Suppose you had $100 in a savings account and the interest rate was 2% per year.

After 5 years, how much do you think you would have in the account if you left the money to grow?

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

Ignore credit risk.

The following equation is called the Dividend Discount Model (DDM), Gordon Growth Model or the perpetuity with growth formula: ### P_0 = \frac{ C_1 }{ r - g } ###

What is ##g##? The value ##g## is the long term expected:

For a price of $102, Andrea will sell you a share which just paid a dividend of $10 yesterday, and is expected to pay dividends every year forever, growing at a rate of 5% pa.

So the next dividend will be ##10(1+0.05)^1=$10.50## in one year from now, and the year after it will be ##10(1+0.05)^2=11.025## and so on.

The required return of the stock is 15% pa.

For a price of $10.20 each, Renee will sell you 100 shares. Each share is expected to pay dividends in perpetuity, growing at a rate of 5% pa. The next dividend is one year away (t=1) and is expected to be $1 per share.

The required return of the stock is 15% pa.

**Question 490** expected and historical returns, accounting ratio

Which of the following is **NOT** a synonym of 'required return'?

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.

In the 'Austin Powers' series of movies, the character Dr. Evil threatens to destroy the world unless the United Nations pays him a ransom (video 1, video 2). Dr. Evil makes the threat on two separate occasions:

- In 1969 he demands a ransom of $1 million (=10^6), and again;
- In 1997 he demands a ransom of $100 billion (=10^11).

If Dr. Evil's demands are equivalent in real terms, in other words $1 million will buy the same basket of goods in 1969 as $100 billion would in 1997, what was the implied inflation rate over the **28** years from 1969 to 1997?

The answer choices below are given as effective annual rates:

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?

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.

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?

**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?

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?

**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.

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?

**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.

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.

**Question 58** NPV, inflation, real and nominal returns and cash flows, Annuity

A project to build a toll bridge will take two years to complete, costing three payments of $100 million at the start of each year for the next three years, that is at t=0, 1 and 2.

After completion, the toll bridge will yield a constant $50 million at the end of each year for the next 10 years. So the first payment will be at t=3 and the last at t=12. After the last payment at t=12, the bridge will be given to the government.

The required return of the project is 21% pa given as an effective annual **nominal** rate.

All cash flows are **real** and the expected inflation rate is 10% pa given as an effective annual rate. Ignore taxes.

The Net Present Value is:

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 ##?

**Question 31** DDM, perpetuity with growth, effective rate conversion

What is the NPV of the following series of cash flows when the discount rate is **5**% given as an effective **annual** rate?

The first payment of $10 is in 4 years, followed by payments every 6 months forever after that which shrink by 2% every 6 months. That is, the growth rate every 6 months is actually **negative 2%**, given as an effective **6 month** rate. So the payment at ## t=4.5 ## years will be ## 10(1-0.02)^1=9.80 ##, and so on.

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 is the current price of the stock?

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 ##?

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

Which expression is **NOT** equal to the expected capital return?

You own an apartment which you rent out as an investment property.

What is the price of the apartment using discounted cash flow (DCF, same as NPV) valuation?

Assume that:

- You just signed a contract to rent the apartment out to a tenant for the next 12 months at $2,000 per month, payable in advance (at the start of the month, t=0). The tenant is just about to pay you the first $2,000 payment.
- The contract states that monthly rental payments are fixed for 12 months. After the contract ends, you plan to sign another contract but with rental payment increases of 3%. You intend to do this every year.

So rental payments will increase at the start of the 13th month (t=12) to be $2,060 (=2,000(1+0.03)), and then they will be constant for the next 12 months.

Rental payments will increase again at the start of the 25th month (t=24) to be $2,121.80 (=2,000(1+0.03)^{2}), and then they will be constant for the next 12 months until the next year, and so on. - The required return of the apartment is 8.732% pa, given as an effective annual rate.
- Ignore all taxes, maintenance, real estate agent, council and strata fees, periods of vacancy and other costs. Assume that the apartment will last forever and so will the rental payments.

