# Fight Finance

#### CoursesTagsRandomAllRecentScores

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

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 ($) 0 -100 1 0 2 121 An investor owns an empty block of land that has local government approval to be developed into a petrol station, car wash or car park. The council will only allow a single development so the projects are mutually exclusive. All of the development projects have the same risk and the required return of each is 10% pa. Each project has an immediate cost and once construction is finished in one year the land and development will be sold. The table below shows the estimated costs payable now, expected sale prices in one year and the internal rates of returns (IRR's).  Mutually Exclusive Projects Project Costnow ($) Sale price inone year ($) IRR(% pa) Petrol station 9,000,000 11,000,000 22.22 Car wash 800,000 1,100,000 37.50 Car park 70,000 110,000 57.14 Which project should the investor accept? 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. 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?

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

Assume the following:

• The degree takes 3 years to complete and all students pass all subjects.
• There are 2 semesters per year and 4 subjects per semester.
• University fees per subject per semester are $1,277, paid at the start of each semester. Fees are expected to remain constant in real terms for the next 3 years. • There are 52 weeks per year. • The first semester is just about to start (t=0). The first semester lasts for 19 weeks (t=0 to 19). • The second semester starts immediately afterwards (t=19) and lasts for another 19 weeks (t=19 to 38). • The summer holidays begin after the second semester ends and last for 14 weeks (t=38 to 52). Then the first semester begins the next year, and so on. • Working full time at the grocery store instead of studying full-time pays$20/hr and you can work 35 hours per week. Wages are paid at the end of each week and are expected to remain constant in real terms.
• Full-time students can work full-time during the summer holiday at the grocery store for the same rate of $20/hr for 35 hours per week. • The discount rate is 9.8% pa. All rates and cash flows are real. Inflation is expected to be 3% pa. All rates are effective annual. The NPV of costs from undertaking the university degree is: 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 ($) 0 -100 1 11 2 121 A project has the following cash flows:  Project Cash Flows Time (yrs) Cash flow ($) 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. 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? You're trying to save enough money to buy your first car which costs$2,500. You can save $100 at the end of each month starting from now. You currently have no money at all. You just opened a bank account with an interest rate of 6% pa payable monthly. How many months will it take to save enough money to buy the car? Assume that the price of the car will stay the same over time. Your main expense is fuel for your car which costs$100 per month. You just refueled, so you won't need any more fuel for another month (first payment at t=1 month).

You have $2,500 in a bank account which pays interest at a rate of 6% pa, payable monthly. Interest rates are not expected to change. Assuming that you have no income, in how many months time will you not have enough money to fully refuel your car? You really want to go on a back packing trip to Europe when you finish university. Currently you have$1,500 in the bank. Bank interest rates are 8% pa, given as an APR compounding per month. If the holiday will cost $2,000, how long will it take for your bank account to reach that amount? You just signed up for a 30 year fully amortising mortgage loan with monthly payments of$1,500 per month. The interest rate is 9% pa which is not expected to change.

To your surprise, you can actually afford to pay $2,000 per month and your mortgage allows early repayments without fees. If you maintain these higher monthly payments, how long will it take to pay off your mortgage? You're trying to save enough money for a deposit to buy a house. You want to buy a house worth$400,000 and the bank requires a 20% deposit ($80,000) before it will give you a loan for the other$320,000 that you need.

You currently have no savings, but you just started working and can save $2,000 per month, with the first payment in one month from now. Bank interest rates on savings accounts are 4.8% pa with interest paid monthly and interest rates are not expected to change. How long will it take to save the$80,000 deposit? Round your answer up to the nearest month.

A student won $1m in a lottery. Currently the money is in a bank account which pays interest at 6% pa, given as an APR compounding per month. She plans to spend$20,000 at the beginning of every month from now on (so the first withdrawal will be at t=0). After each withdrawal, she will check how much money is left in the account. When there is less than $500,000 left, she will donate that remaining amount to charity. In how many months will she make her last withdrawal and donate the remainder to charity? When using the dividend discount model, care must be taken to avoid using a nominal dividend growth rate that exceeds the country's nominal GDP growth rate. Otherwise the firm is forecast to take over the country since it grows faster than the average business forever. Suppose a firm's nominal dividend grows at 10% pa forever, and nominal GDP growth is 5% pa forever. The firm's total dividends are currently$1 billion (t=0). The country's GDP is currently $1,000 billion (t=0). In approximately how many years will the company's total dividends be as large as the country's GDP? The required return of a project is 10%, given as an effective annual rate. Assume that the cash flows shown in the table are paid all at once at the given point in time. What is the Net Present Value (NPV) of the project?  Project Cash Flows Time (yrs) Cash flow ($) 0 -100 1 0 2 121

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?

