Fight Finance

Question 993  inflation, real and nominal returns and cash flows

In February 2020, the RBA cash rate was 0.75% pa and the Australian CPI inflation rate was 1.8% pa.

You currently have $100 in the bank which pays a 0.75% pa interest rate.

Apples currently cost $1 each at the shop and inflation is 1.8% pa which is the expected growth rate in the apple price.

This information is summarised in the table below, with some parts missing that correspond to the answer options. All rates are given as effective annual rates. Note that when payments are not specified as real, as in this question, they're conventionally assumed to be nominal.

Wealth in Dollars and Apples
Time (year)	Bank account wealth ($)	Apple price ($)	Wealth in apples
0	100	1	100
1	100.75	1.018	(a)
2	(b)	(c)	(d)

 

Which of the following statements is NOT correct? Your:

(a) Real wealth at t=1 is $98.96856582 or 98.96856582 apples.

(b) Nominal wealth at t=2 is $101.505625.

(c) Apple price t=2 is $1.036324.

(d) Real wealth at t=2 is $102.0952287 or 102.0952287 apples.

(e) Real interest rate is exactly -1.0314342% pa.

Question 456  inflation, effective rate

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

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

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

The answer choices below are given as effective annual rates:

(a) 0.5086% pa

(b) 1.5086% pa

(c) 5.0859% pa

(d) 50.8591% pa

(e) 150.8591% pa

Question 526  real and nominal returns and cash flows, inflation, no explanation

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

(a) ##C_\text{real, t}=C_\text{nominal,t}.(1+r_\text{inflation})^t##

(b) ##C_\text{real,t}=\dfrac{C_\text{nominal,t}}{(1+r_\text{inflation})^t} ##

(c) ##C_\text{real,t}=\dfrac{C_\text{nominal,t}}{r_\text{inflation}} ##

(d) ##C_\text{real,t}=C_\text{nominal,t}.r_\text{inflation} ##

(e) ##C_\text{real,t}=C_\text{nominal,t}.r_\text{inflation}.t##

Question 574  inflation, real and nominal returns and cash flows, NPV

What is the present value of a nominal payment of $100 in 5 years? The real discount rate is 10% pa and the inflation rate is 3% pa.

(a) $71.2986

(b) $62.0921

(c) $61.5028

(d) $54.276

(e) $53.5612

Question 734  real and nominal returns and cash flows, inflation, DDM, no explanation

An equities analyst is using the dividend discount model to price a company's shares. The company operates domestically and has no plans to expand overseas. It is part of a mature industry with stable positive growth prospects.

The analyst has estimated the real required return (r) of the stock and the value of the dividend that the stock just paid a moment before ##(C_\text{0 before})##.

What is the highest perpetual real growth rate of dividends (g) that can be justified? Select the most correct statement from the following choices. The highest perpetual real expected growth rate of dividends that can be justified is the country's expected:

(a) Inflation rate.

(b) Nominal GDP growth rate.

(c) Real GDP growth rate.

(d) Nominal total return on the share market index.

(e) Real total return on the share market index.

Question 364  PE ratio, Multiples valuation

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

(a) Illiquid small private companies.

(b) Exchange-listed companies operating in stagnant industries with negative growth prospects.

(c) Exchange-listed companies expected to have temporarily high earnings over the next year, but with lower earnings later.

(d) Exchange-listed companies operating in high-risk industries with very high required returns on equity.

(e) Exchange-listed companies whose assets include a very large proportion of cash.

Question 1022  inflation linked bond, breakeven inflation rate, inflation, real and nominal returns and cash flows

Below is a graph of 10-year US treasury fixed coupon bond yields (red), inflation-indexed bond yields (green) and the 'breakeven' inflation rate (blue). Note that inflation-indexed bonds are also called treasury inflation protected securities (TIPS) in the US. In other countries they're called inflation-linked bonds (ILB's). For more information, see PIMCO's great article about inflation linked bonds here.

The 10 year breakeven inflation rate (blue) equals the:

(a) Inflation-linked bond yield (green).

(b) Fixed coupon bond yield (red).

