (t=1). Current liabilities will not be affected.
Assumptions
- The debt-to-assets 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 50% capital gains tax discount is not available since the project is undertaken by a firm, not an individual.
What is the net present value (NPV) of the project?
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.
Question 798 idiom, diversification, market efficiency, sunk cost, no explanation
The following quotes are most closely related to which financial concept?
- “Opportunity is missed by most people because it is dressed in overalls and looks like work” -Thomas Edison
- “The only place where success comes before work is in the dictionary” -Vidal Sassoon
- “The safest way to double your money is to fold it over and put it in your pocket” - Kin Hubbard
In the home loan market, the acronym LVR stands for Loan to Valuation Ratio. If you bought a house worth one million dollars, partly funded by an $800,000 home loan, then your LVR was 80%. The LVR is equivalent to which of the following ratios?
Question 800 leverage, portfolio return, risk, portfolio risk, capital structure, no explanation
Which of the following assets would you expect to have the highest required rate of return? All values are current market values.
The following steps outline the process of ‘negative gearing’ an investment property in Australia. Which of these steps or statements is NOT correct? To successfully achieve negative gearing on an investment property:
Question 802 negative gearing, leverage, capital structure, no explanation
Which of the following statements about ‘negative gearing’ 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?
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?
Short selling is a way to make money from falling prices. In what order must the following steps be completed to short-sell an asset? Let Tom, Dick and Harry be traders in the share market.
- Step P: Purchase the asset from Harry.
- Step G: Give the asset to Tom.
- Step W: Wait and hope that the asset price falls.
- Step B: Borrow the asset from Tom.
- Step S: Sell the asset to Dick.
Select the statement with the correct order of steps.
A firm conducts a two-for-one stock split. Which of the following consequences would NOT be expected?
Question 807 market efficiency, expected and historical returns, CAPM, beta, systematic risk, no explanation
You work in Asia and just woke up. It looked like a nice day but then you read the news and found out that last night the American share market fell by 10% while you were asleep due to surprisingly poor macro-economic world news. You own a portfolio of liquid stocks listed in Asia with a beta of 1.6. When the Asian equity markets open, what do you expect to happen to your share portfolio? Assume that the capital asset pricing model (CAPM) is correct and that the market portfolio contains all shares in the world, of which American shares are a big part. Your portfolio beta is measured against this world market portfolio.
When the Asian equity market opens for trade, you would expect your portfolio value to:
A graph of assets’ expected returns ##(\mu)## versus standard deviations ##(\sigma)## is given in the below diagram.
Each letter corresponds to a separate coloured area. The portfolios at the boundary of the areas, on the black lines, are excluded from each area. Assume that all assets represented in this graph are fairly priced, and that all risky assets can be short-sold.
Which of the following statements about this graph and Markowitz portfolio theory is NOT correct?
Question 809 Markowitz portfolio theory, CAPM, Jensens alpha, CML, systematic and idiosyncratic risk
A graph of assets’ expected returns ##(\mu)## versus standard deviations ##(\sigma)## is given in the graph below. The CML is the capital market line.
Which of the following statements about this graph, Markowitz portfolio theory and the Capital Asset Pricing Model (CAPM) theory is NOT correct?
Question 810 CAPM, systematic and idiosyncratic risk, market efficiency
Examine the graphs below. Assume that asset A is a single stock. Which of the following statements is NOT correct? Asset A:
Question 811 log-normal distribution, mean and median returns, return distribution, arithmetic and geometric averages
Which of the following statements about probability distributions is NOT correct?
A firm is about to conduct a 2-for-7 rights issue with a subscription price of $10 per share. They haven’t announced the capital raising to the market yet and the share price is currently $13 per share. Assume that every shareholder will exercise their rights, the cash raised will simply be put in the bank, and the rights issue is completed so quickly that the time value of money can be ignored. Disregard signalling, taxes and agency-related effects.
Which of the following statements about the rights issue is NOT correct? After the rights issue is completed:
The famous investor Warren Buffett is one of few portfolio managers who appears to have consistently beaten the market. His company Berkshire Hathaway (BRK) appears to have outperformed the US S&P500 market index, shown in the graph below.
