A fairly valued share's current price is $4 and it has a total required return of 30%. Dividends are paid annually and next year's dividend is expected to be $1. After that, dividends are expected to grow by 5% pa in perpetuity. All rates are effective annual returns.
What is the expected dividend income paid at the end of the second year (t=2) and what is the expected capital gain from just after the first dividend (t=1) to just after the second dividend (t=2)? The answers are given in the same order, the dividend and then the capital gain.
Question 535 DDM, real and nominal returns and cash flows, stock pricing
You are an equities analyst trying to value the equity of the Australian telecoms company Telstra, with ticker TLS. In Australia, listed companies like Telstra tend to pay dividends every 6 months. The payment around August is called the final dividend and the payment around February is called the interim dividend. Both occur annually.
- Today is mid-March 2015.
- TLS's last interim dividend of $0.15 was one month ago in mid-February 2015.
- TLS's last final dividend of $0.15 was seven months ago in mid-August 2014.
Judging by TLS's dividend history and prospects, you estimate that the nominal dividend growth rate will be 1% pa. Assume that TLS's total nominal cost of equity is 6% pa. The dividends are nominal cash flows and the inflation rate is 2.5% pa. All rates are quoted as nominal effective annual rates. Assume that each month is exactly one twelfth (1/12) of a year, so you can ignore the number of days in each month.
Calculate the current TLS share price.
Question 488 income and capital returns, payout policy, payout ratio, DDM
Two companies BigDiv and ZeroDiv are exactly the same except for their dividend payouts.
BigDiv pays large dividends and ZeroDiv doesn't pay any dividends.
Currently the two firms have the same earnings, assets, number of shares, share price, expected total return and risk.
Assume a perfect world with no taxes, no transaction costs, no asymmetric information and that all assets including business projects are fairly priced and therefore zero-NPV.
All things remaining equal, which of the following statements is NOT correct?
Which firms tend to have low forward-looking price-earnings (PE) ratios?
Only consider firms with positive earnings, disregard firms with negative earnings and therefore negative PE ratios.
One and a half years ago Frank bought a house for $600,000. Now it's worth only $500,000, based on recent similar sales in the area.
The expected total return on Frank's residential property is 7% pa.
He rents his house out for $1,600 per month, paid in advance. Every 12 months he plans to increase the rental payments.
The present value of 12 months of rental payments is $18,617.27.
The future value of 12 months of rental payments one year in the future is $19,920.48.
What is the expected annual rental yield of the property? Ignore the costs of renting such as maintenance, real estate agent fees and so on.
The expression 'you have to spend money to make money' relates to which business decision?
The expression 'cash is king' emphasizes the importance of having enough cash to pay your short term debts to avoid bankruptcy. Which business decision is this expression most closely related to?
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?
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.
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 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 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).
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?
Bonds X and Y are issued by the same US company. Both bonds yield 10% pa, and they have the same face value ($100), maturity, seniority, and payment frequency.
The only difference is that bond X and Y's coupon rates are 8 and 12% pa respectively. Which of the following statements is true?
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?
In these tough economic times, central banks around the world have cut interest rates so low that they are practically zero. In some countries, government bond yields are also very close to zero.
A three year government bond with a face value of $100 and a coupon rate of 2% pa paid semi-annually was just issued at a yield of 0%. What is the price of the bond?
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.
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:
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:
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?
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?
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:
There are many ways to calculate a firm's free cash flow (FFCF), also called cash flow from assets (CFFA). Some include the annual interest tax shield in the cash flow and some do not.
Which of the below FFCF formulas include the interest tax shield in the cash flow?
###(1) \quad FFCF=NI + Depr - CapEx -ΔNWC + IntExp### ###(2) \quad FFCF=NI + Depr - CapEx -ΔNWC + IntExp.(1-t_c)### ###(3) \quad FFCF=EBIT.(1-t_c )+ Depr- CapEx -ΔNWC+IntExp.t_c### ###(4) \quad FFCF=EBIT.(1-t_c) + Depr- CapEx -ΔNWC### ###(5) \quad FFCF=EBITDA.(1-t_c )+Depr.t_c- CapEx -ΔNWC+IntExp.t_c### ###(6) \quad FFCF=EBITDA.(1-t_c )+Depr.t_c- CapEx -ΔNWC### ###(7) \quad FFCF=EBIT-Tax + Depr - CapEx -ΔNWC### ###(8) \quad FFCF=EBIT-Tax + Depr - CapEx -ΔNWC-IntExp.t_c### ###(9) \quad FFCF=EBITDA-Tax - CapEx -ΔNWC### ###(10) \quad FFCF=EBITDA-Tax - CapEx -ΔNWC-IntExp.t_c###The formulas for net income (NI also called earnings), EBIT and EBITDA are given below. Assume that depreciation and amortisation are both represented by 'Depr' and that 'FC' represents fixed costs such as rent.