A firm is considering a business project which costs $11m now and is expected to pay a constant$1m at the end of every year forever.

Assume that the initial $11m 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? An investor owns a whole level of an old office building which is currently worth$1 million. There are three mutually exclusive projects that can be started by the investor. The office building level can be:

• Rented out to a tenant for one year at $0.1m paid immediately, and then sold for$0.99m in one year.
• Refurbished into more modern commercial office rooms at a cost of $1m now, and then sold for$2.4m when the refurbishment is finished in one year.
• Converted into residential apartments at a cost of $2m now, and then sold for$3.4m when the conversion is finished in one year.

All of the development projects have the same risk so the required return of each is 10% pa. The table below shows the estimated cash flows and internal rates of returns (IRR's).

 Mutually Exclusive Projects Project Cash flownow ($) Cash flow inone year ($) IRR(% pa) Rent then sell as is -900,000 990,000 10 Refurbishment into modern offices -2,000,000 2,400,000 20 Conversion into residential apartments -3,000,000 3,400,000 13.33

Which project should the investor accept?

How many years will it take for an asset's price to double if the price grows by 10% pa?

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 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 11 2 121 A project's NPV is positive. Select the most correct statement: For an asset price to double every 10 years, what must be the expected future capital return, given as an effective annual rate? 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 firm is considering a business project which costs$10m now and is expected to pay a single cash flow of $12.1m in two years. Assume that the initial$10m cost is funded using the firm's existing cash so no new equity or debt will be raised. The cost of capital is 10% pa.

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

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

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

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?

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.

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 stock was bought for $8 and paid a dividend of$0.50 one year later (at t=1 year). Just after the dividend was paid, the stock price was $7 (at t=1 year). What were the total, capital and dividend returns given as effective annual rates? The choices are given in the same order: $r_\text{total}$, $r_\text{capital}$, $r_\text{dividend}$. 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:

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

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: $r_\text{total},r_\text{capital},r_\text{income}$. One and a half years ago Frank bought a house for$600,000. Now it's worth only $500,000, based on recent similar sales in the area. The expected total return on Frank's residential property is 7% pa. He rents his house out for$1,600 per month, paid in advance. Every 12 months he plans to increase the rental payments.

The present value of 12 months of rental payments is $18,617.27. The future value of 12 months of rental payments one year in the future is$19,920.48.

What is the expected annual rental yield of the property? Ignore the costs of renting such as maintenance, real estate agent fees and so on.

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

After one year, would you be able to buy , exactly the as or than today with the money in this account?

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?

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

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

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

The answer choices below are given as effective annual rates:

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.

A residential investment property has an expected nominal total return of 8% 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.

A stock has a real expected total return of 7% pa and a real expected capital return of 2% pa.

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

What is the nominal expected total return, capital return and dividend yield? The answers below are given in the same order.

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

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

You judge that the customer can afford to pay back $1,000,000 in 2 years, given as a nominal cash flow. How much should you lend to her right now? 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? 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? Which of the following statements about book and market equity is NOT correct? One year ago a pharmaceutical firm floated by selling its 1 million shares for$100 each. Its book and market values of equity were both $100m. Its debt totalled$50m. The required return on the firm's assets was 15%, equity 20% and debt 5% pa.

In the year since then, the firm:

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

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

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

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

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

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

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

Similarly for equity and debt.

The investment decision primarily affects which part of a business?

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

The financing decision primarily affects which part of a business?

Payout policy is most closely related to which part of a business?

Business people make lots of important decisions. Which of the following is the most important long term decision?

You're considering making an investment in a particular company. They have preference shares, ordinary shares, senior debt and junior debt.

Which is the safest investment? Which will give the highest returns?

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

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

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

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.

Which of the following statements about cash in the form of notes and coins is NOT correct? Assume that inflation is positive.

Notes and coins:

How can a nominal cash flow be precisely converted into a real cash flow?

You expect a nominal payment of $100 in 5 years. The real discount rate is 10% pa and the inflation rate is 3% pa. Which of the following statements is NOT correct? 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.

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. The expression 'you have to spend money to make money' relates to which business decision? 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. 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? Which of the following statements is NOT correct? Apples and oranges currently cost$1 each. Inflation is 5% pa, and apples and oranges are equally affected by this inflation rate. Note that when payments are not specified as real, as in this question, they're conventionally assumed to be nominal.

Which of the following statements is NOT correct?

Which of the following statements about inflation is NOT correct?

