Fight Finance

Your friend wants to borrow $1,000 and offers to pay you back $100 in 6 months, with more $100 payments at the end of every month for another 11 months. So there will be twelve $100 payments in total. She says that 12 payments of $100 equals $1,200 so she's being generous.

If interest rates are 12% pa, given as an APR compounding monthly, what is the Net Present Value (NPV) of your friend's deal?

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

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

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

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

The Net Present Value is:

The 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?

The following cash flows are expected:

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

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

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?

There are many ways to write the ordinary annuity formula.

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

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.

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.

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?

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?

The following cash flows are expected:

• 10 yearly payments of $80, with the first payment in 6.5 years from now (first payment at t=6.5).
• A single payment of $500 in 4 years and 3 months (t=4.25) from now.

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

You are promised 20 payments of $100, where the first payment is immediate (t=0) and the last is at the end of the 19th year (t=19). The effective annual discount rate is ##r##.

Which of the following equations does NOT give the correct present value of these 20 payments?

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?

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

The first payment of $90 is in 3 years, followed by payments every 6 months in perpetuity after that which shrink by 3% every 6 months. That is, the growth rate every 6 months is actually negative 3%, given as an effective 6 month rate. So the payment at ## t=3.5 ## years will be ## 90(1-0.03)^1=87.3 ##, and so on.

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 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:

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:

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)?

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 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.

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 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 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.

A home loan company advertises an interest rate of 9% pa, payable monthly. Which of the following statements about the interest rate is NOT correct? All rates are given with an accuracy of 4 decimal places.

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

An effective monthly return of 1% ##(r_\text{eff monthly})## is equivalent to an effective annual return ##(r_\text{eff annual})## of:

An effective semi-annual return of 5% ##(r_\text{eff 6mth})## is equivalent to an effective annual return ##(r_\text{eff annual})## of:

Details of two different types of light bulbs are given below:

• Low-energy light bulbs cost $3.50, have a life of nine years, and use about $1.60 of electricity a year, paid at the end of each year.
• Conventional light bulbs cost only $0.50, but last only about a year and use about $6.60 of energy a year, paid at the end of each year.

The real discount rate is 5%, given as an effective annual rate. Assume that all cash flows are real. The inflation rate is 3% given as an effective annual rate.

Find the Equivalent Annual Cost (EAC) of the low-energy and conventional light bulbs. The below choices are listed in that order.

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

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.

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##

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 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.

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

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

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

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

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

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

You own 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.

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.

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.

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

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

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

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

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

For a price of $100, Carol will sell you a 5 year bond paying semi-annual coupons of 16% pa. The face value of the bond is $100. Other bonds with similar risk, maturity and coupon characteristics trade at a yield of 12% pa.

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

For a price of $100, Andrea will sell you a 2 year bond paying annual coupons of 10% pa. The face value of the bond is $100. Other bonds with the same risk, maturity and coupon characteristics trade at a yield of 6% pa.

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.

A three year bond has a face value of $100, a yield of 10% and a fixed coupon rate of 5%, paid semi-annually. What is its 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 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 paying a dividend of $1 in one year and every year after that forever. The required return of the stock is 10% pa.

For a price of $6, Carlos will sell you a share which will pay a dividend of $1 in one year and every year after that forever. The required return of the stock is 10% pa.

For a price of $102, Andrea will sell you a share which just paid a dividend of $10 yesterday, and is expected to pay dividends every year forever, growing at a rate of 5% pa.

So the next dividend will be ##10(1+0.05)^1=$10.50## in one year from now, and the year after it will be ##10(1+0.05)^2=11.025## and so on.

The required return of the stock is 15% pa.

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

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

The required return of the stock is 15% pa.

For a price of $10.20 each, Renee will sell you 100 shares. Each share is expected to pay dividends in perpetuity, growing at a rate of 5% pa. The next dividend is one year away (t=1) and is expected to be $1 per share.

The required return of the stock is 15% pa.

For a price of $129, Joanne will sell you a share which is expected to pay a $30 dividend in one year, and a $10 dividend every year after that forever. So the stock's dividends will be $30 at t=1, $10 at t=2, $10 at t=3, and $10 forever onwards.

The required return of the stock is 10% pa.

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

The required return of the stock is 10% pa.

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 is the discount rate '## r_\text{eff} ##' in this equation?

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 ##?

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?

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?

When using the dividend discount model to price a stock:

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

The growth rate of dividends (g):

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

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

Which expression is NOT equal to the expected dividend yield?

A 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 is 10% pa, given as an effective annual rate.

What is the price of the share now?