(c) Fixed coupon bond yield (red) plus the inflation-linked bond yield (green).

(d) Fixed coupon bond yield (red) less the inflation-linked bond yield (green).

(e) Inflation-linked bond yield (green) less the fixed coupon bond yield (red).

Question 1018  RBA cash rate, monetary policy, foreign exchange rate

RBA Governor Phil Lowe says that when the RBA raises the cash rate (by surprise), the Australian dollar (AUD) tends to:

(a) Appreciate against the USD, so the USD per AUD quote number may increase from say 0.7 to 0.71 USD per AUD.

(b) Appreciate against the USD, so the USD per AUD quote number may decrease from say 0.7 to 0.69 USD per AUD.

(c) Depreciate against the USD, so the USD per AUD quote number may increase from say 0.7 to 0.71 USD per AUD.

(d) Depreciate against the USD, so the USD per AUD quote number may decrease from say 0.7 to 0.69 USD per AUD.

Question 1019  RBA cash rate, monetary policy, wealth effect

Former RBA Governor Phil Lowe says that when the RBA raise the cash rate, asset prices tend to:

(a) Rise, making asset-holders feel wealthier and likely to spend more on consumption at the shops.

(b) Rise, making asset-holders feel poorer and likely to spend less on consumption at the shops.

(c) Fall, making asset-holders feel wealthier and likely to spend more on consumption at the shops.

(d) Fall, making asset-holders feel poorer and likely to spend less on consumption at the shops.

Question 238  CFFA, leverage, interest tax shield

A company increases the proportion of debt funding it uses to finance its assets by issuing bonds and using the cash to repurchase stock, leaving assets unchanged.

Ignoring the costs of financial distress, which of the following statements is NOT correct:

(a) The company is increasing its debt-to-assets and debt-to-equity ratios. These are types of 'leverage' or 'gearing' ratios.

(b) The company will pay less tax to the government due to the benefit of interest tax shields.

(c) The company's net income, also known as earnings or net profit after tax, will fall.

(d) The company's expected levered firm free cash flow (FFCF or CFFA) will be higher due to tax shields.

(e) The company's expected levered equity free cash flow (EFCF) will not change.

Question 344  CFFA, capital budgeting

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?

(a) Point A.

(b) Point B.

(c) Point C.

(d) Any of the points.

(e) None of the points.

Question 361  CFFA

Over the next year, the management of an unlevered company plans to:

• Make $5m in sales, $1.9m in net income and $2m in equity free cash flow (EFCF).
• Pay dividends of $1m.
• Complete a $1.3m share buy-back.

Assume that:

• All amounts are received and paid at the end of the year so you can ignore the time value of money.
• The firm has sufficient retained profits to legally pay the dividend and complete the buy back.
• The firm plans to run a very tight ship, with no excess cash above operating requirements currently or over the next year.

How much new equity financing will the company need? In other words, what is the value of new shares that will need to be issued?

(a) $2m

(b) $1m

(c) $0.4m

(d) $0.3m

(e) No new shares need to be issued, the firm will be sufficiently financed.

Question 370  capital budgeting, NPV, interest tax shield, WACC, CFFA

Project Data
Project life	2 yrs
Initial investment in equipment	$600k
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?

(a) $684.222k

(b) $690.919k

(c) $697.616k

(d) $698.713k

(e) $710.601k

Question 418  capital budgeting, NPV, interest tax shield, WACC, CFFA, CAPM

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?

(a) $5.772m

(b) $4.979m

(c) $4.959m

(d) $4.733m

(e) $4.584m

Question 1006  CAPM, beta, leverage, WACC, real estate

Four retail business people compete in the same city. They are all exactly the same except that they have different ways of funding or leasing the shop real estate needed to run their retail business.

The two main assets that retail stores need are:

• Inventory typically worth $1 million which has a beta of 2, and;
• Shopfront real estate worth $1 million which has a beta of 1. Shops can be bought or leased.

Lease contract prices are fixed for the term of the lease and based on expectations of the future state of the economy. When leases end, a new lease contract is negotiated and the lease cost may be higher or lower depending on the state of the economy and demand and supply if the economy is:

• Booming, shop real estate is worth more and lease costs are higher.
• In recession, shop real estate is worth less and lease costs are low.

