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

You wish to consume an equal amount now (t=0) and in one year (t=1) and have nothing left in the bank at the end (t=1).

How much can you consume at each time?

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?

Your neighbour asks you for a loan of $100 and offers to pay you back $120 in one year.

You don't actually have any money right now, but you can borrow and lend from the bank at a rate of 10% pa. Rates are given as effective annual rates.

Assume that your neighbour will definitely pay you back. Ignore interest tax shields and transaction costs.

The Net Present Value (NPV) of lending to your neighbour is $9.09. Describe what you would do to actually receive a $9.09 cash flow right now with zero net cash flows in the future.

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

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

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

An asset's total expected return over the next year is given by:

###r_\text{total} = \dfrac{c_1+p_1-p_0}{p_0} ###

Where ##p_0## is the current price, ##c_1## is the expected income in one year and ##p_1## is the expected price in one year. The total return can be split into the income return and the capital return.

Which of the following is the expected **capital** return?

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

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

The choices are given in the same order:

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

Total cash flows can be broken into income and capital cash flows. What is the name given to the **income** cash flow from owning shares?

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

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

**Question 278** inflation, real and nominal returns and cash flows

Imagine that the interest rate on your savings account was 1% per year and inflation was 2% per year.

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

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

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

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

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

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

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

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

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

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

Which of the above statements is or are correct?

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

What is the present value of a **real** payment of $500 in 2 years? The **nominal** discount rate is 7% pa and the inflation rate is 4% pa.

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

On his 20th birthday, a man makes a resolution. He will put $**30** cash under his bed at the **end** of every month starting from today. His birthday today is the first day of the month. So the first addition to his cash stash will be in one month. He will write in his will that when he dies the cash under the bed should be given to charity.

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

Also, what will be the **real** value of that cash in today's prices if inflation is expected to **2.5%** pa? Assume that the inflation rate is an effective annual rate and is not expected to change.

The answers are given in the same order, the amount of money under his bed in 60 years, and the real value of that money in today's prices.

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

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

Which business structure or structures have the advantage of limited liability for equity investors?

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

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

The following cash flows are expected:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Which of the following statements about book and market equity is **NOT** correct?

The below screenshot of Commonwealth Bank of Australia's (CBA) details were taken from the Google Finance website on 7 Nov 2014. Some information has been deliberately blanked out.

What was CBA's market capitalisation of equity?

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

The investment decision primarily affects which part of a business?

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

The financing decision primarily affects which part of a business?

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

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

Ignore credit risk.

This annuity formula ##\dfrac{C_1}{r}\left(1-\dfrac{1}{(1+r)^3} \right)## is equivalent to which of the following formulas? Note the **3**.

In the below formulas, ##C_t## is a cash flow at time t. All of the cash flows are equal, but paid at different times.

Your friend overheard that you need some cash and asks if you would like to borrow some money. She can lend you $**5,000** now (t=0), and in return she wants you to pay her back $1,000 in two years (t=2) and every year after that for the next 5 years, so there will be **6** payments of $**1,000** from t=**2** to t=**7** inclusive.

What is the net present value (NPV) of borrowing from your friend?

Assume that banks loan funds at interest rates of **10**% pa, given as an effective annual rate.

Some countries' interest rates are so low that they're zero.

If interest rates are **0**% pa and are expected to stay at that level for the foreseeable future, what is the most that you would be prepared to pay a bank now if it offered to pay you $**10** at the end of every year for the next **5** years?

In other words, what is the present value of five $10 payments at time 1, 2, 3, 4 and 5 if interest rates are 0% pa?

Discounted cash flow (DCF) valuation prices assets by finding the present value of the asset's future cash flows. The single cash flow, annuity, and perpetuity equations are very useful for this.

Which of the following equations is the 'perpetuity with growth' equation?

A stock is expected to pay its **next** dividend of $1 in one year. Future annual dividends are expected to grow by 2% pa. So the first dividend of $1 will be in one year, the year after that $1.02 (=1*(1+0.02)^1), and a year later $1.0404 (=1*(1+0.02)^2) and so on forever.

Its required total return is 10% pa. The total required return and growth rate of dividends are given as effective annual rates.

Calculate the current stock price.