Read the below statements about Warren Buffett and the implications for the Efficient Markets Hypothesis (EMH) theory of Eugene Fama. Assume that the first sentence is true. Analyse the second sentence and select the answer option which is NOT correct. In other words, find the false statement in the second sentence.
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.
Question 707 continuously compounding rate, continuously compounding rate conversion
Convert a 10% effective annual rate ##(r_\text{eff annual})## into a continuously compounded annual rate ##(r_\text{cc annual})##. The equivalent continuously compounded annual rate is:
An effective semi-annual return of 5% ##(r_\text{eff 6mth})## is equivalent to an effective annual return ##(r_\text{eff annual})## of:
Question 711 continuously compounding rate, continuously compounding rate conversion
A continuously compounded semi-annual return of 5% ##(r_\text{cc 6mth})## is equivalent to a continuously compounded annual return ##(r_\text{cc annual})## of:
Question 691 continuously compounding rate, effective rate, continuously compounding rate conversion, no explanation
A bank quotes an interest rate of 6% pa with quarterly compounding. Note that another way of stating this rate is that it is an annual percentage rate (APR) compounding discretely every 3 months.
Which of the following statements about this rate is NOT correct? All percentages are given to 6 decimal places. The equivalent:
If a variable, say X, is normally distributed with mean ##\mu## and variance ##\sigma^2## then mathematicians write ##X \sim \mathcal{N}(\mu, \sigma^2)##.
If a variable, say Y, is log-normally distributed and the underlying normal distribution has mean ##\mu## and variance ##\sigma^2## then mathematicians write ## Y \sim \mathbf{ln} \mathcal{N}(\mu, \sigma^2)##.
The below three graphs show probability density functions (PDF) of three different random variables Red, Green and Blue.
Select the most correct statement:
The below three graphs show probability density functions (PDF) of three different random variables Red, Green and Blue. Let ##P_1## be the unknown price of a stock in one year. ##P_1## is a random variable. Let ##P_0 = 1##, so the share price now is $1. This one dollar is a constant, it is not a variable.
Which of the below statements is NOT correct? Financial practitioners commonly assume that the shape of the PDF represented in the colour:
Question 719 mean and median returns, return distribution, arithmetic and geometric averages, continuously compounding rate
A stock has an arithmetic average continuously compounded return (AALGDR) of 10% pa, a standard deviation of continuously compounded returns (SDLGDR) of 80% pa and current stock price of $1. Assume that stock prices are log-normally distributed. The graph below summarises this information and provides some helpful formulas.
In one year, what do you expect the median and mean prices to be? The answer options are given in the same order.
Question 720 mean and median returns, return distribution, arithmetic and geometric averages, continuously compounding rate
A stock has an arithmetic average continuously compounded return (AALGDR) of 10% pa, a standard deviation of continuously compounded returns (SDLGDR) of 80% pa and current stock price of $1. Assume that stock prices are log-normally distributed.
In 5 years, what do you expect the median and mean prices to be? The answer options are given in the same order.
Question 723 mean and median returns, return distribution, arithmetic and geometric averages, continuously compounding rate
Here is a table of stock prices and returns. Which of the statements below the table is NOT correct?
| Price and Return Population Statistics | ||||
| Time | Prices | LGDR | GDR | NDR |
| 0 | 100 | |||
| 1 | 99 | -0.010050 | 0.990000 | -0.010000 |
| 2 | 180.40 | 0.600057 | 1.822222 | 0.822222 |
| 3 | 112.73 | 0.470181 | 0.624889 | 0.375111 |
| Arithmetic average | 0.0399 | 1.1457 | 0.1457 | |
| Arithmetic standard deviation | 0.4384 | 0.5011 | 0.5011 | |
For a price of $1040, Camille will sell you a share which just paid a dividend of $100, and is expected to pay dividends every year forever, growing at a rate of 5% pa.
So the next dividend will be ##100(1+0.05)^1=$105.00##, and the year after it will be ##100(1+0.05)^2=110.25## and so on.
The required return of the stock is 15% pa.
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?