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. It just paid a dividend of $3. The growth rate in the dividend is 4% 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:

After year 4, the dividend will grow in perpetuity at 4% pa. The required return on the stock is 10% pa. Both the growth rate and required return are given as effective annual rates. Note that the $8 dividend at time zero is about to be paid tonight.

What is the current price of the stock?

A stock is expected to pay the following dividends:

After year 4, the dividend will grow in perpetuity at 4% pa. The required return on the stock is 10% pa. Both the growth rate and required return are given as effective annual rates. Note that the $8 dividend at time zero is about to be paid tonight.

What will be the price of the stock in 5 years (t = 5), just after the dividend at that time has been paid?

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

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

Which of the following statements about the Dividend Discount Model is NOT correct?

A stock pays annual dividends. It just paid a dividend of $5. The growth rate in the dividend is 1% pa. You estimate that the stock's required return is 8% 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:

After year 4, the dividend will grow in perpetuity at 4% pa. 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:

After year 4, the dividend will grow in perpetuity at 4% pa. 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 5 years (t = 5), just after the dividend at that time has been paid?

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

The total required return is 10% pa.

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

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 bathroom and plumbing supplies shop offers credit to its customers. Customers are given 60 days to pay for their goods, but if they pay within 7 days they will get a 2% discount.

What is the effective interest rate implicit in the discount being offered? Assume 365 days in a year and that all customers pay on either the 7th day or the 60th day. All rates given in this question are effective annual rates.

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} ###

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?

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}##

A three year corporate bond yields 12% pa with a coupon rate of 10% pa, paid semi-annually.

Find the effective six month yield, effective annual yield and the effective daily yield. Assume that each month has 30 days and that there are 360 days in a year.

All answers are given in the same order:

##r_\text{eff semi-annual}##, ##r_\text{eff yearly}##, ##r_\text{eff daily}##.

A 2 year government bond yields 5% pa with a coupon rate of 6% pa, paid semi-annually.

Find the effective six month rate, effective annual rate and the effective daily rate. Assume that each month has 30 days and that there are 360 days in a year.

All answers are given in the same order:

##r_\text{eff semi-annual}##, ##r_\text{eff yrly}##, ##r_\text{eff daily}##.

A 2 year corporate bond yields 3% pa with a coupon rate of 5% pa, paid semi-annually.

Find the effective monthly rate, effective six month rate, and effective annual rate.

##r_\text{eff monthly}##, ##r_\text{eff 6 month}##, ##r_\text{eff annual}##.

Jan asks you for a loan. He wants $100 now and offers to pay you back $120 in 1 year. You can borrow and lend from the bank at an interest rate of 10% pa, given as an effective annual rate.

Ignore credit risk. Remember:

### V_0 = \frac{V_t}{(1+r_\text{eff})^t} ###

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.

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?

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 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 stock is expected to pay the following dividends:

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?

A stock is expected to pay the following dividends:

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 will be the price of the stock in four and a half years (t = 4.5)?

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?

In Australia, domestic university students are allowed to buy concession tickets for the bus, train and ferry which sell at a discount of 50% to full-price tickets.

The Australian Government do not allow international university students to buy concession tickets, they have to pay the full price.

Some international students see this as unfair and they are willing to pay for fake university identification cards which have the concession sticker.

What is the most that an international student would be willing to pay for a fake identification card?

Assume that international students:

• consider buying their fake card on the morning of the first day of university from their neighbour, just before they leave to take the train into university.
• buy their weekly train tickets on the morning of the first day of each week.
• ride the train to university and back home again every day seven days per week until summer holidays 40 weeks from now. The concession card only lasts for those 40 weeks. Assume that there are 52 weeks in the year for the purpose of interest rate conversion.
• a single full-priced one-way train ride costs $5.
• have a discount rate of 11% pa, given as an effective annual rate.

Approach this question from a purely financial view point, ignoring the illegality, embarrassment and the morality of committing fraud.

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

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

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

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

A project's net present value (NPV) is negative. Select the most correct statement.

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

Harvey Norman the large retailer often runs sales advertising 2 years interest free when you purchase its products. This offer can be seen as a free personal loan from Harvey Norman to its customers.

Assume that banks charge an interest rate on personal loans of 12% pa given as an APR compounding per month. This is the interest rate that Harvey Norman deserves on the 2 year loan it extends to its customers. Therefore Harvey Norman must implicitly include the cost of this loan in the advertised sale price of its goods.

If you were a customer buying from Harvey Norman, and you were paying immediately, not in 2 years, what is the minimum percentage discount to the advertised sale price that you would insist on? (Hint: if it makes it easier, assume that you’re buying a product with an advertised price of $100).