A stock **just paid** a dividend of $1. Future annual dividends are expected to grow by 2% pa. The next dividend of $1.02 (=1*(1+0.02)^1) will be in one year, and the year after that the dividend will be $1.0404 (=1*(1+0.02)^2), and so on forever.

Its required total return is 10% pa. The total required return and growth rate of dividends are given as effective annual rates.

Calculate the current stock price.

A stock is **just about to pay** a dividend of $1 **tonight**. Future annual dividends are expected to grow by 2% pa. The next dividend of $1 will be paid tonight, and the year after that the dividend will be $1.02 (=1*(1+0.02)^1), and a year later 1.0404 (=1*(1+0.04)^2) and so on forever.

Its required total return is 10% pa. The total required return and growth rate of dividends are given as effective annual rates.

Calculate the current stock price.

For a price of $13, Carla will sell you a share which will pay a dividend of $1 in one year and every year after that forever. The required return of the stock is 10% pa.

For a price of $1040, Camille will sell you a share which just paid a dividend of $100, and is expected to pay dividends every year forever, growing at a rate of 5% pa.

So the next dividend will be ##100(1+0.05)^1=$105.00##, and the year after it will be ##100(1+0.05)^2=110.25## and so on.

The required return of the stock is 15% pa.

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

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

A stock pays dividends annually. It just paid a dividend, but the next dividend (##d_1##) will be paid in one year.

According to the DDM, what is the correct formula for the expected price of the stock in 2.5 years?

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

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

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

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?

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

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

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

A project has the following cash flows:

Project Cash Flows | |

Time (yrs) | Cash flow ($) |

0 | -400 |

1 | 0 |

2 | 500 |

What is the payback period of the project in years?

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

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

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

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

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

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

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

### P_{0} = \frac{C_1}{r_{\text{eff}} - g_{\text{eff}}} ###

What would you call the expression ## C_1/P_0 ##?

Estimate the US bank JP Morgan's share price using a price earnings (PE) multiples approach with the following assumptions and figures only:

- The major US banks JP Morgan Chase (JPM), Citi Group (C) and Wells Fargo (WFC) are comparable companies;
- JP Morgan Chase's historical earnings per share (EPS) is $
**4.37**; - Citi Group's share price is $
**50.05**and historical EPS is $**4.26**; - Wells Fargo's share price is $
**48.98**and historical EPS is $**3.89**.

Note: Figures sourced from Google Finance on 24 March 2014.

Estimate the Chinese bank ICBC's share price using a backward-looking price earnings (PE) multiples approach with the following assumptions and figures only. Note that the renminbi (RMB) is the Chinese currency, also known as the yuan (CNY).

- The 4 major Chinese banks ICBC, China Construction Bank (CCB), Bank of China (BOC) and Agricultural Bank of China (ABC) are comparable companies;
- ICBC 's historical earnings per share (EPS) is RMB
**0.74**; - CCB's backward-looking PE ratio is
**4.59**; - BOC 's backward-looking PE ratio is
**4.78**; - ABC's backward-looking PE ratio is also
**4.78**;

Note: Figures sourced from Google Finance on 25 March 2014. Share prices are from the Shanghai stock exchange.

Estimate Microsoft's (MSFT) share price using a price earnings (PE) multiples approach with the following assumptions and figures only:

- Apple, Google and Microsoft are comparable companies,
- Apple's (AAPL) share price is $526.24 and historical EPS is $40.32.
- Google's (GOOG) share price is $1,215.65 and historical EPS is $36.23.
- Micrsoft's (MSFT) historical earnings per share (EPS) is $2.71.

Source: Google Finance 28 Feb 2014.

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

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

Only consider firms with positive earnings, disregard firms with negative earnings and therefore negative PE ratios.

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.

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

The required return of a project is 10%, given as an effective annual rate. Assume that the cash flows shown in the table are paid all at once at the given point in time.

What is the Net Present Value (NPV) of the project?

Project Cash Flows | |

Time (yrs) | Cash flow ($) |

0 | -100 |

1 | 0 |

2 | 121 |

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 |

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

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

What is the payback period of the project in years?

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

Project Cash Flows | |

Time (yrs) | Cash flow ($) |

0 | -100 |

1 | 11 |

2 | 121 |

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.

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

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

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

What is the current stock price?

Which of the following statements is **NOT** equivalent to the **yield** on debt?