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. 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. 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. 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. Will you or Katya's deal? There are many ways to write the ordinary annuity formula. Which of the following is NOT equal to the ordinary annuity formula? 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. 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 and last at t=12).
• 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? 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.

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:

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?

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

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

For a price of $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.

Would you like to Carla's share or politely ?

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:

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.

Would you like to the share or politely ?

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 $C_1/P_0$?

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

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

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

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?

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 is expected to pay a dividend of $15 in one year (t=1), then$25 for 9 years after that (payments at t=2 ,3,...10), and on the 11th year (t=11) the dividend will be 2% less than at t=10, and will continue to shrink at the same rate every year after that forever. The required return of the stock is 10%. All rates are effective annual rates.

What is the price of the stock now?

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?

In the dividend discount model:

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

The return $r$ is supposed to be the:

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%? What is the NPV of the following series of cash flows when the discount rate is 5% given as an effective annual rate? The first payment of$10 is in 4 years, followed by payments every 6 months forever after that which shrink by 2% every 6 months. That is, the growth rate every 6 months is actually negative 2%, given as an effective 6 month rate. So the payment at $t=4.5$ years will be $10(1-0.02)^1=9.80$, and so on.

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

What is the price of the share now?

A stock pays annual dividends which are expected to continue forever. It just paid a dividend of $10. The growth rate in the dividend is 2% pa. You estimate that the stock's required return is 10% pa. Both the discount rate and growth rate are given as effective annual rates. Using the dividend discount model, what will be the share price? A stock is expected to pay the following dividends:  Cash Flows of a Stock Time (yrs) 0 1 2 3 4 ... Dividend ($) 0.00 1.00 1.05 1.10 1.15 ...

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

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

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

A stock is expected to pay the following dividends:

 Cash Flows of a Stock Time (yrs) 0 1 2 3 4 ... Dividend ($) 0.00 1.00 1.05 1.10 1.15 ... After year 4, the annual dividend will grow in perpetuity at 5% pa, so; • the dividend at t=5 will be$1.15(1+0.05),
• the dividend at t=6 will be $1.15(1+0.05)^2, and so on. The required return on the stock is 10% pa. Both the growth rate and required return are given as effective annual rates. What will be the price of the stock in three and a half years (t = 3.5)? 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, $d_3$? 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? The following equation is the Dividend Discount Model, also known as the 'Gordon Growth Model' or the 'Perpetuity with growth' equation. $$p_0=\frac{d_1}{r_\text{eff}-g_\text{eff}}$$ Which expression is NOT equal to the expected capital return? A fairly valued share's current price is$4 and it has a total required return of 30%. Dividends are paid annually and next year's dividend is expected to be $1. After that, dividends are expected to grow by 5% pa in perpetuity. All rates are effective annual returns. What is the expected dividend income paid at the end of the second year (t=2) and what is the expected capital gain from just after the first dividend (t=1) to just after the second dividend (t=2)? The answers are given in the same order, the dividend and then the capital gain. A stock pays semi-annual dividends. It just paid a dividend of$10. The growth rate in the dividend is 1% every 6 months, given as an effective 6 month rate. You estimate that the stock's required return is 21% pa, as an effective annual rate.

Using the dividend discount model, what will be the share price?

Most listed Australian companies pay dividends twice per year, the 'interim' and 'final' dividends, which are roughly 6 months apart.

You are an equities analyst trying to value the company BHP. You decide to use the Dividend Discount Model (DDM) as a starting point, so you study BHP's dividend history and you find that BHP tends to pay the same interim and final dividend each year, and that both grow by the same rate.

