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 |

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?

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.

**Question 542** price gains and returns over time, IRR, NPV, income and capital returns, effective return

For an asset price to **double** every **10** years, what must be the expected future capital return, given as an effective annual rate?

**Question 353** income and capital returns, inflation, real and nominal returns and cash flows, real estate

A residential investment property has an expected **nominal** total return of **6**% pa and nominal capital return of **3**% pa.

Inflation is expected to be **2**% pa. All rates are given as effective annual rates.

What are the property's expected **real** total, capital and income returns? The answer choices below are given in the same order.

**Question 407** income and capital returns, inflation, real and nominal returns and cash flows

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.

**Question 525** income and capital returns, real and nominal returns and cash flows, inflation

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:

**Question 295** inflation, real and nominal returns and cash flows, NPV

When valuing assets using discounted cash flow (net present value) methods, it is important to consider inflation. To properly deal with inflation:

(I) Discount nominal cash flows by nominal discount rates.

(II) Discount nominal cash flows by real discount rates.

(III) Discount real cash flows by nominal discount rates.

(IV) Discount real cash flows by real discount rates.

Which of the above statements is or are correct?

**Question 526** real and nominal returns and cash flows, inflation, no explanation

How can a **nominal** cash flow be precisely converted into a **real** cash flow?

**Question 575** inflation, real and nominal returns and cash flows

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?

**Question 577** inflation, real and nominal returns and cash flows

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.

**Question 554** inflation, real and nominal returns and cash flows

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.

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?

**Question 531** bankruptcy or insolvency, capital structure, risk, limited liability

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

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?

**Question 444** investment decision, corporate financial decision theory

The investment decision primarily affects which part of a business?

**Question 445** financing decision, corporate financial decision theory

The financing decision primarily affects which part of a business?

**Question 443** corporate financial decision theory, investment decision, financing decision, working capital decision, payout policy

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

The expression 'you have to spend money to make money' relates to which business decision?

Katya offers to pay you $10 at the end of every year for the next 5 years (t=1,2,3,4,5) if you pay her $50 now (t=0). You can borrow and lend from the bank at an interest rate of 10% pa, given as an effective annual rate.

Ignore credit risk.

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.

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.

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 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:

**Question 497** income and capital returns, DDM, ex dividend date

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

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

In the dividend discount model:

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

The return ##r## is supposed to be the:

A stock pays annual dividends which are expected to continue forever. It just paid a dividend of $10. The growth rate in the dividend is 2% pa. You estimate that the stock's required return is 10% pa. Both the discount rate and growth rate are given as effective annual rates. Using the dividend discount model, what will be the share price?

A stock is expected to pay the following dividends:

Cash Flows of a Stock | ||||||

Time (yrs) | 0 | 1 | 2 | 3 | 4 | ... |

Dividend ($) | 0.00 | 1.00 | 1.05 | 1.10 | 1.15 | ... |

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

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

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

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

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

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

Which expression is **NOT** equal to the expected dividend yield?

A fairly valued share's current price is $**4** and it has a total required return of **30**%. Dividends are paid annually and next year's dividend is expected to be $**1**. After that, dividends are expected to grow by **5**% pa in perpetuity. All rates are effective annual returns.

What is the expected dividend income paid at the end of the second year (t=**2**) and what is the expected capital gain from just after the first dividend (t=**1**) to just after the second dividend (t=**2**)? The answers are given in the same order, the dividend and then the capital gain.

**Question 50** DDM, stock pricing, inflation, real and nominal returns and cash flows

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?

**Question 535** DDM, real and nominal returns and cash flows, stock pricing

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

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

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

Calculate the current TLS share price.

**Question 488** income and capital returns, payout policy, payout ratio, DDM

Two companies BigDiv and ZeroDiv are exactly the same except for their dividend payouts.

BigDiv pays large dividends and ZeroDiv doesn't pay any dividends.

Currently the two firms have the same earnings, assets, number of shares, share price, expected total return and risk.

Assume a perfect world with no taxes, no transaction costs, no asymmetric information and that all assets including business projects are fairly priced and therefore zero-NPV.

All things remaining equal, which of the following statements is **NOT** correct?

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.

**Question 180** equivalent annual cash flow, inflation, real and nominal returns and cash flows

Details of two different types of light bulbs are given below:

- Low-energy light bulbs cost $3.50, have a life of nine years, and use about $1.60 of electricity a year, paid at the end of each year.
- Conventional light bulbs cost only $0.50, but last only about a year and use about $6.60 of energy a year, paid at the end of each year.

The real discount rate is 5%, given as an effective annual rate. Assume that all cash flows are real. The inflation rate is 3% given as an effective annual rate.

Find the Equivalent Annual Cost (EAC) of the low-energy and conventional light bulbs. The below choices are listed in that order.

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.

