# Fight Finance

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The required return of a project is 10%, given as an effective annual rate. Assume that the cash flows shown in the table are paid all at once at the given point in time.

What is the Net Present Value (NPV) of the project?

 Project Cash Flows Time (yrs) Cash flow ($) 0 -100 1 0 2 121 What is the Internal Rate of Return (IRR) of the project detailed in the table below? Assume that the cash flows shown in the table are paid all at once at the given point in time. All answers are given as effective annual rates.  Project Cash Flows Time (yrs) Cash flow ($) 0 -100 1 0 2 121

If a project's net present value (NPV) is zero, then its internal rate of return (IRR) will be:

The required return of a building 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.

The building firm is just about to start the project and the client has signed the contract. Initially the firm will pay $100 to the sub-contractors to carry out the work and then will receive an$11 payment from the client in one year and $121 when the project is finished in 2 years. Ignore credit risk. But the building company is considering selling the project to a competitor at different points in time and is pondering the minimum price that they should sell it for.  Project Cash Flows Time (yrs) Cash flow ($) 0 -100 1 11 2 121

Which of the below statements is NOT correct? The project is worth:

The required return of a project is 10%, given as an effective annual rate.

What is the payback period of the project in years?

Assume that the cash flows shown in the table are received smoothly over the year. So the $121 at time 2 is actually earned smoothly from t=1 to t=2.  Project Cash Flows Time (yrs) Cash flow ($) 0 -100 1 11 2 121

A project has the following cash flows:

 Project Cash Flows Time (yrs) Cash flow ($) 0 -400 1 0 2 500 What is the payback period of the project in years? Normally cash flows are assumed to happen at the given time. But here, assume that the cash flows are received smoothly over the year. So the$500 at time 2 is actually earned smoothly from t=1 to t=2.

The below graph shows a project's net present value (NPV) against its annual discount rate.

For what discount rate or range of discount rates would you accept and commence the project?

All answer choices are given as approximations from reading off the graph.

The below graph shows a project's net present value (NPV) against its annual discount rate.

Which of the following statements is NOT correct?

You have $100,000 in the bank. The bank pays interest at 10% pa, given as an effective annual rate. You wish to consume an equal amount now (t=0) and in one year (t=1) and have nothing left in the bank at the end (t=1). How much can you consume at each time? You have$100,000 in the bank. The bank pays interest at 10% pa, given as an effective annual rate.

You wish to consume an equal amount now (t=0), in one year (t=1) and in two years (t=2), and still have $50,000 in the bank after that (t=2). How much can you consume at each time? Your neighbour asks you for a loan of$100 and offers to pay you back $120 in one year. You don't actually have any money right now, but you can borrow and lend from the bank at a rate of 10% pa. Rates are given as effective annual rates. Assume that your neighbour will definitely pay you back. Ignore interest tax shields and transaction costs. The Net Present Value (NPV) of lending to your neighbour is$9.09. Describe what you would do to actually receive a $9.09 cash flow right now with zero net cash flows in the future. An investor owns an empty block of land that has local government approval to be developed into a petrol station, car wash or car park. The council will only allow a single development so the projects are mutually exclusive. All of the development projects have the same risk and the required return of each is 10% pa. Each project has an immediate cost and once construction is finished in one year the land and development will be sold. The table below shows the estimated costs payable now, expected sale prices in one year and the internal rates of returns (IRR's).  Mutually Exclusive Projects Project Costnow ($) 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 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: $r_\text{total}$ , $r_\text{capital}$ , $r_\text{dividend}$. One and a half years ago Frank bought a house for$600,000. Now it's worth only $500,000, based on recent similar sales in the area. The expected total return on Frank's residential property is 7% pa. He rents his house out for$1,600 per month, paid in advance. Every 12 months he plans to increase the rental payments.

The present value of 12 months of rental payments is $18,617.27. The future value of 12 months of rental payments one year in the future is$19,920.48.

What is the expected annual rental yield of the property? Ignore the costs of renting such as maintenance, real estate agent fees and so on.

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?

In February 2020, the RBA cash rate was 0.75% pa and the Australian CPI inflation rate was 1.8% pa.

You currently have $100 in the bank which pays a 0.75% pa interest rate. Apples currently cost$1 each at the shop and inflation is 1.8% pa which is the expected growth rate in the apple price.

This information is summarised in the table below, with some parts missing that correspond to the answer options. All rates are given as effective annual rates. Note that when payments are not specified as real, as in this question, they're conventionally assumed to be nominal.

 Wealth in Dollars and Apples Time (year) Bank account wealth ($) Apple price ($) Wealth in apples 0 100 1 100 1 100.75 1.018 (a) 2 (b) (c) (d)

Which of the following statements is NOT correct? Your:

Which of the following statements is NOT correct?

What is the lowest and highest expected share price and expected return from owning shares in a company over a finite period of time?

Let the current share price be $p_0$, the expected future share price be $p_1$, the expected future dividend be $d_1$ and the expected return be $r$. Define the expected return as:

$r=\dfrac{p_1-p_0+d_1}{p_0}$

The answer choices are stated using inequalities. As an example, the first answer choice "(a) $0≤p<∞$ and $0≤r< 1$", states that the share price must be larger than or equal to zero and less than positive infinity, and that the return must be larger than or equal to zero and less than one.

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.

A stock is just about to pay a dividend of $1 tonight. Future annual dividends are expected to grow by 2% pa. The next dividend of$1 will be paid tonight, and the year after that the dividend will be $1.02 (=1*(1+0.02)^1), and a year later 1.0404 (=1*(1+0.04)^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? 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 $C_1/P_0$? 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)? 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. You currently have$100 in the bank which pays a 10% pa interest rate.

Oranges currently cost $1 each at the shop and inflation is 5% pa which is the expected growth rate in the orange price. This information is summarised in the table below, with some parts missing that correspond to the answer options. All rates are given as effective annual rates. Note that when payments are not specified as real, as in this question, they're conventionally assumed to be nominal.  Wealth in Dollars and Oranges Time (year) Bank account wealth ($) Orange price ($) Wealth in oranges 0 100 1 100 1 110 1.05 (a) 2 (b) (c) (d) Which of the following statements is NOT correct? Your: 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? You just signed up for a 30 year interest-only mortgage with monthly payments of$3,000 per month. The interest rate is 6% pa which is not expected to change.

How much did you borrow? After 15 years, just after the 180th payment at that time, how much will be owing on the mortgage? The interest rate is still 6% and is not expected to change. Remember that the mortgage is interest-only and that mortgage payments are paid in arrears (at the end of the month).

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? A stock just paid its annual dividend of$9. The share price is $60. The required return of the stock is 10% pa as an effective annual rate. What is the implied growth rate of the dividend per year? A residential investment property has an expected nominal total return of 6% pa and nominal capital return of 3% pa. Inflation is expected to be 2% pa. All rates are given as effective annual rates. What are the property's expected real total, capital and income returns? The answer choices below are given in the same order. 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. Which of the following statements about cash in the form of notes and coins is NOT correct? Assume that inflation is positive. Notes and coins: When valuing assets using discounted cash flow (net present value) methods, it is important to consider inflation. To properly deal with inflation: (I) Discount nominal cash flows by nominal discount rates. (II) Discount nominal cash flows by real discount rates. (III) Discount real cash flows by nominal discount rates. (IV) Discount real cash flows by real discount rates. Which of the above statements is or are correct? How can a nominal cash flow be precisely converted into a real cash flow? You expect a nominal payment of$100 in 5 years. The real discount rate is 10% pa and the inflation rate is 3% pa. Which of the following statements is NOT correct?

