# Fight Finance

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The saying "buy low, sell high" suggests that investors should make a:

Total cash flows can be broken into income and capital cash flows. What is the name given to the income cash flow from owning shares?

An asset's total expected return over the next year is given by:

$$r_\text{total} = \dfrac{c_1+p_1-p_0}{p_0}$$

Where $p_0$ is the current price, $c_1$ is the expected income in one year and $p_1$ is the expected price in one year. The total return can be split into the income return and the capital return.

Which of the following is the expected capital return?

A share was bought for $30 (at t=0) and paid its annual dividend of$6 one year later (at t=1).

Just after the dividend was paid, the share price fell to $27 (at t=1). What were the total, capital and income returns given as effective annual rates? The choices are given in the same order: $r_\text{total}$ , $r_\text{capital}$ , $r_\text{dividend}$. For an asset price to double every 10 years, what must be the expected future capital return, given as an effective annual rate? Imagine that the interest rate on your savings account was 1% per year and inflation was 2% per year. After one year, would you be able to buy , exactly the as or than today with the money in this account? A stock has a real expected total return of 7% pa and a real expected capital return of 2% pa. Inflation is expected to be 2% pa. All rates are given as effective annual rates. What is the nominal expected total return, capital return and dividend yield? The answers below are given in the same order. What is the present value of a real payment of$500 in 2 years? The nominal discount rate is 7% pa and the inflation rate is 4% pa.

On his 20th birthday, a man makes a resolution. He will put $30 cash under his bed at the end of every month starting from today. His birthday today is the first day of the month. So the first addition to his cash stash will be in one month. He will write in his will that when he dies the cash under the bed should be given to charity. If the man lives for another 60 years, how much money will be under his bed if he dies just after making his last (720th) addition? Also, what will be the real value of that cash in today's prices if inflation is expected to 2.5% pa? Assume that the inflation rate is an effective annual rate and is not expected to change. The answers are given in the same order, the amount of money under his bed in 60 years, and the real value of that money in today's prices. 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? An investor bought a bond for$100 (at t=0) and one year later it paid its annual coupon of $1 (at t=1). Just after the coupon was paid, the bond price was$100.50 (at t=1). Inflation over the past year (from t=0 to t=1) was 3% pa, given as an effective annual rate.

Which of the following statements is NOT correct? The bond investment produced a:

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

Which is the safest investment? Which will give the highest returns?

Which business structure or structures have the advantage of limited liability for equity investors?

Who is most in danger of being personally bankrupt? Assume that all of their businesses' assets are highly liquid and can therefore be sold immediately.

Which of the following statements about book and market equity is NOT correct?

The below screenshot of Commonwealth Bank of Australia's (CBA) details were taken from the Google Finance website on 7 Nov 2014. Some information has been deliberately blanked out.

What was CBA's market capitalisation of equity?

The investment decision primarily affects which part of a business?

The financing decision primarily affects which part of a business?

Business people make lots of important decisions. Which of the following is the most important long term decision?

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.

Will you or Katya's deal?

This annuity formula $\dfrac{C_1}{r}\left(1-\dfrac{1}{(1+r)^3} \right)$ is equivalent to which of the following formulas? Note the 3.

In the below formulas, $C_t$ is a cash flow at time t. All of the cash flows are equal, but paid at different times.

Your friend overheard that you need some cash and asks if you would like to borrow some money. She can lend you $5,000 now (t=0), and in return she wants you to pay her back$1,000 in two years (t=2) and every year after that for the next 5 years, so there will be 6 payments of $1,000 from t=2 to t=7 inclusive. What is the net present value (NPV) of borrowing from your friend? Assume that banks loan funds at interest rates of 10% pa, given as an effective annual rate. Some countries' interest rates are so low that they're zero. If interest rates are 0% pa and are expected to stay at that level for the foreseeable future, what is the most that you would be prepared to pay a bank now if it offered to pay you$10 at the end of every year for the next 5 years?

