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

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.

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 |

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?

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:

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.

**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?

**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.

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.

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

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

**Question 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.

**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 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.

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).

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 phone company Telstra 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 $50 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 $71 per month. This plan includes the latest smart phone.

Neither plan has any additional payments at the start or end.

The only difference between the plans is the phone, so what is the implied cost of the phone as a present value?

Assume that the discount rate is 2% per month given as an effective monthly rate, the same high interest rate on credit cards.

**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?

A two year Government bond has a face value of $100, a yield of 2.5% pa and a fixed coupon rate of 0.5% pa, paid semi-annually. What is its price?

**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:

A company's shares just paid their annual dividend of $2 each.

The stock price is now $40 (just after the dividend payment). The annual dividend is expected to grow by 3% every year forever. The assumptions of the dividend discount model are valid for this company.

What do you expect the effective annual **dividend yield** to be in 3 years (dividend yield from t=3 to t=4)?

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.

In the dividend discount model:

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

The pronumeral ##g## is supposed to be the:

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?

**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.

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 just signed up for a 30 year **interest-only** mortgage with monthly payments of $3,000 per month. The interest rate is 6% pa which is not expected to change.

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

**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?

**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.

Due to floods overseas, there is a cut in the supply of the mineral iron ore and its price increases dramatically. An Australian iron ore mining company therefore expects a large but temporary increase in its profit and cash flows. The mining company does not have any positive NPV projects to begin, so what should it do? Select the most correct answer.

You want to buy an apartment worth $500,000. You have saved a deposit of $50,000. The bank has agreed to lend you the $450,000 as a **fully amortising** mortgage loan with a term of 25 years. The interest rate is 6% pa and is not expected to change.

What will be your monthly payments?

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:

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?

When using the dividend discount model to price a stock:

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

The growth rate of dividends (g):

A student just won the lottery. She won $1 million in cash after tax. She is trying to calculate how much she can spend per month for the rest of her life. She assumes that she will live for another 60 years. She wants to withdraw equal amounts at the beginning of every month, starting right now.

All of the cash is currently sitting in a bank account which pays interest at a rate of 6% pa, given as an APR compounding per month. On her last withdrawal, she intends to have nothing left in her bank account. How much can she withdraw at the beginning of each month?

**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?

You just signed up for a 30 year **fully amortising** mortgage with monthly payments of $1,000 per month. The interest rate is 6% pa which is not expected to change.

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

A highly leveraged risky firm is trying to raise more debt. The types of debt being considered, in no particular order, are senior bonds, junior bonds, bank accepted bills, promissory notes and bank loans.

Which of these forms of debt is the safest from the perspective of the debt investors who are thinking of investing in the firm's new debt?

Currently, a mining company has a share price of $6 and pays constant annual dividends of $0.50. The next dividend will be paid in 1 year. Suddenly and unexpectedly the mining company announces that due to higher than expected profits, all of these windfall profits will be paid as a special dividend of $0.30 in 1 year.

If investors believe that the windfall profits and dividend is a one-off event, what will be the new share price? If investors believe that the additional dividend is actually permanent and will continue to be paid, what will be the new share price? Assume that the required return on equity is unchanged. Choose from the following, where the first share price includes the one-off increase in earnings and dividends for the first year only ##(P_\text{0 one-off})## , and the second assumes that the increase is permanent ##(P_\text{0 permanent})##:

Note: When a firm makes excess profits they sometimes pay them out as special dividends. Special dividends are just like ordinary dividends but they are one-off and investors do not expect them to continue, unlike ordinary dividends which are expected to persist.

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?

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 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.

**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.

What is the net present value (NPV) of undertaking a full-time Australian undergraduate business degree as an Australian citizen? Only include the cash flows over the duration of the degree, ignore any benefits or costs of the degree after it's completed.