You expect BHP will pay a $0.55 interim dividend in six months and a$0.55 final dividend in one year. You expect each to grow by 4% next year and forever, so the interim and final dividends next year will be $0.572 each, and so on in perpetuity. Assume BHP's cost of equity is 8% pa. All rates are quoted as nominal effective rates. The dividends are nominal cash flows and the inflation rate is 2.5% pa. What is the current price of a BHP share? You own an apartment which you rent out as an investment property. What is the price of the apartment using discounted cash flow (DCF, same as NPV) valuation? Assume that: • You just signed a contract to rent the apartment out to a tenant for the next 12 months at$2,000 per month, payable in advance (at the start of the month, t=0). The tenant is just about to pay you the first $2,000 payment. • The contract states that monthly rental payments are fixed for 12 months. After the contract ends, you plan to sign another contract but with rental payment increases of 3%. You intend to do this every year. So rental payments will increase at the start of the 13th month (t=12) to be$2,060 (=2,000(1+0.03)), and then they will be constant for the next 12 months.
Rental payments will increase again at the start of the 25th month (t=24) to be $2,121.80 (=2,000(1+0.03)2), and then they will be constant for the next 12 months until the next year, and so on. • The required return of the apartment is 8.732% pa, given as an effective annual rate. • Ignore all taxes, maintenance, real estate agent, council and strata fees, periods of vacancy and other costs. Assume that the apartment will last forever and so will the rental payments. Two companies BigDiv and ZeroDiv are exactly the same except for their dividend payouts. BigDiv pays large dividends and ZeroDiv doesn't pay any dividends. Currently the two firms have the same earnings, assets, number of shares, share price, expected total return and risk. Assume a perfect world with no taxes, no transaction costs, no asymmetric information and that all assets including business projects are fairly priced and therefore zero-NPV. All things remaining equal, which of the following statements is NOT correct? The boss of WorkingForTheManCorp has a wicked (and unethical) idea. He plans to pay his poor workers one week late so that he can get more interest on his cash in the bank. Every week he is supposed to pay his 1,000 employees$1,000 each. So $1 million is paid to employees every week. The boss was just about to pay his employees today, until he thought of this idea so he will actually pay them one week (7 days) later for the work they did last week and every week in the future, forever. Bank interest rates are 10% pa, given as a real effective annual rate. So $r_\text{eff annual, real} = 0.1$ and the real effective weekly rate is therefore $r_\text{eff weekly, real} = (1+0.1)^{1/52}-1 = 0.001834569$ All rates and cash flows are real, the inflation rate is 3% pa and there are 52 weeks per year. The boss will always pay wages one week late. The business will operate forever with constant real wages and the same number of employees. What is the net present value (NPV) of the boss's decision to pay later? A business project is expected to cost$100 now (t=0), then pay $10 at the end of the third (t=3), fourth, fifth and sixth years, and then grow by 5% pa every year forever. So the cash flow will be$10.5 at the end of the seventh year (t=7), then $11.025 at the end of the eighth year (t=8) and so on perpetually. The total required return is 10℅ pa. Which of the following formulas will NOT give the correct net present value of the project? 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. Details of two different types of light bulbs are given below: • Low-energy light bulbs cost$3.50, have a life of nine years, and use about $1.60 of electricity a year, paid at the end of each year. • Conventional light bulbs cost only$0.50, but last only about a year and use about $6.60 of energy a year, paid at the end of each year. The real discount rate is 5%, given as an effective annual rate. Assume that all cash flows are real. The inflation rate is 3% given as an effective annual rate. Find the Equivalent Annual Cost (EAC) of the low-energy and conventional light bulbs. The below choices are listed in that order. You're advising your superstar client 40-cent who is weighing up buying a private jet or a luxury yacht. 40-cent is just as happy with either, but he wants to go with the more cost-effective option. These are the cash flows of the two options: • The private jet can be bought for$6m now, which will cost $12,000 per month in fuel, piloting and airport costs, payable at the end of each month. The jet will last for 12 years. • Or the luxury yacht can be bought for$4m now, which will cost $20,000 per month in fuel, crew and berthing costs, payable at the end of each month. The yacht will last for 20 years. What's unusual about 40-cent is that he is so famous that he will actually be able to sell his jet or yacht for the same price as it was bought since the next generation of superstar musicians will buy it from him as a status symbol. Bank interest rates are 10% pa, given as an effective annual rate. You can assume that 40-cent will live for another 60 years and that when the jet or yacht's life is at an end, he will buy a new one with the same details as above. Would you advise 40-cent to buy the or the ? Note that the effective monthly rate is $r_\text{eff monthly}=(1+0.1)^{1/12}-1=0.00797414$ An industrial chicken farmer grows chickens for their meat. Chickens: 1. Cost$0.50 each to buy as chicks. They are bought on the day they’re born, at t=0.
2. Grow at a rate of $0.70 worth of meat per chicken per week for the first 6 weeks (t=0 to t=6). 3. Grow at a rate of$0.40 worth of meat per chicken per week for the next 4 weeks (t=6 to t=10) since they’re older and grow more slowly.
4. Feed costs are $0.30 per chicken per week for their whole life. Chicken feed is bought and fed to the chickens once per week at the beginning of the week. So the first amount of feed bought for a chicken at t=0 costs$0.30, and so on.
5. Can be slaughtered (killed for their meat) and sold at no cost at the end of the week. The price received for the chicken is their total value of meat (note that the chicken grows fast then slow, see above).