In other words, what is the present value of five $10 payments at time 1, 2, 3, 4 and 5 if interest rates are 0% pa? Discounted cash flow (DCF) valuation prices assets by finding the present value of the asset's future cash flows. The single cash flow, annuity, and perpetuity equations are very useful for this. Which of the following equations is the 'perpetuity with growth' equation? A stock is expected to pay its next dividend of$1 in one year. Future annual dividends are expected to grow by 2% pa. So the first dividend of $1 will be in one year, the year after that$1.02 (=1*(1+0.02)^1), and a year later $1.0404 (=1*(1+0.02)^2) and so on forever. Its required total return is 10% pa. The total required return and growth rate of dividends are given as effective annual rates. Calculate the current stock price. A stock just paid a dividend of$1. Future annual dividends are expected to grow by 2% pa. The next dividend of $1.02 (=1*(1+0.02)^1) will be in one year, and the year after that the dividend will be$1.0404 (=1*(1+0.02)^2), and so on forever.

Its required total return is 10% pa. The total required return and growth rate of dividends are given as effective annual rates.

Calculate the current stock price.

For a price of $13, Carla 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.

Would you like to Carla's share or politely ?

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.

Would you like to the share or politely ?

The perpetuity with growth formula, also known as the dividend discount model (DDM) or Gordon growth model, is appropriate for valuing a company's shares. $P_0$ is the current share price, $C_1$ is next year's expected dividend, $r$ is the total required return and $g$ is the expected growth rate of the dividend.

$$P_0=\dfrac{C_1}{r-g}$$

The below graph shows the expected future price path of the company's shares. Which of the following statements about the graph is NOT correct?

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

$$P_0=\frac{d_1}{r-g}$$

A stock pays dividends annually. It just paid a dividend, but the next dividend ($d_1$) will be paid in one year.

According to the DDM, what is the correct formula for the expected price of the stock in 2.5 years?

A stock will pay you a dividend of $10 tonight if you buy it today. Thereafter the annual dividend is expected to grow by 5% pa, so the next dividend after the$10 one tonight will be $10.50 in one year, then in two years it will be$11.025 and so on. The stock's required return is 10% pa.

What is the stock price today and what do you expect the stock price to be tomorrow, approximately?

In the dividend discount model:

$$P_0 = \dfrac{C_1}{r-g}$$

The return $r$ is supposed to be the:

A stock pays annual dividends which are expected to continue forever. It just paid a dividend of $10. The growth rate in the dividend is 2% pa. You estimate that the stock's required return is 10% pa. Both the discount rate and growth rate are given as effective annual rates. Using the dividend discount model, what will be the share price? A stock is expected to pay the following dividends:  Cash Flows of a Stock Time (yrs) 0 1 2 3 4 ... Dividend ($) 0.00 1.00 1.05 1.10 1.15 ...

After year 4, the annual dividend will grow in perpetuity at 5% pa, so;

• the dividend at t=5 will be $1.15(1+0.05), • the dividend at t=6 will be$1.15(1+0.05)^2, and so on.

The required return on the stock is 10% pa. Both the growth rate and required return are given as effective annual rates.

What will be the price of the stock in three and a half years (t = 3.5)?

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

$$p_0 = \frac{d_1}{r - g}$$

Which expression is NOT equal to the expected dividend yield?

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.

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?

A stock is expected to pay a dividend of $15 in one year (t=1), then$25 for 9 years after that (payments at t=2 ,3,...10), and on the 11th year (t=11) the dividend will be 2% less than at t=10, and will continue to shrink at the same rate every year after that forever. The required return of the stock is 10%. All rates are effective annual rates.

What is the price of the stock now?

Estimate the US bank JP Morgan's share price using a price earnings (PE) multiples approach with the following assumptions and figures only:

• The major US banks JP Morgan Chase (JPM), Citi Group (C) and Wells Fargo (WFC) are comparable companies;
• JP Morgan Chase's historical earnings per share (EPS) is $4.37; • Citi Group's share price is$50.05 and historical EPS is $4.26; • Wells Fargo's share price is$48.98 and historical EPS is $3.89. Note: Figures sourced from Google Finance on 24 March 2014. Estimate Microsoft's (MSFT) share price using a price earnings (PE) multiples approach with the following assumptions and figures only: • Apple, Google and Microsoft are comparable companies, • Apple's (AAPL) share price is$526.24 and historical EPS is $40.32. • Google's (GOOG) share price is$1,215.65 and historical EPS is $36.23. • Micrsoft's (MSFT) historical earnings per share (EPS) is$2.71.