Assume the following:

- The degree takes
**3**years to complete and all students pass all subjects. - There are
**2**semesters per year and**4**subjects per semester. - University fees per subject per semester are
**$1,277**, paid at the**start**of each semester. Fees are expected to stay constant for the next 3 years. - There are
**52**weeks per year. - The first semester is just about to start (t=0). The first semester lasts for 19 weeks (t=
**0**to**19**). - The second semester starts immediately afterwards (t=19) and lasts for another 19 weeks (t=
**19**to**38**). - The summer holidays begin after the second semester ends and last for
**14**weeks (t=**38**to**52**). Then the first semester begins the next year, and so on. - Working full time at the grocery store instead of studying full-time pays
**$20**/hr and you can work**35**hours per week. Wages are paid at the**end**of each week. - Full-time students can work full-time during the summer holiday at the grocery store for the same rate of $20/hr for 35 hours per week. Wages are paid at the end of each week.
- The discount rate is
**9.8%**pa. All rates and cash flows are real. Inflation is expected to be**3%**pa. All rates are effective annual.

The NPV of costs from undertaking the university degree is:

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

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

You're trying to save enough money for a deposit to buy a house. You want to buy a house worth $400,000 and the bank requires a 20% deposit ($80,000) before it will give you a loan for the other $320,000 that you need.

You currently have no savings, but you just started working and can save $2,000 per month, with the first payment in one month from now. Bank interest rates on savings accounts are 4.8% pa with interest paid monthly and interest rates are not expected to change.

How long will it take to save the $80,000 deposit? Round your answer up to the nearest month.

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?

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?

A stock **just paid** its annual dividend of $9. The share price is $60. The required return of the stock is 10% pa as an effective annual rate.

What is the implied growth rate of the dividend per year?

**Question 498** NPV, Annuity, perpetuity with growth, multi stage growth model

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

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

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

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

**Question 215** equivalent annual cash flow, effective rate conversion

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

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

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

Should you buy the or the ?

**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.

Over the next year, the management of an unlevered company plans to:

- Achieve firm free cash flow (FFCF or CFFA) of $1m.
- Pay dividends of $1.8m
- Complete a $1.3m share buy-back.
- Spend $0.8m on new buildings without buying or selling any other fixed assets. This capital expenditure is included in the CFFA figure quoted above.

Assume that:

- All amounts are received and paid at the end of the year so you can ignore the time value of money.
- The firm has sufficient retained profits to pay the dividend and complete the buy back.
- The firm plans to run a very tight ship, with no excess cash above operating requirements currently or over the next year.

How much new equity financing will the company need? In other words, what is the value of new shares that will need to be issued?

Over the next year, the management of an **unlevered** company plans to:

- Make $
**5**m in sales, $**1.9m**in net income and $**2**m in equity free cash flow (EFCF). - Pay dividends of $
**1**m. - Complete a $
**1.3**m share buy-back.

Assume that:

- All amounts are received and paid at the end of the year so you can ignore the time value of money.
- The firm has sufficient retained profits to legally pay the dividend and complete the buy back.
- The firm plans to run a very tight ship, with no excess cash above operating requirements currently or over the next year.

How much new equity financing will the company need? In other words, what is the value of new shares that will need to be issued?

A person is thinking about borrowing $100 from the bank at 7% pa and investing it in shares with an expected return of 10% pa. One year later the person will sell the shares and pay back the loan in full. Both the loan and the shares are fairly priced.

What is the Net Present Value (NPV) of this one year investment? Note that you are asked to find the present value (##V_0##), not the value in one year (##V_1##).

You just started work at your new job which pays $48,000 per year.

The human resources department have given you the option of being paid at the end of every week or every month.

Assume that there are 4 weeks per month, 12 months per year and 48 weeks per year.

Bank interest rates are 12% pa given as an APR compounding per month.

What is the dollar gain over one year, as a net present value, of being paid every week rather than every month?

Your friend is trying to find the net present value of a project. The project is expected to last for just one year with:

- a negative cash flow of
**-**$**1**million initially (t=0), and - a positive cash flow of $
**1.1**million in one year (t=1).

The project has a total required return of 10% pa due to its moderate level of undiversifiable risk.

Your friend is aware of the importance of opportunity costs and the time value of money, but he is unsure of how to find the NPV of the project.

He knows that the opportunity cost of investing the $1m in the project is the expected gain from investing the money in shares instead. Like the project, shares also have an expected return of 10% since they have moderate undiversifiable risk. This opportunity cost is $0.1m ##(=1m \times 10\%)## which occurs in one year (t=1).