An industrial chicken farmer grows chickens for their meat. Chickens:

- Cost $
**0.50**each to buy as chicks. They are bought on the day they’re born, at t=**0**. - Grow at a rate of $
**0.70**worth of meat per chicken per week for the first 6 weeks (t=**0**to t=**6**). - Grow at a rate of $
**0.40**worth of meat per chicken per week for the next 4 weeks (t=**6**to t=**10**) since they’re older and grow more slowly. - Feed costs are $
**0.30**per chicken per week for their whole life. Chicken feed is bought and fed to the chickens once per week at the beginning of the week. So the first amount of feed bought for a chicken at t=**0**costs $0.30, and so on. - Can be slaughtered (killed for their meat) and sold at no cost at the
**end**of the week. The price received for the chicken is their total value of meat (note that the chicken grows fast then slow, see above).

The required return of the chicken farm is **0.5%** given as an effective **weekly** rate.

Ignore taxes and the fixed costs of the factory. Ignore the chicken’s welfare and other environmental and ethical concerns.

Find the equivalent **weekly** cash flow of slaughtering a chicken at **6** weeks and at **10** weeks so the farmer can figure out the best time to slaughter his chickens. The choices below are given in the same order, 6 and 10 weeks.

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

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

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

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

**Question 543** price gains and returns over time, IRR, NPV, income and capital returns, effective return

For an asset price to **triple** every **5** years, what must be the expected future capital return, given as an effective annual rate?

A newly floated farming company is financed with senior bonds, junior bonds, cumulative non-voting preferred stock and common stock. The new company has no retained profits and due to floods it was unable to record any revenues this year, leading to a loss. The firm is not bankrupt yet since it still has substantial contributed equity (same as paid-up capital).

On which securities must it pay interest or dividend payments in this terrible financial year?

**Question 452** limited liability, expected and historical returns

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

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

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

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

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?

**Question 524** risk, expected and historical returns, bankruptcy or insolvency, capital structure, corporate financial decision theory, limited liability

Which of the following statements is **NOT** correct?

**Question 604** inflation, real and nominal returns and cash flows

Apples and oranges currently cost $**1** each. Inflation is **5**% pa, and apples and oranges are equally affected by this inflation rate. Note that when payments are not specified as real, as in this question, they're conventionally assumed to be nominal.

Which of the following statements is **NOT** correct?

**Question 578** inflation, real and nominal returns and cash flows

Which of the following statements about inflation is **NOT** correct?

**Question 576** inflation, real and nominal returns and cash flows

What is the present value of a **nominal** payment of $1,000 in 4 years? The **nominal** discount rate is 8% pa and the inflation rate is 2% pa.

**Question 522** income and capital returns, real and nominal returns and cash flows, inflation, real estate

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

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

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

The answer choices below are given in the same order.

**Question 523** income and capital returns, real and nominal returns and cash flows, inflation

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

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

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

The answer choices below are given in the same order.

The following cash flows are expected:

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

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

**Question 727** inflation, real and nominal returns and cash flows

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

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

**Question 728** inflation, real and nominal returns and cash flows, income and capital returns, no explanation

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

**Question 729** book and market values, balance sheet, no explanation

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

**Question 730** DDM, income and capital returns, no explanation

A stock’s current price is $**1**. Its expected total return is **10**% pa and its long term expected capital return is **4**% pa. It pays an annual dividend and the next one will be paid in **one year**. All rates are given as effective annual rates. The dividend discount model is thought to be a suitable model for the stock. Ignore taxes. Which of the following statements about the stock is **NOT** correct?

**Question 731** DDM, income and capital returns, no explanation

In the dividend discount model (DDM), share prices fall when dividends are paid. Let the high price before the fall be called the peak, and the low price after the fall be called the trough.

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

Which of the following statements about the DDM is **NOT** correct?

**Question 732** real and nominal returns and cash flows, inflation, income and capital returns

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:

A share’s current price is $**60**. It’s expected to pay a dividend of $**1.50** in one year. The growth rate of the dividend is **0.5**% pa and the stock’s required total return is **3**% pa. The stock’s price can be modeled using the dividend discount model (DDM):

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

Which of the following methods is **NOT** equal to the stock’s expected price in one year and six months (t=**1.5** years)? Note that the symbolic formulas shown in each line below do equal the formulas with numbers. The formula is just repeated with symbols and then numbers in case it helps you to identify the incorrect statement more quickly.

**Question 734** real and nominal returns and cash flows, inflation, DDM, no explanation

An equities analyst is using the dividend discount model to price a company's shares. The company operates domestically and has no plans to expand overseas. It is part of a mature industry with stable positive growth prospects.

The analyst has estimated the **real** required return (r) of the stock and the value of the dividend that the stock **just paid** a moment before ##(C_\text{0 before})##.

What is the highest perpetual **real** growth rate of dividends (g) that can be justified? Select the most correct statement from the following choices. The highest perpetual real expected growth rate of dividends that can be justified is the country's expected:

A share currently worth $**100** is expected to pay a constant dividend of $**4** for the next **5** years with the first dividend in one year (t=1) and the last in 5 years (t=5).