Assume that the debt being referred to is fairly priced, but do not assume that it's priced at par.

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

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

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

All answers are given in the same order:

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

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

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

All answers are given in the same order:

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

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

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

All answers are given in the same order:

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

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

In Germany, nominal yields on **semi**-annual coupon paying Government Bonds with 2 years until maturity are currently **0.04**% pa.

The inflation rate is currently **1.4**% 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?

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

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

You just signed up for a 30 year **fully amortising** mortgage 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.

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

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

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

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

You want to buy a house priced at $400,000. You have saved a deposit of $40,000. The bank has agreed to lend you $360,000 as a **fully amortising** loan with a term of 30 years. The interest rate is 8% pa payable monthly and is not expected to change.

What will be your monthly payments?

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

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

You just 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).

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

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

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

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

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

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

**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?

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.

In Australia in the 1980's, inflation was around 8% pa, and residential mortgage loan interest rates were around 14%.

In 2013, inflation was around 2.5% pa, and residential mortgage loan interest rates were around 4.5%.

If a person can afford constant mortgage loan payments of $**2,000** per month, how much more can they borrow when interest rates are **4.5**% pa compared with **14.0**% pa?

Give your answer as a proportional increase over the amount you could borrow when interest rates were high ##(V_\text{high rates})##, so:

###\text{Proportional increase} = \dfrac{V_\text{low rates}-V_\text{high rates}}{V_\text{high rates}} ###

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 (
**APR**'s) compounding per**month**.

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

For a price of $100, Vera will sell you a 2 year bond paying semi-annual coupons of 10% pa. The face value of the bond is $100. Other bonds with similar risk, maturity and coupon characteristics trade at a yield of 8% pa.

For a price of $95, Nicole will sell you a 10 year bond paying semi-annual coupons of 8% pa. The face value of the bond is $100. Other bonds with the same risk, maturity and coupon characteristics trade at a yield of 8% pa.

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?

Bonds A and B are issued by the same company. They have the same face value, maturity, seniority and coupon payment frequency. The only difference is that bond A has a 5% coupon rate, while bond B has a 10% coupon rate. The yield curve is flat, which means that yields are expected to stay the same.

Which bond would have the higher current price?

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

**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 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.

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

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

A bond maturing in 10 years has a coupon rate of 4% pa, paid semi-annually. The bond's yield is currently 6% pa. The face value of the bond is $100. What is its price?

Bonds A and B are issued by the same Australian company. Both bonds yield 7% pa, and they have the same face value ($100), maturity, seniority, and payment frequency.

The only difference is that bond A pays coupons of 10% pa and bond B pays coupons of 5% pa. Which of the following statements is true about the bonds' prices?

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?

A three year bond has a fixed coupon rate of 12% pa, paid semi-annually. The bond's yield is currently 6% pa. The face value is $100. What is its price?

A four year bond has a face value of $100, a yield of 6% and a fixed coupon rate of 12%, paid semi-annually. What is its price?

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), maturity (3 years) and yield (10%) as each other.

Which of the following statements is true?

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

A firm wishes to raise $20 million now. They will issue 8% pa semi-annual coupon bonds that will mature in 5 years and have a face value of $100 each. Bond yields are 6% pa, given as an APR compounding every 6 months, and the yield curve is flat.

How many bonds should the firm issue?

A five year bond has a face value of $100, a yield of 12% and a fixed coupon rate of 6%, paid semi-annually.

What is the bond's price?

Which one of the following bonds is trading at par?

A firm wishes to raise $8 million now. They will issue 7% pa semi-annual coupon bonds that will mature in 10 years and have a face value of $100 each. Bond yields are 10% pa, given as an APR compounding every 6 months, and the yield curve is flat.

How many bonds should the firm issue?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Select the most correct statement.

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

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

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

The only difference is that bond X pays coupons of 6% pa and bond Y pays coupons of 8% pa. Which of the following statements is true?

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

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

A **10** year Australian government bond was just issued at **par** with a yield of **3.9**% pa. The fixed coupon payments are **semi-annual**. The bond has a face value of $**1,000**.

**Six months** later, just **after** the first coupon is paid, the yield of the bond decreases to **3.65**% pa. What is the bond's **new price**?