The boss of WorkingForTheManCorp has a wicked (and unethical) idea. He plans to pay his poor workers one week late so that he can get more interest on his cash in the bank.

Every week he is supposed to pay his 1,000 employees $1,000 each. So $**1** million is paid to employees every week.

The boss was just about to pay his employees today, until he thought of this idea so he will actually pay them one week (**7** days) later for the work they did last week and every week in the future, forever.

Bank interest rates are **10**% pa, given as a real effective annual rate. So ##r_\text{eff annual, real} = 0.1## and the real effective weekly rate is therefore ##r_\text{eff weekly, real} = (1+0.1)^{1/52}-1 = 0.001834569##

All rates and cash flows are real, the inflation rate is **3**% pa and there are **52** weeks per year. The boss will always pay wages one week late. The business will operate forever with constant real wages and the same number of employees.

What is the net present value (**NPV**) of the boss's decision to pay later?

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

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

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.

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

Which of the following 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} ###

**Question 49** inflation, real and nominal returns and cash flows, APR, effective rate

In Australia, nominal yields on **semi**-annual coupon paying Government Bonds with 2 years until maturity are currently **2.83**% pa.

The inflation rate is currently **2.2**% pa, given as an APR compounding per **quarter**. The inflation rate is not expected to change over the next 2 years.

What is the real yield on these bonds, given as an APR compounding every 6 months?

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.

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.

**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 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?

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?

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 444** investment decision, corporate financial decision theory

The investment decision primarily affects which part of a business?

**Question 446** working capital decision, corporate financial decision theory

The working capital decision primarily affects which part of a business?

The expression 'cash is king' emphasizes the importance of having enough cash to pay your short term debts to avoid bankruptcy. Which business decision is this expression most closely related to?

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 461** book and market values, ROE, ROA, market efficiency

One year ago a pharmaceutical firm floated by selling its 1 million shares for $100 each. Its book and market values of equity were both $100m. Its debt totalled $50m. The required return on the firm's assets was 15%, equity 20% and debt 5% pa.

In the year since then, the firm:

- Earned net income of $29m.
- Paid dividends totaling $10m.
- Discovered a valuable new drug that will lead to a massive 1,000 times increase in the firm's net income in 10 years after the research is commercialised. News of the discovery was publicly announced. The firm's systematic risk remains unchanged.

Which of the following statements is **NOT** correct? All statements are about current figures, not figures one year ago.

**Hint**: Book return on assets (ROA) and book return on equity (ROE) are ratios that accountants like to use to measure a business's *past* performance.

###\text{ROA}= \dfrac{\text{Net income}}{\text{Book value of assets}}###

###\text{ROE}= \dfrac{\text{Net income}}{\text{Book value of equity}}###

The required return on assets ##r_V## is a return that financiers like to use to estimate a business's *future* required performance which compensates them for the firm's assets' risks. If the business were to achieve realised historical returns equal to its required returns, then investment into the business's assets would have been a zero-NPV decision, which is neither good nor bad but fair.

###r_\text{V, 0 to 1}= \dfrac{\text{Cash flow from assets}_\text{1}}{\text{Market value of assets}_\text{0}} = \dfrac{CFFA_\text{1}}{V_\text{0}}###

Similarly for equity and debt.

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?

"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:

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 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.

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 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?

**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?

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

**Question 207** income and capital returns, bond pricing, coupon rate, no explanation

For a bond that pays fixed semi-annual coupons, how is the annual coupon rate defined, and how is the bond's annual income yield from time 0 to 1 defined mathematically?

Let: ##P_0## be the bond price now,

##F_T## be the bond's face value,

##T## be the bond's maturity in years,

##r_\text{total}## be the bond's total yield,

##r_\text{income}## be the bond's income yield,

##r_\text{capital}## be the bond's capital yield, and

##C_t## be the bond's coupon at time t in years. So ##C_{0.5}## is the coupon in 6 months, ##C_1## is the coupon in 1 year, and so on.