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? The expression 'you have to spend money to make money' relates to which business decision? The following is the Dividend Discount Model (DDM) used to price stocks: $$P_0=\dfrac{C_1}{r-g}$$ If the assumptions of the DDM hold, which one of the following statements is NOT correct? The long term expected: 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? Most listed Australian companies pay dividends twice per year, the 'interim' and 'final' dividends, which are roughly 6 months apart. You are an equities analyst trying to value the company BHP. You decide to use the Dividend Discount Model (DDM) as a starting point, so you study BHP's dividend history and you find that BHP tends to pay the same interim and final dividend each year, and that both grow by the same rate. You expect BHP will pay a$0.55 interim dividend in six months and a $0.55 final dividend in one year. You expect each to grow by 4% next year and forever, so the interim and final dividends next year will be$0.572 each, and so on in perpetuity.

Assume BHP's cost of equity is 8% pa. All rates are quoted as nominal effective rates. The dividends are nominal cash flows and the inflation rate is 2.5% pa.

What is the current price of a BHP share?

You are an equities analyst trying to value the equity of the Australian telecoms company Telstra, with ticker TLS. In Australia, listed companies like Telstra tend to pay dividends every 6 months. The payment around August is called the final dividend and the payment around February is called the interim dividend. Both occur annually.

• Today is mid-March 2015.
• TLS's last interim dividend of $0.15 was one month ago in mid-February 2015. • TLS's last final dividend of$0.15 was seven months ago in mid-August 2014.

Judging by TLS's dividend history and prospects, you estimate that the nominal dividend growth rate will be 1% pa. Assume that TLS's total nominal cost of equity is 6% pa. The dividends are nominal cash flows and the inflation rate is 2.5% pa. All rates are quoted as nominal effective annual rates. Assume that each month is exactly one twelfth (1/12) of a year, so you can ignore the number of days in each month.

Calculate the current TLS share price.

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. You own a nice suit which you wear once per week on nights out. You bought it one year ago for$600. In your experience, suits used once per week last for 6 years. So you expect yours to last for another 5 years.

Your younger brother said that retro is back in style so he wants to wants to borrow your suit once a week when he goes out. With the increased use, your suit will only last for another 4 years rather than 5.

What is the present value of the cost of letting your brother use your current suit for the next 4 years?

Assume: that bank interest rates are 10% pa, given as an effective annual rate; you will buy a new suit when your current one wears out and your brother will not use the new one; your brother will only use your current suit so he will only use it for the next four years; and the price of a new suit never changes.

You own some nice shoes which you use once per week on date nights. You bought them 2 years ago for $500. In your experience, shoes used once per week last for 6 years. So you expect yours to last for another 4 years. Your younger sister said that she wants to borrow your shoes once per week. With the increased use, your shoes will only last for another 2 years rather than 4. What is the present value of the cost of letting your sister use your current shoes for the next 2 years? Assume: that bank interest rates are 10% pa, given as an effective annual rate; you will buy a new pair of shoes when your current pair wears out and your sister will not use the new ones; your sister will only use your current shoes so she will only use it for the next 2 years; and the price of new shoes never changes. 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. Which of the below statements about effective rates and annualised percentage rates (APR's) is NOT correct? A credit card offers an interest rate of 18% pa, compounding monthly. Find the effective monthly rate, effective annual rate and the effective daily rate. Assume that there are 365 days in a year. All answers are given in the same order: $$r_\text{eff monthly} , r_\text{eff yearly} , r_\text{eff daily}$$ Calculate the effective annual rates of the following three APR's: • A credit card offering an interest rate of 18% pa, compounding monthly. • A bond offering a yield of 6% pa, compounding semi-annually. • An annual dividend-paying stock offering a return of 10% pa compounding annually. All answers are given in the same order: $r_\text{credit card, eff yrly}$, $r_\text{bond, eff yrly}$, $r_\text{stock, eff yrly}$ On his 20th birthday, a man makes a resolution. He will deposit$30 into a bank account at the end of every month starting from now, which is the start of the month. So the first payment will be in one month. He will write in his will that when he dies the money in the account should be given to charity.

The bank account pays interest at 6% pa compounding monthly, which is not expected to change.

If the man lives for another 60 years, how much money will be in the bank account if he dies just after making his last (720th) payment?

You want to buy an apartment priced at $300,000. You have saved a deposit of$30,000. The bank has agreed to lend you the $270,000 as a fully amortising loan with a term of 25 years. The interest rate is 12% pa and is not expected to change. What will be your monthly payments? Remember that mortgage loan payments are paid in arrears (at the end of the month). You want to buy an apartment worth$400,000. You have saved a deposit of $80,000. The bank has agreed to lend you the$320,000 as a fully amortising mortgage loan with a term of 30 years. The interest rate is 6% pa and is not expected to change. What will be your monthly payments?

You just signed up for a 30 year fully amortising mortgage loan with monthly payments of $2,000 per month. The interest rate is 9% pa which is not expected to change. How much did you borrow? After 5 years, how much will be owing on the mortgage? The interest rate is still 9% and is not expected to change. You just signed up for a 30 year fully amortising mortgage loan with monthly payments of$1,500 per month. The interest rate is 9% pa which is not expected to change.

How much did you borrow? After 10 years, how much will be owing on the mortgage? The interest rate is still 9% and is not expected to change.

You just agreed to a 30 year fully amortising mortgage loan with monthly payments of $2,500. The interest rate is 9% pa which is not expected to change. How much did you borrow? After 10 years, how much will be owing on the mortgage? The interest rate is still 9% and is not expected to change. The below choices are given in the same order. You want to buy an apartment priced at$300,000. You have saved a deposit of $30,000. The bank has agreed to lend you the$270,000 as an interest only loan with a term of 25 years. The interest rate is 12% pa and is not expected to change.

What will be your monthly payments? Remember that mortgage payments are paid in arrears (at the end of the month).

You just borrowed $400,000 in the form of a 25 year interest-only mortgage with monthly payments of$3,000 per month. The interest rate is 9% pa which is not expected to change.

You actually plan to pay more than the required interest payment. You plan to pay $3,300 in mortgage payments every month, which your mortgage lender allows. These extra payments will reduce the principal and the minimum interest payment required each month. At the maturity of the mortgage, what will be the principal? That is, after the last (300th) interest payment of$3,300 in 25 years, how much will be owing on the mortgage?

A bank grants a borrower an interest-only residential mortgage loan with a very large 50% deposit and a nominal interest rate of 6% that is not expected to change. Assume that inflation is expected to be a constant 2% pa over the life of the loan. Ignore credit risk.

From the bank's point of view, what is the long term expected nominal capital return of the loan asset?

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? Let the 'income return' of a bond be the coupon at the end of the period divided by the market price now at the start of the period $(C_1/P_0)$. The expected income return of a premium fixed coupon bond is: Which one of the following bonds is trading at a premium? 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.

A European 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 company's forward rate over the second year (from t=1 to t=2)? Give your answer as an effective annual rate, which is how the above bond yields are quoted.

An Australian company just issued two bonds:

• A 6-month zero coupon bond at a yield of 6% pa, and
• A 12 month zero coupon bond at a yield of 7% pa.