Bonds X and Y are issued by the same US company. Both bonds yield **6**% pa, and they have the same face value ($100), maturity, seniority, and payment frequency.

The only difference is that bond X pays coupons of **8**% pa and bond Y pays coupons of **12**% pa. Which of the following statements is true?

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.

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

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

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

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

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

Calculate the price of a newly issued **ten** year bond with a face value of $**100**, a yield of **8**% pa and a fixed coupon rate of **6**% pa, paid **semi**-annually. So there are two coupons per year, paid in arrears every six months.

"Buy low, sell high" is a phrase commonly heard in financial markets. It states that traders should try to buy assets at low prices and sell at high prices.

Traders in the fixed-coupon bond markets often quote promised bond yields rather than prices. Fixed-coupon bond traders should try to:

A 10 year bond has a face value of $100, a yield of 6% pa and a fixed coupon rate of 8% pa, paid semi-annually. What is its price?

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

An Australian company just issued two bonds:

- A 6-month zero coupon bond at a yield of 6% pa, and
- A 12 month zero coupon bond at a yield of 7% pa.

What is the company's forward rate from 6 to 12 months? Give your answer as an APR compounding every 6 months, which is how the above bond yields are quoted.

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

An Australian company just issued two bonds:

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

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

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?

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).

Why is Capital Expenditure (CapEx) subtracted in the Cash Flow From Assets (CFFA) formula?

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

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.

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

Remember:

###NI = (Rev-COGS-FC-Depr-IntExp).(1-t_c )### ###CFFA=NI+Depr-CapEx - \Delta NWC+IntExp###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?

Which one of the following will have no effect on net income (NI) but decrease cash flow from assets (CFFA or FFCF) in this year for a tax-paying firm, all else remaining constant?

Remember:

###NI=(Rev-COGS-FC-Depr-IntExp).(1-t_c )### ###CFFA=NI+Depr-CapEx - ΔNWC+IntExp###Find Ching-A-Lings Corporation's Cash Flow From Assets (CFFA), also known as Free Cash Flow to the Firm (FCFF), over the year ending 30th June 2013.

Ching-A-Lings Corp | ||

Income Statement for | ||

year ending 30th June 2013 | ||

$m | ||

Sales | 100 | |

COGS | 20 | |

Depreciation | 20 | |

Rent expense | 11 | |

Interest expense | 19 | |

Taxable Income | 30 | |

Taxes at 30% | 9 | |

Net income | 21 | |

Ching-A-Lings Corp | ||

Balance Sheet | ||

as at 30th June | 2013 | 2012 |

$m | $m | |

Inventory | 49 | 38 |

Trade debtors | 14 | 2 |

Rent paid in advance | 5 | 5 |

PPE | 400 | 400 |

Total assets | 468 | 445 |

Trade creditors | 4 | 10 |

Bond liabilities | 200 | 190 |

Contributed equity | 145 | 145 |

Retained profits | 119 | 100 |

Total L and OE | 468 | 445 |

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

The cash flow from assets was:

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?

Read the following financial statements and calculate the firm's free cash flow over the 2014 financial year.

UBar Corp | ||

Income Statement for | ||

year ending 30th June 2014 | ||

$m | ||

Sales | 293 | |

COGS | 200 | |

Rent expense | 15 | |

Gas expense | 8 | |

Depreciation | 10 | |

EBIT | 60 | |

Interest expense | 0 | |

Taxable income | 60 | |

Taxes | 18 | |

Net income | 42 | |

UBar Corp | ||

Balance Sheet | ||

as at 30th June | 2014 | 2013 |

$m | $m | |

Assets | ||

Cash | 30 | 29 |

Accounts receivable | 5 | 7 |

Pre-paid rent expense | 1 | 0 |

Inventory | 50 | 46 |

PPE | 290 | 300 |

Total assets | 376 | 382 |

Liabilities | ||

Trade payables | 20 | 18 |

Accrued gas expense | 3 | 2 |

Non-current liabilities | 0 | 0 |

Contributed equity | 212 | 212 |

Retained profits | 136 | 150 |

Asset revaluation reserve | 5 | 0 |

Total L and OE | 376 | 382 |

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

The firm's free cash flow over the 2014 financial year was:

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

Trademark Corp | ||

Income Statement for | ||

year ending 30th June 2013 | ||

$m | ||

Sales | 100 | |

COGS | 25 | |

Operating expense | 5 | |

Depreciation | 20 | |

Interest expense | 20 | |

Income before tax | 30 | |

Tax at 30% | 9 | |

Net income | 21 | |

Trademark Corp | ||

Balance Sheet | ||

as at 30th June | 2013 | 2012 |

$m | $m | |

Assets | ||

Current assets | 120 | 80 |

PPE | ||

Cost | 150 | 140 |

Accumul. depr. | 60 | 40 |

Carrying amount | 90 | 100 |

Total assets | 210 | 180 |

Liabilities | ||

Current liabilities | 75 | 65 |

Non-current liabilities | 75 | 55 |

Owners' equity | ||

Retained earnings | 10 | 10 |

Contributed equity | 50 | 50 |

Total L and OE | 210 | 180 |

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

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

UniBar Corp | ||

Income Statement for | ||

year ending 30th June 2013 | ||

$m | ||

Sales | 80 | |

COGS | 40 | |

Operating expense | 15 | |

Depreciation | 10 | |

Interest expense | 5 | |

Income before tax | 10 | |

Tax at 30% | 3 | |

Net income | 7 | |

UniBar Corp | ||

Balance Sheet | ||

as at 30th June | 2013 | 2012 |

$m | $m | |

Assets | ||

Current assets | 120 | 90 |

PPE | ||

Cost | 360 | 320 |

Accumul. depr. | 40 | 30 |

Carrying amount | 320 | 290 |

Total assets | 440 | 380 |

Liabilities | ||

Current liabilities | 110 | 60 |

Non-current liabilities | 190 | 180 |

Owners' equity | ||

Retained earnings | 95 | 95 |

Contributed equity | 45 | 45 |

Total L and OE | 440 | 380 |

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

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

Piano Bar | ||

Income Statement for | ||

year ending 30th June 2013 | ||

$m | ||

Sales | 310 | |

COGS | 185 | |

Operating expense | 20 | |

Depreciation | 15 | |

Interest expense | 10 | |

Income before tax | 80 | |

Tax at 30% | 24 | |

Net income | 56 | |

Piano Bar | ||

Balance Sheet | ||

as at 30th June | 2013 | 2012 |

$m | $m | |

Assets | ||

Current assets | 240 | 230 |

PPE | ||

Cost | 420 | 400 |

Accumul. depr. | 50 | 35 |

Carrying amount | 370 | 365 |

Total assets | 610 | 595 |

Liabilities | ||

Current liabilities | 180 | 190 |

Non-current liabilities | 290 | 265 |

Owners' equity | ||

Retained earnings | 90 | 90 |

Contributed equity | 50 | 50 |

Total L and OE | 610 | 595 |

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

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

World Bar | ||

Income Statement for | ||

year ending 30th June 2013 | ||

$m | ||

Sales | 300 | |

COGS | 150 | |

Operating expense | 50 | |

Depreciation | 40 | |

Interest expense | 10 | |

Taxable income | 50 | |

Tax at 30% | 15 | |

Net income | 35 | |

World Bar | ||

Balance Sheet | ||

as at 30th June | 2013 | 2012 |

$m | $m | |

Assets | ||

Current assets | 200 | 230 |

PPE | ||

Cost | 400 | 400 |

Accumul. depr. | 75 | 35 |

Carrying amount | 325 | 365 |

Total assets | 525 | 595 |

Liabilities | ||

Current liabilities | 150 | 205 |

Non-current liabilities | 235 | 250 |

Owners' equity | ||

Retained earnings | 100 | 100 |

Contributed equity | 40 | 40 |

Total L and OE | 525 | 595 |

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

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

Scubar Corp | ||

Income Statement for | ||

year ending 30th June 2013 | ||

$m | ||

Sales | 200 | |

COGS | 60 | |

Depreciation | 20 | |

Rent expense | 11 | |

Interest expense | 19 | |

Taxable Income | 90 | |

Taxes at 30% | 27 | |

Net income | 63 | |

Scubar Corp | ||

Balance Sheet | ||

as at 30th June | 2013 | 2012 |

$m | $m | |

Inventory | 60 | 50 |

Trade debtors | 19 | 6 |

Rent paid in advance | 3 | 2 |

PPE | 420 | 400 |

Total assets | 502 | 458 |

Trade creditors | 10 | 8 |

Bond liabilities | 200 | 190 |

Contributed equity | 130 | 130 |

Retained profits | 162 | 130 |

Total L and OE | 502 | 458 |

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

The cash flow from assets was:

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 young lady is trying to decide if she should attend university or not.