A stock is expected to pay the following dividends:

After year 4, the dividend will grow in perpetuity at 5% pa. The required return of 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:

After year 4, the dividend will grow in perpetuity at 5% pa. The required return of 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 7 years (t = 7), just after the dividend at that time has been paid?

A stock is expected to pay the following dividends:

After year 4, the dividend will grow in perpetuity at 5% pa. The required return of the stock is 10% pa. Both the growth rate and required return are given as effective annual rates.

If all of the dividends since time period zero were deposited into a bank account yielding 8% pa as an effective annual rate, how much money will be in the bank account in 2.5 years (in other words, at t=2.5)?

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} ##.

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 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.

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

What is the bond's price?

Which one of the following bonds is trading at par?

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

How many bonds should the firm issue?

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

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? All numbers are rounded up.

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?

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.

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

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

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

A firm wishes to raise $10 million now. They will issue 6% pa semi-annual coupon bonds that will mature in 3 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?

An investor bought a 10 year 2.5% pa fixed coupon government bond priced at par. The face value is $100. Coupons are paid semi-annually and the next one is in 6 months.

Six months later, just after the coupon at that time was paid, yields suddenly and unexpectedly fell to 2% pa. Note that all yields above are given as APR's compounding semi-annually.

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

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

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

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

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

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

A 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 4.5% fixed coupon Australian Government bond was issued at par in mid-April 2009. Coupons are paid semi-annually in arrears in mid-April and mid-October each year. The face value is $1,000. The bond will mature in mid-April 2020, so the bond had an original tenor of 11 years.

Today is mid-September 2015 and similar bonds now yield 1.9% pa.

What is the bond's new price? Note: there are 10 semi-annual coupon payments remaining from now (mid-September 2015) until maturity (mid-April 2020); both yields are given as APR's compounding semi-annually; assume that the yield curve was flat before the change in yields, and remained flat afterwards as well.

An investor bought a 5 year government bond with a 2% pa coupon rate at par. Coupons are paid semi-annually. The face value is $100.

Calculate the bond's new price 8 months later after yields have increased to 3% pa. Note that both yields are given as APR's compounding semi-annually. Assume that the yield curve was flat before the change in yields, and remained flat afterwards as well.

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?

Value the following business project to manufacture a new product.

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?

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.

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.

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).

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

Note 1: Due to the project, the firm will have to purchase $40m of inventory initially (at t=0). Half of this inventory will be sold at t=1 and the other half at t=2.

Note 2: The equipment will have a book value of $2m at the end of the project for tax purposes. However, the equipment is expected to fetch $1m when it is sold. Assume that the full capital loss is tax-deductible and taxed at the full corporate tax rate.

Note 3: The project will be fully funded by equity which investors will expect to pay dividends totaling $10m at the end of each year.

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

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.

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###

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.

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.

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.

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

Cash Flow From Assets (CFFA) can be defined as:

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.

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.

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

The cash flow from assets was:

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.

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

The cash flow from assets was:

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.

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?

A method commonly seen in textbooks for calculating a levered firm's free cash flow (FFCF, or CFFA) is the following:

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

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:

One formula for calculating a levered firm's free cash flow (FFCF, or CFFA) is to use net operating profit after tax (NOPAT).

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

What do you think will be the stock's expected return over the next year, given as an effective annual rate?

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

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

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

Government bonds currently have a return of 5% pa. A stock has an expected return of 6% pa and the market return is 7% pa. What is the beta of the stock?

Stock A has a beta of 0.5 and stock B has a beta of 1. Which statement is NOT correct?

A firm's weighted average cost of capital before tax (##r_\text{WACC before tax}##) would increase due to:

A company has:

• 50 million shares outstanding.
• The market price of one share is currently $6.
• The risk-free rate is 5% and the market return is 10%.
• Market analysts believe that the company's ordinary shares have a beta of 2.
• The company has 1 million preferred stock which have a face (or par) value of $100 and pay a constant dividend of 10% of par. They currently trade for $80 each.
• The company's debentures are publicly traded and their market price is equal to 90% of their face value.
• The debentures have a total face value of $60,000,000 and the current yield to maturity of corporate debentures is 10% per annum. The corporate tax rate is 30%.

What is the company's after-tax weighted average cost of capital (WACC)? Assume a classical tax system.

Government bonds currently have a return of 5%. A stock has a beta of 2 and the market return is 7%. What is the expected return of the stock?

A company has:

• 140 million shares outstanding.
• The market price of one share is currently $2.
• The company's debentures are publicly traded and their market price is equal to 93% of the face value.
• The debentures have a total face value of $50,000,000 and the current yield to maturity of corporate debentures is 12% per annum.
• The risk-free rate is 8.50% and the market return is 13.7%.
• Market analysts estimated that the company's stock has a beta of 0.90.
• The corporate tax rate is 30%.