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

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

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

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

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

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

Every time Edwin buys a second hand 4 year old car he immediately has to spend $1,000 on repairs, and then$1,000 every year after that for the next 10 years. So there are 11 payments in total from when the second hand car is bought at t=0 to the last payment at t=10. One year later (t=11) the old car is at the end of its total 15 year life and can be scrapped for $2,000. Assuming that Carlos and Edwin maintain their love of Commodores and keep up their habits of buying new ones and second hand ones respectively, how much larger is Carlos' equivalent annual cost of car ownership compared with Edwin's? The real discount rate is 10% pa. All cash flows are real and are expected to remain constant. Inflation is forecast to be 3% pa. All rates are effective annual. Ignore capital gains tax and tax savings from depreciation since cars are tax-exempt for individuals. You're about to buy a car. These are the cash flows of the two different cars that you can buy: • You can buy an old car for$5,000 now, for which you will have to buy $90 of fuel at the end of each week from the date of purchase. The old car will last for 3 years, at which point you will sell the old car for$500.
• Or you can buy a new car for $14,000 now for which you will have to buy$50 of fuel at the end of each week from the date of purchase. The new car will last for 4 years, at which point you will sell the new car for $1,000. Bank interest rates are 10% pa, given as an effective annual rate. Assume that there are exactly 52 weeks in a year. Ignore taxes and environmental and pollution factors. Should you buy the or the ? Details of two different types of desserts or edible treats are given below: • High-sugar treats like candy, chocolate and ice cream make a person very happy. High sugar treats are cheap at only$2 per day.
• Low-sugar treats like nuts, cheese and fruit make a person equally happy if these foods are of high quality. Low sugar treats are more expensive at $4 per day. The advantage of low-sugar treats is that a person only needs to pay the dentist$2,000 for fillings and root canal therapy once every 15 years. Whereas with high-sugar treats, that treatment needs to be done every 5 years.

The real discount rate is 10%, given as an effective annual rate. Assume that there are 365 days in every year and that all cash flows are real. The inflation rate is 3% given as an effective annual rate.

Find the equivalent annual cash flow (EAC) of the high-sugar treats and low-sugar treats, including dental costs. The below choices are listed in that order.

Ignore the pain of dental therapy, personal preferences and other factors.

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

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

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

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

You own some nice shoes which you use once per week on date nights. You bought them 2 years ago for $500. In your experience, shoes used once per week last for 6 years. So you expect yours to last for another 4 years. Your younger sister said that she wants to borrow your shoes once per week. With the increased use, your shoes will only last for another 2 years rather than 4. What is the present value of the cost of letting your sister use your current shoes for the next 2 years? Assume: that bank interest rates are 10% pa, given as an effective annual rate; you will buy a new pair of shoes when your current pair wears out and your sister will not use the new ones; your sister will only use your current shoes so she will only use it for the next 2 years; and the price of new shoes never changes. 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? Which firms tend to have high forward-looking price-earnings (PE) ratios? Which firms tend to have low forward-looking price-earnings (PE) ratios? Only consider firms with positive PE ratios. Which of the below statements about effective rates and annualised percentage rates (APR's) is NOT correct? Which of the following statements about effective rates and annualised percentage rates (APR's) is NOT correct? Private equity firms are known to buy medium sized private companies operating in the same industry, merge them together into a larger company, and then sell it off in a public float (initial public offering, IPO). If medium-sized private companies trade at PE ratios of 5 and larger listed companies trade at PE ratios of 15, what return can be achieved from this strategy? Assume that: • The medium-sized companies can be bought, merged and sold in an IPO instantaneously. • There are no costs of finding, valuing, merging and restructuring the medium sized companies. Also, there is no competition to buy the medium-sized companies from other private equity firms. • The large merged firm's earnings are the sum of the medium firms' earnings. • The only reason for the difference in medium and large firm's PE ratios is due to the illiquidity of the medium firms' shares. • Return is defined as: $r_{0→1} = (p_1-p_0+c_1)/p_0$ , where time zero is just before the merger and time one is just after. A 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: $r_\text{credit card, eff yrly}$, $r_\text{bond, eff yrly}$, $r_\text{stock, eff yrly}$ 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? 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?

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.

The perpetuity with growth formula, also known as the dividend discount model (DDM) or Gordon growth model, is appropriate for valuing a company's shares. $P_0$ is the current share price, $C_1$ is next year's expected dividend, $r$ is the total required return and $g$ is the expected growth rate of the dividend.

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

The below graph shows the expected future price path of the company's shares. Which of the following statements about the graph is NOT correct?

You are an equities analyst trying to value the equity of the Australian telecoms company Telstra, with ticker TLS. In Australia, listed companies like Telstra tend to pay dividends every 6 months. The payment around August is called the final dividend and the payment around February is called the interim dividend. Both occur annually.