The young lady's parents say that she must attend university because otherwise all of her hard work studying and attending school during her childhood was a waste.

What's the correct way to classify this item from a capital budgeting perspective when trying to decide whether to attend university?

The hard work studying at school in her childhood should be classified as:

A 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 man has taken a day off from his casual painting job to relax.

It's the end of the day and he's thinking about the hours that he could have spent working (in the past) which are now:

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 the cash flow from assets (CFFA) of the following project.

One Year Mining Project Data | ||

Project life | 1 year | |

Initial investment in building mine and equipment | $9m | |

Depreciation of mine and equipment over the year | $8m | |

Kilograms of gold mined at end of year | 1,000 | |

Sale price per kilogram | $0.05m | |

Variable cost per kilogram | $0.03m | |

Before-tax cost of closing mine at end of year | $4m | |

Tax rate | 30% | |

Note 1: Due to the project, the firm also anticipates finding some rare diamonds which will give before-tax revenues of $1m at the end of the year.

Note 2: The land that will be mined actually has thermal springs and a family of koalas that could be sold to an eco-tourist resort for an after-tax amount of $3m right now. However, if the mine goes ahead then this natural beauty will be destroyed.

Note 3: The mining equipment will have a book value of $1m at the end of the year for tax purposes. However, the equipment is expected to fetch $2.5m when it is sold.

Find the project's CFFA at time zero and one. Answers are given in millions of dollars ($m), with the first cash flow at time zero, and the second at time one.

Find the cash flow from assets (CFFA) of the following project.

Project Data | ||

Project life | 2 years | |

Initial investment in equipment | $6m | |

Depreciation of equipment per year for tax purposes | $1m | |

Unit sales per year | 4m | |

Sale price per unit | $8 | |

Variable cost per unit | $3 | |

Fixed costs per year, paid at the end of each year | $1.5m | |

Tax rate | 30% | |

Note 1: The equipment will have a book value of $4m at the end of the project for tax purposes. However, the equipment is expected to fetch $0.9 million when it is sold at t=2.

Note 2: Due to the project, the firm will have to purchase $0.8m of inventory initially, which it will sell at t=1. The firm will buy another $0.8m at t=1 and sell it all again at t=2 with zero inventory left. The project will have no effect on the firm's current liabilities.

Find the project's CFFA at time zero, one and two. Answers are given in millions of dollars ($m).

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.

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).

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

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

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

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

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

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:

Which one of the following will increase the Cash Flow From Assets in this year for a tax-paying firm, all else remaining constant?

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

Remember:

###NI=(Rev-COGS-FC-Depr-IntExp).(1-t_c )### ###CFFA=NI+Depr-CapEx - ΔNWC+IntExp###A retail furniture company buys furniture wholesale and distributes it through its retail stores. The owner believes that she has some good ideas for making stylish new furniture. She is considering a project to buy a factory and employ workers to manufacture the new furniture she's designed. Furniture manufacturing has more systematic risk than furniture retailing.

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

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

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

Assume the following:

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

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

The mobile phone manufacturing project's:

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

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

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

###NI=(Rev - COGS - Depr - FC - IntExp).(1-t_c )### ###EBIT=Rev - COGS - FC-Depr### ###EBITDA=Rev - COGS - FC### ###Tax =(Rev - COGS - Depr - FC - IntExp).t_c= \dfrac{NI.t_c}{1-t_c}###A method commonly seen in textbooks for calculating a levered firm's free cash flow (FFCF, or CFFA) is the following:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Project Data | ||

Project life | 2 yrs | |

Initial investment in equipment | $600k | |

Depreciation of equipment per year | $250k | |

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

Revenue per job | $12k | |

Variable cost per job | $4k | |

Quantity of jobs per year | 120 | |

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

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

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

Tax rate | 30% | |

Government treasury bond yield | 5% | |

Bank loan debt yield | 6% | |

Levered cost of equity | 12.5% | |

Market portfolio return | 10% | |

Beta of assets | 1.24 | |

Beta of levered equity | 1.5 | |

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

**Notes**

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

**Assumptions**

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

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

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

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

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

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

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

Fill in the missing words in the following sentence:

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

**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?

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

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

Use the below information to value a levered company with constant annual perpetual cash flows from assets. The next cash flow will be generated in one year from now, so a perpetuity can be used to value this firm. Both the cash flow from assets including and excluding interest tax shields are constant (but not equal to each other).