What is the company's forward rate from 6 to 12 months? Give your answer as an APR compounding every 6 months, which is how the above bond yields are quoted.

An Australian company just issued two bonds paying semi-annual coupons:

• 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're trying to save enough money to buy your first car which costs $2,500. You can save$100 at the end of each month starting from now. You currently have no money at all. You just opened a bank account with an interest rate of 6% pa payable monthly.

How many months will it take to save enough money to buy the car? Assume that the price of the car will stay the same over time.

Your main expense is fuel for your car which costs $100 per month. You just refueled, so you won't need any more fuel for another month (first payment at t=1 month). You have$2,500 in a bank account which pays interest at a rate of 6% pa, payable monthly. Interest rates are not expected to change.

Assuming that you have no income, in how many months time will you not have enough money to fully refuel your car?

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?

A young lady is trying to decide if she should attend university. Her friends say that she should go to university because she is more likely to meet a clever young man than if she begins full time work straight away.

What's the correct way to classify this item from a capital budgeting perspective when trying to find the Net Present Value of going to university rather than working?

The opportunity to meet a desirable future spouse should be classified as:

A man is thinking about taking a day off from his casual painting job to relax.

He just woke up early in the morning and he's about to call his boss to say that he won't be coming in to work.

But he's thinking about the hours that he could work today (in the future) which are:

A man has taken a day off from his casual painting job to relax.

It's the end of the day and he's thinking about the hours that he could have spent working (in the past) which are now:

Find Candys Corporation's Cash Flow From Assets (CFFA), also known as Free Cash Flow to the Firm (FCFF), over the year ending 30th June 2013.

 Candys Corp Income Statement for year ending 30th June 2013 $m Sales 200 COGS 50 Operating expense 10 Depreciation 20 Interest expense 10 Income before tax 110 Tax at 30% 33 Net income 77  Candys Corp Balance Sheet as at 30th June 2013 2012$m $m Assets Current assets 220 180 PPE Cost 300 340 Accumul. depr. 60 40 Carrying amount 240 300 Total assets 460 480 Liabilities Current liabilities 175 190 Non-current liabilities 135 130 Owners' equity Retained earnings 50 60 Contributed equity 100 100 Total L and OE 460 480 Note: all figures are given in millions of dollars ($m).

Find Ching-A-Lings Corporation's Cash Flow From Assets (CFFA), also known as Free Cash Flow to the Firm (FCFF), over the year ending 30th June 2013.

 Ching-A-Lings Corp Income Statement for year ending 30th June 2013 $m Sales 100 COGS 20 Depreciation 20 Rent expense 11 Interest expense 19 Taxable Income 30 Taxes at 30% 9 Net income 21  Ching-A-Lings Corp Balance Sheet as at 30th June 2013 2012$m $m Inventory 49 38 Trade debtors 14 2 Rent paid in advance 5 5 PPE 400 400 Total assets 468 445 Trade creditors 4 10 Bond liabilities 200 190 Contributed equity 145 145 Retained profits 119 100 Total L and OE 468 445 Note: All figures are given in millions of dollars ($m).

The cash flow from assets was:

To value a business's assets, the free cash flow of the firm (FCFF, also called CFFA) needs to be calculated. This requires figures from the firm's income statement and balance sheet. For what figures is the balance sheet needed? Note that the balance sheet is sometimes also called the statement of financial position.

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.

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.

Why is Capital Expenditure (CapEx) subtracted in the Cash Flow From Assets (CFFA) formula?

$$CFFA=NI+Depr-CapEx - \Delta NWC+IntExp$$

Find Trademark Corporation's Cash Flow From Assets (CFFA), also known as Free Cash Flow to the Firm (FCFF), over the year ending 30th June 2013.

 Trademark Corp Income Statement for year ending 30th June 2013 $m Sales 100 COGS 25 Operating expense 5 Depreciation 20 Interest expense 20 Income before tax 30 Tax at 30% 9 Net income 21  Trademark Corp Balance Sheet as at 30th June 2013 2012$m $m Assets Current assets 120 80 PPE Cost 150 140 Accumul. depr. 60 40 Carrying amount 90 100 Total assets 210 180 Liabilities Current liabilities 75 65 Non-current liabilities 75 55 Owners' equity Retained earnings 10 10 Contributed equity 50 50 Total L and OE 210 180 Note: all figures are given in millions of dollars ($m).

Find UniBar Corp's Cash Flow From Assets (CFFA), also known as Free Cash Flow to the Firm (FCFF), over the year ending 30th June 2013.

 UniBar Corp Income Statement for year ending 30th June 2013 $m Sales 80 COGS 40 Operating expense 15 Depreciation 10 Interest expense 5 Income before tax 10 Tax at 30% 3 Net income 7  UniBar Corp Balance Sheet as at 30th June 2013 2012$m $m Assets Current assets 120 90 PPE Cost 360 320 Accumul. depr. 40 30 Carrying amount 320 290 Total assets 440 380 Liabilities Current liabilities 110 60 Non-current liabilities 190 180 Owners' equity Retained earnings 95 95 Contributed equity 45 45 Total L and OE 440 380 Note: all figures are given in millions of dollars ($m).

Find Piano Bar's Cash Flow From Assets (CFFA), also known as Free Cash Flow to the Firm (FCFF), over the year ending 30th June 2013.

 Piano Bar Income Statement for year ending 30th June 2013 $m Sales 310 COGS 185 Operating expense 20 Depreciation 15 Interest expense 10 Income before tax 80 Tax at 30% 24 Net income 56  Piano Bar Balance Sheet as at 30th June 2013 2012$m $m Assets Current assets 240 230 PPE Cost 420 400 Accumul. depr. 50 35 Carrying amount 370 365 Total assets 610 595 Liabilities Current liabilities 180 190 Non-current liabilities 290 265 Owners' equity Retained earnings 90 90 Contributed equity 50 50 Total L and OE 610 595 Note: all figures are given in millions of dollars ($m).

Which one of the following will increase the Cash Flow From Assets in this year for a tax-paying firm, all else remaining constant?

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 World Bar's Cash Flow From Assets (CFFA), also known as Free Cash Flow to the Firm (FCFF), over the year ending 30th June 2013.

 World Bar Income Statement for year ending 30th June 2013 $m Sales 300 COGS 150 Operating expense 50 Depreciation 40 Interest expense 10 Taxable income 50 Tax at 30% 15 Net income 35  World Bar Balance Sheet as at 30th June 2013 2012$m $m Assets Current assets 200 230 PPE Cost 400 400 Accumul. depr. 75 35 Carrying amount 325 365 Total assets 525 595 Liabilities Current liabilities 150 205 Non-current liabilities 235 250 Owners' equity Retained earnings 100 100 Contributed equity 40 40 Total L and OE 525 595 Note: all figures above and below are given in millions of dollars ($m).

Value the following business project to manufacture a new product.

 Project Data Project life 2 yrs Initial investment in equipment $6m Depreciation of equipment per year$3m Expected sale price of equipment at end of project $0.6m Unit sales per year 4m Sale price per unit$8 Variable cost per unit $5 Fixed costs per year, paid at the end of each year$1m Interest expense per year 0 Tax rate 30% Weighted average cost of capital after tax per annum 10%

Notes

1. The firm's current assets and current liabilities are $3m and$2m respectively right now. This net working capital will not be used in this project, it will be used in other unrelated projects.
Due to the project, current assets (mostly inventory) will grow by $2m initially (at t = 0), and then by$0.2m at the end of the first year (t=1).
Current liabilities (mostly trade creditors) will increase by $0.1m at the end of the first year (t=1). At the end of the project, the net working capital accumulated due to the project can be sold for the same price that it was bought. 2. The project cost$0.5m to research which was incurred one year ago.