Assume that the market’s expected return is 10% pa, required returns are expected to remain constant, shop assets can be valued as a perpetuity of lease profits, and that buying, selling, shutting down, moving out, moving in and opening a new shop has negligible (low) cost. Store owners can invest surplus funds in alternative investments that also earn the 10% pa market return.

Which retail business person will have the LOWEST beta of equity (or net wealth)?

(a) Anne owns her shop, funded with equity.

(b) Bob owns his shop, funded with fixed rate debt that matures in 10 years.

(c) Carla leases her shop on a 1 year contract.

(d) Dan leases his shop on a 5 year contract.

(e) All business people have the same equity beta.

Question 69  interest tax shield, capital structure, leverage, WACC

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

(a) The before-tax cost of debt is less than the before-tax cost of equity. Therefore debt is a cheaper form of financing than equity so companies should try to finance their projects with debt only.

(b) Debt makes a firm's equity more risky. Therefore the higher the amount of debt, the higher the cost of equity.

(c) The more debt a firm has, the higher its tax shields. Therefore firms should seek to have as much debt and as little equity as possible.

(d) The more debt, the lower the firm's after tax WACC. The after tax WACC is the discount rate that discounts the firm's cash flows, so the lower it is the more the firm is worth. Therefore firms should try to make their after tax WACC as low as possible by using as much debt as possible.

(e) The less debt, the lower the chance of bankruptcy. Therefore firms should try to pay off all of their debt so that they are financed by equity only.

Question 115  capital structure, leverage, WACC

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) The debt-to-assets (D/V) ratio will decrease.

(b) The debt-to-equity ratio (D/E) will decrease.

(c) The firm's cost of equity will decrease.

(d) The company's after-tax WACC will decrease.

(e) The company's before-tax WACC will decrease.

Question 121  capital structure, leverage, financial distress, interest tax shield

Fill in the missing words in the following sentence:

All things remaining equal, as a firm's amount of debt funding falls, benefits of interest tax shields __________ and the costs of financial distress __________.

(a) Fall, fall.

(b) Fall, rises.

(c) Rise, fall.

(d) Rise, rise.

(e) Remain unchanged, remain unchanged.

Question 337  capital structure, interest tax shield, leverage, real and nominal returns and cash flows, multi stage growth model

A fast-growing firm is suitable for valuation using a multi-stage growth model.

It's nominal unlevered cash flow from assets (##CFFA_U##) at the end of this year (t=1) is expected to be $1 million. After that it is expected to grow at a rate of:

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

Assume that:

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

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

(a) $13.19m

(b) $12.36m

(c) $11.77m

(d) $11.53m

(e) $11.20m

Question 378  leverage, capital structure, no explanation

A levered company's required return on debt is always less than its required return on equity. or ?

Question 1031  Multiples valuation

Investment bank Canaccord's Think Childcare (TNK) initiation of coverage states: "What's the Differentiator? TNK are operators, not consolidators - Other listed childcare companies have led highly successful consolidation strategies involving multiple arbitrage combined with scale benefits and operating efficiencies. TNK’s focus is on operating the centres to the best of their individual potentials..." (Canaccord, 2016). Multiples arbitrage involves:

(a) Buying existing childcare centres at higher PE ratios than TNK's.

(b) Buying existing childcare centres at lower PE ratios than TNK's.

(c) Negotiating cheaper garden and building maintenance contracts on a per site basis due to having more sites.

(d) Maximising the occupancy proportion, which is the number of enrolled children divided by the maximum possible number allowed.

(e) Cross-selling additional services in addition to childcare such as piano lessons and speech therapy.

Question 1032  inflation, percent of sales forecasting, no explanation

Investment bank Canaccord's Think Childcare (TNK) initiation of coverage states: "Building lease costs – Rent expense is the second largest cost and TNK reported rent/sales of 12.1%, within the industry range that we typically see as 12-14% of sales. TNK lease all their properties and do not intend to own property. Leases are generally long term with 10-15 year terms and additional options. Although terms vary across properties and landlords, rental increases are generally tied to the consumer price index (CPI)" (Canaccord, 2016).