The total required return is **10**% pa.

What do you expected the share price to be in **5** years, just **after** the dividend at that time has been paid?

**Question 548** equivalent annual cash flow, time calculation, no explanation

An Apple iPhone 6 smart phone can be bought now for $**999**. An Android Kogan Agora 4G+ smart phone can be bought now for $**240**.

If the Kogan phone lasts for **one** year, approximately how long must the Apple phone last for to have the same equivalent annual cost?

Assume that both phones have equivalent features besides their lifetimes, that both are worthless once they've outlasted their life, the discount rate is **10**% pa given as an effective annual rate, and there are no extra costs or benefits from either phone.

Stocks in the United States usually pay **quarterly** dividends. For example, the software giant Microsoft paid a $0.23 dividend every quarter over the 2013 financial year and plans to pay a $0.28 dividend every quarter over the 2014 financial year.

Using the dividend discount model and net present value techniques, calculate the stock price of Microsoft assuming that:

- The time now is the beginning of July 2014. The next dividend of $
**0.28**will be received in**3**months (end of September 2014), with another 3 quarterly payments of $0.28 after this (end of December 2014, March 2015 and June 2015). - The quarterly dividend will increase by
**2.5**% every year, but each quarterly dividend over the year will be equal. So each quarterly dividend paid in the financial year beginning in September 2015 will be $ 0.287 ##(=0.28×(1+0.025)^1)##, with the last at the end of June 2016. In the next financial year beginning in September 2016 each quarterly dividend will be $0.294175 ##(=0.28×(1+0.025)^2)##, with the last at the end of June 2017, and so on forever. - The total required return on equity is
**6**% pa. - The required return and growth rate are given as effective annual rates.
- Dividend payment dates and ex-dividend dates are at the same time.
- Remember that there are 4 quarters in a year and 3 months in a quarter.

What is the current stock price?

A home loan company advertises an interest rate of 6% pa, payable monthly. Which of the following statements about the interest rate is **NOT** correct? All rates are given to four decimal places.

A semi-annual coupon bond has a yield of 3% pa. Which of the following statements about the yield is **NOT** correct? All rates are given to four decimal places.

Which of the below statements about effective rates and annualised percentage rates (APR's) is **NOT** correct?

A credit card offers an interest rate of 18% pa, compounding monthly.

Find the effective monthly rate, effective annual rate and the effective daily rate. Assume that there are 365 days in a year.

All answers are given in the same order:

### r_\text{eff monthly} , r_\text{eff yearly} , r_\text{eff daily} ###

Calculate the effective annual rates of the following three APR's:

- A credit card offering an interest rate of 18% pa, compounding monthly.
- A bond offering a yield of 6% pa, compounding semi-annually.
- An annual dividend-paying stock offering a return of 10% pa compounding annually.

All answers are given in the same order:

##r_\text{credit card, eff yrly}##, ##r_\text{bond, eff yrly}##, ##r_\text{stock, eff yrly}##

On his 20th birthday, a man makes a resolution. He will deposit $**30** into a bank account at the **end** of every month starting from now, which is the start of the month. So the first payment will be in one month. He will write in his will that when he dies the money in the account should be given to charity.

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

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

You want to buy an apartment priced at $300,000. You have saved a deposit of $30,000. The bank has agreed to lend you the $270,000 as a **fully amortising** loan with a term of 25 years. The interest rate is 12% pa and is not expected to change.

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

You want to buy an apartment worth $400,000. You have saved a deposit of $80,000. The bank has agreed to lend you the $320,000 as a **fully amortising** mortgage loan with a term of 30 years. The interest rate is 6% pa and is not expected to change. What will be your monthly payments?

You just signed up for a 30 year **fully amortising** mortgage loan with monthly payments of $2,000 per month. The interest rate is 9% pa which is not expected to change.

How much did you borrow? After 5 years, how much will be owing on the mortgage? The interest rate is still 9% and is not expected to change.

You just signed up for a 30 year **fully amortising** mortgage loan with monthly payments of $1,500 per month. The interest rate is 9% pa which is not expected to change.

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

You just agreed to a 30 year **fully amortising** mortgage loan with monthly payments of $2,500. The interest rate is 9% pa which is not expected to change.

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

You want to buy an apartment priced at $300,000. You have saved a deposit of $30,000. The bank has agreed to lend you the $270,000 as an **interest only** loan with a term of 25 years. The interest rate is 12% pa and is not expected to change.

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

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

You actually plan to pay more than the required interest payment. You plan to pay $3,300 in mortgage payments every month, which your mortgage lender allows. These extra payments will reduce the principal and the minimum interest payment required each month.

At the maturity of the mortgage, what will be the principal? That is, after the last (300th) interest payment of $3,300 in 25 years, how much will be owing on the mortgage?

You want to buy an apartment worth $300,000. You have saved a deposit of $60,000.

The bank has agreed to lend you $240,000 as an **interest only** mortgage loan with a term of 30 years. The interest rate is 6% pa and is not expected to change. What will be your monthly payments?