Assumptions

• All cash flows occur at the start or end of the year as appropriate, not in the middle or throughout the year.
• All rates and cash flows are real. The inflation rate is 3% pa.
• All rates are given as effective annual rates.
• The business considering the project is run as a 'sole tradership' (run by an individual without a company) and is therefore eligible for a 50% capital gains tax discount when the equipment is sold, as permitted by the Australian Tax Office.

What is the expected net present value (NPV) of the project?

Find Scubar Corporation's Cash Flow From Assets (CFFA), also known as Free Cash Flow to the Firm (FCFF), over the year ending 30th June 2013.

 Scubar Corp Income Statement for year ending 30th June 2013 $m Sales 200 COGS 60 Depreciation 20 Rent expense 11 Interest expense 19 Taxable Income 90 Taxes at 30% 27 Net income 63  Scubar Corp Balance Sheet as at 30th June 2013 2012$m $m Inventory 60 50 Trade debtors 19 6 Rent paid in advance 3 2 PPE 420 400 Total assets 502 458 Trade creditors 10 8 Bond liabilities 200 190 Contributed equity 130 130 Retained profits 162 130 Total L and OE 502 458 Note: All figures are given in millions of dollars ($m).

The cash flow from assets was:

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:

$$NI=(Rev-COGS-FC-Depr-IntExp).(1-t_c )$$ $$CFFA=NI+Depr-CapEx - ΔNWC+IntExp$$

Find Sidebar Corporation's Cash Flow From Assets (CFFA), also known as Free Cash Flow to the Firm (FCFF), over the year ending 30th June 2013.

 Sidebar Corp Income Statement for year ending 30th June 2013 $m Sales 405 COGS 100 Depreciation 34 Rent expense 22 Interest expense 39 Taxable Income 210 Taxes at 30% 63 Net income 147  Sidebar Corp Balance Sheet as at 30th June 2013 2012$m $m Cash 0 0 Inventory 70 50 Trade debtors 11 16 Rent paid in advance 4 3 PPE 700 680 Total assets 785 749 Trade creditors 11 19 Bond liabilities 400 390 Contributed equity 220 220 Retained profits 154 120 Total L and OE 785 749 Note: All figures are given in millions of dollars ($m).

The cash flow from assets was:

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?

Read the following financial statements and calculate the firm's free cash flow over the 2014 financial year.

 UBar Corp Income Statement for year ending 30th June 2014 $m Sales 293 COGS 200 Rent expense 15 Gas expense 8 Depreciation 10 EBIT 60 Interest expense 0 Taxable income 60 Taxes 18 Net income 42  UBar Corp Balance Sheet as at 30th June 2014 2013$m $m Assets Cash 30 29 Accounts receivable 5 7 Pre-paid rent expense 1 0 Inventory 50 46 PPE 290 300 Total assets 376 382 Liabilities Trade payables 20 18 Accrued gas expense 3 2 Non-current liabilities 0 0 Contributed equity 212 212 Retained profits 136 150 Asset revaluation reserve 5 0 Total L and OE 376 382 Note: all figures are given in millions of dollars ($m).

The firm's free cash flow over the 2014 financial year was:

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).

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).

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.

In the below term structure of interest rates equation, all rates are effective annual yields and the numbers in subscript represent the years that the yields are measured over:

$$(1+r_{0-3})^3 = (1+r_{0-1})(1+r_{1-2})(1+r_{2-3})$$

Which of the following statements is NOT correct?

In the below term structure of interest rates equation, all rates are effective annual yields and the numbers in subscript represent the years that the yields are measured over:

$$(1+r_{0-3})^3 = (1+r_{0-1})(1+r_{1-2})(1+r_{2-3})$$

Which of the following statements is NOT correct?

Which of the following statements about yield curves is NOT correct?

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.

An Australian company just issued two bonds:

• A 1 year zero coupon bond at a yield of 10% pa, and
• A 2 year zero coupon bond at a yield of 8% 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 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?

You're trying to save enough money for a deposit to buy a house. You want to buy a house worth $400,000 and the bank requires a 20% deposit ($80,000) before it will give you a loan for the other $320,000 that you need. You currently have no savings, but you just started working and can save$2,000 per month, with the first payment in one month from now. Bank interest rates on savings accounts are 4.8% pa with interest paid monthly and interest rates are not expected to change.

How long will it take to save the $80,000 deposit? Round your answer up to the nearest month. Jan asks you for a loan. He wants$100 now and offers to pay you back $120 in 1 year. You can borrow and lend from the bank at an interest rate of 10% pa, given as an effective annual rate. Ignore credit risk. Remember: $$V_0 = \frac{V_t}{(1+r_\text{eff})^t}$$ Will you or Jan's deal? For a price of$129, Joanne will sell you a share which is expected to pay a $30 dividend in one year, and a$10 dividend every year after that forever. So the stock's dividends will be $30 at t=1,$10 at t=2, $10 at t=3, and$10 forever onwards.

The required return of the stock is 10% pa.

Would you like to the share or politely ?

Your friend wants to borrow $1,000 and offers to pay you back$100 in 6 months, with more $100 payments at the end of every month for another 11 months. So there will be twelve$100 payments in total. She says that 12 payments of $100 equals$1,200 so she's being generous.

If interest rates are 12% pa, given as an APR compounding monthly, what is the Net Present Value (NPV) of your friend's deal?

Which of the following investable assets are NOT suitable for valuation using PE multiples techniques?

Which firms tend to have low forward-looking price-earnings (PE) ratios?

Only consider firms with positive earnings, disregard firms with negative earnings and therefore negative PE ratios.

Estimate the Chinese bank ICBC's share price using a backward-looking price earnings (PE) multiples approach with the following assumptions and figures only. Note that the renminbi (RMB) is the Chinese currency, also known as the yuan (CNY).

• The 4 major Chinese banks ICBC, China Construction Bank (CCB), Bank of China (BOC) and Agricultural Bank of China (ABC) are comparable companies;
• ICBC 's historical earnings per share (EPS) is RMB 0.74;
• CCB's backward-looking PE ratio is 4.59;
• BOC 's backward-looking PE ratio is 4.78;
• ABC's backward-looking PE ratio is also 4.78;

Note: Figures sourced from Google Finance on 25 March 2014. Share prices are from the Shanghai stock exchange.

Which firms tend to have high forward-looking price-earnings (PE) ratios?

Which firms tend to have low forward-looking price-earnings (PE) ratios? Only consider firms with positive PE ratios.

Estimate the French bank Societe Generale's share price using a backward-looking price earnings (PE) multiples approach with the following assumptions and figures only. Note that EUR is the euro, the European monetary union's currency.

• The 4 major European banks Credit Agricole (ACA), Deutsche Bank AG (DBK), UniCredit (UCG) and Banco Santander (SAN) are comparable companies to Societe Generale (GLE);
• Societe Generale's (GLE's) historical earnings per share (EPS) is EUR 2.92;
• ACA's backward-looking PE ratio is 16.29 and historical EPS is EUR 0.84;
• DBK's backward-looking PE ratio is 25.01 and historical EPS is EUR 1.26;
• SAN's backward-looking PE ratio is 14.71 and historical EPS is EUR 0.47;
• UCG's backward-looking PE ratio is 15.78 and historical EPS is EUR 0.40;

Note: Figures sourced from Google Finance on 27 March 2015.