**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:

A four year bond has a face value of $100, a yield of 9% and a fixed coupon rate of 6%, paid semi-annually. What is its 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?

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?

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

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.

A **30** year Japanese government bond was just issued at **par** with a yield of **1.7**% pa. The fixed coupon payments are **semi-annual**. The bond has a face value of $**100**.

**Six months** later, just **after** the first coupon is paid, the yield of the bond increases to **2**% pa. What is the bond's **new** price?

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**?

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 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?

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

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

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

A 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.

When using the dividend discount model, care must be taken to avoid using a nominal dividend growth rate that exceeds the country's nominal GDP growth rate. Otherwise the firm is forecast to take over the country since it grows faster than the average business forever.

Suppose a firm's nominal dividend grows at **10**% pa forever, and nominal GDP growth is **5**% pa forever. The firm's total dividends are currently $**1** billion (t=0). The country's GDP is currently $**1,000** billion (t=0).

In approximately how many years will the company's total dividends be as large as the country's GDP?

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.

A student won $**1**m in a lottery. Currently the money is in a bank account which pays interest at **6**% pa, given as an APR compounding per month.

She plans to spend $**20,000** at the **beginning** of every month from now on (so the first withdrawal will be at t=0). After each withdrawal, she will check how much money is left in the account. When there is less than $**500,000** left, she will donate that remaining amount to charity.

In how many months will she make her last withdrawal and donate the remainder to charity?

**Question 573** bond pricing, zero coupon bond, term structure of interest rates, expectations hypothesis, liquidity premium theory, forward interest rate, yield curve

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?

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.

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 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?

**Question 547** PE ratio, Multiples valuation, DDM, income and capital returns, no explanation

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.

Which of the following companies is most suitable for valuation using PE multiples techniques?

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##.

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

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

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

**Question 398** financial distress, capital raising, leverage, capital structure, NPV

A levered firm has zero-coupon bonds which mature in one year and have a combined face value of $**9.9**m.

Investors are risk-neutral and therefore all debt and equity holders demand the same required return of **10**% pa.

In one year the firm's assets will be worth:

- $
**13.2**m with probability 0.5 in the good state of the world, or - $
**6.6**m with probability 0.5 in the bad state of the world.

A new project presents itself which requires an investment of $**2**m and will provide a certain cash flow of $**3.3**m in one year.

The firm doesn't have any excess cash to make the initial $2m investment, but the funds can be raised from shareholders through a fairly priced rights issue. Ignore all transaction costs.

Should shareholders vote to proceed with the project and equity raising? What will be the gain in shareholder **wealth** if they decide to proceed?

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:

**Question 237** WACC, Miller and Modigliani, interest tax shield

Which of the following discount rates should be the **highest** for a levered company? Ignore the costs of financial distress.

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 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:

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 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}###

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?

An old company's Firm Free Cash Flow (FFCF, same as CFFA) is forecast in the graph below.

To value the firm's assets, the terminal value needs to be calculated using the perpetuity with growth formula:

###V_{\text{terminal, }t-1} = \dfrac{FFCF_{\text{terminal, }t}}{r-g}###

Which point corresponds to the best time to calculate the terminal value?

A new company's Firm Free Cash Flow (FFCF, same as CFFA) is forecast in the graph below.

To value the firm's assets, the terminal value needs to be calculated using the perpetuity with growth formula:

###V_{\text{terminal, }t-1} = \dfrac{FFCF_{\text{terminal, }t}}{r-g}###

Which point corresponds to the best time to calculate the terminal value?

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

**Question 657** systematic and idiosyncratic risk, CAPM, no explanation

A stock's **required** total return will **decrease** when its:

When using the dividend discount model to price a stock:

### p_{0} = \frac{d_1}{r - g} ###

The growth rate of dividends (g):

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:

A very low-risk stock just paid its semi-annual dividend of $0.14, as it has for the last 5 years. You conservatively estimate that from now on the dividend will fall at a rate of 1% every 6 months.