Assuming that sales grow faster than the CPI, when Canaccord forecast TNK's building lease costs using the 'percent of sales' method, that proportion should:

(a) Rise over time.

(b) Fall over time.

(c) Remain constant over time.

(d) Insufficient information to make a conclusion.

Question 1029  Buffett ratio

Tesla CEO Elon Musk asked a question to ARK Invest CEO Cathie Wood on 6 April 2021: "What do you think of the unusually high ratio of the S&P market cap to GDP?", to which Cathie Wood replied.

What are the units of this S&P500 market cap to GDP ratio, commonly known as the Buffett ratio?

(a) Dollars.

(b) Dollars per time.

(c) Time.

(d) Per time.

(e) Pure number.

Question 1026  CFFA, WACC, interest tax shield

Meier and Tarhan (2006) conducted an interesting survey of corporate managers. The results are copied in Table 7 below. What proportion of managers are evaluating levered projects correctly?

Table 7: Consistency between hurdle rate and the calculation of cash flows
Hurdle rate	Cash flow calculation (see below notes)
	(i)	(ii)	(iii)	(iv)	(v)	Other	Total
WACC	11.3%	34.8%	1.7%	3.5%	18.3%	1.7%	71.3%
Equity levered	0.0%	2.6%	0.9%	0.0%	0.9%	0.9%	6.1%
Equity unlevered	1.7%	1.7%	0.9%	0.9%	1.7%	0.9%	7.8%
Other	2.6%	5.2%	1.7%	0.9%	3.5%	0.9%	14.8%
Total	16.5%	44.4%	5.2%	5.2%	24.4%	4.4%	100.0%

 

The rows of the cross-tabulation indicate what the self-reported hurdle rate represents and the columns denote five different ways to calculate cash flows, (i) to (v), plus the “other” category. Each cell then displays the fraction of all 113 respondents for a given combination of what the hurdle rate represents and how the firm calculates its cash flows when evaluating a project.

The definitions of the cash flow calculations (i)-(v) are as follows:

(i) Earnings before interest and after taxes (EBIAT) + depreciation

(ii) Earnings before interest and after taxes (EBIAT) + depreciation – capital expenditures – net change in working capital

(iii) Earnings

(iv) Earnings + depreciation

(v) Earnings + depreciation – capital expenditures – net change in working capital

Assume that the WACC is after tax, the required return on unlevered equity is the WACC before tax, all projects are levered, the benefit of interest tax shields should be included in the valuation, earnings = net profit after tax (NPAT) and EBIAT = EBIT*(1-tc) which is often also called net operating profit after tax (NOPAT).

What proportion of managers are evaluating levered projects correctly?

(a) 46.1%

(b) 44.4%

(c) 34.8%

(d) 11.3%

(e) 16.5%

Question 1027  duration

Below is a table showing GMO's 2016 estimates of different assets' durations, appearing in Slater (2017).

If you were certain that interest rates would fall more than the market expects, into what asset might you allocate more funds?

(a) Value stocks

(b) Growth stocks

(c) Real estate

(d) 10 year bond

(e) Cash

Question 1028  duration, beta, CAPM, DDM

A stock has a beta of 0.5. Its next dividend is expected to be $3, paid one year from now. Dividends are expected to be paid annually and grow by 2% pa forever. Treasury bonds yield 3% pa and the market risk premium (MRP) is 6% pa. All returns are effective annual rates.

Which of the following statements is NOT correct?

(a) 6% pa is the stock's required return.

(b) $75 is the stock's fair price.

(c) 26.5 years is the stock's Macaulay duration.

(d) If the market portfolio were to fall 1% today, the stock is expected to fall by 0.5%.

(e) If the Treasury bond yield were to fall 1 percentage point today, then the stock price is expected to fall by 25% approximately, ceteris paribus.

Question 1007  WACC, leverage, CFFA, EFCF

An analyst is valuing a levered company whose owners insist on keeping the dollar amount of debt funding fixed. So the company cannot issue or repay its debt, its dollar value must remain constant. Any funding gaps will be met with equity.