Source: Google Finance 28 Feb 2014.

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.

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 $2,000. Assuming that Carlos and Edwin maintain their love of Commodores and keep up their habits of buying new ones and second hand ones respectively, how much larger is Carlos' equivalent annual cost of car ownership compared with Edwin's? The real discount rate is 10% pa. All cash flows are real and are expected to remain constant. Inflation is forecast to be 3% pa. All rates are effective annual. Ignore capital gains tax and tax savings from depreciation since cars are tax-exempt for individuals. The required return of a project is 10%, given as an effective annual rate. Assume that the cash flows shown in the table are paid all at once at the given point in time. What is the Net Present Value (NPV) of the project?  Project Cash Flows Time (yrs) Cash flow ($) 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 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. 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 Costnow ($) Sale price inone year ($) 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 $3.4m when the conversion is finished in one year. All of the development projects have the same risk so the required return of each is 10% pa. The table below shows the estimated cash flows and internal rates of returns (IRR's).  Mutually Exclusive Projects Project Cash flownow ($) Cash flow inone 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? How many years will it take for an asset's price to double if the price grows by 10% pa? 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:

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?

Which of the following equations is NOT equal to the total return of an asset?

Let $p_0$ be the current price, $p_1$ the expected price in one year and $c_1$ the expected income in one year.

Total cash flows can be broken into income and capital cash flows.

What is the name given to the cash flow generated from selling shares at a higher price than they were bought?

The below screenshot of Microsoft's (MSFT) details were taken from the Google Finance website on 28 Nov 2014. Some information has been deliberately blanked out.

What was MSFT's market capitalisation of equity?

Which of the following statements is NOT correct?

Apples and oranges currently cost $1 each. Inflation is 5% pa, and apples and oranges are equally affected by this inflation rate. Note that when payments are not specified as real, as in this question, they're conventionally assumed to be nominal. Which of the following statements is NOT correct? Which of the following statements about inflation is NOT correct? What is the present value of a nominal payment of$1,000 in 4 years? The nominal discount rate is 8% pa and the inflation rate is 2% pa.

A residential investment property has an expected nominal total return of 6% pa and nominal capital return of 2.5% pa. Inflation is expected to be 2.5% pa.

All of the above are effective nominal rates and investors believe that they will stay the same in perpetuity.

What are the property's expected real total, capital and income returns?

The answer choices below are given in the same order.

A low-growth mature stock has an expected nominal total return of 6% pa and nominal capital return of 2% pa. Inflation is expected to be 3% pa.

All of the above are effective nominal rates and investors believe that they will stay the same in perpetuity.

What are the stock's expected real total, capital and income returns?

The answer choices below are given in the same order.

The Australian Federal Government lends money to domestic students to pay for their university education. This is known as the Higher Education Contribution Scheme (HECS). The nominal interest rate on the HECS loan is set equal to the consumer price index (CPI) inflation rate. The interest is capitalised every year, which means that the interest is added to the principal. The interest and principal does not need to be repaid by students until they finish study and begin working.

Which of the following statements about HECS loans is NOT correct?

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'.

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

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

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

The following cash flows are expected:

• 10 yearly payments of $80, with the first payment in 3 years from now (first payment at t=3). • 1 payment of$600 in 5 years and 6 months (t=5.5) from now.

What is the NPV of the cash flows if the discount rate is 10% given as an effective annual rate?

Which of the following statements about gold is NOT correct? Assume that the gold price increases by inflation. Gold:

If a firm makes a profit and pays no dividends, which of the firm’s accounts will increase?