Your friend wants to borrow $1,000 and offers to pay you back $100 in 6 months, with more $100 payments at the end of every month for another 11 months. So there will be twelve $100 payments in total. She says that 12 payments of $100 equals $1,200 so she's being generous.
If interest rates are 12% pa, given as an APR compounding monthly, what is the Net Present Value (NPV) of your friend's deal?
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 really want to go on a back packing trip to Europe when you finish university. Currently you have $1,500 in the bank. Bank interest rates are 8% pa, given as an APR compounding per month. If the holiday will cost $2,000, how long will it take for your bank account to reach that amount?
Question 49 inflation, real and nominal returns and cash flows, APR, effective rate
In Australia, nominal yields on semi-annual coupon paying Government Bonds with 2 years until maturity are currently 2.83% pa.
The inflation rate is currently 2.2% pa, given as an APR compounding per quarter. The inflation rate is not expected to change over the next 2 years.
What is the real yield on these bonds, given as an APR compounding every 6 months?
Question 64 inflation, real and nominal returns and cash flows, APR, effective rate
In Germany, nominal yields on semi-annual coupon paying Government Bonds with 2 years until maturity are currently 0.04% pa.
The inflation rate is currently 1.4% pa, given as an APR compounding per quarter. The inflation rate is not expected to change over the next 2 years.
What is the real yield on these bonds, given as an APR compounding every 6 months?
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?
Your credit card shows a $600 debt liability. The interest rate is 24% pa, payable monthly. You can't pay any of the debt off, except in 6 months when it's your birthday and you'll receive $50 which you'll use to pay off the credit card. If that is your only repayment, how much will the credit card debt liability be one year from now?
Which of the following statements about effective rates and annualised percentage rates (APR's) is NOT correct?
Question 22 NPV, perpetuity with growth, effective rate, effective rate conversion
What is the NPV of the following series of cash flows when the discount rate is 10% given as an effective annual rate?
The first payment of $90 is in 3 years, followed by payments every 6 months in perpetuity after that which shrink by 3% every 6 months. That is, the growth rate every 6 months is actually negative 3%, given as an effective 6 month rate. So the payment at ## t=3.5 ## years will be ## 90(1-0.03)^1=87.3 ##, and so on.
Question 24 implicit interest rate in wholesale credit, effective rate
A bathroom and plumbing supplies shop offers credit to its customers. Customers are given 60 days to pay for their goods, but if they pay within 7 days they will get a 2% discount.
What is the effective interest rate implicit in the discount being offered? Assume 365 days in a year and that all customers pay on either the 7th day or the 60th day. All rates given in this question are effective annual rates.
You're trying to save enough money to buy your first car which costs $2,500. You can save $100 at the end of each month starting from now. You currently have no money at all. You just opened a bank account with an interest rate of 6% pa payable monthly.
How many months will it take to save enough money to buy the car? Assume that the price of the car will stay the same over time.
A three year corporate bond yields 12% pa with a coupon rate of 10% pa, paid semi-annually.
Find the effective six month yield, effective annual yield and the effective daily yield. Assume that each month has 30 days and that there are 360 days in a year.
All answers are given in the same order:
##r_\text{eff semi-annual}##, ##r_\text{eff yearly}##, ##r_\text{eff daily}##.
A share just paid its semi-annual dividend of $10. The dividend is expected to grow at 2% every 6 months forever. This 2% growth rate is an effective 6 month rate. Therefore the next dividend will be $10.20 in six months. The required return of the stock is 10% pa, given as an effective annual rate.
What is the price of the share now?
A 2 year government bond yields 5% pa with a coupon rate of 6% pa, paid semi-annually.
Find the effective six month rate, effective annual rate and the effective daily rate. Assume that each month has 30 days and that there are 360 days in a year.
All answers are given in the same order:
##r_\text{eff semi-annual}##, ##r_\text{eff yrly}##, ##r_\text{eff daily}##.
A 2 year corporate bond yields 3% pa with a coupon rate of 5% pa, paid semi-annually.
Find the effective monthly rate, effective six month rate, and effective annual rate.