A firm pays out all of its earnings as dividends. Because of this, the firm has no real growth in earnings, dividends or stock price since there is no re-investment back into the firm to buy new assets and make higher earnings. The dividend discount model is suitable to value this company.

The firm's revenues and costs are expected to increase by inflation in the foreseeable future. The firm has no debt. It operates in the services industry and has few physical assets so there is negligible depreciation expense and negligible net working capital required.

Which of the following statements about this firm's PE ratio is NOT correct? The PE ratio should:

Note: The inverse of x is 1/x.

Question 749  Multiples valuation, PE ratio, price to revenue ratio, price to book ratio, NPV

A real estate agent says that the price of a house in Sydney Australia is approximately equal to the gross weekly rent times 1000.

What type of valuation method is the real estate agent using?

A three year project's NPV is negative. The cash flows of the project include a negative cash flow at the very start and positive cash flows over its short life. The required return of the project is 10% pa. Select the most correct statement.

A project has an internal rate of return (IRR) which is greater than its required return. Select the most correct statement.

A project's net present value (NPV) is negative. Select the most correct statement.

A project's NPV is positive. Select the most correct statement:

A project has the following cash flows:

 Project Cash Flows Time (yrs) Cash flow ($) 0 -400 1 0 2 500 The required return on the project is 10%, given as an effective annual rate. What is the Internal Rate of Return (IRR) of this project? The following choices are effective annual rates. Assume that the cash flows shown in the table are paid all at once at the given point in time. A project's Profitability Index (PI) is less than 1. Select the most correct statement: Question 218 NPV, IRR, profitability index, average accounting return Which of the following statements is NOT correct? All other things remaining equal, a project is worse if its: 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?

For a price of $100, Vera will sell you a 2 year bond paying semi-annual coupons of 10% pa. The face value of the bond is$100. Other bonds with similar risk, maturity and coupon characteristics trade at a yield of 8% pa.

Would you like to her bond or politely ?

For a price of $100, Carol will sell you a 5 year bond paying semi-annual coupons of 16% pa. The face value of the bond is$100. Other bonds with similar risk, maturity and coupon characteristics trade at a yield of 12% pa.

Would you like to her bond or politely ?

For a price of $100, Andrea will sell you a 2 year bond paying annual coupons of 10% pa. The face value of the bond is$100. Other bonds with the same risk, maturity and coupon characteristics trade at a yield of 6% pa.

Would you like to the bond or politely ?

A three year bond has a face value of $100, a yield of 10% and a fixed coupon rate of 5%, paid semi-annually. What is its price? A fixed coupon bond was bought for$90 and paid its annual coupon of $3 one year later (at t=1 year). Just after the coupon was paid, the bond price was$92 (at t=1 year). What was the total return, capital return and income return? Calculate your answers as effective annual rates.

The choices are given in the same order: $r_\text{total},r_\text{capital},r_\text{income}$.

Bonds A and B are issued by the same company. They have the same face value, maturity, seniority and coupon payment frequency. The only difference is that bond A has a 5% coupon rate, while bond B has a 10% coupon rate. The yield curve is flat, which means that yields are expected to stay the same.

Which bond would have the higher current price?

Bonds A and B are issued by the same Australian company. Both bonds yield 7% pa, and they have the same face value ($100), maturity, seniority, and payment frequency. The only difference is that bond A pays coupons of 10% pa and bond B pays coupons of 5% pa. Which of the following statements is true about the bonds' prices? Bonds X and Y are issued by different companies, but they both pay a semi-annual coupon of 10% pa and they have the same face value ($100) and maturity (3 years).

The only difference is that bond X and Y's yields are 8 and 12% pa respectively. Which of the following statements is true?

Bonds X and Y are issued by different companies, but they both pay a semi-annual coupon of 10% pa and they have the same face value ($100), maturity (3 years) and yield (10%) as each other. Which of the following statements is true? A firm wishes to raise$20 million now. They will issue 8% pa semi-annual coupon bonds that will mature in 5 years and have a face value of $100 each. Bond yields are 6% pa, given as an APR compounding every 6 months, and the yield curve is flat. How many bonds should the firm issue? Which one of the following bonds is trading at par? The coupon rate of a fixed annual-coupon bond is constant (always the same). What can you say about the income return ($r_\text{income}$) of a fixed annual coupon bond? Remember that: $$r_\text{total} = r_\text{income} + r_\text{capital}$$ $$r_\text{total, 0 to 1} = \frac{c_1}{p_0} + \frac{p_1-p_0}{p_0}$$ Assume that there is no change in the bond's total annual yield to maturity from when it is issued to when it matures. Select the most correct statement. From its date of issue until maturity, the income return of a fixed annual coupon: Bonds X and Y are issued by the same 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 pays coupons of 6% pa and bond Y pays coupons of 8% pa. Which of the following statements is true?

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? Bonds X and Y are issued by the same US company. Both bonds yield 6% pa, and they have the same face value ($100), maturity, seniority, and payment frequency.

The only difference is that bond X pays coupons of 8% pa and bond Y pays coupons of 12% pa. Which of the following statements is true?

The expression 'my word is my bond' is often used in everyday language to make a serious promise.

Why do you think this expression uses the metaphor of a bond rather than a share?

Risk-free government bonds that have coupon rates greater than their yields:

A 'fully amortising' loan can also be called a:

An investor bought a 20 year 5% pa fixed coupon government bond priced at par. The face value is $100. Coupons are paid semi-annually and the next one is in 6 months. Six months later, just after the coupon at that time was paid, yields suddenly and unexpectedly rose to 5.5% pa. Note that all yields above are given as APR's compounding semi-annually. What was the bond investors' historical total return over that first 6 month period, given as an effective semi-annual rate? The following equation is called the Dividend Discount Model (DDM), Gordon Growth Model or the perpetuity with growth formula: $$P_0 = \frac{ C_1 }{ r - g }$$ What is $g$? The value $g$ is the long term expected: For a price of$6, Carlos will sell you a share which will pay a dividend of $1 in one year and every year after that forever. The required return of the stock is 10% pa. Would you like to his share or politely ? You want to buy an apartment worth$500,000. You have saved a deposit of $50,000. The bank has agreed to lend you the$450,000 as a fully amortising mortgage loan with a term of 25 years. The interest rate is 6% pa and is not expected to change.

What will be your monthly payments?

You 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 with monthly payments of$1,000 per month. The interest rate is 6% pa which is not expected to change.

How much did you borrow? After 20 years, how much will be owing on the mortgage? The interest rate is still 6% and is not expected to change.

Which of the following statements about the capital and income returns of a 25 year fully amortising loan asset is correct?

Assume that the yield curve (which shows total returns over different maturities) is flat and is not expected to change.

Over the 25 years from issuance to maturity, a fully amortising loan's expected annual effective:

Many Australian home loans that are interest-only actually require payments to be made on a fully amortising basis after a number of years.

You decide to borrow $600,000 from the bank at an interest rate of 4.25% pa for 25 years. The payments will be interest-only for the first 10 years (t=0 to 10 years), then they will have to be paid on a fully amortising basis for the last 15 years (t=10 to 25 years). Assuming that interest rates will remain constant, what will be your monthly payments over the first 10 years from now, and then the next 15 years after that? The answer options are given in the same order. You just entered into a fully amortising home loan with a principal of$600,000, a variable interest rate of 4.25% pa and a term of 25 years.