**Question 239** income and capital returns, inflation, real and nominal returns and cash flows, interest only loan

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

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

Calculate the price of a newly issued **ten** year bond with a face value of $**100**, a yield of **8**% pa and a fixed coupon rate of **6**% pa, paid **annually**. So there's only one coupon per year, paid in arrears every year.

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?

**Question 48** IRR, NPV, bond pricing, premium par and discount bonds, market efficiency

The theory of fixed interest bond pricing is an application of the theory of Net Present Value (NPV). Also, a 'fairly priced' asset is not over- or under-priced. Buying or selling a fairly priced asset has an NPV of zero.

Considering this, which of the following statements is **NOT** correct?

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.

**Question 35** bond pricing, zero coupon bond, term structure of interest rates, forward interest rate

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.

**Question 143** bond pricing, zero coupon bond, term structure of interest rates, forward interest rate

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.

**Question 96** bond pricing, zero coupon bond, term structure of interest rates, forward interest rate

An Australian company just issued two bonds:

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

What is the forward rate on the company's debt from years 1 to 2? Give your answer as an APR compounding every **6** months, which is how the above bond yields are quoted.

You'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.

You really want to go on a back packing trip to Europe when you finish university. Currently you have $**1,500** in the bank. Bank interest rates are **8**% pa, given as an APR compounding per month. If the holiday will cost $**2,000**, how long will it take for your bank account to reach that amount?

**Question 370** capital budgeting, NPV, interest tax shield, WACC, CFFA

Project Data | ||

Project life | 2 yrs | |

Initial investment in equipment | $600k | |

Depreciation of equipment per year | $250k | |

Expected sale price of equipment at end of project | $200k | |

Revenue per job | $12k | |

Variable cost per job | $4k | |

Quantity of jobs per year | 120 | |

Fixed costs per year, paid at the end of each year | $100k | |

Interest expense in first year (at t=1) | $16.091k | |

Interest expense in second year (at t=2) | $9.711k | |

Tax rate | 30% | |

Government treasury bond yield | 5% | |

Bank loan debt yield | 6% | |

Levered cost of equity | 12.5% | |

Market portfolio return | 10% | |

Beta of assets | 1.24 | |

Beta of levered equity | 1.5 | |

Firm's and project's debt-to-equity ratio |
25% | |

**Notes**

- The project will require an immediate purchase of $
**50**k of inventory, which will all be sold at cost when the project ends. Current liabilities are negligible so they can be ignored.

**Assumptions**

- The debt-to-equity ratio will be kept constant throughout the life of the project. The amount of interest expense at the end of each period has been correctly calculated to maintain this constant debt-to-equity ratio. Note that interest expense is different in each year.
- Thousands are represented by 'k' (kilo).
- All cash flows occur at the start or end of the year as appropriate, not in the middle or throughout the year.
- All rates and cash flows are nominal. The inflation rate is 2% pa.
- All rates are given as effective annual rates.
- The 50% capital gains tax discount is not available since the project is undertaken by a firm, not an individual.

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

A company issues a large amount of bonds to raise money for new projects of similar risk to the company's existing projects. The net present value (NPV) of the new projects is positive but small. Assume a classical tax system. Which statement is **NOT** correct?

A firm has a debt-to-assets ratio of 50%. The firm then issues a large amount of equity to raise money for new projects of similar systematic risk to the company's existing projects. Assume a classical tax system. Which statement is correct?

A firm has a debt-to-assets ratio of 50%. The firm then issues a large amount of debt to raise money for new projects of similar risk to the company's existing projects. Assume a classical tax system. Which statement is correct?

**Question 337** capital structure, interest tax shield, leverage, real and nominal returns and cash flows, multi stage growth model

A fast-growing firm is suitable for valuation using a multi-stage growth model.

It's **nominal** unlevered cash flow from assets (##CFFA_U##) at the end of this year (**t=1**) is expected to be $**1** million. After that it is expected to grow at a rate of:

**12**% pa for the next two years (from t=1 to 3),**5**% over the fourth year (from t=3 to 4), and**-1**% forever after that (from t=4 onwards). Note that this is a negative one percent growth rate.

Assume that:

- The nominal WACC
**after**tax is**9.5**% pa and is not expected to change. - The nominal WACC
**before**tax is**10**% pa and is not expected to change. - The firm has a target debt-to-
**equity**ratio that it plans to maintain. - The inflation rate is
**3**% pa. - All rates are given as
**nominal**effective annual rates.

What is the levered value of this fast growing firm's assets?

Your friend just bought a house for $400,000. He financed it using a $320,000 mortgage loan and a deposit of $80,000.

In the context of residential housing and mortgages, the 'equity' tied up in the value of a person's house is the value of the house less the value of the mortgage. So the initial equity your friend has in his house is $80,000. Let this amount be E, let the value of the mortgage be D and the value of the house be V. So ##V=D+E##.

