# Fight Finance

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Two companies BigDiv and ZeroDiv are exactly the same except for their dividend payouts.

BigDiv pays large dividends and ZeroDiv doesn't pay any dividends.

Currently the two firms have the same earnings, assets, number of shares, share price, expected total return and risk.

Assume a perfect world with no taxes, no transaction costs, no asymmetric information and that all assets including business projects are fairly priced and therefore zero-NPV.

All things remaining equal, which of the following statements is NOT correct?

The boss of WorkingForTheManCorp has a wicked (and unethical) idea. He plans to pay his poor workers one week late so that he can get more interest on his cash in the bank.

Every week he is supposed to pay his 1,000 employees $1,000 each. So$1 million is paid to employees every week.

The boss was just about to pay his employees today, until he thought of this idea so he will actually pay them one week (7 days) later for the work they did last week and every week in the future, forever.

Bank interest rates are 10% pa, given as a real effective annual rate. So $r_\text{eff annual, real} = 0.1$ and the real effective weekly rate is therefore $r_\text{eff weekly, real} = (1+0.1)^{1/52}-1 = 0.001834569$

All rates and cash flows are real, the inflation rate is 3% pa and there are 52 weeks per year. The boss will always pay wages one week late. The business will operate forever with constant real wages and the same number of employees.

What is the net present value (NPV) of the boss's decision to pay later?

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

For a share price to double over 7 years, what must its capital return be as an effective annual rate?

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.

Note that the effective monthly rate is $r_\text{eff monthly}=(1+0.1)^{1/12}-1=0.00797414$

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? An 'interest only' loan can also be called a: "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: 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? 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? 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.

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? Which of the following statements about gold is NOT correct? Assume that the gold price increases by inflation. Gold: Which of the following statements about book and market equity is NOT correct? One year ago a pharmaceutical firm floated by selling its 1 million shares for$100 each. Its book and market values of equity were both $100m. Its debt totalled$50m. The required return on the firm's assets was 15%, equity 20% and debt 5% pa.

In the year since then, the firm:

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

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

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

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

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

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

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

Similarly for equity and debt.

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

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

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

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

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

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 $0.30, and so on. 5. Can be slaughtered (killed for their meat) and sold at no cost at the end of the week. The price received for the chicken is their total value of meat (note that the chicken grows fast then slow, see above). The required return of the chicken farm is 0.5% given as an effective weekly rate. Ignore taxes and the fixed costs of the factory. Ignore the chicken’s welfare and other environmental and ethical concerns. Find the equivalent weekly cash flow of slaughtering a chicken at 6 weeks and at 10 weeks so the farmer can figure out the best time to slaughter his chickens. The choices below are given in the same order, 6 and 10 weeks. Which of the following investable assets are NOT suitable for valuation using PE multiples techniques? Find Sidebar Corporation's Cash Flow From Assets (CFFA), also known as Free Cash Flow to the Firm (FCFF), over the year ending 30th June 2013.  Sidebar Corp Income Statement for year ending 30th June 2013$m Sales 405 COGS 100 Depreciation 34 Rent expense 22 Interest expense 39 Taxable Income 210 Taxes at 30% 63 Net income 147
 Sidebar Corp Balance Sheet as at 30th June 2013 2012 $m$m Inventory 70 50 Trade debtors 11 16 Rent paid in advance 4 3 PPE 700 680 Total assets 785 749 Trade creditors 11 19 Bond liabilities 400 390 Contributed equity 220 220 Retained profits 154 120 Total L and OE 785 749

Note: All figures are given in millions of dollars ($m). The cash flow from assets was: A firm has forecast its Cash Flow From Assets (CFFA) for this year and management is worried that it is too low. Which one of the following actions will lead to a higher CFFA for this year (t=0 to 1)? Only consider cash flows this year. Do not consider cash flows after one year, or the change in the NPV of the firm. Consider each action in isolation. Your friend is trying to find the net present value of a project. The project is expected to last for just one year with: • a negative cash flow of -$1 million initially (t=0), and
• a positive cash flow of $1.1 million in one year (t=1). The project has a total required return of 10% pa due to its moderate level of undiversifiable risk. Your friend is aware of the importance of opportunity costs and the time value of money, but he is unsure of how to find the NPV of the project. He knows that the opportunity cost of investing the$1m in the project is the expected gain from investing the money in shares instead. Like the project, shares also have an expected return of 10% since they have moderate undiversifiable risk. This opportunity cost is 0.1m $(=1m \times 10\%)$ which occurs in one year (t=1). He knows that the time value of money should be accounted for, and this can be done by finding the present value of the cash flows in one year. Your friend has listed a few different ways to find the NPV which are written down below. (I) $-1m + \dfrac{1.1m}{(1+0.1)^1}$ (II) $-1m + \dfrac{1.1m}{(1+0.1)^1} - \dfrac{1m}{(1+0.1)^1} \times 0.1$ (III) $-1m + \dfrac{1.1m}{(1+0.1)^1} - \dfrac{1.1m}{(1+0.1)^1} \times 0.1$ (IV) $-1m + 1.1m - \dfrac{1.1m}{(1+0.1)^1} \times 0.1$ (V) $-1m + 1.1m - 1.1m \times 0.1$ Which of the above calculations give the correct NPV? Select the most correct answer. 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: One method for calculating a firm's free cash flow (FFCF, or CFFA) is to ignore interest expense. That is, pretend that interest expense $(IntExp)$ is zero: \begin{aligned} FFCF &= (Rev - COGS - Depr - FC - IntExp)(1-t_c) + Depr - CapEx -\Delta NWC + IntExp \\ &= (Rev - COGS - Depr - FC - 0)(1-t_c) + Depr - CapEx -\Delta NWC - 0\\ \end{aligned} Does this annual FFCF with zero interest expense or the annual interest tax shield?  Project Data Project life 2 yrs Initial investment in equipment600k Depreciation of equipment per year $250k Expected sale price of equipment at end of project$200k Revenue per job $12k Variable cost per job$4k Quantity of jobs per year 120 Fixed costs per year, paid at the end of each year $100k Interest expense in first year (at t=1)$16.091k Interest expense in second year (at t=2) $9.711k Tax rate 30% Government treasury bond yield 5% Bank loan debt yield 6% Levered cost of equity 12.5% Market portfolio return 10% Beta of assets 1.24 Beta of levered equity 1.5 Firm's and project's debt-to-equity ratio 25% Notes 1. The project will require an immediate purchase of$50k of inventory, which will all be sold at cost when the project ends. Current liabilities are negligible so they can be ignored.

Assumptions

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

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

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

Let: $P_0$ be the bond price now,

$F_T$ be the bond's face value,

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

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

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

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

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

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

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

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

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

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

Select the most correct statement.

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

A 30-day Bank Accepted Bill has a face value of $1,000,000. The interest rate is 2.5% pa and there are 365 days in the year. What is its price now? A fast-growing firm is suitable for valuation using a multi-stage growth model. It's nominal unlevered cash flow from assets ($CFFA_U$) at the end of this year (t=1) is expected to be$1 million. After that it is expected to grow at a rate of:

• 12% pa for the next two years (from t=1 to 3),
• 5% over the fourth year (from t=3 to 4), and
• -1% forever after that (from t=4 onwards). Note that this is a negative one percent growth rate.

Assume that:

• The nominal WACC after tax is 9.5% pa and is not expected to change.
• The nominal WACC before tax is 10% pa and is not expected to change.
• The firm has a target debt-to-equity ratio that it plans to maintain.
• The inflation rate is 3% pa.
• All rates are given as nominal effective annual rates.

What is the levered value of this fast growing firm's assets?

Diversification in a portfolio of two assets works best when the correlation between their returns is:

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

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

The covariance and correlation of two stocks X and Y's annual returns are calculated over a number of years. The units of the returns are in percent per annum $(\% pa)$.

What are the units of the covariance $(\sigma_{X,Y})$ and correlation $(\rho_{X,Y})$ of returns respectively?

Hint: Visit Wikipedia to understand the difference between percentage points $(\text{pp})$ and percent $(\%)$.

Let the standard deviation of returns for a share per month be $\sigma_\text{monthly}$.

What is the formula for the standard deviation of the share's returns per year $(\sigma_\text{yearly})$?

Assume that returns are independently and identically distributed (iid) so they have zero auto correlation, meaning that if the return was higher than average today, it does not indicate that the return tomorrow will be higher or lower than average.

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

Investment projects that plot above the SML would have:

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

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 $r_f$?

 Project Data Project life 1 year Initial investment in equipment $8m Depreciation of equipment per year$8m Expected sale price of equipment at end of project 0 Unit sales per year 4m Sale price per unit $10 Variable cost per unit$5 Fixed costs per year, paid at the end of each year $2m Interest expense in first year (at t=1)$0.562m Corporate tax rate 30% Government treasury bond yield 5% Bank loan debt yield 9% Market portfolio return 10% Covariance of levered equity returns with market 0.32 Variance of market portfolio returns 0.16 Firm's and project's debt-to-equity ratio 50%

Notes

1. Due to the project, current assets will increase by $6m now (t=0) and fall by$6m at the end (t=1). Current liabilities will not be affected.

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.
• Millions are represented by 'm'.
• 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 2% pa. All rates are given as effective annual rates.
• The project is undertaken by a firm, not an individual.

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