Fight Finance

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.

Suppose you had $100 in a savings account and the interest rate was 2% per year.

After 5 years, how much do you think you would have in the account if you left the money to grow?

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 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 $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.

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, 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.

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##).

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

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.

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 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?

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?

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).

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 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} ##.

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.

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?

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 ##?

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).

A share was bought for $20 (at t=0) and paid its annual dividend of $3 one year later (at t=1). Just after the dividend was paid, the share price was $16 (at t=1). 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 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 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.

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?

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

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?

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 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?

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 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 Profitability Index (PI) of the project?

A wholesale horticulture nursery offers credit to its customers.

Customers are given 60 days to pay for their goods, but if they pay immediately they will get a 3% discount.

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

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 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?

A three year project's NPV is negative. The cash flows of the project include a negative cash flow at the very start and positive cash flows over its short life. The required return of the project is 10% pa. Select the most correct statement.

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?

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)?

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 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 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.

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.

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?

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.

What is the standard deviation (not variance) of the above portfolio? Note that the stocks' covariance is given, not correlation.

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.

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?

What is the expected return of the above portfolio?

What is the standard deviation (not variance) of returns of the above portfolio?

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 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?

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?

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.

A company runs a number of slaughterhouses which supply hamburger meat to McDonalds. The company is afraid that live cattle prices will increase over the next year, even though there is widespread belief in the market that they will be stable. What can the company do to hedge against the risk of increasing live cattle prices? Which statement(s) are correct?

(i) buy call options on live cattle.

(ii) buy put options on live cattle.

(iii) sell call options on live cattle.

Select the most correct response:

Below are 4 option graphs. Note that the y-axis is payoff at maturity (T). What options do they depict? List them in the order that they are numbered.

A fairly priced stock has an expected return of 15% pa. Treasury bonds yield 5% pa and the market portfolio's expected return is 10% pa. What is the beta of the stock?

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?

An Australian company just issued two bonds:

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

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

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

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

All things remaining equal, the variance of a portfolio of two positively-weighted stocks rises as:

According to the theory of the Capital Asset Pricing Model (CAPM), total risk can be broken into two components, systematic risk and idiosyncratic risk. Which of the following events would be considered a systematic, undiversifiable event according to the theory of the CAPM?

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?

A firm can issue 5 year annual coupon bonds at a yield of 8% pa and a coupon rate of 12% pa.

The beta of its levered equity is 1. Five year government bonds yield 5% pa with a coupon rate of 6% pa. The market's expected dividend return is 4% pa and its expected capital return is 6% pa.

The firm's debt-to-equity ratio is 2:1. The corporate tax rate is 30%.

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

Below are 4 option graphs. Note that the y-axis is payoff at maturity (T). What options do they depict? List them in the order that they are numbered

You operate a cattle farm that supplies hamburger meat to the big fast food chains. You buy a lot of grain to feed your cattle, and you sell the fully grown cattle on the livestock market.

You're afraid of adverse movements in grain and livestock prices. What options should you buy to hedge your exposures in the grain and cattle livestock markets?

Select the most correct response:

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.

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 90-day Bank Accepted Bill (BAB) has a face value of $1,000,000. The simple interest rate is 10% pa and there are 365 days in the year. What is its price now?

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?

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?

Your credit card shows a $600 debt liability. The interest rate is 24% pa, payable monthly. You can't pay any of the debt off, except in 6 months when it's your birthday and you'll receive $50 which you'll use to pay off the credit card. If that is your only repayment, how much will the credit card debt liability be one year from now?

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}##.

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?

A wholesale shop offers credit to its customers. The customers are given 21 days to pay for their goods. But if they pay straight away (now) they get a 1% discount.

What is the effective interest rate given to customers who pay in 21 days? All rates given below are effective annual rates. Assume 365 days in a year.

A project has an internal rate of return (IRR) which is greater than its required return. Select the most correct statement.

When using the dividend discount model to price a stock:

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

The growth rate of dividends (g):

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 30-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?

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?

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

A 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 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}##.

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 wholesale vitamin supplements store offers credit to its customers. Customers are given 30 days to pay for their goods, but if they pay within 5 days they will get a 1% 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 5th day or the 30th day. All of the below answer choices are given as effective annual interest rates.

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 90-day Bank Accepted Bill has a face value of $1,000,000. The interest rate is 6% pa and there are 365 days in the year. What is its price?

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

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

Which expression is NOT equal to the expected capital return?

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?

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 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 share was bought for $10 (at t=0) and paid its annual dividend of $0.50 one year later (at t=1). Just after the dividend was paid, the share price was $11 (at t=1).

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{dividend}##.

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 wholesale store offers credit to its customers. Customers are given 60 days to pay for their goods, but if they pay immediately they will get a 1.5% discount.

What is the effective interest rate implicit in the discount being offered? Assume 365 days in a year and that all customers pay either immediately or the 60th day. All of the below answer choices are given as effective annual interest rates.

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

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?

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?

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.

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).

A project has the following cash flows:

What is the Profitability Index (PI) of the project? Assume that the cash flows shown in the table are paid all at once at the given point in time. The required return is 10% pa, given as an effective annual rate.

A project has the following cash flows. 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 $250 at time 2 is actually earned smoothly from t=1 to t=2:

What is the payback period of the project in years?

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

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

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

A furniture distributor offers credit to its customers. Customers are given 25 days to pay for their goods, but if they pay immediately they will get a 1% discount.

What is the effective interest rate implicit in the discount being offered? Assume 365 days in a year and that all customers pay either immediately or on the 25th day. All rates given below are effective annual rates.

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?

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.

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

In the dividend discount model:

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

The return ##r## is supposed to be the:

Bonds with lower (worse) credit ratings tend to have:

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 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?

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).

A project has the following cash flows:

The required return on the project is 10%, given as an effective annual rate.

What is the Internal Rate of Return (IRR) of this project? The following choices are effective annual rates. Assume that the cash flows shown in the table are paid all at once at the given point in time.

A project has the following cash flows:

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's Profitability Index (PI) is less than 1. Select the most correct statement:

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?

A share pays annual dividends. It just paid a dividend of $2. The growth rate in the dividend is 3% 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 is the share price?

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)?

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 and the stock is fairly priced, which one of the following statements is NOT correct? The long term expected:

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.

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?

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:

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).

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'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 ?

Which of the following statements is NOT correct?

A project has the following cash flows:

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 Profitability Index (PI) of the project?

A project has the following cash flows. 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 $105 at time 2 is actually earned smoothly from t=1 to t=2:

What is the payback period of the project in years?

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.

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

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