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

You have $100,000 in the bank. The bank pays interest at 10% pa, given as an effective annual rate.

You wish to consume an equal amount now (t=0), in one year (t=1) and in two years (t=2), and still have $50,000 in the bank after that (t=2).

How much can you consume at each time?

An investor owns an empty block of land that has local government approval to be developed into a petrol station, car wash or car park. The council will only allow a single development so the projects are mutually exclusive.

All of the development projects have the same risk and the required return of each is 10% pa. Each project has an immediate cost and once construction is finished in one year the land and development will be sold. The table below shows the estimated costs payable now, expected sale prices in one year and the internal rates of returns (IRR's).

Mutually Exclusive Projects | |||

Project | Cost now ($) |
Sale price in one year ($) |
IRR (% pa) |

Petrol station | 9,000,000 | 11,000,000 | 22.22 |

Car wash | 800,000 | 1,100,000 | 37.50 |

Car park | 70,000 | 110,000 | 57.14 |

Which project should the investor accept?

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 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?

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're considering a business project which costs $**11**m now and is expected to pay a single cash flow of $**11**m in one year. So you pay $11m now, then one year later you receive $11m.

Assume that the initial $**11**m cost is funded using the your firm's **existing cash** so no new equity or debt will be raised. The cost of capital is **10**% pa.

Which of the following statements about the net present value (NPV), internal rate of return (IRR) and payback period is **NOT** correct?

The following cash flows are expected:

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

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

**Question 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?

Bonds X and Y are issued by the same US company. Both bonds yield **10**% pa, and they have the same face value ($100), maturity, seniority, and payment frequency.

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

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.

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.

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}###**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?

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 remain constant in real terms 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 and are expected to remain constant in real terms. - 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.
- 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 | |

Cash | 0 | 0 |

Inventory | 70 | 50 |

Trade debtors | 11 | 16 |

Rent paid in advance | 4 | 3 |

PPE | 700 | 680 |

Total assets | 785 | 749 |

Trade creditors | 11 | 19 |

Bond liabilities | 400 | 390 |

Contributed equity | 220 | 220 |

Retained profits | 154 | 120 |

Total L and OE | 785 | 749 |

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

The cash flow from assets was:

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?

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

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

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

Two years ago Fred bought a house for $**300,000**.

Now it's worth $**500,000**, based on recent similar sales in the area.

Fred's residential property has an expected total return of **8**% pa.

He rents his house out for $**2,000** 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 $**23,173.86**.

The future value of 12 months of rental payments one year ahead is $**25,027.77**.

What is the expected annual growth rate of the rental payments? In other words, by what percentage increase will Fred have to raise the monthly rent by each year to sustain the expected annual total return of 8%?

Private equity firms are known to buy medium sized private companies operating in the same industry, merge them together into a larger company, and then sell it off in a public float (initial public offering, IPO).

If medium-sized private companies trade at PE ratios of **5** and larger listed companies trade at PE ratios of **15**, what return can be achieved from this strategy?

Assume that:

- The medium-sized companies can be bought, merged and sold in an IPO instantaneously.
- There are no costs of finding, valuing, merging and restructuring the medium sized companies. Also, there is no competition to buy the medium-sized companies from other private equity firms.
- The large merged firm's earnings are the sum of the medium firms' earnings.
- The only reason for the difference in medium and large firm's PE ratios is due to the illiquidity of the medium firms' shares.
- Return is defined as: ##r_{0→1} = (p_1-p_0+c_1)/p_0## , where time zero is just before the merger and time one is just after.

A share was bought for $30 (at t=0) and paid its annual dividend of $6 one year later (at t=1).

Just after the dividend was paid, the share price fell to $27 (at t=1). What were the total, capital and income returns given as effective annual rates?

The choices are given in the same order:

##r_\text{total}## , ##r_\text{capital}## , ##r_\text{dividend}##.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

The 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 760** time calculation, interest only loan, no explanation

**Five** years ago (##t=-5## years) you entered into an **interest-only** home loan with a principal of $**500,000**, an interest rate of **4.5**% pa compounding monthly with a term of **25** years.

Then interest rates suddenly fall to **3**% pa (##t=0##), but you continue to pay the same monthly home loan payments as you did before. Will your home loan be paid off by the end of its remaining term? If so, in how many years from now? Measure the time taken to pay off the home loan from the current time which is 5 years after the home loan was first entered into.

Assume that the lower interest rate was given to you immediately after the loan repayment at the end of year 5, which was the 60th payment since the loan was granted. Also assume that rates were and are expected to remain constant.

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

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

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

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

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

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

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

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

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

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

The CAPM can be used to find a business's expected opportunity cost of capital:

###r_i=r_f+β_i (r_m-r_f)###

What should be used as the risk free rate ##r_f##?

**Question 418** capital budgeting, NPV, interest tax shield, WACC, CFFA, CAPM

Project Data | ||

Project life | 1 year | |

Initial investment in equipment | $8m | |

Depreciation of equipment per year | $8m | |

Expected sale price of equipment at end of project | 0 | |

Unit sales per year | 4m | |

Sale price per unit | $10 | |

Variable cost per unit | $5 | |

Fixed costs per year, paid at the end of each year | $2m | |

Interest expense in first year (at t=1) | $0.562m | |

Corporate tax rate | 30% | |

Government treasury bond yield | 5% | |

Bank loan debt yield | 9% | |

Market portfolio return | 10% | |

Covariance of levered equity returns with market | 0.32 | |

Variance of market portfolio returns | 0.16 | |

Firm's and project's debt-to-equity ratio |
50% | |

**Notes**

- Due to the project, current assets will increase by $
**6**m now (t=0) and fall by $**6**m at the end (t=1). Current liabilities will not be affected.

**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.
- Millions are represented by 'm'.
- 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 2% pa. All rates are given as effective annual rates.
- The project is undertaken by a firm, not an individual.

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

**Question 119** market efficiency, fundamental analysis, joint hypothesis problem

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

(i) Weak form market efficiency is broken.

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

(iii) Strong form market efficiency is broken.

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

Select the most correct response:

**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 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.

**Question 708** continuously compounding rate, continuously compounding rate conversion

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

**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 | 0.9802 | 1.0607 | 1.0607 | |

**Question 626** cross currency interest rate parity, foreign exchange rate, forward foreign exchange rate

The Australian cash rate is expected to be **2**% pa over the next one year, while the Japanese cash rate is expected to be **0**% pa, both given as nominal effective annual rates. The current exchange rate is **100** JPY per AUD.

What is the implied **1** year forward foreign exchange rate?

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 772** interest tax shield, capital structure, leverage

A firm issues debt and uses the funds to buy back equity. Assume that there are no costs of financial distress or transactions costs. Which of the following statements about interest tax shields is **NOT** correct?