A stock’s current price is $1. Its expected total return is 10% pa and its long term expected capital return is 4% pa. It pays an annual dividend and the next one will be paid in one year. All rates are given as effective annual rates. The dividend discount model is thought to be a suitable model for the stock. Ignore taxes. Which of the following statements about the stock is NOT correct? In the dividend discount model (DDM), share prices fall when dividends are paid. Let the high price before the fall be called the peak, and the low price after the fall be called the trough. $$P_0=\dfrac{C_1}{r-g}$$ Which of the following statements about the DDM is NOT correct? A share’s current price is$60. It’s expected to pay a dividend of $1.50 in one year. The growth rate of the dividend is 0.5% pa and the stock’s required total return is 3% pa. The stock’s price can be modeled using the dividend discount model (DDM): $P_0=\dfrac{C_1}{r-g}$ Which of the following methods is NOT equal to the stock’s expected price in one year and six months (t=1.5 years)? Note that the symbolic formulas shown in each line below do equal the formulas with numbers. The formula is just repeated with symbols and then numbers in case it helps you to identify the incorrect statement more quickly. An equities analyst is using the dividend discount model to price a company's shares. The company operates domestically and has no plans to expand overseas. It is part of a mature industry with stable positive growth prospects. The analyst has estimated the real required return (r) of the stock and the value of the dividend that the stock just paid a moment before $(C_\text{0 before})$. What is the highest perpetual real growth rate of dividends (g) that can be justified? Select the most correct statement from the following choices. The highest perpetual real expected growth rate of dividends that can be justified is the country's expected: A share currently worth$100 is expected to pay a constant dividend of $4 for the next 5 years with the first dividend in one year (t=1) and the last in 5 years (t=5). The total required return is 10% pa. What do you expected the share price to be in 5 years, just after the dividend at that time has been paid? An Apple iPhone 6 smart phone can be bought now for$999. An Android Kogan Agora 4G+ smart phone can be bought now for $240. If the Kogan phone lasts for one year, approximately how long must the Apple phone last for to have the same equivalent annual cost? Assume that both phones have equivalent features besides their lifetimes, that both are worthless once they've outlasted their life, the discount rate is 10% pa given as an effective annual rate, and there are no extra costs or benefits from either phone. Stocks in the United States usually pay quarterly dividends. For example, the software giant Microsoft paid a$0.23 dividend every quarter over the 2013 financial year and plans to pay a $0.28 dividend every quarter over the 2014 financial year. Using the dividend discount model and net present value techniques, calculate the stock price of Microsoft assuming that: • The time now is the beginning of July 2014. The next dividend of$0.28 will be received in 3 months (end of September 2014), with another 3 quarterly payments of $0.28 after this (end of December 2014, March 2015 and June 2015). • The quarterly dividend will increase by 2.5% every year, but each quarterly dividend over the year will be equal. So each quarterly dividend paid in the financial year beginning in September 2015 will be$ 0.287 $(=0.28×(1+0.025)^1)$, with the last at the end of June 2016. In the next financial year beginning in September 2016 each quarterly dividend will be $0.294175 $(=0.28×(1+0.025)^2)$, with the last at the end of June 2017, and so on forever. • The total required return on equity is 6% pa. • The required return and growth rate are given as effective annual rates. • Dividend payment dates and ex-dividend dates are at the same time. • Remember that there are 4 quarters in a year and 3 months in a quarter. What is the current stock price? An 'interest payment' is the same thing as a 'coupon payment'. or ? An 'interest rate' is the same thing as a 'coupon rate'. or ? An 'interest rate' is the same thing as a 'yield'. or ? An 'interest only' loan can also be called a: 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.

Calculate the price of a newly issued ten year bond with a face value of $100, a yield of 8% pa and a fixed coupon rate of 6% pa, paid semi-annually. So there are two coupons per year, paid in arrears every six months. "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: 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?

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?

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?

A bond maturing in 10 years has a coupon rate of 4% pa, paid semi-annually. The bond's yield is currently 6% pa. The face value of the bond is $100. What is its price? A three year bond has a fixed coupon rate of 12% pa, paid semi-annually. The bond's yield is currently 6% pa. The face value is$100. What is its price?

Which one of the following bonds is trading at a discount?