If house prices suddenly fall by **10**%, what would be your friend's percentage change in equity (E)? Assume that the value of the mortgage is unchanged and that no income (rent) was received from the house during the short time over which house prices fell.

Remember:

### r_{0\rightarrow1}=\frac{p_1-p_0+c_1}{p_0} ###

where ##r_{0-1}## is the return (percentage change) of an asset with price ##p_0## initially, ##p_1## one period later, and paying a cash flow of ##c_1## at time ##t=1##.

One year ago you bought $**100,000** of shares partly funded using a margin loan. The margin loan size was $**70,000** and the other $**30,000** was your own wealth or 'equity' in the share assets.

The interest rate on the margin loan was **7.84**% pa.

Over the year, the shares produced a dividend yield of **4**% pa and a capital gain of **5**% pa.

What was the **total** return on your **wealth**? Ignore taxes, assume that all cash flows (interest payments and dividends) were paid and received at the end of the year, and all rates above are effective annual rates.

Hint: Remember that wealth in this context is your equity (E) in the house asset (V = D+E) which is funded by the loan (D) and your deposit or equity (E).

Interest expense (IntExp) is an important part of a company's income statement (or 'profit and loss' or 'statement of financial performance').

How does an **accountant** calculate the annual interest expense of a fixed-coupon bond that has a liquid secondary market? Select the most correct answer:

Annual interest expense is equal to:

A firm has a debt-to-equity ratio of 25%. What is its debt-to-assets ratio?

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

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

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

Assume the following:

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

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

The mobile phone manufacturing project's:

There are many ways to calculate a firm's free cash flow (FFCF), also called cash flow from assets (CFFA). Some include the annual interest tax shield in the cash flow and some do not.

Which of the below FFCF formulas include the interest tax shield in the cash flow?

###(1) \quad FFCF=NI + Depr - CapEx -ΔNWC + IntExp### ###(2) \quad FFCF=NI + Depr - CapEx -ΔNWC + IntExp.(1-t_c)### ###(3) \quad FFCF=EBIT.(1-t_c )+ Depr- CapEx -ΔNWC+IntExp.t_c### ###(4) \quad FFCF=EBIT.(1-t_c) + Depr- CapEx -ΔNWC### ###(5) \quad FFCF=EBITDA.(1-t_c )+Depr.t_c- CapEx -ΔNWC+IntExp.t_c### ###(6) \quad FFCF=EBITDA.(1-t_c )+Depr.t_c- CapEx -ΔNWC### ###(7) \quad FFCF=EBIT-Tax + Depr - CapEx -ΔNWC### ###(8) \quad FFCF=EBIT-Tax + Depr - CapEx -ΔNWC-IntExp.t_c### ###(9) \quad FFCF=EBITDA-Tax - CapEx -ΔNWC### ###(10) \quad FFCF=EBITDA-Tax - CapEx -ΔNWC-IntExp.t_c###The formulas for net income (NI also called earnings), EBIT and EBITDA are given below. Assume that depreciation and amortisation are both represented by 'Depr' and that 'FC' represents fixed costs such as rent.

###NI=(Rev - COGS - Depr - FC - IntExp).(1-t_c )### ###EBIT=Rev - COGS - FC-Depr### ###EBITDA=Rev - COGS - FC### ###Tax =(Rev - COGS - Depr - FC - IntExp).t_c= \dfrac{NI.t_c}{1-t_c}###One formula for calculating a levered firm's free cash flow (FFCF, or CFFA) is to use earnings before interest and tax (EBIT).

###\begin{aligned} FFCF &= (EBIT)(1-t_c) + Depr - CapEx -\Delta NWC + IntExp.t_c \\ &= (Rev - COGS - Depr - FC)(1-t_c) + Depr - CapEx -\Delta NWC + IntExp.t_c \\ \end{aligned} \\###

One formula for calculating a levered firm's free cash flow (FFCF, or CFFA) is to use net operating profit after tax (NOPAT).

###\begin{aligned} FFCF &= NOPAT + Depr - CapEx -\Delta NWC \\ &= (Rev - COGS - Depr - FC)(1-t_c) + Depr - CapEx -\Delta NWC \\ \end{aligned} \\###

Your friend just bought a house for $**1,000,000**. He financed it using a $**900,000** mortgage loan and a deposit of $**100,000**.

In the context of residential housing and mortgages, the 'equity' or 'net wealth' tied up in a house is the value of the house less the value of the mortgage loan. Assuming that your friend's only asset is his house, his net wealth is $100,000.

If house prices suddenly fall by **15%**, what would be your friend's percentage change in net wealth?

Assume that:

- No income (rent) was received from the house during the short time over which house prices fell.
- Your friend will not declare bankruptcy, he will always pay off his debts.

Here are the Net Income (NI) and Cash Flow From Assets (CFFA) equations:

###NI=(Rev-COGS-FC-Depr-IntExp).(1-t_c)###

###CFFA=NI+Depr-CapEx - \varDelta NWC+IntExp###

What is the formula for calculating annual interest expense (IntExp) which is used in the equations above?