Immediately after settling the loan, the variable interest rate suddenly falls to 4% pa! You can't believe your luck. Despite this, you plan to continue paying the same home loan payments as you did before. How long will it now take to pay off your home loan?

Assume that the lower interest rate was granted immediately and that rates were and are now again expected to remain constant. Round your answer up to the nearest whole month.

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: $$\text{Proportional Increase} = \dfrac{V_\text{0,interest only}}{V_\text{0,fully amortising}} - 1$$ 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.

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? 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.

In Australia in the 1980's, inflation was around 8% pa, and residential mortgage loan interest rates were around 14%.

In 2013, inflation was around 2.5% pa, and residential mortgage loan interest rates were around 4.5%.

If a person can afford constant mortgage loan payments of $2,000 per month, how much more can they borrow when interest rates are 4.5% pa compared with 14.0% pa? Give your answer as a proportional increase over the amount you could borrow when interest rates were high $(V_\text{high rates})$, so: $$\text{Proportional increase} = \dfrac{V_\text{low rates}-V_\text{high rates}}{V_\text{high rates}}$$ 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 (APR's) compounding per month. Which of the following statements about the capital and income returns of an interest-only loan is correct? Assume that the yield curve (which shows total returns over different maturities) is flat and is not expected to change. An interest-only loan's expected: 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:

$$\text{Proportional Increase} = \dfrac{V_\text{0,interest only}}{V_\text{0,fully amortising}} - 1$$

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?

A business project is expected to cost $100 now (t=0), then pay$10 at the end of the third (t=3), fourth, fifth and sixth years, and then grow by 5% pa every year forever. So the cash flow will be $10.5 at the end of the seventh year (t=7), then$11.025 at the end of the eighth year (t=8) and so on perpetually. The total required return is 10℅ pa.

Which of the following formulas will NOT give the correct net present value of the project?

A stock is expected to pay its first dividend of $20 in 3 years (t=3), which it will continue to pay for the next nine years, so there will be ten$20 payments altogether with the last payment in year 12 (t=12).

From the thirteenth year onward, the dividend is expected to be 4% more than the previous year, forever. So the dividend in the thirteenth year (t=13) will be $20.80, then$21.632 in year 14, and so on forever. The required return of the stock is 10% pa. All rates are effective annual rates. Calculate the current (t=0) stock price.

A 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 project has the following cash flows. 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 $250 at time 2 is actually earned smoothly from t=1 to t=2:  Project Cash Flows Time (yrs) Cash flow ($) 0 -400 1 200 2 250

What is the payback period of the project in years?

A project has the following cash flows. 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 $105 at time 2 is actually earned smoothly from t=1 to t=2:  Project Cash Flows Time (yrs) Cash flow ($) 0 -90 1 30 2 105

What is the payback period of the project in years?

A firm is considering a business project which costs $11m now and is expected to pay a constant$1m at the end of every year forever.

Assume that the initial $11m cost is funded using the firm's existing cash so no new equity or debt will be raised. The cost of capital is 10% pa. Which of the following statements about net present value (NPV), internal rate of return (IRR) and payback period is NOT correct? Which of the following companies is most suitable for valuation using PE multiples techniques? Which of the following investable assets is the LEAST suitable for valuation using PE multiples techniques? A mature firm has constant expected future earnings and dividends. Both amounts are equal. So earnings and dividends are expected to be equal and unchanging. Which of the following statements is NOT correct? Private equity firms are known to buy medium sized private companies operating in the same industry, merge them together into a larger company, and then sell it off in a public float (initial public offering, IPO). If medium-sized private companies trade at PE ratios of 5 and larger listed companies trade at PE ratios of 15, what return can be achieved from this strategy? Assume that: • The medium-sized companies can be bought, merged and sold in an IPO instantaneously. • There are no costs of finding, valuing, merging and restructuring the medium sized companies. Also, there is no competition to buy the medium-sized companies from other private equity firms. • The large merged firm's earnings are the sum of the medium firms' earnings. • The only reason for the difference in medium and large firm's PE ratios is due to the illiquidity of the medium firms' shares. • Return is defined as: $r_{0→1} = (p_1-p_0+c_1)/p_0$ , where time zero is just before the merger and time one is just after. A firm has 1 million shares which trade at a price of$30 each. The firm is expected to announce earnings of $3 million at the end of the year and pay an annual dividend of$1.50 per share.

What is the firm's (forward looking) price/earnings (PE) ratio?

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 backwards-looking price-earnings ratio?

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 backwards-looking price-earnings ratio?

A firm has 2m shares and a market capitalisation of equity of $30m. The firm just announced earnings of$5m and paid an annual dividend of $0.75 per share. What is the firm's (backward looking) price/earnings (PE) ratio? 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. 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 is the discount rate '$r_\text{eff}$' in this equation? A share was bought for$20 (at t=0) and paid its annual dividend of $3 one year later (at t=1). Just after the dividend was paid, the share price was$16 (at t=1). What was the total return, capital return and income return? Calculate your answers as effective annual rates.

The choices are given in the same order: $r_\text{total},r_\text{capital},r_\text{income}$.

The following is the Dividend Discount Model (DDM) used to price stocks:

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

Assume that the assumptions of the DDM hold and that the time period is measured in years.

Which of the following is equal to the expected dividend in 3 years, $d_3$?

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

$$p_0=\frac{d_1}{r_\text{eff}-g_\text{eff}}$$

Which expression is NOT equal to the expected capital return?

You're about to buy a car. These are the cash flows of the two different cars that you can buy:

• You can buy an old car for $5,000 now, for which you will have to buy$90 of fuel at the end of each week from the date of purchase. The old car will last for 3 years, at which point you will sell the old car for $500. • Or you can buy a new car for$14,000 now for which you will have to buy $50 of fuel at the end of each week from the date of purchase. The new car will last for 4 years, at which point you will sell the new car for$1,000.

Bank interest rates are 10% pa, given as an effective annual rate. Assume that there are exactly 52 weeks in a year. Ignore taxes and environmental and pollution factors.

Should you buy the or the ?

Details of two different types of desserts or edible treats are given below:

• High-sugar treats like candy, chocolate and ice cream make a person very happy. High sugar treats are cheap at only $2 per day. • Low-sugar treats like nuts, cheese and fruit make a person equally happy if these foods are of high quality. Low sugar treats are more expensive at$4 per day.

The advantage of low-sugar treats is that a person only needs to pay the dentist $2,000 for fillings and root canal therapy once every 15 years. Whereas with high-sugar treats, that treatment needs to be done every 5 years. The real discount rate is 10%, given as an effective annual rate. Assume that there are 365 days in every year and that all cash flows are real. The inflation rate is 3% given as an effective annual rate. Find the equivalent annual cash flow (EAC) of the high-sugar treats and low-sugar treats, including dental costs. The below choices are listed in that order. Ignore the pain of dental therapy, personal preferences and other factors. You just bought a nice dress which you plan to wear once per month on nights out. You bought it a moment ago for$600 (at t=0). In your experience, dresses used once per month last for 6 years.

Your younger sister is a student with no money and wants to borrow your dress once a month when she hits the town. With the increased use, your dress will only last for another 3 years rather than 6.

What is the present value of the cost of letting your sister use your current dress for the next 3 years?