An investor bought two fixed-coupon bonds issued by the same company, a zero-coupon bond and a 7% pa semi-annual coupon bond. Both bonds have a face value of $1,000, mature in 10 years, and had a yield at the time of purchase of 8% pa. A few years later, yields fell to 6% pa. Which of the following statements is correct? Note that a capital gain is an increase in price. 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?

A 10 year bond has a face value of $100, a yield of 6% pa and a fixed coupon rate of 8% pa, paid semi-annually. What is its price? Below are some statements about loans and bonds. The first descriptive sentence is correct. But one of the second sentences about the loans' or bonds' prices is not correct. Which statement is NOT correct? Assume that interest rates are positive. Note that coupons or interest payments are the periodic payments made throughout a bond or loan's life. The face or par value of a bond or loan is the amount paid at the end when the debt matures. An Australian company just issued two bonds: • A 1 year zero coupon bond at a yield of 8% pa, and • A 2 year zero coupon bond at a yield of 10% pa. What is the forward rate on the company's debt from years 1 to 2? Give your answer as an APR compounding every 6 months, which is how the above bond yields are quoted. 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? Which of the following statements is NOT correct? Borrowers: Which of the following statements is NOT correct? Lenders: 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. 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? You deposit cash into your bank account. Have you or your money? You deposit cash into your bank account. Have you or debt? You deposit cash into your bank account. Does the deposit account represent a debt or to you? You owe money. Are you a or a ? You own a debt asset. Are you a or a ? Which of the following statements is NOT correct? Bond investors: 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. Which of the following statements about effective rates and annualised percentage rates (APR's) is NOT correct? A European bond paying annual coupons of 6% offers a yield of 10% pa. Convert the yield into an effective monthly rate, an effective annual rate and an effective daily rate. Assume that there are 365 days in a year. All answers are given in the same order: $$r_\text{eff, monthly} , r_\text{eff, yearly} , r_\text{eff, daily}$$ You are owed money. Are you a or a ? You want to buy an apartment priced at$500,000. You have saved a deposit of $50,000. The bank has agreed to lend you the$450,000 as an interest only loan with a term of 30 years. The interest rate is 6% pa and is not expected to change. What will be your monthly payments?

You want to buy an apartment priced at $500,000. You have saved a deposit of$50,000. The bank has agreed to lend you the $450,000 as a fully amortising loan with a term of 30 years. The interest rate is 6% pa and is not expected to change. What will be your monthly payments? You just signed up for a 30 year fully amortising mortgage loan with monthly payments of$1,500 per month. The interest rate is 9% pa which is not expected to change.

To your surprise, you can actually afford to pay $2,000 per month and your mortgage allows early repayments without fees. If you maintain these higher monthly payments, how long will it take to pay off your mortgage? A prospective home buyer can afford to pay$2,000 per month in mortgage loan repayments. The central bank recently lowered its policy rate by 0.25%, and residential home lenders cut their mortgage loan rates from 4.74% to 4.49%.

How much more can the prospective home buyer borrow now that interest rates are 4.49% rather than 4.74%? Give your answer as a proportional increase over the original amount he could borrow ($V_\text{before}$), so:

$$\text{Proportional increase} = \frac{V_\text{after}-V_\text{before}}{V_\text{before}}$$

Assume that:

• Interest rates are expected to be constant over the life of the loan.

• Loans are interest-only and have a life of 30 years.

• Mortgage loan payments are made every month in arrears and all interest rates are given as annualised percentage rates compounding per month.

Which of the following statements about risk free government bonds is NOT correct?

Hint: Total return can be broken into income and capital returns as follows:

\begin{aligned} r_\text{total} &= \frac{c_1}{p_0} + \frac{p_1-p_0}{p_0} \\ &= r_\text{income} + r_\text{capital} \end{aligned}

The capital return is the growth rate of the price.
The income return is the periodic cash flow. For a bond this is the coupon payment.