He knows that the time value of money should be accounted for, and this can be done by finding the present value of the cash flows in one year.

Your friend has listed a few different ways to find the NPV which are written down below.

(I) ##-1m + \dfrac{1.1m}{(1+0.1)^1} ##

(II) ##-1m + \dfrac{1.1m}{(1+0.1)^1} - \dfrac{1m}{(1+0.1)^1} \times 0.1 ##

(III) ##-1m + \dfrac{1.1m}{(1+0.1)^1} - \dfrac{1.1m}{(1+0.1)^1} \times 0.1 ##

(IV) ##-1m + 1.1m - \dfrac{1.1m}{(1+0.1)^1} \times 0.1 ##

(V) ##-1m + 1.1m - 1.1m \times 0.1 ##

Which of the above calculations give the correct NPV? Select the most correct answer.

A pharmaceutical firm has just discovered a valuable new drug. So far the news has been kept a secret.

The net present value of making and commercialising the drug is $**200** million, but $**600** million of bonds will need to be issued to fund the project and buy the necessary plant and equipment.

The firm will release the news of the discovery and bond raising to shareholders simultaneously in the same announcement. The bonds will be issued shortly after.

Once the announcement is made and the bonds are issued, what is the expected increase in the value of the firm's assets (ΔV), market capitalisation of debt (ΔD) and market cap of equity (ΔE)?

The triangle symbol is the Greek letter capital delta which means change or increase in mathematics.

Ignore the benefit of interest tax shields from having more debt.

Remember: ##ΔV = ΔD+ΔE##

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?

The following cash flows are expected:

- Constant perpetual yearly payments of $70, with the first payment in 2.5 years from now (first payment at t=2.5).
- A single payment of $600 in 3 years and 9 months (t=3.75) from now.

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

**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?

Value the following business project to manufacture a new product.

Project Data | ||

Project life | 2 yrs | |

Initial investment in equipment | $6m | |

Depreciation of equipment per year | $3m | |

Expected sale price of equipment at end of project | $0.6m | |

Unit sales per year | 4m | |

Sale price per unit | $8 | |

Variable cost per unit | $5 | |

Fixed costs per year, paid at the end of each year | $1m | |

Interest expense per year | 0 | |

Tax rate | 30% | |

Weighted average cost of capital after tax per annum | 10% | |

**Notes**

- The firm's current assets and current liabilities are $3m and $2m respectively right now. This net working capital will not be used in this project, it will be used in other unrelated projects.

Due to the project, current assets (mostly inventory) will grow by $2m initially (at t = 0), and then by $0.2m at the end of the first year (t=1).

Current liabilities (mostly trade creditors) will increase by $0.1m at the end of the first year (t=1).

At the end of the project, the net working capital accumulated due to the project can be sold for the same price that it was bought. - The project cost $0.5m to research which was incurred one year ago.

**Assumptions**

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

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

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

Candys Corp | ||

Income Statement for | ||

year ending 30th June 2013 | ||

$m | ||

Sales | 200 | |

COGS | 50 | |

Operating expense | 10 | |

Depreciation | 20 | |

Interest expense | 10 | |

Income before tax | 110 | |

Tax at 30% | 33 | |

Net income | 77 | |

Candys Corp | ||

Balance Sheet | ||

as at 30th June | 2013 | 2012 |

$m | $m | |

Assets | ||

Current assets | 220 | 180 |

PPE | ||

Cost | 300 | 340 |

Accumul. depr. | 60 | 40 |

Carrying amount | 240 | 300 |

Total assets | 460 | 480 |

Liabilities | ||

Current liabilities | 175 | 190 |

Non-current liabilities | 135 | 130 |

Owners' equity | ||

Retained earnings | 50 | 60 |

Contributed equity | 100 | 100 |

Total L and OE | 460 | 480 |

Note: all figures are given in millions of dollars ($m).

There are a number of ways that assets can be depreciated. Generally the government's tax office stipulates a certain method.

But if it didn't, what would be the ideal way to depreciate an asset from the perspective of a businesses owner?