If the stock currently sells for $3 per share, what must be its required total return as an effective annual rate?

If risk free government bonds are trading at a yield of 4% pa, given as an effective annual rate, would you consider buying or selling the stock?

The stock's required total return is:

**Question 271** CAPM, option, risk, systematic risk, systematic and idiosyncratic risk

All things remaining equal, according to the capital asset pricing model, if the systematic variance of an asset increases, its required return will increase and its price will decrease.

If the idiosyncratic variance of an asset increases, its price will be unchanged.

What is the relationship between the price of a call or put **option** and the total, systematic and idiosyncratic variance of the **underlying asset** that the option is based on? Select the most correct answer.

Call and put option prices **in**crease when the:

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

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

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

The accounting identity states that the book value of a company's assets (A) equals its liabilities (L) plus owners equity (OE), so A = L + OE.

The finance version states that the market value of a company's assets (V) equals the market value of its debt (D) plus equity (E), so V = D + E.

Therefore a business's assets can be seen as a portfolio of the debt and equity that fund the assets.

Let ##\sigma_\text{V total}^2## be the total variance of returns on assets, ##\sigma_\text{V syst}^2## be the systematic variance of returns on assets, and ##\sigma_\text{V idio}^2## be the idiosyncratic variance of returns on assets, and ##\rho_\text{D idio, E idio}## be the correlation between the idiosyncratic returns on debt and equity.

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

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

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

Mr Blue, Miss Red and Mrs Green are people with different utility functions. Which of the statements about the 3 utility functions is **NOT** correct?

**Question 699** utility, risk aversion, utility function, gamble

Mr Blue, Miss Red and Mrs Green are people with different utility functions.

Each person has $50 of initial wealth. A coin toss game is offered to each person at a casino where the player can win or lose $50. Each player can flip a coin and if they flip heads, they receive $50. If they flip tails then they will lose $50. Which of the following statements is **NOT** correct?

Which of the below statements about utility is **NOT** generally accepted by economists? Most people are thought to:

Mr Blue, Miss Red and Mrs Green are people with different utility functions.

Note that a fair gamble is a bet that has an expected value of zero, such as paying $0.50 to win $1 in a coin flip with heads or nothing if it lands tails. Fairly priced insurance is when the expected present value of the insurance premiums is equal to the expected loss from the disaster that the insurance protects against, such as the cost of rebuilding a home after a catastrophic fire.

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

A stock's total standard deviation of returns is **20**% pa. The market portfolio's total standard deviation of returns is **15**% pa. The beta of the stock is **0.8**.

What is the stock's **diversifiable** standard deviation?

**Question 624** franking credit, personal tax on dividends, imputation tax system, no explanation

Which of the following statements about Australian franking credits is **NOT** correct? Franking credits:

**Question 494** franking credit, personal tax on dividends, imputation tax system

A firm pays a fully franked cash dividend of $**100** to one of its Australian shareholders who has a personal marginal tax rate of **15**%. The corporate tax rate is **30**%.

What will be the shareholder's personal tax payable due to the dividend payment?

**Question 513** stock split, reverse stock split, stock dividend, bonus issue, rights issue

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

In mid 2009 the listed mining company Rio Tinto announced a 21-for-40 renounceable rights issue. Below is the chronology of events:

- 04/06/2009. Share price opens at $69.00 and closes at $66.90.
- 05/06/2009. 21-for-40 rights issue announced at a subscription price of $28.29.
- 16/06/2009. Last day that shares trade cum-rights. Share price opens at $76.40 and closes at $75.50.
- 17/06/2009. Shares trade ex-rights. Rights trading commences.

All things remaining equal, what would you expect Rio Tinto's stock price to open at on the first day that it trades ex-rights (17/6/2009)? Ignore the time value of money since time is negligibly short. Also ignore taxes.