Data on a Levered Firm with Perpetual Cash Flows | ||

Item abbreviation | Value | Item full name |

##\text{CFFA}_\text{U}## | $100m | Cash flow from assets excluding interest tax shields (unlevered) |

##\text{CFFA}_\text{L}## | $112m | Cash flow from assets including interest tax shields (levered) |

##g## | 0% pa | Growth rate of cash flow from assets, levered and unlevered |

##\text{WACC}_\text{BeforeTax}## | 7% pa | Weighted average cost of capital before tax |

##\text{WACC}_\text{AfterTax}## | 6.25% pa | Weighted average cost of capital after tax |

##r_\text{D}## | 5% pa | Cost of debt |

##r_\text{EL}## | 9% pa | Cost of levered equity |

##D/V_L## | 50% pa | Debt to assets ratio, where the asset value includes tax shields |

##t_c## | 30% | Corporate tax rate |

What is the value of the levered firm including interest tax shields?

Use the below information to value a levered company with constant annual perpetual cash flows from assets. The next cash flow will be generated in one year from now, so a perpetuity can be used to value this firm. Both the cash flow from assets including and excluding interest tax shields are constant (but not equal to each other).

Data on a Levered Firm with Perpetual Cash Flows | ||

Item abbreviation | Value | Item full name |

##\text{CFFA}_\text{U}## | $48.5m | Cash flow from assets excluding interest tax shields (unlevered) |

##\text{CFFA}_\text{L}## | $50m | Cash flow from assets including interest tax shields (levered) |

##g## | 0% pa | Growth rate of cash flow from assets, levered and unlevered |

##\text{WACC}_\text{BeforeTax}## | 10% pa | Weighted average cost of capital before tax |

##\text{WACC}_\text{AfterTax}## | 9.7% pa | Weighted average cost of capital after tax |

##r_\text{D}## | 5% pa | Cost of debt |

##r_\text{EL}## | 11.25% pa | Cost of levered equity |

##D/V_L## | 20% pa | Debt to assets ratio, where the asset value includes tax shields |

##t_c## | 30% | Corporate tax rate |

What is the value of the levered firm including interest tax shields?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

A real estate agent says that the price of a house in Sydney Australia is approximately equal to the gross weekly rent times 1000.

What type of valuation method is the real estate agent using?

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

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

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

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

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

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

The following cash flows are expected:

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

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

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

How many bonds should the firm issue?

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

How many bonds should the firm issue?

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

How many bonds should the firm issue?

**Question 759** time calculation, fully amortising loan, no explanation

**Five** years ago you entered into a **fully amortising** 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. 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 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.

**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.

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?

Radio-Rentals.com offers the Apple iphone 5S smart phone for rent at $**12.95** per week paid in **advance** on a **2** year contract. After renting the phone, you must return it to Radio-Rentals.

Kogan.com offers the Apple iphone 5S smart phone for sale at $**699**. You estimate that the phone will last for **3** years before it will break and be worthless.

Currently, the effective annual interest rate is **11.351**%, the effective monthly interest rate **0.9**% and the effective weekly interest rate is **0.207**%. Assume that there are exactly **52** weeks per year and **12** months per year.

Find the equivalent annual cost of renting the phone and also buying the phone. The answers below are listed in the same order.

A stock is expected to pay its first dividend of $**20** in **3** years (t=3), which it will continue to pay for the next nine years, so there will be **ten** $20 payments altogether with the last payment in year 12 (t=12).

From the thirteenth year onward, the dividend is expected to be **4**% more than the previous year, forever. So the dividend in the thirteenth year (t=13) will be $20.80, then $21.632 in year 14, and so on forever. The required return of the stock is **10**% pa. All rates are effective annual rates. Calculate the current (t=0) stock price.