• Today is mid-March 2015.
• TLS's last interim dividend of $0.15 was one month ago in mid-February 2015. • TLS's last final dividend of$0.15 was seven months ago in mid-August 2014.

Judging by TLS's dividend history and prospects, you estimate that the nominal dividend growth rate will be 1% pa. Assume that TLS's total nominal cost of equity is 6% pa. The dividends are nominal cash flows and the inflation rate is 2.5% pa. All rates are quoted as nominal effective annual rates. Assume that each month is exactly one twelfth (1/12) of a year, so you can ignore the number of days in each month.

Calculate the current TLS share price.

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.

An 'interest payment' is the same thing as a 'coupon payment'. or ?

An 'interest rate' is the same thing as a 'coupon rate'. or ?

An 'interest rate' is the same thing as a 'yield'. or ?

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.

An 'interest only' loan can also be called a:

Which of the following statements is NOT correct? Borrowers:

Which of the following statements is NOT correct? Lenders:

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

What will be your monthly payments?

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 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?

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. 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. 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? 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:

$$\text{Proportional increase} = \frac{V_\text{after}-V_\text{before}}{V_\text{before}}$$

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.

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. 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. Would you like to her bond or politely ? 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. Would you like to the bond or politely ? 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? 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?

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?

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? 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?

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?

Which one of the following bonds is trading at par?

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

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

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?

A four year bond has a face value of $100, a yield of 9% and a fixed coupon rate of 6%, paid semi-annually. What is its price? In these tough economic times, central banks around the world have cut interest rates so low that they are practically zero. In some countries, government bond yields are also very close to zero. A three year government bond with a face value of$100 and a coupon rate of 2% pa paid semi-annually was just issued at a yield of 0%. What is the price of the bond?

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? 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. "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: Let the 'income return' of a bond be the coupon at the end of the period divided by the market price now at the start of the period $(C_1/P_0)$. The expected income return of a premium fixed coupon bond is: A European 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 company's forward rate over the second year (from t=1 to t=2)? Give your answer as an effective annual rate, which is how the above bond yields are quoted. 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. An Australian company just issued two bonds paying semi-annual coupons: • 1 year zero coupon bond at a yield of 8% pa, and a • 2 year zero coupon bond at a yield of 10% pa. What is the forward rate on the company's debt from years 1 to 2? Give your answer as an APR compounding every 6 months, which is how the above bond yields are quoted. You deposit cash into your bank account. Have you or your money? You deposit cash into your bank account. Have you or debt? You deposit cash into your bank account. Have you or debt? You deposit cash into your bank account. Does the deposit account represent a debt or to you? You owe money. Are you a or a ? You are owed money. Are you a or a ? You own a debt asset. Are you a or a ? Which of the following statements is NOT correct? Bond investors: 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. A European company just issued two bonds, a • 2 year zero coupon bond at a yield of 8% pa, and a • 3 year zero coupon bond at a yield of 10% pa. What is the company's forward rate over the third year (from t=2 to t=3)? Give your answer as an effective annual rate, which is how the above bond yields are quoted. 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? $$CFFA=NI+Depr-CapEx - \Delta NWC+IntExp$$ Cash Flow From Assets (CFFA) can be defined as: 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. A company increases the proportion of debt funding it uses to finance its assets by issuing bonds and using the cash to repurchase stock, leaving assets unchanged. Ignoring the costs of financial distress, which of the following statements is NOT correct: 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: $$NI = (Rev-COGS-FC-Depr-IntExp).(1-t_c )$$ $$CFFA=NI+Depr-CapEx - \Delta NWC+IntExp$$ 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 Sidebar Corporation's Cash Flow From Assets (CFFA), also known as Free Cash Flow to the Firm (FCFF), over the year ending 30th June 2013.  Sidebar Corp Income Statement for year ending 30th June 2013$m Sales 405 COGS 100 Depreciation 34 Rent expense 22 Interest expense 39 Taxable Income 210 Taxes at 30% 63 Net income 147
 Sidebar Corp Balance Sheet as at 30th June 2013 2012 $m$m Cash 0 0 Inventory 70 50 Trade debtors 11 16 Rent paid in advance 4 3 PPE 700 680 Total assets 785 749 Trade creditors 11 19 Bond liabilities 400 390 Contributed equity 220 220 Retained profits 154 120 Total L and OE 785 749