Select one of the following answers. Note that D is the value of debt which is constant through time, and ##r_D## is the cost of debt.

Which one of the following will **decrease** net income (NI) but **increase** cash flow from assets (CFFA) in this year for a tax-paying firm, all else remaining constant?

Remember:

###NI=(Rev-COGS-FC-Depr-IntExp).(1-t_c )### ###CFFA=NI+Depr-CapEx - ΔNWC+IntExp###A firm has a debt-to-equity ratio of 60%. What is its debt-to-assets ratio?

A retail furniture company buys furniture wholesale and distributes it through its retail stores. The owner believes that she has some good ideas for making stylish new furniture. She is considering a project to buy a factory and employ workers to manufacture the new furniture she's designed. Furniture manufacturing has more systematic risk than furniture retailing.

Her furniture retailing firm's after-tax WACC is 20%. Furniture manufacturing firms have an after-tax WACC of 30%. Both firms are optimally geared. Assume a classical tax system.

Which method(s) will give the correct valuation of the new furniture-making project? Select the most correct answer.

A company increases the proportion of debt funding it uses to finance its assets by issuing bonds and using the cash to repurchase stock, leaving assets unchanged.

Ignoring the costs of financial distress, which of the following statements is **NOT** correct:

A method commonly seen in textbooks for calculating a levered firm's free cash flow (FFCF, or CFFA) is the following:

###\begin{aligned} FFCF &= (Rev - COGS - Depr - FC - IntExp)(1-t_c) + \\ &\space\space\space+ Depr - CapEx -\Delta NWC + IntExp(1-t_c) \\ \end{aligned}###

One method for calculating a firm's free cash flow (FFCF, or CFFA) is to ignore interest expense. That is, pretend that interest expense ##(IntExp)## is zero:

###\begin{aligned} FFCF &= (Rev - COGS - Depr - FC - IntExp)(1-t_c) + Depr - CapEx -\Delta NWC + IntExp \\ &= (Rev - COGS - Depr - FC - 0)(1-t_c) + Depr - CapEx -\Delta NWC - 0\\ \end{aligned}###

**Question 413** CFFA, interest tax shield, depreciation tax shield

There are many ways to calculate a firm's free cash flow (FFCF), also called cash flow from assets (CFFA).

One method is to use the following formulas to transform net income (NI) into FFCF including interest and depreciation tax shields:

###FFCF=NI + Depr - CapEx -ΔNWC + IntExp###

###NI=(Rev - COGS - Depr - FC - IntExp).(1-t_c )###

Another popular method is to use EBITDA rather than net income. EBITDA is defined as:

###EBITDA=Rev - COGS - FC###

One of the below formulas correctly calculates FFCF from EBITDA, including interest and depreciation tax shields, giving an identical answer to that above. Which formula is correct?

**Question 69** interest tax shield, capital structure, leverage, WACC

Which statement about risk, required return and capital structure is the most correct?

A firm is considering a new project of similar risk to the current risk of the firm. This project will expand its existing business. The cash flows of the project have been calculated assuming that there is no interest expense. In other words, the cash flows assume that the project is all-equity financed.

In fact the firm has a target debt-to-equity ratio of 1, so the project will be financed with 50% debt and 50% equity. To find the levered value of the firm's assets, what discount rate should be applied to the project's unlevered cash flows? Assume a classical tax system.

**Question 99** capital structure, interest tax shield, Miller and Modigliani, trade off theory of capital structure

A firm changes its capital structure by issuing a large amount of debt and using the funds to repurchase shares. Its assets are unchanged.

Assume that:

- The firm and individual investors can borrow at the same rate and have the same tax rates.
- The firm's debt and shares are fairly priced and the shares are repurchased at the market price, not at a premium.
- There are no market frictions relating to debt such as asymmetric information or transaction costs.
- Shareholders wealth is measured in terms of utiliity. Shareholders are wealth-maximising and risk-averse. They have a preferred level of overall leverage. Before the firm's capital restructure all shareholders were optimally levered.

According to Miller and Modigliani's theory, which statement is correct?

**Question 121** capital structure, leverage, costs of financial distress, interest tax shield

Fill in the missing words in the following sentence:

All things remaining equal, as a firm's amount of debt funding falls, benefits of interest tax shields __________ and the costs of financial distress __________.

A firm plans to issue equity and use the cash raised to pay off its debt. No assets will be bought or sold. Ignore the costs of financial distress.

Which of the following statements is **NOT** correct, all things remaining equal?

A credit card company advertises an interest rate of 18% pa, payable monthly. Which of the following statements about the interest rate is **NOT** correct? All rates are given to four decimal places.

Which of the following statements about effective rates and annualised percentage rates (APR's) is **NOT** correct?

A European bond paying annual coupons of 6% offers a yield of 10% pa.

Convert the yield into an effective monthly rate, an effective annual rate and an effective daily rate. Assume that there are 365 days in a year.