Assume: that bank interest rates are 10% pa, given as an effective annual rate; you will buy a new dress when your current one wears out; your sister will only use the current dress, not the next one that you will buy; and the price of a new dress never changes.

A low-quality second-hand car can be bought now for $1,000 and will last for 1 year before it will be scrapped for nothing. A high-quality second-hand car can be bought now for$4,900 and it will last for 5 years before it will be scrapped for nothing.

What is the equivalent annual cost of each car? Assume a discount rate of 10% pa, given as an effective annual rate.

The answer choices are given as the equivalent annual cost of the low-quality car and then the high quality car.

A stock is expected to pay a dividend of $1 in one year. Its future annual dividends are expected to grow by 10% pa. So the first dividend of$1 is in one year, and the year after that the dividend will be $1.1 (=1*(1+0.1)^1), and a year later$1.21 (=1*(1+0.1)^2) and so on forever.

Its required total return is 30% pa. The total required return and growth rate of dividends are given as effective annual rates. The stock is fairly priced.

Calculate the pay back period of buying the stock and holding onto it forever, assuming that the dividends are received as at each time, not smoothly over each year.

One year ago you bought $100,000 of shares partly funded using a margin loan. The margin loan size was$70,000 and the other $30,000 was your own wealth or 'equity' in the share assets. The interest rate on the margin loan was 7.84% pa. Over the year, the shares produced a dividend yield of 4% pa and a capital gain of 5% pa. What was the total return on your wealth? Ignore taxes, assume that all cash flows (interest payments and dividends) were paid and received at the end of the year, and all rates above are effective annual rates. Hint: Remember that wealth in this context is your equity (E) in the house asset (V = D+E) which is funded by the loan (D) and your deposit or equity (E). You just bought a house worth$1,000,000. You financed it with an $800,000 mortgage loan and a deposit of$200,000.

You estimate that:

• The house has a beta of 1;
• The mortgage loan has a beta of 0.2.

What is the beta of the equity (the $200,000 deposit) that you have in your house? Also, if the risk free rate is 5% pa and the market portfolio's return is 10% pa, what is the expected return on equity in your house? Ignore taxes, assume that all cash flows (interest payments and rent) were paid and received at the end of the year, and all rates are effective annual rates. 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 $r_f$? A firm wishes to raise$100 million now. The firm's current market value of equity is $300m and the market price per share is$5. They estimate that they'll be able to issue shares in a rights issue at a subscription price of $4. All answers are rounded to 6 decimal places. Ignore the time value of money and assume that all shareholders exercise their rights. Which of the following statements is NOT correct? 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: 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 ? 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 ? A firm has a debt-to-equity ratio of 60%. What is its debt-to-assets ratio? 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?

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 manufacturing company is considering a new project in the more risky services industry. The cash flows from assets (CFFA) are estimated for the new project, with interest expense excluded from the calculations. To get the levered value of the project, what should these unlevered cash flows be discounted by?

Assume that the manufacturing firm has a target debt-to-assets ratio that it sticks to.

The US firm Google operates in the online advertising business. In 2011 Google bought Motorola Mobility which manufactures mobile phones.

Assume the following:

• Google had a 10% after-tax weighted average cost of capital (WACC) before it bought Motorola.
• Motorola had a 20% after-tax WACC before it merged with Google.
• Google and Motorola have the same level of gearing.
• Both companies operate in a classical tax system.

You are a manager at Motorola. You must value a project for making mobile phones. Which method(s) will give the correct valuation of the mobile phone manufacturing project? Select the most correct answer.

The mobile phone manufacturing project's:

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?

The hardest and most important aspect of business project valuation is the estimation of the:

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?

One of Miller and Modigliani's (M&M's) important insights is that a firm's managers should not try to achieve a particular level of leverage in a world with zero taxes and perfect information since investors can make their own leverage. Therefore corporate capital structure policy is irrelevant since investors can achieve their own desired leverage at the personal level by borrowing or lending on their own.

This principal of 'home-made' or 'do-it-yourself' leverage can also be applied to other topics. Read the following statements to decide which are true:

(I) Payout policy: a firm's managers should not try to achieve a particular pattern of equity payout.

(II) Agency costs: a firm's managers should not try to minimise agency costs.

(III) Diversification: a firm's managers should not try to diversify across industries.

(IV) Shareholder wealth: a firm's managers should not try to maximise shareholders' wealth.

Which of the above statement(s) are true?

The following table shows a sample of historical total returns of shares in two different companies A and B.

 Stock Returns Total effective annual returns Year $r_A$ $r_B$ 2007 0.2 0.4 2008 0.04 -0.2 2009 -0.1 -0.3 2010 0.18 0.5

What is the historical sample covariance ($\hat{\sigma}_{A,B}$) and correlation ($\rho_{A,B}$) of stock A and B's total effective annual returns?

Stock A and B's returns have a correlation of 0.3. Which statement is NOT correct?

 Portfolio Details Stock Expected return Standard deviation Correlation Dollars invested A 0.1 0.4 0.5 60 B 0.2 0.6 140

What is the expected return of the above portfolio?

 Portfolio Details Stock Expected return Standard deviation Covariance $(\sigma_{A,B})$ Beta Dollars invested A 0.2 0.4 0.12 0.5 40 B 0.3 0.8 1.5 80

What is the standard deviation (not variance) of the above portfolio? Note that the stocks' covariance is given, not correlation.

You're the boss of an investment bank's equities research team. Your five analysts are each trying to find the expected total return over the next year of shares in a mining company. The mining firm:

• Is regarded as a mature company since it's quite stable in size and was floated around 30 years ago. It is not a high-growth company;
• Share price is very sensitive to changes in the price of the market portfolio, economic growth, the exchange rate and commodities prices. Due to this, its standard deviation of total returns is much higher than that of the market index;
• Experienced tough times in the last 10 years due to unexpected falls in commodity prices.
• Shares are traded in an active liquid market.
Your team of analysts present their findings, and everyone has different views. While there's no definitive true answer, whose calculation of the expected total return is the most plausible?

Assume that:

• The analysts' source data is correct and true, but their inferences might be wrong;
• All returns and yields are given as effective annual nominal rates.

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 itself?

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

What is the covariance of a variable X with a constant C?

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

The standard deviation and variance of a stock's annual returns are calculated over a number of years. The units of the returns are percent per annum $(\% pa)$.

What are the units of the standard deviation $(\sigma)$ and variance $(\sigma^2)$ of returns respectively?

Hint: Visit Wikipedia to understand the difference between percentage points $(\text{pp})$ and percent $(\%)$.

Let the variance of returns for a share per month be $\sigma_\text{monthly}^2$.

What is the formula for the variance of the share's returns per year $(\sigma_\text{yearly}^2)$?

Assume that returns are independently and identically distributed (iid) so they have zero auto correlation, meaning that if the return was higher than average today, it does not indicate that the return tomorrow will be higher or lower than average.

Let the standard deviation of returns for a share per month be $\sigma_\text{monthly}$.

What is the formula for the standard deviation of the share's returns per year $(\sigma_\text{yearly})$?

Assume that returns are independently and identically distributed (iid) so they have zero auto correlation, meaning that if the return was higher than average today, it does not indicate that the return tomorrow will be higher or lower than average.

Diversification in a portfolio of two assets works best when the correlation between their returns is:

Diversification is achieved by investing in a large amount of stocks. What type of risk is reduced by diversification?