There are many different ways to value a firm's assets. Which of the following will **NOT** give the correct market value of a levered firm's assets ##(V_L)##? Assume that:

- The firm is financed by listed common stock and vanilla annual fixed coupon bonds, which are both traded in a liquid market.
- The bonds' yield is equal to the coupon rate, so the bonds are issued at par. The yield curve is flat and yields are not expected to change. When bonds mature they will be rolled over by issuing the same number of new bonds with the same expected yield and coupon rate, and so on forever.
- Tax rates on the dividends and capital gains received by investors are equal, and capital gains tax is paid every year, even on unrealised gains regardless of when the asset is sold.
- There is no re-investment of the firm's cash back into the business. All of the firm's excess cash flow is paid out as dividends so real growth is zero.
- The firm operates in a mature industry with zero real growth.
- All cash flows and rates in the below equations are real (not nominal) and are expected to be stable forever. Therefore the perpetuity equation with no growth is suitable for valuation.

Where:

###r_\text{WACC before tax} = r_D.\frac{D}{V_L} + r_{EL}.\frac{E_L}{V_L} = \text{Weighted average cost of capital before tax}### ###r_\text{WACC after tax} = r_D.(1-t_c).\frac{D}{V_L} + r_{EL}.\frac{E_L}{V_L} = \text{Weighted average cost of capital after tax}### ###NI_L=(Rev-COGS-FC-Depr-\mathbf{IntExp}).(1-t_c) = \text{Net Income Levered}### ###CFFA_L=NI_L+Depr-CapEx - \varDelta NWC+\mathbf{IntExp} = \text{Cash Flow From Assets Levered}### ###NI_U=(Rev-COGS-FC-Depr).(1-t_c) = \text{Net Income Unlevered}### ###CFFA_U=NI_U+Depr-CapEx - \varDelta NWC= \text{Cash Flow From Assets Unlevered}###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?

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 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}###

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

Assume the following:

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

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

The mobile phone manufacturing project's:

A 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 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.

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?

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:

**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?

**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?

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

Portfolio Details | ||||||

Stock | Expected return |
Standard deviation |
Correlation ##(\rho_{A,B})## |
Dollars invested |
||

A | 0.1 | 0.4 | 0.5 | 60 | ||

B | 0.2 | 0.6 | 140 | |||

What is the standard deviation (not variance) of the above portfolio?

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

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

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 covariance and correlation of two stocks X and Y's annual returns are calculated over a number of years. The units of the returns are in percent per annum ##(\% pa)##.

What are the units of the covariance ##(\sigma_{X,Y})## and correlation ##(\rho_{X,Y})## of returns respectively?

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

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?

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

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

**Question 704** utility, risk aversion, utility function, gamble

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

Each person has $256 of initial wealth. A coin toss game is offered to each person at a casino where the player can win or lose $256. Each player can flip a coin and if they flip heads, they receive $256. If they flip tails then they will lose $256. Which of the following statements is **NOT** correct?

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

Investment projects that plot **above** the SML would have:

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

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

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

**Question 339** bond pricing, inflation, market efficiency, income and capital returns

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

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

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

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

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

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

**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.

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 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:

A company announces that it will pay a dividend, as the market expected. The company's shares trade on the stock exchange which is open from 10am in the morning to 4pm in the afternoon each weekday. When would the share price be expected to fall by the amount of the dividend? Ignore taxes.

The share price is expected to fall during the:

In late 2003 the listed bank ANZ announced a 2-for-11 rights issue to fund the takeover of New Zealand bank NBNZ. Below is the chronology of events:

- 23/10/2003. Share price closes at $18.30.
- 24/10/2003. 2-for-11 rights issue announced at a subscription price of $13. The proceeds of the rights issue will be used to acquire New Zealand bank NBNZ. Trading halt announced in morning before market opens.
- 28/10/2003. Trading halt lifted. Last (and only) day that shares trade cum-rights. Share price opens at $18.00 and closes at $18.14.
- 29/10/2003. Shares trade ex-rights.

All things remaining equal, what would you expect ANZ's stock price to open at on the first day that it trades ex-rights (29/10/2003)? Ignore the time value of money since time is negligibly short. Also ignore taxes.

The below three graphs show probability density functions (PDF) of three different random variables Red, Green and Blue.