##r_\text{eff monthly}##, ##r_\text{eff 6 month}##, ##r_\text{eff annual}##.
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 31 DDM, perpetuity with growth, effective rate conversion
What is the NPV of the following series of cash flows when the discount rate is 5% given as an effective annual rate?
The first payment of $10 is in 4 years, followed by payments every 6 months forever after that which shrink by 2% every 6 months. That is, the growth rate every 6 months is actually negative 2%, given as an effective 6 month rate. So the payment at ## t=4.5 ## years will be ## 10(1-0.02)^1=9.80 ##, and so on.
Question 155 inflation, real and nominal returns and cash flows, Loan, effective rate conversion
You are a banker about to grant a 2 year loan to a customer. The loan's principal and interest will be repaid in a single payment at maturity, sometimes called a zero-coupon loan, discount loan or bullet loan.
You require a real return of 6% pa over the two years, given as an effective annual rate. Inflation is expected to be 2% this year and 4% next year, both given as effective annual rates.
You judge that the customer can afford to pay back $1,000,000 in 2 years, given as a nominal cash flow. How much should you lend to her right now?
Question 215 equivalent annual cash flow, effective rate conversion
You're about to buy a car. These are the cash flows of the two different cars that you can buy:
- You can buy an old car for $5,000 now, for which you will have to buy $90 of fuel at the end of each week from the date of purchase. The old car will last for 3 years, at which point you will sell the old car for $500.
- Or you can buy a new car for $14,000 now for which you will have to buy $50 of fuel at the end of each week from the date of purchase. The new car will last for 4 years, at which point you will sell the new car for $1,000.
Bank interest rates are 10% pa, given as an effective annual rate. Assume that there are exactly 52 weeks in a year. Ignore taxes and environmental and pollution factors.
Should you buy the or the ?
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:
| 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 180 equivalent annual cash flow, inflation, real and nominal returns and cash flows
Details of two different types of light bulbs are given below:
- Low-energy light bulbs cost $3.50, have a life of nine years, and use about $1.60 of electricity a year, paid at the end of each year.
- Conventional light bulbs cost only $0.50, but last only about a year and use about $6.60 of energy a year, paid at the end of each year.
The real discount rate is 5%, given as an effective annual rate. Assume that all cash flows are real. The inflation rate is 3% given as an effective annual rate.
Find the Equivalent Annual Cost (EAC) of the low-energy and conventional light bulbs. The below choices are listed in that order.
An industrial chicken farmer grows chickens for their meat. Chickens:
- Cost $0.50 each to buy as chicks. They are bought on the day they’re born, at t=0.
- Grow at a rate of $0.70 worth of meat per chicken per week for the first 6 weeks (t=0 to t=6).
- Grow at a rate of $0.40 worth of meat per chicken per week for the next 4 weeks (t=6 to t=10) since they’re older and grow more slowly.
- Feed costs are $0.30 per chicken per week for their whole life. Chicken feed is bought and fed to the chickens once per week at the beginning of the week. So the first amount of feed bought for a chicken at t=0 costs $0.30, and so on.
- Can be slaughtered (killed for their meat) and sold at no cost at the end of the week. The price received for the chicken is their total value of meat (note that the chicken grows fast then slow, see above).
The required return of the chicken farm is 0.5% given as an effective weekly rate.
Ignore taxes and the fixed costs of the factory. Ignore the chicken’s welfare and other environmental and ethical concerns.
Find the equivalent weekly cash flow of slaughtering a chicken at 6 weeks and at 10 weeks so the farmer can figure out the best time to slaughter his chickens. The choices below are given in the same order, 6 and 10 weeks.
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 249 equivalent annual cash flow, effective rate conversion
Details of two different types of desserts or edible treats are given below:
- High-sugar treats like candy, chocolate and ice cream make a person very happy. High sugar treats are cheap at only $2 per day.
- Low-sugar treats like nuts, cheese and fruit make a person equally happy if these foods are of high quality. Low sugar treats are more expensive at $4 per day.
The advantage of low-sugar treats is that a person only needs to pay the dentist $2,000 for fillings and root canal therapy once every 15 years. Whereas with high-sugar treats, that treatment needs to be done every 5 years.