Note: All figures are given in millions of dollars ($m). The cash flow from assets was: 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 $0.8m on new buildings without buying or selling any other fixed assets. This capital expenditure is included in the CFFA figure quoted above. Assume that: • All amounts are received and paid at the end of the year so you can ignore the time value of money. • The firm has sufficient retained profits to pay the dividend and complete the buy back. • The firm plans to run a very tight ship, with no excess cash above operating requirements currently or over the next year. How much new equity financing will the company need? In other words, what is the value of new shares that will need to be issued? Find Ching-A-Lings Corporation's Cash Flow From Assets (CFFA), also known as Free Cash Flow to the Firm (FCFF), over the year ending 30th June 2013.  Ching-A-Lings Corp Income Statement for year ending 30th June 2013$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$5m in sales, $1.9m in net income and$2m in equity free cash flow (EFCF).
• Pay dividends of $1m. • Complete a$1.3m 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 an investment which:

• Costs $1 million initially (t=0); and • Pays a single positive cash flow of$1.1 million in one year (t=1).

The investment 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.

Method 1: $-1m + \dfrac{1.1m}{(1+0.1)^1}$

Method 2: $-1m + 1.1m - 1m \times 0.1$

Method 3: $-1m + \dfrac{1.1m}{(1+0.1)^1} - 1m \times 0.1$

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

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

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

A man is thinking about taking a day off from his casual painting job to relax.

He just woke up early in the morning and he's about to call his boss to say that he won't be coming in to work.

But he's thinking about the hours that he could work today (in the future) which are:

A 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:

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).

Value the following business project to manufacture a new product.

 Project Data Project life 2 yrs Initial investment in equipment $6m Depreciation of equipment per year$3m Expected sale price of equipment at end of project $0.6m Unit sales per year 4m Sale price per unit$8 Variable cost per unit $5 Fixed costs per year, paid at the end of each year$1m Interest expense per year 0 Tax rate 30% Weighted average cost of capital after tax per annum 10%

Notes

1. The firm's current assets and current liabilities are $3m and$2m respectively right now. This net working capital will not be used in this project, it will be used in other unrelated projects.
Due to the project, current assets (mostly inventory) will grow by $2m initially (at t = 0), and then by$0.2m at the end of the first year (t=1).
Current liabilities (mostly trade creditors) will increase by $0.1m at the end of the first year (t=1). At the end of the project, the net working capital accumulated due to the project can be sold for the same price that it was bought. 2. The project cost$0.5m to research which was incurred one year ago.

Assumptions

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

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

To value a business's assets, the free cash flow of the firm (FCFF, also called CFFA) needs to be calculated. This requires figures from the firm's income statement and balance sheet. For what figures is the balance sheet needed? Note that the balance sheet is sometimes also called the statement of financial position.

Issuing debt doesn't give away control of the firm because debt holders can't cast votes to determine the company's affairs, such as at the annual general meeting (AGM), and can't appoint directors to the board. or ?

Companies must pay interest and principal payments to debt-holders. They're compulsory. But companies are not forced to pay dividends to share holders. or ?

Your friend just bought a house for $400,000. He financed it using a$320,000 mortgage loan and a deposit of $80,000. In the context of residential housing and mortgages, the 'equity' tied up in the value of a person's house is the value of the house less the value of the mortgage. So the initial equity your friend has in his house is$80,000. Let this amount be E, let the value of the mortgage be D and the value of the house be V. So $V=D+E$.

If house prices suddenly fall by 10%, what would be your friend's percentage change in equity (E)? Assume that the value of the mortgage is unchanged and that no income (rent) was received from the house during the short time over which house prices fell.

Remember:

$$r_{0\rightarrow1}=\frac{p_1-p_0+c_1}{p_0}$$

where $r_{0-1}$ is the return (percentage change) of an asset with price $p_0$ initially, $p_1$ one period later, and paying a cash flow of $c_1$ at time $t=1$.

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 manufacturing company is considering a new project in the more risky services industry. The cash flows from assets (CFFA) are estimated for the new project, with interest expense excluded from the calculations. To get the levered value of the project, what should these unlevered cash flows be discounted by? Assume that the manufacturing firm has a target debt-to-assets ratio that it sticks to. A 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: 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} Does this annual FFCF or the annual interest tax shield? 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} \\ Does this annual FFCF or the annual interest tax shield? 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} Does this annual FFCF with zero interest expense or the annual interest tax shield? One formula for calculating a levered firm's free cash flow (FFCF, or CFFA) is to use net operating profit after tax (NOPAT). \begin{aligned} FFCF &= NOPAT + Depr - CapEx -\Delta NWC \\ &= (Rev - COGS - Depr - FC)(1-t_c) + Depr - CapEx -\Delta NWC \\ \end{aligned} \\ Does this annual FFCF or the annual interest tax shield? 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. $$NI=(Rev - COGS - Depr - FC - IntExp).(1-t_c )$$ $$EBIT=Rev - COGS - FC-Depr$$ $$EBITDA=Rev - COGS - FC$$ $$Tax =(Rev - COGS - Depr - FC - IntExp).t_c= \dfrac{NI.t_c}{1-t_c}$$ 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?  Project Data Project life 2 yrs Initial investment in equipment600k 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 1. The project will require an immediate purchase of$50k 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?