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

In the below term structure of interest rates equation, all rates are effective annual yields and the numbers in subscript represent the years that the yields are measured over:

###(1+r_{0-3})^3 = (1+r_{0-1})(1+r_{1-2})(1+r_{2-3}) ###

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

**Question 536** idiom, bond pricing, capital structure, leverage

The expression 'my word is my bond' is often used in everyday language to make a serious promise.

Why do you think this expression uses the metaphor of a bond rather than a share?

**Question 538** bond pricing, income and capital returns, no explanation

Risk-free government bonds that have coupon rates greater than their yields:

**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.

**Question 108** bond pricing, zero coupon bond, term structure of interest rates, forward interest rate

An Australian company just issued two bonds:

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

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

A fixed coupon bond was bought for $90 and paid its annual coupon of $3 one year later (at t=1 year). Just after the coupon was paid, the bond price was $92 (at t=1 year). What was the total return, capital return and income return? Calculate your answers as effective annual rates.

The choices are given in the same order: ## r_\text{total},r_\text{capital},r_\text{income} ##.

An investor bought a **20** year **5**% pa fixed coupon government bond priced at **par**. The face value is $100. Coupons are paid semi-annually and the next one is in 6 months.

Six months later, just after the coupon at that time was paid, yields suddenly and unexpectedly rose to **5.5**% pa. Note that all yields above are given as APR's compounding semi-annually.

What was the bond investors' historical total return over that first 6 month period, given as an effective semi-annual rate?

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

**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?

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

You wish to consume **twice** as much now (t=0) as in one year (t=1) and have nothing left in the bank at the end.

How much can you consume at time zero and one? The answer choices are given in the same order.

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

You wish to consume **half** as much now (t=0) as in one year (t=1) and have nothing left in the bank at the end.

How much can you consume at time zero and one? The answer choices are given in the same order.

A project to build a toll road will take **3** years to complete, costing three payments of $**50** million, paid at the start of each year (at times 0, 1, and 2).

After completion, the toll road will yield a constant $**10** million at the end of each year forever with no costs. So the first payment will be at t=**4**.

The required return of the project is 10% pa given as an effective nominal rate. All cash flows are nominal.

What is the **payback period**?

A firm is considering a business project which costs $**10**m now and is expected to pay a single cash flow of $**12.1**m in two years.

Assume that the initial $**10**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?

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

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

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

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

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

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

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

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

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

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

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

The below screenshot of Microsoft's (MSFT) details were taken from the Google Finance website on 28 Nov 2014. Some information has been deliberately blanked out.

What was MSFT's market capitalisation of equity?

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

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

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

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

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

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

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

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

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

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

The answer choices below are given in the same order.

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

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

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

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

The answer choices below are given in the same order.

There are many ways to write the ordinary annuity formula.

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

The following cash flows are expected:

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

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

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

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

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

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

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

The Net Present Value is:

The first payment of a constant perpetual annual cash flow is received at time 5. Let this cash flow be ##C_5## and the required return be ##r##.

So there will be equal annual cash flows at time 5, 6, 7 and so on forever, and all of the cash flows will be equal so ##C_5 = C_6 = C_7 = ...##

When the perpetuity formula is used to value this stream of cash flows, it will give a value (V) at time:

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?

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%?

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

### P_0 = \frac{d_1}{r-g} ###Assume that the assumptions of the DDM hold and that the time period is measured in years.

Which of the following is equal to the expected dividend in 3 years, ## d_3 ##?

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

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

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 low-quality second-hand car can be bought now for $**1,000** and will last for **1** year before it will be scrapped for nothing.

A high-quality second-hand car can be bought now for $**4,900** and it will last for **5** years before it will be scrapped for nothing.

What is the equivalent annual cost of each car? Assume a discount rate of **10**% pa, given as an effective annual rate.

The answer choices are given as the equivalent annual cost of the low-quality car and then the high quality car.

You just bought a nice dress which you plan to wear once per month on nights out. You bought it a moment ago for $600 (at t=0). In your experience, dresses used once per month last for 6 years.

Your younger sister is a student with no money and wants to borrow your dress once a month when she hits the town. With the increased use, your dress will only last for another 3 years rather than 6.

What is the present value of the cost of letting your sister use your current dress for the next 3 years?

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

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

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

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

How many bonds should the firm issue?