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:

**Question 546** income and capital returns, interest only loan, no explanation

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:

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

Which of the following statements about futures contracts on shares is **NOT** correct, assuming that markets are efficient?

When an equity future is first negotiated (at t=0):

A company advertises an investment costing $**1,000** which they say is underpriced. They say that it has an expected total return of **15**% pa, but a required return of only **10**% pa. Assume that there are no dividend payments so the entire 15% total return is all capital return.

Assuming that the company's statements are correct, what is the **NPV** of buying the investment if the 15% return lasts for the next **100** years (t=0 to 100), then reverts to 10% pa after that time? Also, what is the NPV of the investment if the 15% return lasts forever?

In both cases, assume that the required return of 10% remains constant. All returns are given as effective annual rates.

The answer choices below are given in the same order (15% for 100 years, and 15% forever):

**Question 455** income and capital returns, payout policy, DDM, market efficiency

A fairly priced **unlevered** firm plans to pay a dividend of $**1** next year (t=1) which is expected to grow by **3**% pa every year after that. The firm's required return on equity is **8**% pa.

The firm is thinking about reducing its future dividend payments by **10**% so that it can use the extra cash to invest in more projects which are expected to return **8**% pa, and have the same risk as the existing projects. Therefore, next year's dividend will be $**0.90**. No new equity or debt will be issued to fund the new projects, they'll all be funded by the cut in dividends.

What will be the stock's new annual **capital** return (proportional increase in price per year) if the change in payout policy goes ahead?

Assume that payout policy is irrelevant to firm value (so there's no signalling effects) and that all rates are effective annual rates.

A managed fund charges fees based on the amount of money that you keep with them. The fee is **2**% of the **end**-of-year amount, paid at the **end** of every year.

This fee is charged regardless of whether the fund makes gains or losses on your money.

The fund offers to invest your money in shares which have an expected return of **10%** pa before fees.

You are thinking of investing $**100,000** in the fund and keeping it there for **40** years when you plan to retire.

How much money do you expect to have in the fund in 40 years? Also, what is the future value of the fees that the fund expects to earn from you? Give both amounts as future values in 40 years. Assume that:

- The fund has no private information.
- Markets are weak and semi-strong form efficient.
- The fund's transaction costs are negligible.
- The cost and trouble of investing your money in shares by yourself, without the managed fund, is negligible.
- The fund invests its fees in the same companies as it invests your funds in, but with no fees.

The below answer choices list your expected wealth in 40 years and then the fund's expected wealth in 40 years.

**Question 416** real estate, market efficiency, income and capital returns, DDM, CAPM

A residential real estate investor believes that house prices will grow at a rate of **5**% pa and that rents will grow by **2**% pa forever.

All rates are given as nominal effective annual returns. Assume that:

- His forecast is true.
- Real estate is and always will be fairly priced and the capital asset pricing model (CAPM) is true.
- Ignore all costs such as taxes, agent fees, maintenance and so on.
- All rental income cash flow is paid out to the owner, so there is no re-investment and therefore no additions or improvements made to the property.
- The non-monetary benefits of owning real estate and renting remain constant.

Which one of the following statements is **NOT** correct? Over time:

Suppose that the US government recently announced that subsidies for fresh milk producers will be gradually phased out over the next year. Newspapers say that there are expectations of a 40% increase in the spot price of fresh milk over the next year.

Option prices on fresh milk trading on the Chicago Mercantile Exchange (CME) reflect expectations of this 40% increase in spot prices over the next year. Similarly to the rest of the market, you believe that prices will rise by 40% over the next year.

What option trades are likely to be profitable, or to be more specific, result in a positive Net Present Value (NPV)?

Assume that:

- Only the spot price is expected to increase and there is no change in expected volatility or other variables that affect option prices.
- No taxes, transaction costs, information asymmetry, bid-ask spreads or other market frictions.