###NI=(Rev - COGS - Depr - FC - IntExp).(1-t_c )### ###EBIT=Rev - COGS - FC-Depr### ###EBITDA=Rev - COGS - FC### ###Tax =(Rev - COGS - Depr - FC - IntExp).t_c= \dfrac{NI.t_c}{1-t_c}###Question 69 interest tax shield, capital structure, leverage, WACC
Which statement about risk, required return and capital structure is the most 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 __________.
All things remaining equal, the variance of a portfolio of two positively-weighted stocks rises as:
| 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.
What is the correlation of a variable X with a constant C?
The corr(X, C) or ##\rho_{X,C}## equals:
Question 418 capital budgeting, NPV, interest tax shield, WACC, CFFA, CAPM
| Project Data | ||
| Project life | 1 year | |
| Initial investment in equipment | $8m | |
| Depreciation of equipment per year | $8m | |
| Expected sale price of equipment at end of project | 0 | |
| Unit sales per year | 4m | |
| Sale price per unit | $10 | |
| Variable cost per unit | $5 | |
| Fixed costs per year, paid at the end of each year | $2m | |
| Interest expense in first year (at t=1) | $0.562m | |
| Corporate tax rate | 30% | |
| Government treasury bond yield | 5% | |
| Bank loan debt yield | 9% | |
| Market portfolio return | 10% | |
| Covariance of levered equity returns with market | 0.32 | |
| Variance of market portfolio returns | 0.16 | |
| Firm's and project's debt-to-equity ratio | 50% | |
Notes
- Due to the project, current assets will increase by $6m now (t=0) and fall by $6m at the end (t=1). Current liabilities will not be affected.
Assumptions
- The debt-to-equity ratio will be kept constant throughout the life of the project. The amount of interest expense at the end of each period has been correctly calculated to maintain this constant debt-to-equity ratio.
- Millions are represented by 'm'.
- All cash flows occur at the start or end of the year as appropriate, not in the middle or throughout the year.
- All rates and cash flows are real. The inflation rate is 2% pa. All rates are given as effective annual rates.
- The project is undertaken by a firm, not an individual.
What is the net present value (NPV) of the project?
Question 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:
Question 339 bond pricing, inflation, market efficiency, income and capital returns
Economic statistics released this morning were a surprise: they show a strong chance of consumer price inflation (CPI) reaching 5% pa over the next 2 years.
This is much higher than the previous forecast of 3% pa.
A vanilla fixed-coupon 2-year risk-free government bond was issued at par this morning, just before the economic news was released.
What is the expected change in bond price after the economic news this morning, and in the next 2 years? Assume that:
- Inflation remains at 5% over the next 2 years.
- Investors demand a constant real bond yield.
- The bond price falls by the (after-tax) value of the coupon the night before the ex-coupon date, as in real life.
A managed fund charges fees based on the amount of money that you keep with them. The fee is 2% of the start-of-year amount, but it is paid at the end of every year.
This fee is charged regardless of whether the fund makes gains or losses on your money.
The fund offers to invest your money in shares which have an expected return of 10% pa before fees.
You are thinking of investing $100,000 in the fund and keeping it there for 40 years when you plan to retire.
What is the Net Present Value (NPV) of investing your money in the fund? Note that the question is not asking how much money you will have in 40 years, it is asking: what is the NPV of investing in the fund? Assume that:
- The fund has no private information.
- Markets are weak and semi-strong form efficient.
- The fund's transaction costs are negligible.
- The cost and trouble of investing your money in shares by yourself, without the managed fund, is negligible.
Question 319 foreign exchange rate, monetary policy, American and European terms
Investors expect the Reserve Bank of Australia (RBA) to keep the policy rate steady at their next meeting.
Then unexpectedly, the RBA announce that they will increase the policy rate by 25 basis points due to fears that the economy is growing too fast and that inflation will be above their target rate of 2 to 3 per cent.
What do you expect to happen to Australia's exchange rate in the short term? The Australian dollar is likely to:
Question 246 foreign exchange rate, forward foreign exchange rate, cross currency interest rate parity
Suppose the Australian cash rate is expected to be 8.15% pa and the US federal funds rate is expected to be 3.00% pa over the next 2 years, both given as nominal effective annual rates. The current exchange rate is at parity, so 1 USD = 1 AUD.
What is the implied 2 year forward foreign exchange rate?
The Chinese government attempts to fix its exchange rate against the US dollar and at the same time use monetary policy to fix its interest rate at a set level.
To be able to fix its exchange rate and interest rate in this way, what does the Chinese government actually do?
- Adopts capital controls to prevent financial arbitrage by private firms and individuals.
- Adopts the same interest rate (monetary policy) as the United States.
- Fixes inflation so that the domestic real interest rate is equal to the United States' real interest rate.
Which of the above statements is or are true?
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).
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?