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

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 equity to raise money for new projects of similar systematic risk to the company's existing projects. Assume a classical tax system. Which statement is correct?

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

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 99  capital structure, interest tax shield, Miller and Modigliani, trade off theory of capital structure

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

Assume that:

• The firm and individual investors can borrow at the same rate and have the same tax rates.
• The firm's debt and shares are fairly priced and the shares are repurchased at the market price, not at a premium.
• There are no market frictions relating to debt such as asymmetric information or transaction costs.
• Shareholders wealth is measured in terms of utiliity. Shareholders are wealth-maximising and risk-averse. They have a preferred level of overall leverage. Before the firm's capital restructure all shareholders were optimally levered.

According to Miller and Modigliani's theory, which statement is correct?

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?

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 has a debt-to-equity ratio of 25%. What is its debt-to-assets ratio? A firm has a debt-to-equity ratio of 60%. What is its debt-to-assets ratio? 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? Where can a publicly listed firm's book value of equity be found? It can be sourced from the company's: Where can a private firm's market value of equity be found? It can be sourced from the company's: 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'. 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? 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. How many years will it take for an asset's price to triple (increase from say$1 to $3) if it grows by 5% pa? If someone says "my shares rose by 10% last year", what do you assume that they mean? 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? 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? 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? Question 749 Multiples valuation, PE ratio, price to revenue ratio, price to book ratio, NPV 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. All other things remaining equal, a project is worse if its: 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 $570 in one month from now. The effective annual interest rate is 15.8%, and the effective monthly interest rate is 1.23%. What is the present value of the savings? A stock is expected to pay the following dividends:  Cash Flows of a Stock Time (yrs) 0 1 2 3 4 ... Dividend ($) 0.00 1.15 1.10 1.05 1.00 ...

After year 4, the annual dividend will grow in perpetuity at -5% pa. Note that this is a negative growth rate, so the dividend will actually shrink. So,

• the dividend at t=5 will be $1(1-0.05) = 0.95$,
• the dividend at t=6 will be $1(1-0.05)^2 = 0.9025$, and so on.

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

What is the current price of the stock?

The following 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?

How much more can you borrow using an interest-only loan compared to a 25-year fully amortising loan if interest rates are 4% pa compounding per month and are not expected to change? If it makes it easier, assume that you can afford to pay $2,000 per month on either loan. Express your answer as a proportional increase using the following formula: $$\text{Proportional Increase} = \dfrac{V_\text{0,interest only}}{V_\text{0,fully amortising}} - 1$$ 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? You just entered into a fully amortising home loan with a principal of$600,000, a variable interest rate of 4.25% pa and a term of 25 years.

Immediately after settling the loan, the variable interest rate suddenly falls to 4% pa! You can't believe your luck. Despite this, you plan to continue paying the same home loan payments as you did before. How long will it now take to pay off your home loan?

Assume that the lower interest rate was granted immediately and that rates were and are now again expected to remain constant. Round your answer up to the nearest whole month.

Two years ago you entered into a fully amortising home loan with a principal of $1,000,000, an interest rate of 6% pa compounding monthly with a term of 25 years. Then interest rates suddenly fall to 4.5% pa (t=0), but you continue to pay the same monthly home loan payments as you did before. How long will it now take to pay off your home loan? Measure the time taken to pay off the home loan from the current time which is 2 years after the home loan was first entered into. Assume that the lower interest rate was given to you immediately after the loan repayment at the end of year 2, which was the 24th payment since the loan was granted. Also assume that rates were and are expected to remain constant. The phone company Telstra have 2 mobile service plans on offer which both have the same amount of phone call, text message and internet data credit. Both plans have a contract length of 24 months and the monthly cost is payable in advance. The only difference between the two plans is that one is a: • 'Bring Your Own' (BYO) mobile service plan, costing$50 per month. There is no phone included in this plan. The other plan is a:
• 'Bundled' mobile service plan that comes with the latest smart phone, costing $71 per month. This plan includes the latest smart phone. Neither plan has any additional payments at the start or end. The only difference between the plans is the phone, so what is the implied cost of the phone as a present value? Assume that the discount rate is 2% per month given as an effective monthly rate, the same high interest rate on credit cards. 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?