**Question 100** market efficiency, technical analysis, joint hypothesis problem

A company selling charting and technical analysis software claims that independent academic studies have shown that its software makes significantly positive abnormal returns. Assuming the claim is true, which statement(s) are correct?

(I) Weak form market efficiency is broken.

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

(III) Strong form market efficiency is broken.

(IV) The asset pricing model used to measure the abnormal returns (such as the CAPM) had mis-specification error so the returns may not be abnormal but rather fair for the level of risk.

Select the most correct response:

An established mining firm announces that it expects large losses over the following year due to flooding which has temporarily stalled production at its mines. Which statement(s) are correct?

(i) If the firm adheres to a full dividend payout policy it will not pay any dividends over the following year.

(ii) If the firm wants to signal that the loss is temporary it will maintain the same level of dividends. It can do this so long as it has enough retained profits.

(iii) By law, the firm will be unable to pay a dividend over the following year because it cannot pay a dividend when it makes a loss.

Select the most correct response:

**Question 338** market efficiency, CAPM, opportunity cost, technical analysis

A man inherits $**500,000** worth of shares.

He believes that by learning the secrets of trading, keeping up with the financial news and doing complex trend analysis with charts that he can quit his job and become a self-employed day trader in the equities markets.

What is the expected gain from doing this over the first year? Measure the net gain in wealth received at the end of this first year due to the decision to become a day trader. Assume the following:

- He earns $
**60,000**pa in his current job, paid in a lump sum at the end of each year. - He enjoys examining share price graphs and day trading just as much as he enjoys his current job.
- Stock markets are weak form and semi-strong form efficient.
- He has no inside information.
- He makes
**1**trade every day and there are**250**trading days in the year. Trading costs are $**20**per trade. His broker invoices him for the trading costs at the end of the year. - The shares that he currently owns and the shares that he intends to trade have the same level of systematic risk as the market portfolio.
- The market portfolio's expected return is
**10**% pa.

Measure the **net gain** over the **first** year as an expected wealth increase at the **end** of the year.

**Question 693** boot strapping zero coupon yield, forward interest rate, term structure of interest rates

Information about three risk free Government bonds is given in the table below.

Federal Treasury Bond Data |
||||

Maturity |
Yield to maturity |
Coupon rate |
Face value |
Price |

(years) | (pa, compounding semi-annually) | (pa, paid semi-annually) | ($) | ($) |

0.5 | 3% | 4% | 100 | 100.4926 |

1 | 4% | 4% | 100 | 100.0000 |

1.5 | 5% | 4% | 100 | 98.5720 |

Based on the above government bonds' yields to maturity, which of the below statements about the spot zero rates and forward zero rates is **NOT** correct?

**Question 155** inflation, real and nominal returns and cash flows, Loan, effective rate conversion

You are a banker about to grant a 2 year loan to a customer. The loan's principal and interest will be repaid in a single payment at maturity, sometimes called a zero-coupon loan, discount loan or bullet loan.

You require a **real** return of **6**% pa over the two years, given as an effective annual rate. Inflation is expected to be **2**% this year and **4**% next year, both given as effective annual rates.

You judge that the customer can afford to pay back $**1,000,000** in **2** years, given as a **nominal** cash flow. How much should you lend to her right now?

**Question 580** price gains and returns over time, time calculation, effective rate

How many years will it take for an asset's price to **quadruple** (be four times as big, say from $1 to $4) if the price grows by **15**% pa?

A 2 year government bond yields 5% pa with a coupon rate of 6% pa, paid semi-annually.

Find the effective six month rate, effective annual rate and the effective daily rate. Assume that each month has 30 days and that there are 360 days in a year.

All answers are given in the same order:

##r_\text{eff semi-annual}##, ##r_\text{eff yrly}##, ##r_\text{eff daily}##.

A share just paid its semi-annual dividend of $10. The dividend is expected to grow at 2% every 6 months forever. This 2% growth rate is an effective 6 month rate. Therefore the next dividend will be $10.20 in six months. The required return of the stock is 10% pa, given as an effective annual rate.