A two year Government bond has a face value of $100, a yield of 0.5% and a fixed coupon rate of 0.5%, paid semi-annually. What is its price? A firm wishes to raise$10 million now. They will issue 6% pa semi-annual coupon bonds that will mature in 8 years and have a face value of $1,000 each. Bond yields are 10% pa, given as an APR compounding every 6 months, and the yield curve is flat. How many bonds should the firm issue? A European company just issued two bonds, a • 2 year zero coupon bond at a yield of 8% pa, and a • 3 year zero coupon bond at a yield of 10% pa. What is the company's forward rate over the third year (from t=2 to t=3)? Give your answer as an effective annual rate, which is how the above bond yields are quoted. A 10 year Australian government bond was just issued at par with a yield of 3.9% pa. The fixed coupon payments are semi-annual. The bond has a face value of$1,000.

Six months later, just after the first coupon is paid, the yield of the bond decreases to 3.65% pa. What is the bond's new price?

A 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:

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.

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 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.

Cash Flow From Assets (CFFA) can be defined as:

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.

Issuing debt doesn't give away control of the firm because debt holders can't cast votes to determine the company's affairs, such as at the annual general meeting (AGM), and can't appoint directors to the board. or ?

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 $t=1$.

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 $g$ 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?

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:

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} \\
Does this annual FFCF or the annual interest tax shield?

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} \\
Does this annual FFCF or the annual interest tax shield?

 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

1. 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 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? 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? Companies must pay interest and principal payments to debt-holders. They're compulsory. But companies are not forced to pay dividends to share holders. or ? 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} Does this annual FFCF or the annual interest tax shield? One method for calculating a firm's free cash flow (FFCF, or CFFA) is to ignore interest expense. That is, pretend that interest expense $(IntExp)$ is zero: \begin{aligned} FFCF &= (Rev - COGS - Depr - FC - IntExp)(1-t_c) + Depr - CapEx -\Delta NWC + IntExp \\ &= (Rev - COGS - Depr - FC - 0)(1-t_c) + Depr - CapEx -\Delta NWC - 0\\ \end{aligned} Does this annual FFCF with zero interest expense or the annual interest tax shield? 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 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? You bought a house, primarily funded using a home loan from a bank. Which of the following statements is NOT correct? Where can a publicly listed firm's book value of equity be found? It can be sourced from the company's: Where can a private firm's market value of equity be found? It can be sourced from the company's: 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? For an asset's price to quintuple every 5 years, what must be its effective annual capital return? Note that a stock's price quintuples when it increases from say1 to $5. 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? If someone says "my shares rose by 10% last year", what do you assume that they mean? 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? 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? 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 24/7/15. 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? All other things remaining equal, a project is worse if its: 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?

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. 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.

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?

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.

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:

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 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?

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?

What is the correlation of a variable X with itself?

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

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?

Do you think that the following statement is or ? “Buying a single company stock usually provides a safer return than a stock mutual fund.”

Which of the following statements about short-selling is NOT true?

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 a constant C?

The cov(X, C) or $\sigma_{X,C}$ equals:

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.

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 $(\%)$.

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?

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.

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?

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?

According to the theory of the Capital Asset Pricing Model (CAPM), total variance can be broken into two components, systematic variance and idiosyncratic variance. Which of the following events would be considered the most diversifiable according to the theory of the CAPM?

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

Treasury bonds currently have a return of 5% pa. A stock has a beta of 0.5 and the market return is 10% pa. What is the expected return of the stock?

