**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?

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?

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.

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

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

If the assumptions of the DDM hold, which one of the following statements is **NOT** correct? The long term expected:

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

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

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

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

A stock is expected to pay the following dividends:

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

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

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

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

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

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

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

**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.

Carlos and Edwin are brothers and they both love Holden Commodore cars.

Carlos likes to buy the latest Holden Commodore car for **$40,000** every **4** years as soon as the new model is released. As soon as he buys the new car, he sells the old one on the second hand car market for **$20,000**. Carlos never has to bother with paying for repairs since his cars are brand new.

Edwin also likes Commodores, but prefers to buy 4-year old cars for **$20,000** and keep them for **11** years until the end of their life (new ones last for 15 years in total but the 4-year old ones only last for another 11 years). Then he sells the old car for **$2,000** and buys another 4-year old second hand car, and so on.

Every time Edwin buys a second hand 4 year old car he **immediately** has to spend **$1,000** on repairs, and then $1,000 every year after that for the next 10 years. So there are **11** payments in total from when the second hand car is bought at t=0 to the last payment at t=10. One year later (t=11) the old car is at the end of its total 15 year life and can be scrapped for $2,000.

Assuming that Carlos and Edwin maintain their love of Commodores and keep up their habits of buying new ones and second hand ones respectively, how much **larger** is Carlos' **equivalent annual cost** of car ownership compared with Edwin's?

The real discount rate is **10%** pa. All cash flows are real and are expected to remain constant. Inflation is forecast to be **3**% pa. All rates are effective annual. Ignore capital gains tax and tax savings from depreciation since cars are tax-exempt for individuals.

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

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

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

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

You own some nice shoes which you use once per week on date nights. You bought them **2** years ago for $**500**. In your experience, shoes used once per week last for **6** years. So you expect yours to last for another **4** years.

Your younger sister said that she wants to borrow your shoes once per week. With the increased use, your shoes will only last for another **2** years rather than 4.

What is the present value of the cost of letting your sister use your current shoes for the next 2 years?

Assume: that bank interest rates are **10**% pa, given as an effective annual rate; you will buy a new pair of shoes when your current pair wears out and your sister will not use the new ones; your sister will only use your current shoes so she will only use it for the next 2 years; and the price of new shoes never changes.

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

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

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

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

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

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:

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?

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

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.

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?

**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:

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

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

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

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?

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.

For a price of $95, Sherylanne will sell you a share which is expected to pay its first dividend of $10 in 7 years (t=7), and will continue to pay the same $10 dividend every year after that forever.

The required return of the stock is 10% pa.

For a price of $100, Rad will sell you a 5 year bond paying semi-annual coupons of 16% pa. The face value of the bond is $100. Other bonds with the same risk, maturity and coupon characteristics trade at a yield of 6% pa.

**Question 539** debt terminology, fully amortising loan, bond pricing

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

"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:

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

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

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

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

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

You 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?

**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?

Let the 'income return' of a bond be the coupon at the end of the period divided by the market price now at the start of the period ##(C_1/P_0)##. The expected income return of a **premium** fixed coupon bond is:

An investor bought two fixed-coupon bonds issued by the same company, a zero-coupon bond and a 7% pa semi-annual coupon bond. Both bonds have a face value of $1,000, mature in 10 years, and had a yield at the time of purchase of 8% pa.

A few years later, yields fell to 6% pa. Which of the following statements is correct? Note that a capital gain is an increase in price.

In these tough economic times, central banks around the world have cut interest rates so low that they are practically zero. In some countries, government bond yields are also very close to zero.

A three year government bond with a face value of $100 and a coupon rate of 2% pa paid semi-annually was just issued at a yield of 0%. What is the price of the bond?

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

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

Your main expense is fuel for your car which costs $100 per month. You just refueled, so you won't need any more fuel for another month (first payment at t=1 month).

You have $2,500 in a bank account which pays interest at a rate of 6% pa, payable monthly. Interest rates are not expected to change.

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

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

A young lady is trying to decide if she should attend university 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:

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

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

Assume that:

- Interest rates are expected to be
**constant**over the life of the loan. - Loans are
**interest-only**and have a life of 30 years. - Mortgage loan payments are made every month in arrears and all interest rates are given as annualised percentage rates compounding per month.