The analyst is wondering, as he changes inputs into his valuation, such as the forecast growth rate of sales, then asset values and other things will change. This makes it hard to figure out which values can be held constant and would therefore make good model inputs, rather than outputs which vary depending on the inputs. Assume that the cost of debt (yield) remains constant and the company’s asset beta will also remain constant since any expansion (or downsize) will involve buying (or selling) more of the same assets.

Which of the following values can be assumed to stay constant when projected sales growth increases?

(a) Debt to assets ratio.

(b) Equity Free Cash Flow.

(c) WACC before tax.

(d) WACC after tax.

(e) Required return on equity.

Question 1008  WACC, leverage, CFFA, EFCF

An analyst is valuing a levered company whose owners insist on keeping a constant market debt to assets ratio into the future.

The analyst is wondering how asset values and other things in her model will change when she changes the forecast sales growth rate.

Which of the below values will increase as the forecast growth rate of sales increases, with the debt to assets ratio remaining constant?

Assume that the cost of debt (yield) remains constant and the company’s asset beta will also remain constant since any expansion (or downsize) will involve buying (or selling) more of the same assets.

The analyst should expect which value or ratio to increase when the forecast growth rate of sales increases and the debt to assets ratio remains unchanged? In other words, which of the following values will NOT remain constant?

(a) Ratio of Equity Free Cash Flow to Debt Cash Flow.

(b) Equity Free Cash Flow.

(c) WACC before tax.

(d) WACC after tax.

(e) Required return on equity.

Question 941  negative gearing, leverage, capital structure, interest tax shield, real estate

Last year, two friends Lev and Nolev each bought similar investment properties for $1 million. Both earned net rents of $30,000 pa over the past year. They funded their purchases in different ways:

• Lev used $200,000 of his own money and borrowed $800,000 from the bank in the form of an interest-only loan with an interest rate of 5% pa.
• Nolev used $1,000,000 of his own money, he has no mortgage loan on his property.

Both Lev and Nolev also work in high-paying jobs and are subject personal marginal tax rates of 45%.

Which of the below statements about the past year is NOT correct?

(a) Lev’s annual interest expense would have been $40,000.

(b) Lev’s annual loss before tax on the investment property was $10,000

(c) Lev’s annual loss after tax on the investment property was $5,500

(d) Lev’s personal tax saving due to the investment property was $5,500.

(e) Nolev’s personal tax payable due to the investment property was $13,500.

Question 959  negative gearing, leverage, capital structure, interest tax shield, real estate

Last year, two friends Gear and Nogear invested in residential apartments. Each invested $1 million of their own money (their net wealth).

Apartments cost $1,000,000 last year and they earned net rents of $30,000 pa over the last year. Net rents are calculated as rent revenues less the costs of renting such as property maintenance, land tax and council rates. However, interest expense and personal income taxes are not deducted from net rents.

Gear and Nogear funded their purchases in different ways:

• Gear used $1,000,000 of her own money and borrowed $4,000,000 from the bank in the form of an interest-only loan with an interest rate of 5% pa to buy 5 apartments.
• Nogear used $1,000,000 of his own money to buy one apartment. He has no mortgage loan on his property.

Both Gear and Nogear also work in high-paying jobs and are subject personal marginal tax rates of 45%.

Which of the below statements about the past year is NOT correct?

(a) Gear’s total annual interest expense would have been $200,000.

(b) Gear’s total annual loss before tax on the investment properties was $50,000

(c) Gear’s total annual loss after tax on the investment properties was $27,500

(d) Gear’s total personal tax saving due to the investment properties was $22,500.

(e) Nogear’s total personal tax payable due to the investment property was $16,500.

Question 774  leverage, WACC, real estate

One year ago you bought a $1,000,000 house partly funded using a mortgage loan. The loan size was $800,000 and the other $200,000 was your wealth or 'equity' in the house asset.

The interest rate on the home loan was 4% pa.

Over the year, the house produced a net rental yield of 2% pa and a capital gain of 2.5% pa.

Assuming that all cash flows (interest payments and net rental payments) were paid and received at the end of the year, and all rates are given as effective annual rates, what was the total return on your wealth over the past year?