A stock has a beta of 0.5. Its next dividend is expected to be $3, paid one year from now. Dividends are expected to be paid annually and grow by 2% pa forever. Treasury bonds yield 5% pa and the market portfolio's expected return is 10% pa. All returns are effective annual rates. What is the price of the stock now? The security market line (SML) shows the relationship between beta and expected return. Investment projects that plot on the SML would have: Examine the following graph which shows stocks' betas $(\beta)$ and expected returns $(\mu)$: Assume that the CAPM holds and that future expectations of stocks' returns and betas are correctly measured. Which statement is NOT correct?  Portfolio Details Stock Expected return Standard deviation Correlation Beta Dollars invested A 0.2 0.4 0.12 0.5 40 B 0.3 0.8 1.5 80 What is the beta of the above portfolio? Which statement(s) are correct? (i) All stocks that plot on the Security Market Line (SML) are fairly priced. (ii) All stocks that plot above the Security Market Line (SML) are overpriced. (iii) All fairly priced stocks that plot on the Capital Market Line (CML) have zero idiosyncratic risk. Select the most correct response: 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: $$r_\text{WACC before tax} = r_D.\frac{D}{V_L} + r_{EL}.\frac{E_L}{V_L} = \text{Weighted average cost of capital before tax}$$ $$r_\text{WACC after tax} = r_D.(1-t_c).\frac{D}{V_L} + r_{EL}.\frac{E_L}{V_L} = \text{Weighted average cost of capital after tax}$$ $$NI_L=(Rev-COGS-FC-Depr-\mathbf{IntExp}).(1-t_c) = \text{Net Income Levered}$$ $$CFFA_L=NI_L+Depr-CapEx - \varDelta NWC+\mathbf{IntExp} = \text{Cash Flow From Assets Levered}$$ $$NI_U=(Rev-COGS-FC-Depr).(1-t_c) = \text{Net Income Unlevered}$$ $$CFFA_U=NI_U+Depr-CapEx - \varDelta NWC= \text{Cash Flow From Assets Unlevered}$$ Mr Blue, Miss Red and Mrs Green are people with different utility functions. Which of the following statements is NOT correct? 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? 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? 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. 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? 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 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):

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:

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? 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:

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: $\Delta V = \Delta D+ \Delta E$ 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?

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.

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. 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? If a stock's future expected effective annual returns are log-normally distributed, what will be bigger, the stock's or effective annual return? Or would you expect them to be ? 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?

Which of the following statements about ‘negative gearing’ is NOT correct?

Which one of the following capital raisings or payouts involve the sale of shares to existing shareholders only?

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.

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?

Which of the following statements about probability distributions is NOT correct?

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?

Which of the following statements is NOT correct? Assume that all 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.

You deposit money into a bank account. Which of the following statements about this deposit 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). 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? 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.

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?

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?

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): 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). A stock's required total return will decrease when its: 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. 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?

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?

What is the present value of real payments of $100 every year forever, with the first payment in one year? The nominal discount rate is 7% pa and the inflation rate is 4% pa. Question 668 buy and hold, market efficiency, idiom A quote from the famous investor Warren Buffet: "Much success can be attributed to inactivity. Most investors cannot resist the temptation to constantly buy and sell." Buffet is referring to the buy-and-hold strategy which is to buy and never sell shares. Which of the following is a disadvantage of a buy-and-hold strategy? Assume that share markets are semi-strong form efficient. Which of the following is NOT an advantage of the strict buy-and-hold strategy? A disadvantage of the buy-and-hold strategy is that it reduces: Which of the following is NOT a valid method for estimating the beta of a company's stock? Assume that markets are efficient, a long history of past data is available, the stock possesses idiosyncratic and market risk. The variances and standard deviations below denote total risks. For certain shares, the forward-looking Price-Earnings Ratio ($P_0/EPS_1$) is equal to the inverse of the share's total expected return ($1/r_\text{total}$). For what shares is this true? Assume: • The general accounting definition of 'payout ratio' which is dividends per share (DPS) divided by earnings per share (EPS). • All cash flows, earnings and rates are real. Three years ago Frederika bought a house for$400,000.

Now it's worth $600,000, based on recent similar sales in the area. Frederika's residential property has an expected total return of 7% pa. She rents her house out for$2,500 per month, paid in advance. Every 12 months she plans to increase the rental payments.

The present value of 12 months of rental payments is $29,089.48. The future value of 12 months of rental payments one year ahead is$31,125.74.

What is the expected annual capital yield of the property?

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:

An effective semi-annual return of 5% $(r_\text{eff 6mth})$ is equivalent to an effective annual return $(r_\text{eff annual})$ of:

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: If a stock's future expected continuously compounded annual returns are normally distributed, what will be bigger, the stock's or continuously compounded annual return? Or would you expect them to be ? If a stock's expected future prices are log-normally distributed, what will be bigger, the stock's or future price? Or would you expect them to be ? 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 one year, what do you expect the mean and median prices to be? The answer options are given in the same order.

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 mean and median prices to be? The answer options are given in the same order.

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