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

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

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

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

The capital return is the growth rate of the price.

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

Bonds X and Y are issued by different companies, but they both pay a semi-annual coupon of **10**% pa and they have the same face value ($100) and maturity (3 years).

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

**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:

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:

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

Sidebar Corp | ||

Income Statement for | ||

year ending 30th June 2013 | ||

$m | ||

Sales | 405 | |

COGS | 100 | |

Depreciation | 34 | |

Rent expense | 22 | |

Interest expense | 39 | |

Taxable Income | 210 | |

Taxes at 30% | 63 | |

Net income | 147 | |

Sidebar Corp | ||

Balance Sheet | ||

as at 30th June | 2013 | 2012 |

$m | $m | |

Inventory | 70 | 50 |

Trade debtors | 11 | 16 |

Rent paid in advance | 4 | 3 |

PPE | 700 | 680 |

Total assets | 785 | 749 |

Trade creditors | 11 | 19 |

Bond liabilities | 400 | 390 |

Contributed equity | 220 | 220 |

Retained profits | 154 | 120 |

Total L and OE | 785 | 749 |

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

The cash flow from assets was:

A firm has forecast its Cash Flow From Assets (CFFA) for this year and management is worried that it is too low. Which one of the following actions will lead to a higher CFFA for this year (t=0 to 1)? Only consider cash flows this year. Do not consider cash flows after one year, or the change in the NPV of the firm. Consider each action in isolation.

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?

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

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

Annual interest expense is equal to:

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

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

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

Assume the following:

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

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

The mobile phone manufacturing project's:

One formula for calculating a levered firm's free cash flow (FFCF, or CFFA) is to use earnings before interest and tax (EBIT).

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

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?

**Question 559** variance, standard deviation, covariance, correlation

Which of the following statements about standard statistical mathematics notation is **NOT** correct?

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 ##(\%)##.

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.

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

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

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

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

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

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

**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 are 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):

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.

**Question 625** dividend re-investment plan, capital raising

Which of the following statements about dividend re-investment plans (DRP's) is **NOT** correct?

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

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

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

A firm can issue 3 year annual coupon bonds at a yield of 10% pa and a coupon rate of 8% pa.

The beta of its levered equity is 2. The market's expected return is 10% pa and 3 year government bonds yield 6% pa with a coupon rate of 4% pa.

The market value of equity is $1 million and the market value of debt is $1 million. The corporate tax rate is 30%.

What is the firm's after-tax WACC? Assume a classical tax system.

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

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

The total return of any asset can be broken down in different ways. One possible way is to use the dividend discount model (or Gordon growth model):

###p_0 = \frac{c_1}{r_\text{total}-r_\text{capital}}###

Which, since ##c_1/p_0## is the income return (##r_\text{income}##), can be expressed as:

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

So the total return of an asset is the income component plus the capital or price growth component.

Another way to break up total return is to use the Capital Asset Pricing Model:

###r_\text{total}=r_\text{f}+β(r_\text{m}- r_\text{f})###

###r_\text{total}=r_\text{time value}+r_\text{risk premium}###

So the risk free rate is the time value of money and the term ##β(r_\text{m}- r_\text{f})## is the compensation for taking on systematic risk.

Using the above theory and your general knowledge, which of the below equations, if any, are correct?

(I) ##r_\text{income}=r_\text{time value}##

(II) ##r_\text{income}=r_\text{risk premium}##

(III) ##r_\text{capital}=r_\text{time value}##

(IV) ##r_\text{capital}=r_\text{risk premium}##

(V) ##r_\text{income}+r_\text{capital}=r_\text{time value}+r_\text{risk premium}##

Which of the equations are correct?

**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:

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

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

A company conducts a **10** for **3** stock split. What is the percentage increase in the stock price and the number of shares outstanding? The answers are given in the same order.

Which of the following interest rate quotes is **NOT** equivalent to a **10**% effective annual rate of return? Assume that each year has 12 months, each month has 30 days, each day has 24 hours, each hour has 60 minutes and each minute has 60 seconds. APR stands for Annualised Percentage Rate.

**Question 710** continuously compounding rate, continuously compounding rate conversion

A continuously compounded **monthly** return of 1% ##(r_\text{cc monthly})## is equivalent to a continuously compounded **annual** return ##(r_\text{cc 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?

**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.

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: