# Fight Finance

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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 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 stock is expected to pay the following dividends:  Cash Flows of a Stock Time (yrs) 0 1 2 3 4 ... Dividend ($) 0.00 1.00 1.05 1.10 1.15 ...

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

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

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

A stock is expected to pay the following dividends:

 Cash Flows of a Stock Time (yrs) 0 1 2 3 4 ... Dividend ($) 0.00 1.00 1.05 1.10 1.15 ... After year 4, the annual dividend will grow in perpetuity at 5% pa, so; • the dividend at t=5 will be$1.15(1+0.05),
• the dividend at t=6 will be $1.15(1+0.05)^2, and so on. The required return on the stock is 10% pa. Both the growth rate and required return are given as effective annual rates. What will be the price of the stock in three and a half years (t = 3.5)? 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 $10 million at the end of each year forever with no costs. So the first payment will be at t=4. The required return of the project is 10% pa given as an effective nominal rate. All cash flows are nominal. What is the payback period? The required return of a project is 10%, given as an effective annual rate. Assume that the cash flows shown in the table are paid all at once at the given point in time. What is the Profitability Index (PI) of the project?  Project Cash Flows Time (yrs) Cash flow ($) 0 -100 1 0 2 121

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?

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

 Portfolio Details Stock Expected return Standard deviation Covariance $(\sigma_{A,B})$ Beta Dollars invested A 0.2 0.4 0.12 0.5 40 B 0.3 0.8 1.5 80

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?

 Portfolio Details Stock Expected return Standard deviation Correlation Dollars invested A 0.1 0.4 0.5 60 B 0.2 0.6 140

What is the expected return of the above portfolio?

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.

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

A stock's correlation with the market portfolio increases while its total risk is unchanged. What will happen to the stock's expected return and systematic risk?

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 formula for the present value of interest tax shields if the tax shields occur in perpetuity?

You may assume:

• the value of debt (D) is constant through time,
• The cost of debt and the yield on debt are equal and given by $r_D$.
• the appropriate rate to discount interest tax shields is $r_D$.
• $\text{IntExp}=D.r_D$

A company has:

• 10 million common shares outstanding, each trading at a price of $90. • 1 million preferred shares which have a face (or par) value of$100 and pay a constant dividend of 9% of par. They currently trade at a price of $120 each. • Debentures that have a total face value of$60,000,000 and a yield to maturity of 6% per annum. They are publicly traded and their market price is equal to 90% of their face value.
• The risk-free rate is 5% and the market return is 10%.
• Market analysts estimate that the company's common stock has a beta of 1.2. The corporate tax rate is 30%.

What is the company's after-tax Weighted Average Cost of Capital (WACC)? Assume a classical tax system.

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:

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

A firm's WACC before tax would decrease due to:

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 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?

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

(i) Weak form market efficiency is broken.

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

(iii) Strong form market efficiency is broken.

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

Select the most correct response:

A zero coupon bond that matures in 6 months has a face value of $1,000. The firm that issued this bond is trying to forecast its income statement for the year. It needs to calculate the interest expense of the bond this year. The bond is highly illiquid and hasn't traded on the market. But the finance department have assessed the bond's fair value to be$950 and this is its book value right now at the start of the year.

Assume that:

• the firm uses the 'effective interest method' to calculate interest expense.
• the market value of the bond is the same as the book value.
• the firm is only interested in this bond's interest expense. Do not include the interest expense for a new bond issued to refinance the current one, as would normally happen.

What will be the interest expense of the bond this year for the purpose of forecasting the income statement?

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

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.

You're trying to save enough money to buy your first car which costs $2,500. You can save$100 at the end of each month starting from now. You currently have no money at all. You just opened a bank account with an interest rate of 6% pa payable monthly.

How many months will it take to save enough money to buy the car? Assume that the price of the car will stay the same over time.

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 $250 at time 2 is actually earned smoothly from t=1 to t=2:  Project Cash Flows Time (yrs) Cash flow ($) 0 -400 1 200 2 250

What is the payback period of the project in years?

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. A highly leveraged risky firm is trying to raise more debt. The types of debt being considered, in no particular order, are senior bonds, junior bonds, bank accepted bills, promissory notes and bank loans. Which of these forms of debt is the safest from the perspective of the debt investors who are thinking of investing in the firm's new debt? There are a number of ways that assets can be depreciated. Generally the government's tax office stipulates a certain method. But if it didn't, what would be the ideal way to depreciate an asset from the perspective of a businesses owner? 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: 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 $r_\text{eff monthly}=(1+0.1)^{1/12}-1=0.00797414$ In mid 2009 the listed mining company Rio Tinto announced a 21-for-40 renounceable rights issue. Below is the chronology of events: • 04/06/2009. Share price opens at$69.00 and closes at $66.90. • 05/06/2009. 21-for-40 rights issue announced at a subscription price of$28.29.

• 16/06/2009. Last day that shares trade cum-rights. Share price opens at $76.40 and closes at$75.50.

All things remaining equal, what would you expect Rio Tinto's stock price to open at on the first day that it trades ex-rights (17/6/2009)? Ignore the time value of money since time is negligibly short. Also ignore taxes.

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

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

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

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

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

Select the most correct statement.

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

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 ?

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

What is the price of the stock now?

Question 218  NPV, IRR, profitability index, average accounting return

Which of the following statements is NOT correct?

An investor bought two fixed-coupon bonds issued by the same company, a zero-coupon bond and a 7% pa semi-annual coupon bond. Both bonds have a face value of $1,000, mature in 10 years, and had a yield at the time of purchase of 8% pa. A few years later, yields fell to 6% pa. Which of the following statements is correct? Note that a capital gain is an increase in price. A stock will pay you a dividend of$10 tonight if you buy it today. Thereafter the annual dividend is expected to grow by 5% pa, so the next dividend after the $10 one tonight will be$10.50 in one year, then in two years it will be $11.025 and so on. The stock's required return is 10% pa. What is the stock price today and what do you expect the stock price to be tomorrow, approximately? On which date would the stock price increase if the dividend and earnings are higher than expected? Question 245 foreign exchange rate, monetary policy, foreign exchange rate direct quote, no explanation Investors expect Australia's central bank, the RBA, to leave the policy rate unchanged at their next meeting. Then unexpectedly, the policy rate is reduced due to fears that Australia's GDP growth is slowing. What do you expect to happen to Australia's exchange rate? Direct and indirect quotes are given from the perspective of an Australian. The Australian dollar will: If the AUD appreciates against the USD, the American terms quote of the AUD will or ? If the Reserve Bank of Australia is expected to keep its interbank overnight cash rate at 2% pa while the US Federal Reserve is expected to keep its federal funds rate at 0% pa over the next year, is the AUD is expected to , , or remain against the USD over the next year? Below is a graph of the USD against the JPY and EUR from 1980 to 2015, compiled by the RBA. Select the correct statement about what occurred between 1980 and 2015. Note that in 1980 the euro was around 1.3 USD per EUR and the Yen was around 250 JPY per USD. Suppose the yield curve in the USA and Germany is flat and the: • USD federal funds rate at the Federal Reserve is 1% pa; • EUR deposit facility at the European Central Bank is -0.4% pa (note the negative sign); • Spot EUR exchange rate is 1 USD per EUR; • One year forward EUR exchange rate is 1.011 USD per EUR. You suspect that there’s an arbitrage opportunity. Which one of the following statements about the potential arbitrage opportunity is NOT correct? The current Australian exchange rate is 0.8 USD per AUD. If you think that the AUD will depreciate against the USD, contrary to the rest of the market, how could you profit? Right now you should: The Chinese central bank has the largest amount of foreign currency reserves. What could the large amounts of foreign exchange reserves held by the Chinese government be used for in a currency crisis? China's currency is called the Renminbi (RMB) or Yuan (CNY). In a Chinese currency crisis the Chinese government is likely to use its FX reserves to: Suppose the current Australian exchange rate is 0.8 USD per AUD. If you think that the AUD will appreciate against the USD, contrary to the rest of the market, how could you profit? Right now you should: A firm pays a fully franked cash dividend of$100 to one of its Australian shareholders who has a personal marginal tax rate of 15%. The corporate tax rate is 30%.

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

Which of the following statements about Australian franking credits is NOT correct? Franking credits:

A graph of assets’ expected returns $(\mu)$ versus standard deviations $(\sigma)$ is given in the graph below. The CML is the capital market line.

Which of the following statements about this graph, Markowitz portfolio theory and the Capital Asset Pricing Model (CAPM) theory is NOT correct?

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

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

Which of the following statements is NOT correct?

A man inherits $500,000 worth of shares. He believes that by learning the secrets of trading, keeping up with the financial news and doing complex trend analysis with charts that he can quit his job and become a self-employed day trader in the equities markets. What is the expected gain from doing this over the first year? Measure the net gain in wealth received at the end of this first year due to the decision to become a day trader. Assume the following: • He earns$60,000 pa in his current job, paid in a lump sum at the end of each year.
• He enjoys examining share price graphs and day trading just as much as he enjoys his current job.
• Stock markets are weak form and semi-strong form efficient.
• He has no inside information.
• He makes 1 trade every day and there are 250 trading days in the year. Trading costs are $20 per trade. His broker invoices him for the trading costs at the end of the year. • The shares that he currently owns and the shares that he intends to trade have the same level of systematic risk as the market portfolio. • The market portfolio's expected return is 10% pa. Measure the net gain over the first year as an expected wealth increase at the end of the year. Economic statistics released this morning were a surprise: they show a strong chance of consumer price inflation (CPI) reaching 5% pa over the next 2 years. This is much higher than the previous forecast of 3% pa. A vanilla fixed-coupon 2-year risk-free government bond was issued at par this morning, just before the economic news was released. What is the expected change in bond price after the economic news this morning, and in the next 2 years? Assume that: • Inflation remains at 5% over the next 2 years. • Investors demand a constant real bond yield. • The bond price falls by the (after-tax) value of the coupon the night before the ex-coupon date, as in real life. A managed fund charges fees based on the amount of money that you keep with them. The fee is 2% of the end-of-year amount, paid at the end of every year. This fee is charged regardless of whether the fund makes gains or losses on your money. The fund offers to invest your money in shares which have an expected return of 10% pa before fees. You are thinking of investing$100,000 in the fund and keeping it there for 40 years when you plan to retire.

How much money do you expect to have in the fund in 40 years? Also, what is the future value of the fees that the fund expects to earn from you? Give both amounts as future values in 40 years. Assume that:

• The fund has no private information.
• Markets are weak and semi-strong form efficient.
• The fund's transaction costs are negligible.
• The cost and trouble of investing your money in shares by yourself, without the managed fund, is negligible.
• The fund invests its fees in the same companies as it invests your funds in, but with no fees.

The below answer choices list your expected wealth in 40 years and then the fund's expected wealth in 40 years.

A fairly priced unlevered firm plans to pay a dividend of $1 next year (t=1) which is expected to grow by 3% pa every year after that. The firm's required return on equity is 8% pa. The firm is thinking about reducing its future dividend payments by 10% so that it can use the extra cash to invest in more projects which are expected to return 8% pa, and have the same risk as the existing projects. Therefore, next year's dividend will be$0.90. No new equity or debt will be issued to fund the new projects, they'll all be funded by the cut in dividends.

What will be the stock's new annual capital return (proportional increase in price per year) if the change in payout policy goes ahead?

Assume that payout policy is irrelevant to firm value (so there's no signalling effects) and that all rates are effective annual rates.

One year ago a pharmaceutical firm floated by selling its 1 million shares for $100 each. Its book and market values of equity were both$100m. Its debt totalled $50m. The required return on the firm's assets was 15%, equity 20% and debt 5% pa. In the year since then, the firm: • Earned net income of$29m.
• Paid dividends totaling $10m. • Discovered a valuable new drug that will lead to a massive 1,000 times increase in the firm's net income in 10 years after the research is commercialised. News of the discovery was publicly announced. The firm's systematic risk remains unchanged. Which of the following statements is NOT correct? All statements are about current figures, not figures one year ago. Hint: Book return on assets (ROA) and book return on equity (ROE) are ratios that accountants like to use to measure a business's past performance. $$\text{ROA}= \dfrac{\text{Net income}}{\text{Book value of assets}}$$ $$\text{ROE}= \dfrac{\text{Net income}}{\text{Book value of equity}}$$ The required return on assets $r_V$ is a return that financiers like to use to estimate a business's future required performance which compensates them for the firm's assets' risks. If the business were to achieve realised historical returns equal to its required returns, then investment into the business's assets would have been a zero-NPV decision, which is neither good nor bad but fair. $$r_\text{V, 0 to 1}= \dfrac{\text{Cash flow from assets}_\text{1}}{\text{Market value of assets}_\text{0}} = \dfrac{CFFA_\text{1}}{V_\text{0}}$$ Similarly for equity and debt. A company advertises an investment costing$1,000 which they say is underpriced. They say that it has an expected total return of 15% pa, but a required return of only 10% pa. Assume that there are no dividend payments so the entire 15% total return is all capital return.

Assuming that the company's statements are correct, what is the NPV of buying the investment if the 15% return lasts for the next 100 years (t=0 to 100), then reverts to 10% pa after that time? Also, what is the NPV of the investment if the 15% return lasts forever?

In both cases, assume that the required return of 10% remains constant. All returns are given as effective annual rates.

The answer choices below are given in the same order (15% for 100 years, and 15% forever):

The efficient markets hypothesis (EMH) and no-arbitrage pricing theory are most closely related to which of the following concepts?

Which of the following statements about returns is NOT correct? A stock's:

The following quotes are most closely related to which financial concept?

• “Opportunity is missed by most people because it is dressed in overalls and looks like work” -Thomas Edison
• “The only place where success comes before work is in the dictionary” -Vidal Sassoon
• “The safest way to double your money is to fold it over and put it in your pocket” - Kin Hubbard

A graph of assets’ expected returns $(\mu)$ versus standard deviations $(\sigma)$ is given in the below diagram.

Each letter corresponds to a separate coloured area. The portfolios at the boundary of the areas, on the black lines, are excluded from each area. Assume that all assets represented in this graph are fairly priced, and that all risky assets can be short-sold.

Three important classes of investable risky assets are:

• Corporate debt which has low total risk,
• Real estate which has medium total risk,
• Equity which has high total risk.

Assume that the correlation between total returns on:

• Corporate debt and real estate is 0.1,
• Corporate debt and equity is 0.1,
• Real estate and equity is 0.5.

You are considering investing all of your wealth in one or more of these asset classes. Which portfolio will give the lowest total risk? You are restricted from shorting any of these assets. Disregard returns and the risk-return trade-off, pretend that you are only concerned with minimising risk.

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

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

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

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

What is the covariance of a variable X with itself?

The cov(X, X) or $\sigma_{X,X}$ equals:

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

The cov(X, C) or $\sigma_{X,C}$ equals:

 Price Data Time Series Sourced from Yahoo Finance Historical Price Data Date S&P500 Index (^GSPC) Apple (AAPL) Open High Low Close Adj close Open High Low Close Adj close 2007, Wed 3 Jan 1418 1429 1408 1417 1417 12.33 12.37 11.7 11.97 10.42 2008, Wed 2 Jan 1468 1472 1442 1447 1447 28.47 28.61 27.51 27.83 24.22 2009, Fri 2 Jan 903 935 899 932 932 12.27 13.01 12.17 12.96 11.28 2010, Mon 4 Jan 1117 1134 1117 1133 1133 30.49 30.64 30.34 30.57 26.6 Source: Yahoo Finance.

Which of the following statements about the above table which is used to calculate Apple's equity beta is NOT correct?

What is the correlation of a variable X with itself?

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

An old 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?

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?

Your friend just bought a house for $1,000,000. He financed it using a$900,000 mortgage loan and a deposit of $100,000. In the context of residential housing and mortgages, the 'equity' or 'net wealth' tied up in a house is the value of the house less the value of the mortgage loan. Assuming that your friend's only asset is his house, his net wealth is$100,000.

If house prices suddenly fall by 15%, what would be your friend's percentage change in net wealth?

Assume that:

• No income (rent) was received from the house during the short time over which house prices fell.
• Your friend will not declare bankruptcy, he will always pay off his debts.

A levered firm has a market value of assets of $10m. Its debt is all comprised of zero-coupon bonds which mature in one year and have a combined face value of$9.9m.

Investors are risk-neutral and therefore all debt and equity holders demand the same required return of 10% pa.

Therefore the current market capitalisation of debt $(D_0)$ is $9m and equity $(E_0)$ is$1m.

A new project presents itself which requires an investment of $2m and will provide a: •$6.6m cash flow with probability 0.5 in the good state of the world, and a
• -$4.4m (notice the negative sign) cash flow with probability 0.5 in the bad state of the world. The project can be funded using the company's excess cash, no debt or equity raisings are required. What would be the new market capitalisation of equity $(E_\text{0, with project})$ if shareholders vote to proceed with the project, and therefore should shareholders proceed with the project? A pharmaceutical firm has just discovered a valuable new drug. So far the news has been kept a secret. The net present value of making and commercialising the drug is$200 million, but $600 million of bonds will need to be issued to fund the project and buy the necessary plant and equipment. The firm will release the news of the discovery and bond raising to shareholders simultaneously in the same announcement. The bonds will be issued shortly after. Once the announcement is made and the bonds are issued, what is the expected increase in the value of the firm's assets (ΔV), market capitalisation of debt (ΔD) and market cap of equity (ΔE)? The triangle symbol is the Greek letter capital delta which means change or increase in mathematics. Ignore the benefit of interest tax shields from having more debt. Remember: $ΔV = ΔD+ΔE$ A firm plans to issue equity and use the cash raised to pay off its debt. No assets will be bought or sold. Ignore the costs of financial distress. Which of the following statements is NOT correct, all things remaining equal? A stock's required total return will increase when its: A stock's standard deviation of returns is expected to be: • 0.09 per month for the first 5 months; • 0.14 per month for the next 7 months. What is the expected standard deviation of the stock per year $(\sigma_\text{annual})$? Assume that returns are independently and identically distributed (iid) and therefore have zero auto-correlation. A stock has an arithmetic average continuously compounded return (AALGDR) of 10% pa, a standard deviation of continuously compounded returns (SDLGDR) of 80% pa and current stock price of$1. Assume that stock prices are log-normally distributed.

In 5 years, what do you expect the mean and median prices to be? The answer options are given in the same order.

Fred owns some BHP shares. He has calculated BHP’s monthly returns for each month in the past 30 years using this formula:

$$r_\text{t monthly}=\ln⁡ \left( \dfrac{P_t}{P_{t-1}} \right)$$

He then took the arithmetic average and found it to be 0.8% per month using this formula:

$$\bar{r}_\text{monthly}= \dfrac{ \displaystyle\sum\limits_{t=1}^T{\left( r_\text{t monthly} \right)} }{T} =0.008=0.8\% \text{ per month}$$

He also found the standard deviation of these monthly returns which was 15% per month:

$$\sigma_\text{monthly} = \dfrac{ \displaystyle\sum\limits_{t=1}^T{\left( \left( r_\text{t monthly} - \bar{r}_\text{monthly} \right)^2 \right)} }{T} =0.15=15\%\text{ per month}$$

Assume that the past historical average return is the true population average of future expected returns and the stock's returns calculated above $(r_\text{t monthly})$ are normally distributed. Which of the below statements about Fred’s BHP shares is NOT correct?

The accounting identity states that the book value of a company's assets (A) equals its liabilities (L) plus owners equity (OE), so A = L + OE.

The finance version states that the market value of a company's assets (V) equals the market value of its debt (D) plus equity (E), so V = D + E.

Therefore a business's assets can be seen as a portfolio of the debt and equity that fund the assets.

Let $\sigma_\text{V total}^2$ be the total variance of returns on assets, $\sigma_\text{V syst}^2$ be the systematic variance of returns on assets, and $\sigma_\text{V idio}^2$ be the idiosyncratic variance of returns on assets, and $\rho_\text{D idio, E idio}$ be the correlation between the idiosyncratic returns on debt and equity.

Which of the following equations is NOT correct?

Use the below information to value a mature levered company with growing annual perpetual cash flows and a constant debt-to-assets ratio. The next cash flow will be generated in one year from now, so a perpetuity can be used to value this firm. The firm's debt funding comprises annual fixed coupon bonds that all have the same seniority and coupon rate. When these bonds mature, new bonds will be re-issued, and so on in perpetuity. The yield curve is flat.

 Data on a Levered Firm with Perpetual Cash Flows Item abbreviation Value Item full name $\text{OFCF}_1$ $12.5m Operating free cash flow at time 1 $\text{FFCF}_1 \text{ or }\text{CFFA}_1$$14m Firm free cash flow or cash flow from assets at time 1 $\text{EFCF}_1$ $11m Equity free cash flow at time 1 $\text{BondCoupons}_1$$1.2m Bond coupons paid to debt holders at time 1 $g$ 2% pa Growth rate of OFCF, FFCF, EFCF and Debt cash flow $\text{WACC}_\text{BeforeTax}$ 9% pa Weighted average cost of capital before tax $\text{WACC}_\text{AfterTax}$ 8.25% pa Weighted average cost of capital after tax $r_\text{D}$ 5% pa Bond yield $r_\text{EL}$ 13% pa Cost or required return of levered equity $D/V_L$ 50% pa Debt to assets ratio, where the asset value includes tax shields $n_\text{shares}$ 1m Number of shares $t_c$ 30% Corporate tax rate

Which of the following statements is NOT correct?

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 income statement needed? Note that the income statement is sometimes also called the profit and loss, P&L, or statement of financial performance.

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

 UBar Corp Income Statement for year ending 30th June 2014 $m Sales 293 COGS 200 Rent expense 15 Gas expense 8 Depreciation 10 EBIT 60 Interest expense 0 Taxable income 60 Taxes 18 Net income 42  UBar Corp Balance Sheet as at 30th June 2014 2013$m $m Assets Cash 30 29 Accounts receivable 5 7 Pre-paid rent expense 1 0 Inventory 50 46 PPE 290 300 Total assets 376 382 Liabilities Trade payables 20 18 Accrued gas expense 3 2 Non-current liabilities 0 0 Contributed equity 212 212 Retained profits 136 150 Asset revaluation reserve 5 0 Total L and OE 376 382 Note: all figures are given in millions of dollars ($m).

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

Question 449  personal tax on dividends, classical tax system

A small private company has a single shareholder. This year the firm earned a \$100 profit before tax. All of the firm's after tax profits will be paid out as dividends to the owner.

The corporate tax rate is 30% and the sole shareholder's personal marginal tax rate is 45%.

The United States' classical tax system applies because the company generates all of its income in the US and pays corporate tax to the Internal Revenue Service. The shareholder is also an American for tax purposes.

What will be the personal tax payable by the shareholder and the corporate tax payable by the company?