What is the company's after-tax weighted average cost of capital (WACC) in a classical tax system?

Treasury bonds currently have a return of 5% pa. A stock has a beta of 0.5 and the market return is 10% pa. What is the expected return of the stock?

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

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

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

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

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

Buying investment projects that plot above the SML would lead to:

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

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

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

Investment projects that plot on the SML would have:

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

###r_i=r_f+β_i (r_m-r_f)###

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

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.

The equations for Net Income (NI, also known as Earnings or Net Profit After Tax) and Cash Flow From Assets (CFFA, also known as Free Cash Flow to the Firm) per year are:

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

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

For a firm with debt, what is the amount of the interest tax shield per year?

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 __________.

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?

Unrestricted negative gearing is allowed in Australia, New Zealand and Japan. Negative gearing laws allow income losses on investment properties to be deducted from a tax-payer's pre-tax personal income. Negatively geared investors benefit from this tax advantage. They also hope to benefit from capital gains which exceed the income losses.

For example, a property investor buys an apartment funded by an interest only mortgage loan. Interest expense is $2,000 per month. The rental payments received from the tenant living on the property are $1,500 per month. The investor can deduct this income loss of $500 per month from his pre-tax personal income. If his personal marginal tax rate is 46.5%, this saves $232.5 per month in personal income tax.

The advantage of negative gearing is an example of the benefits of:

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?

One of Miller and Modigliani's (M&M's) important insights is that a firm's managers should not try to achieve a particular level of leverage in a world with zero taxes and perfect information since investors can make their own leverage. Therefore corporate capital structure policy is irrelevant since investors can achieve their own desired leverage at the personal level by borrowing or lending on their own.

This principal of 'home-made' or 'do-it-yourself' leverage can also be applied to other topics. Read the following statements to decide which are true:

(I) Payout policy: a firm's managers should not try to achieve a particular pattern of equity payout.

(II) Agency costs: a firm's managers should not try to minimise agency costs.

(III) Diversification: a firm's managers should not try to diversify across industries.

(IV) Shareholder wealth: a firm's managers should not try to maximise shareholders' wealth.

Which of the above statement(s) are true?

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

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

The 'time value of money' is most closely related to which of the following concepts?

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?

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

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?

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

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

An established mining firm announces that it expects large losses over the following year due to flooding which has temporarily stalled production at its mines. Which statement(s) are correct?

(i) If the firm adheres to a full dividend payout policy it will not pay any dividends over the following year.

(ii) If the firm wants to signal that the loss is temporary it will maintain the same level of dividends. It can do this so long as it has enough retained profits.

(iii) By law, the firm will be unable to pay a dividend over the following year because it cannot pay a dividend when it makes a loss.

Select the most correct response:

Assume that there exists a perfect world with no transaction costs, no asymmetric information, no taxes, no agency costs, equal borrowing rates for corporations and individual investors, the ability to short the risk free asset, semi-strong form efficient markets, the CAPM holds, investors are rational and risk-averse and there are no other market frictions.

For a firm operating in this perfect world, which statement(s) are correct?

(i) When a firm changes its capital structure and/or payout policy, share holders' wealth is unaffected.

(ii) When the idiosyncratic risk of a firm's assets increases, share holders do not expect higher returns.

(iii) When the systematic risk of a firm's assets increases, share holders do not expect higher returns.

Select the most correct response:

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

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

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

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?

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.

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.

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:

A new company's Firm Free Cash Flow (FFCF, same as CFFA) is forecast in the graph below.

To value the firm's assets, the terminal value needs to be calculated using the perpetuity with growth formula:

###V_{\text{terminal, }t-1} = \dfrac{FFCF_{\text{terminal, }t}}{r-g}###

Which point corresponds to the best time to calculate the terminal value?

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.

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.

All other things remaining equal, a project is worse if its:

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?

Accountants and finance professionals have lots of names for the same things which can be quite confusing.

Which of the following groups of items are NOT synonyms?

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

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:

A firm pays a fully franked cash dividend of $70 to one of its Australian shareholders who has a personal marginal tax rate of 45%. The corporate tax rate is 30%.

What will be the shareholder's personal tax payable due to the dividend payment?

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

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

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

High risk firms in danger of bankruptcy tend to have:

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?

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?

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).

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

What is the price of the stock now?

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?

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?

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

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.

A $100 stock has a continuously compounded expected total return of 10% pa. Its dividend yield is 2% pa with continuous compounding. What do you expect its price to be in one year?

A 180-day Bank Accepted Bill has a face value of $1,000,000. The interest rate is 8% pa and there are 365 days in the year. What is its price now?