All answers are given in the same order:

### r_\text{eff, monthly} , r_\text{eff, yearly} , r_\text{eff, daily} ###

You want to buy an apartment priced at $500,000. You have saved a deposit of $50,000. The bank has agreed to lend you the $450,000 as an **interest only** loan with a term of 30 years. The interest rate is 6% pa and is not expected to change. What will be your monthly payments?

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

You just signed up for a 30 year **fully amortising** mortgage loan with monthly payments of $1,500 per month. The interest rate is 9% pa which is not expected to change.

To your surprise, you can actually afford to pay $2,000 per month and your mortgage allows early repayments without fees. If you maintain these higher monthly payments, how long will it take to pay off your mortgage?

A prospective home buyer can afford to pay $2,000 per month in mortgage loan repayments. The central bank recently lowered its policy rate by 0.25%, and residential home lenders cut their mortgage loan rates from 4.74% to 4.49%.

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

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.

**Question 56** income and capital returns, bond pricing, premium par and discount bonds

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

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

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

The capital return is the growth rate of the price.

The income return is the periodic cash flow. For a bond this is the coupon payment.

A two year Government bond has a face value of $100, a yield of 0.5% and a fixed coupon rate of 0.5%, paid semi-annually. What is its price?

A firm wishes to raise $10 million now. They will issue 6% pa semi-annual coupon bonds that will mature in 8 years and have a face value of $1,000 each. Bond yields are 10% pa, given as an APR compounding every 6 months, and the yield curve is flat.

How many bonds should the firm issue?

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?

**Question 25** bond pricing, zero coupon bond, term structure of interest rates, forward interest rate

A European company just issued two bonds, a

- 2 year zero coupon bond at a yield of 8% pa, and a
- 3 year zero coupon bond at a yield of 10% pa.

What is the company's forward rate over the third year (from t=2 to t=3)? Give your answer as an effective annual rate, which is how the above bond yields are quoted.

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**?

**Question 213** income and capital returns, bond pricing, premium par and discount bonds

The coupon rate of a fixed annual-coupon bond is constant (always the same).

What can you say about the income return (##r_\text{income}##) of a fixed annual coupon bond? Remember that:

###r_\text{total} = r_\text{income} + r_\text{capital}###

###r_\text{total, 0 to 1} = \frac{c_1}{p_0} + \frac{p_1-p_0}{p_0}###

Assume that there is no change in the bond's total annual yield to maturity from when it is issued to when it matures.

Select the most correct statement.

From its date of issue until maturity, the **income return** of a fixed annual coupon:

There are many ways to write the ordinary annuity formula.

Which of the following is **NOT** equal to the ordinary annuity formula?

The following cash flows are expected:

- 10 yearly payments of $60, with the first payment in 3 years from now (first payment at t=3).
- 1 payment of $400 in 5 years and 6 months (t=5.5) from now.

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

You deposit money into a bank. Which of the following statements is **NOT** correct? You:

You bought a house, primarily funded using a home loan from a bank. Which of the following statements is **NOT** correct?

**Question 737** financial statement, balance sheet, income statement

Where can a publicly listed firm's book value of equity be found? It can be sourced from the company's:

**Question 738** financial statement, balance sheet, income statement

Where can a private firm's market value of equity be found? It can be sourced from the company's:

**Question 739** real and nominal returns and cash flows, inflation

There are a number of different formulas involving real and nominal returns and cash flows. Which one of the following formulas is **NOT** correct? All returns are effective annual rates. Note that the symbol ##\approx## means 'approximately equal to'.

**Question 740** real and nominal returns and cash flows, DDM, inflation

Taking inflation into account when using the DDM can be hard. Which of the following formulas will **NOT** give a company's current stock price ##(P_0)##? Assume that the annual dividend was just paid ##(C_0)##, and the next dividend will be paid in one year ##(C_1)##.

A home loan company advertises an interest rate of **4.5**% pa, payable monthly. Which of the following statements about the interest rate is **NOT** correct?

**Question 742** price gains and returns over time, no explanation

For an asset's price to quintuple every **5** years, what must be its effective annual capital return? Note that a stock's price quintuples when it increases from say $1 to $5.

**Question 743** price gains and returns over time, no explanation

How many years will it take for an asset's price to **triple** (increase from say $1 to $3) if it grows by **5**% pa?

**Question 744** income and capital returns, real and nominal returns and cash flows, inflation

If someone says "my shares rose by 10% last year", what do you assume that they mean?

**Question 745** real and nominal returns and cash flows, inflation, income and capital returns

If the nominal gold price is expected to increase at the same rate as inflation which is 3% pa, which of the following statements is **NOT** correct?

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

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

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

A share will pay its next dividend of ##C_1## in one year, and will continue to pay a dividend every year after that forever, growing at a rate of ##g##. So the next dividend will be ##C_2=C_1 (1+g)^1##, then ##C_3=C_2 (1+g)^1##, and so on forever.