The real discount rate is 10%, given as an effective annual rate. Assume that there are 365 days in every year and that all cash flows are real. The inflation rate is 3% given as an effective annual rate.
Find the equivalent annual cash flow (EAC) of the high-sugar treats and low-sugar treats, including dental costs. The below choices are listed in that order.
Ignore the pain of dental therapy, personal preferences and other factors.
You own a nice suit which you wear once per week on nights out. You bought it one year ago for $600. In your experience, suits used once per week last for 6 years. So you expect yours to last for another 5 years.
Your younger brother said that retro is back in style so he wants to wants to borrow your suit once a week when he goes out. With the increased use, your suit will only last for another 4 years rather than 5.
What is the present value of the cost of letting your brother use your current suit for the next 4 years?
Assume: that bank interest rates are 10% pa, given as an effective annual rate; you will buy a new suit when your current one wears out and your brother will not use the new one; your brother will only use your current suit so he will only use it for the next four years; and the price of a new suit never changes.
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.
Carlos and Edwin are brothers and they both love Holden Commodore cars.
Carlos likes to buy the latest Holden Commodore car for $40,000 every 4 years as soon as the new model is released. As soon as he buys the new car, he sells the old one on the second hand car market for $20,000. Carlos never has to bother with paying for repairs since his cars are brand new.
Edwin also likes Commodores, but prefers to buy 4-year old cars for $20,000 and keep them for 11 years until the end of their life (new ones last for 15 years in total but the 4-year old ones only last for another 11 years). Then he sells the old car for $2,000 and buys another 4-year old second hand car, and so on.
Every time Edwin buys a second hand 4 year old car he immediately has to spend $1,000 on repairs, and then $1,000 every year after that for the next 10 years. So there are 11 payments in total from when the second hand car is bought at t=0 to the last payment at t=10. One year later (t=11) the old car is at the end of its total 15 year life and can be scrapped for $2,000.
Assuming that Carlos and Edwin maintain their love of Commodores and keep up their habits of buying new ones and second hand ones respectively, how much larger is Carlos' equivalent annual cost of car ownership compared with Edwin's?
The real discount rate is 10% pa. All cash flows are real and are expected to remain constant. Inflation is forecast to be 3% pa. All rates are effective annual. Ignore capital gains tax and tax savings from depreciation since cars are tax-exempt for individuals.
Question 104 CAPM, payout policy, capital structure, Miller and Modigliani, risk
Assume that there exists a perfect world with no transaction costs, no asymmetric information, no taxes, no agency costs, equal borrowing rates for corporations and individual investors, the ability to short the risk free asset, semi-strong form efficient markets, the CAPM holds, investors are rational and risk-averse and there are no other market frictions.
For a firm operating in this perfect world, which statement(s) are correct?
(i) When a firm changes its capital structure and/or payout policy, share holders' wealth is unaffected.
(ii) When the idiosyncratic risk of a firm's assets increases, share holders do not expect higher returns.
(iii) When the systematic risk of a firm's assets increases, share holders do not expect higher returns.
Select the most correct response:
Question 237 WACC, Miller and Modigliani, interest tax shield
Which of the following discount rates should be the highest for a levered company? Ignore the costs of financial distress.
Question 241 Miller and Modigliani, leverage, payout policy, diversification, NPV
One of Miller and Modigliani's (M&M's) important insights is that a firm's managers should not try to achieve a particular level of leverage in a world with zero taxes and perfect information since investors can make their own leverage. Therefore corporate capital structure policy is irrelevant since investors can achieve their own desired leverage at the personal level by borrowing or lending on their own.
This principal of 'home-made' or 'do-it-yourself' leverage can also be applied to other topics. Read the following statements to decide which are true:
(I) Payout policy: a firm's managers should not try to achieve a particular pattern of equity payout.
(II) Agency costs: a firm's managers should not try to minimise agency costs.
(III) Diversification: a firm's managers should not try to diversify across industries.
(IV) Shareholder wealth: a firm's managers should not try to maximise shareholders' wealth.
Which of the above statement(s) are true?