What is the price of the share now?

**Question 24** implicit interest rate in wholesale credit, effective rate

A bathroom and plumbing supplies shop offers credit to its customers. Customers are given 60 days to pay for their goods, but if they pay within 7 days they will get a 2% discount.

What is the effective interest rate implicit in the discount being offered? Assume 365 days in a year and that all customers pay on either the 7th day or the 60th day. All rates given in this question are effective annual rates.

**Question 22** NPV, perpetuity with growth, effective rate, effective rate conversion

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

The first payment of $90 is in 3 years, followed by payments every 6 months in perpetuity after that which shrink by 3% every 6 months. That is, the growth rate every 6 months is actually negative 3%, given as an effective 6 month rate. So the payment at ## t=3.5 ## years will be ## 90(1-0.03)^1=87.3 ##, and so on.

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 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?

**Question 662** APR, effective rate, effective rate conversion, no explanation

Which of the following interest rate labels does **NOT** make sense?

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?

An effective **monthly** return of 1% ##(r_\text{eff monthly})## is equivalent to an effective **annual** return ##(r_\text{eff annual})## of:

The symbol ##\text{GDR}_{0\rightarrow 1}## represents a stock's gross discrete return per annum over the first year. ##\text{GDR}_{0\rightarrow 1} = P_1/P_0##. The subscript indicates the time period that the return is mentioned over. So for example, ##\text{AAGDR}_{1 \rightarrow 3}## is the arithmetic average GDR measured over the two year period from years 1 to 3, but it is expressed as a per annum rate.

Which of the below statements about the arithmetic and geometric average GDR is **NOT** correct?

A share was bought for $10 (at t=0) and paid its annual dividend of $0.50 one year later (at t=1). Just after the dividend was paid, the share price was $11 (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{dividend}##.

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

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

All rates are effective annual rates and the cash flows (##d_1##) are received every year. Note that the r and g terms in the above DDM could also be labelled as below: ###r = r_{\text{total, 0}\rightarrow\text{1yr, eff 1yr}}### ###g = r_{\text{capital, 0}\rightarrow\text{1yr, eff 1yr}}### Which of the following statements is **NOT** correct?

**Question 707** continuously compounding rate, continuously compounding rate conversion

Convert a **10**% effective annual rate ##(r_\text{eff annual})## into a continuously compounded annual rate ##(r_\text{cc annual})##. The equivalent continuously compounded annual rate is:

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

The below three graphs show probability density functions (PDF) of three different random variables Red, Green and Blue. Let ##P_1## be the unknown price of a stock in one year. ##P_1## is a random variable. Let ##P_0 = 1##, so the share price now is $1. This one dollar is a constant, it is not a variable.

Which of the below statements is **NOT** correct? Financial practitioners commonly assume that the shape of the PDF represented in the colour:

A managed fund charges fees based on the amount of money that you keep with them. The fee is **2**% of the **start**-of-year amount, but it is paid at the **end** of every year.

This fee is charged regardless of whether the fund makes gains or losses on your money.

The fund offers to invest your money in shares which have an expected return of **10**% pa before fees.

You are thinking of investing $**100,000** in the fund and keeping it there for **40** years when you plan to retire.

What is the Net Present Value (NPV) of investing your money in the fund? Note that the question is **not** asking how much money you will have in 40 years, it is asking: what is the **NPV** of investing in the fund? Assume that:

- The fund has no private information.
- Markets are weak and semi-strong form efficient.
- The fund's transaction costs are negligible.
- The cost and trouble of investing your money in shares by yourself, without the managed fund, is negligible.

Alice, Bob, Chris and Delta are traders in the futures market. The following trades occur over a single day in a newly-opened equity index future that matures in one year which the exchange just made available.

1. Alice buys a future from Bob.

2. Chris buys a future from Delta.

3. Delta buys a future from Bob.

These were the only trades made in this equity index future. What was the trading volume and what is the open interest?