The current price of the share is ##P_0## and its required return is ##r##

Which of the following is **NOT** equal to the expected share price in 2 years ##(P_2)## just after the dividend at that time ##(C_2)## has been paid?

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?

**Question 748** income and capital returns, DDM, ex dividend date

A stock will pay you a dividend of $**2** tonight if you buy it **today**.

Thereafter the annual dividend is expected to grow by **3**% pa, so the next dividend after the $2 one tonight will be $2.06 in one year, then in two years it will be $2.1218 and so on. The stock's required return is 8% pa.

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

Itau Unibanco is a major listed bank in Brazil with a market capitalisation of equity equal to BRL **85.744** billion, EPS of **BRL 3.96** and **2.97** billion shares on issue.

Banco Bradesco is another major bank with total earnings of BRL **8.77** billion and **2.52** billion shares on issue.

Estimate Banco Bradesco's current share price using a price-earnings multiples approach assuming that Itau Unibanco is a comparable firm.

Note that BRL is the Brazilian Real, their currency. Figures sourced from Google Finance on the market close of the BVMF on 24/7/15.

Telsa Motors advertises that its Model S electric car saves $**570** per **month** in fuel costs. Assume that Tesla cars last for **10** years, fuel and electricity costs remain the same, and savings are made at the end of each month with the first saving of $570 in one month from now.

The effective annual interest rate is **15.8**%, and the effective monthly interest rate is **1.23**%. What is the present value of the savings?

The following cash flows are expected:

- A
**perpetuity**of yearly payments of $**30**, with the first payment in**5**years (first payment at t=5, which continues every year after that forever). **One**payment of $**100**in 6 years and 3 months (t=**6.25**).

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

How much more can you borrow using an **interest-only** loan compared to a **25**-year **fully amortising** loan if interest rates are **4**% pa compounding per month and are not expected to change? If it makes it easier, assume that you can afford to pay $2,000 per month on either loan. Express your answer as a proportional increase using the following formula:

A firm wishes to raise $**50** million now. They will issue **7**% pa semi-annual coupon bonds that will mature in **6** years and have a face value of $**100** each. Bond yields are **5**% pa, given as an APR compounding every 6 months, and the yield curve is flat.

How many bonds should the firm issue?

A firm wishes to raise $**50** million now. They will issue **5**% pa semi-annual coupon bonds that will mature in **3** years and have a face value of $**100** each. Bond yields are **6**% pa, given as an APR compounding every 6 months, and the yield curve is flat.

How many bonds should the firm issue?

A firm wishes to raise $**50** million now. They will issue **5**% pa semi-annual coupon bonds that will mature in **10** years and have a face value of $**100** each. Bond yields are **5**% pa, given as an APR compounding every 6 months, and the yield curve is flat.

How many bonds should the firm issue?

**Question 758** time calculation, fully amortising loan, no explanation

**Two** years ago you entered into a **fully amortising** home loan with a principal of $**1,000,000**, an interest rate of **6**% pa compounding monthly with a term of **25** years.

Then interest rates suddenly fall to **4.5**% pa (t=0), but you continue to pay the same monthly home loan payments as you did before. How long will it now take to pay off your home loan? Measure the time taken to pay off the home loan from the current time which is 2 years after the home loan was first entered into.

Assume that the lower interest rate was given to you immediately after the loan repayment at the end of year 2, which was the 24th payment since the loan was granted. Also assume that rates were and are expected to remain constant.

The phone company Optus have 2 mobile service plans on offer which both have the same amount of phone call, text message and internet data credit. Both plans have a contract length of **24** months and the monthly cost is payable in **advance**. The only difference between the two plans is that one is a:

- 'Bring Your Own' (BYO) mobile service plan, costing $
**80**per month. There is no phone included in this plan. The other plan is a: - 'Bundled' mobile service plan that comes with the latest smart phone, costing $
**100**per month. This plan includes the latest smart phone.

Neither plan has any additional payments at the start or end. Assume that the discount rate is **1**% per month given as an effective monthly rate.

The only difference between the plans is the phone, so what is the implied cost of the phone as a present value? Given that the latest smart phone actually costs $**600** to purchase outright from another retailer, should you commit to the BYO plan or the bundled plan?

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 |

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

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

What is the payback period of the project in years?

Assume that the cash flows shown in the table are received smoothly over the year. So the $121 at time 2 is actually earned smoothly from t=1 to t=2.

Project Cash Flows | |

Time (yrs) | Cash flow ($) |

0 | -100 |

1 | 11 |

2 | 121 |

A project has the following cash flows:

Project Cash Flows | |

Time (yrs) | Cash flow ($) |

0 | -400 |

1 | 0 |

2 | 500 |

What is the payback period of the project in years?

Normally cash flows are assumed to happen at the given time. But here, assume that the cash flows are received smoothly over the year. So the $500 at time 2 is actually earned smoothly from t=1 to t=2.

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

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

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

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

Which of the following statements is **NOT** correct?

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

Assume that the initial $**11**m 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?