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

A fairly priced stock has an expected return equal to the market's. Treasury bonds yield 5% pa and the market portfolio's expected return is 10% pa. What is the stock's beta?

The security market line (SML) shows the relationship between beta and expected return.

Investment projects that plot above the SML would have:

Stock A has a beta of 0.5 and stock B has a beta of 1. Which statement is NOT correct?

Which statement is the most correct?

A stock's correlation with the market portfolio increases while its total risk is unchanged. What will happen to the stock's expected return and systematic risk?

Assets A, B, M and $r_f$ are shown on the graphs above. Asset M is the market portfolio and $r_f$ is the risk free yield on government bonds. Which of the below statements is NOT correct?

Assets A, B, M and $r_f$ are shown on the graphs above. Asset M is the market portfolio and $r_f$ is the risk free yield on government bonds. Assume that investors can borrow and lend at the risk free rate. Which of the below statements is NOT correct?

A stock has a beta of 1.5. The market's expected total return is 10% pa and the risk free rate is 5% pa, both given as effective annual rates.

What do you think will be the stock's expected return over the next year, given as an effective annual rate?

A stock has a beta of 1.5. The market's expected total return is 10% pa and the risk free rate is 5% pa, both given as effective annual rates.

In the last 5 minutes, bad economic news was released showing a higher chance of recession. Over this time the share market fell by 1%. The risk free rate was unchanged.

What do you think was the stock's historical return over the last 5 minutes, given as an effective 5 minute rate?

A stock has a beta of 1.5. The market's expected total return is 10% pa and the risk free rate is 5% pa, both given as effective annual rates.

Over the last year, bad economic news was released showing a higher chance of recession. Over this time the share market fell by 1%. So $r_{m} = (P_{0} - P_{-1})/P_{-1} = -0.01$, where the current time is zero and one year ago is time -1. The risk free rate was unchanged.

What do you think was the stock's historical return over the last year, given as an effective annual rate?

A firm changes its capital structure by issuing a large amount of equity and using the funds to repay debt. Its assets are unchanged. Ignore interest tax shields.

According to the Capital Asset Pricing Model (CAPM), which statement is correct?

A firm's WACC before tax would decrease due to:

Which of the following statements about the weighted average cost of capital (WACC) is NOT correct?

Your friend claims that by reading 'The Economist' magazine's economic news articles, she can identify shares that will have positive abnormal expected returns over the next 2 years. Assuming that her claim is true, which statement(s) are correct?

(i) Weak form market efficiency is broken.

(ii) Semi-strong form market efficiency is broken.

(iii) Strong form market efficiency is broken.

(iv) The asset pricing model used to measure the abnormal returns (such as the CAPM) is either wrong (mis-specification error) or is measured using the wrong inputs (data errors) so the returns may not be abnormal but rather fair for the level of risk.

Select the most correct response:

Fundamentalists who analyse company financial reports and news announcements (but who don't have inside information) will make positive abnormal returns if:

Economic statistics released this morning were a surprise: they show a strong chance of consumer price inflation (CPI) reaching 5% pa over the next 2 years.

This is much higher than the previous forecast of 3% pa.

A vanilla fixed-coupon 2-year risk-free government bond was issued at par this morning, just before the economic news was released.

What is the expected change in bond price after the economic news this morning, and in the next 2 years? Assume that:

• Inflation remains at 5% over the next 2 years.
• Investors demand a constant real bond yield.
• The bond price falls by the (after-tax) value of the coupon the night before the ex-coupon date, as in real life.

The efficient markets hypothesis (EMH) and no-arbitrage pricing theory are most closely related to which of the following concepts?

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? Which of the following statements about Australian franking credits is NOT correct? Franking credits: 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: $\Delta V = \Delta D+ \Delta E$ A company conducts a 1 for 5 rights issue at a subscription price of$7 when the pre-announcement stock price was $10. What is the percentage change in the stock price and the number of shares outstanding? The answers are given in the same order. Ignore all taxes, transaction costs and signalling effects. Question 625 dividend re-investment plan, capital raising Which of the following statements about dividend re-investment plans (DRP's) is NOT correct? In late 2003 the listed bank ANZ announced a 2-for-11 rights issue to fund the takeover of New Zealand bank NBNZ. Below is the chronology of events: • 23/10/2003. Share price closes at$18.30.

• 24/10/2003. 2-for-11 rights issue announced at a subscription price of $13. The proceeds of the rights issue will be used to acquire New Zealand bank NBNZ. Trading halt announced in morning before market opens. • 28/10/2003. Trading halt lifted. Last (and only) day that shares trade cum-rights. Share price opens at$18.00 and closes at $18.14. • 29/10/2003. Shares trade ex-rights. All things remaining equal, what would you expect ANZ's stock price to open at on the first day that it trades ex-rights (29/10/2003)? Ignore the time value of money since time is negligibly short. Also ignore taxes. When someone says that they're "buying American dollars" (USD), what type of asset are they probably buying? They're probably buying: An Indonesian lady wishes to convert 1 million Indonesian rupiah (IDR) to Australian dollars (AUD). Exchange rates are 13,125 IDR per USD and 0.79 USD per AUD. How many AUD is the IDR 1 million worth? Australians usually quote the Australian dollar in USD per 1 AUD. For example, in October 2015 the Australian dollar was quoted as 0.72 USD per AUD. Is this an or terms quote? Chinese people usually quote the Chinese Yuan or Renminbi in RMB per 1 USD. For example, in October 2015 the Chinese Renminbi was 6.35 RMB per USD. Is this an or terms quote? If the AUD appreciates against the USD, the American terms quote of the AUD will or ? If the current AUD exchange rate is USD 0.9686 = AUD 1, what is the European terms quote of the AUD against the USD? If the USD appreciates against the AUD, the European terms quote of the AUD will or ? Investors expect the Reserve Bank of Australia (RBA) to keep the policy rate steady at their next meeting. Then unexpectedly, the RBA announce that they will increase the policy rate by 25 basis points due to fears that the economy is growing too fast and that inflation will be above their target rate of 2 to 3 per cent. What do you expect to happen to Australia's exchange rate in the short term? The Australian dollar is likely to: The market expects the Reserve Bank of Australia (RBA) to increase the policy rate by 25 basis points at their next meeting. Then unexpectedly, the RBA announce that they will increase the policy rate by 50 basis points due to high future GDP and inflation forecasts. What do you expect to happen to Australia's exchange rate in the short term? The Australian dollar will: The Australian cash rate is expected to be 2% pa over the next one year, while the Japanese cash rate is expected to be 0% pa, both given as nominal effective annual rates. The current exchange rate is 100 JPY per AUD. What is the implied 1 year forward foreign exchange rate? Suppose the Australian cash rate is expected to be 8.15% pa and the US federal funds rate is expected to be 3.00% pa over the next 2 years, both given as nominal effective annual rates. The current exchange rate is at parity, so 1 USD = 1 AUD. What is the implied 2 year forward foreign exchange rate? The Chinese government attempts to fix its exchange rate against the US dollar and at the same time use monetary policy to fix its interest rate at a set level. To be able to fix its exchange rate and interest rate in this way, what does the Chinese government actually do? 1. Adopts capital controls to prevent financial arbitrage by private firms and individuals. 2. Adopts the same interest rate (monetary policy) as the United States. 3. Fixes inflation so that the domestic real interest rate is equal to the United States' real interest rate. Which of the above statements is or are true? 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.