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

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?

**Question 721** mean and median returns, return distribution, arithmetic and geometric averages, continuously compounding rate

Fred owns some Commonwealth Bank (CBA) shares. He has calculated CBA’s monthly returns for each month in the past 20 years using this formula:

###r_\text{t monthly}=\ln \left( \dfrac{P_t}{P_{t-1}} \right)###He then took the arithmetic average and found it to be **1**% per month using this formula:

He also found the standard deviation of these monthly returns which was **5**% per month:

Which of the below statements about Fred’s CBA shares is **NOT** correct? Assume that the past historical average return is the true population average of future expected returns.

**Question 722** mean and median returns, return distribution, arithmetic and geometric averages, continuously compounding rate

Here is a table of stock prices and returns. Which of the statements below the table is **NOT** correct?

Price and Return Population Statistics |
||||

Time | Prices | LGDR | GDR | NDR |

0 | 100 | |||

1 | 50 | -0.6931 | 0.5 | -0.5 |

2 | 100 | 0.6931 | 2 | 1 |

Arithmetic average | 0 | 1.25 | 0.25 | |

Arithmetic standard deviation | -0.6931 | 0.75 | 0.75 | |

**Question 668** buy and hold, market efficiency, idiom

A quote from the famous investor Warren Buffet: "Much success can be attributed to inactivity. Most investors cannot resist the temptation to constantly buy and sell."

Buffet is referring to the buy-and-hold strategy which is to buy and never sell shares. Which of the following is a disadvantage of a buy-and-hold strategy? Assume that share markets are semi-strong form efficient. Which of the following is **NOT** an advantage of the strict buy-and-hold strategy? A disadvantage of the buy-and-hold strategy is that it reduces:

An economy has only two investable assets: stocks and cash.

Stocks had a historical nominal average total return of negative two percent per annum (-2% pa) over the last 20 years. Stocks are liquid and actively traded. Stock returns are variable, they have risk.

Cash is riskless and has a nominal constant return of zero percent per annum (0% pa), which it had in the past and will have in the future. Cash can be kept safely at zero cost. Cash can be converted into shares and vice versa at zero cost.

The nominal total return of the shares over the **next** year is **expected** to be:

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. Of the **15**% pa total expected return, the dividend yield is expected to always be **7**% pa and rest is the capital yield.

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

In both cases, assume that the required return of 10% remains constant, the dividends can only be re-invested at **10**% pa and all returns are given as effective annual rates.

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

**Question 719** mean and median returns, return distribution, arithmetic and geometric averages, continuously compounding rate

A stock has an arithmetic average continuously compounded return (AALGDR) of **10**% pa, a standard deviation of continuously compounded returns (SDLGDR) of **80**% pa and current stock price of $**1**. Assume that stock prices are log-normally distributed.

In **one** year, what do you expect the mean and median prices to be? The answer options are given in the same order.

A 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.

A stock has a beta of **0.5**. Its next dividend is expected to be $**3**, paid **one** year from now. Dividends are expected to be paid annually and grow by **2**% pa forever. Treasury bonds yield **5**% pa and the market portfolio's expected return is **10**% pa. All returns are effective annual rates.

What is the price of the stock now?

**Question 235** SML, NPV, CAPM, risk

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

Investment projects that plot * on* the SML would have:

**Question 244** CAPM, SML, NPV, risk

Examine the following graph which shows stocks' betas ##(\beta)## and expected returns ##(\mu)##:

Assume that the CAPM holds and that future expectations of stocks' returns and betas are correctly measured. Which statement is **NOT** correct?

**Question 408** leverage, portfolio beta, portfolio risk, real estate, CAPM

You just bought a house worth $**1,000,000**. You financed it with an $**800,000** mortgage loan and a deposit of $**200,000**.

You estimate that:

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

What is the beta of the equity (the $200,000 deposit) that you have in your house?

Also, if the risk free rate is **5**% pa and the market portfolio's return is **10**% pa, what is the expected return on equity in your house? Ignore taxes, assume that all cash flows (interest payments and rent) were paid and received at the end of the year, and all rates are effective annual rates.

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

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

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

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

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

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

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

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

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

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

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.

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

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