(a) 0.4808% pa

(b) 2% pa

(c) 4.5% pa

(d) 6.5% pa

(e) 8.5% pa

Hint: Remember that wealth in this context is your equity (E) in the house asset (V = D+E) which is funded by the loan (D) and your deposit or equity (E).

Question 84  WACC, capital structure, capital budgeting

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) The required return on equity, ##r_E##

(b) The required return on debt, ##r_D##

(c) The after-tax required return on debt, ##r_D.(1-t_c)##

(d) The after-tax WACC, ##\text{WACC after tax}=\frac{D}{V_L}.r_D.(1-t_c )+\frac{E_L}{V_L}.r_E##

(e) The pre-tax WACC, ##\text{WACC before tax}=\frac{D}{V_L}.r_D+\frac{E_L}{V_L}.r_E##

Question 1037  gross domestic product, no explanation

What effect is being referred to in the following quote from the MARTIN model description?  

Economy-wide models also account for feedback between economic variables. For example, an increase in aggregate demand will encourage firms to hire more workers, which raises employment and lowers the unemployment rate. The tightening of the labour market is likely to lead to an increase in wages growth. The resulting increase in household incomes is likely to lead to an increase in consumption, further raising aggregate demand. (Ballantyne et al, 2019)

The name of the effect being referred to is:

(a) Inflation

(b) Wage-price spiral

(c) Multiplier

(d) Monetary policy stimulus

(e) Fiscal policy stimulus

Question 1014  book build, initial public offering, capital raising, demand schedule

A firm is floating its stock in an IPO and its underwriter has received the following bids, listed in order from highest to lowest share price:

IPO Book Build Bids
Bidders	Share price	Number of shares
	$/share	millions
BidderA	2.5	2
BidderB	2	1.5
BidderC	1.5	4
BidderD	1	3
BidderE	0.5	2

 

Suppose that the firm's owner wishes to raise $6 million to expand the business by selling new stock in the initial public offering (IPO). The owner currently holds 8 million stock which are not for sale. Which of the following statements is NOT correct?

(a) The IPO share price will be $2 per share

(b) The pre-money equity market capitalisation is $16 million.

(c) The post-money equity market capitalisation is $22 million.

(d) Bidder A will be allocated their entire bid, while Bidders C, D and E will be unsuccessful.

(e) Bidder B will be allocated only 0.5m stock of their 1.5m stock bid.

Question 101  payout policy, no explanation

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

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

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

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

Select the most correct response:

(a) Only (i) is true.

(b) Only (ii) is true.

(c) Only (iii) is true.

(d) Only (i) and (ii) is true.

(e) All statements (i), (ii) and (iii) are true.

Question 202  DDM, payout policy

Currently, a mining company has a share price of $6 and pays constant annual dividends of $0.50. The next dividend will be paid in 1 year. Suddenly and unexpectedly the mining company announces that due to higher than expected profits, all of these windfall profits will be paid as a special dividend of $0.30 in 1 year.

If investors believe that the windfall profits and dividend is a one-off event, what will be the new share price? If investors believe that the additional dividend is actually permanent and will continue to be paid, what will be the new share price? Assume that the required return on equity is unchanged. Choose from the following, where the first share price includes the one-off increase in earnings and dividends for the first year only ##(P_\text{0 one-off})## , and the second assumes that the increase is permanent ##(P_\text{0 permanent})##:

(a) ##P_\text{0 one-off} = 9.6000, \space \space P_\text{0 permanent} = 6.2766##

(b) ##P_\text{0 one-off} = 6.3000, \space \space P_\text{0 permanent} = 6.2769##

(c) ##P_\text{0 one-off} = 9.6000, \space \space P_\text{0 permanent} = 6.3000##

(d) ##P_\text{0 one-off} = 6.2769, \space \space P_\text{0 permanent} = 9.6000##

(e) ##P_\text{0 one-off} = 6.3000, \space \space P_\text{0 permanent} = 9.6000##

Note: When a firm makes excess profits they sometimes pay them out as special dividends. Special dividends are just like ordinary dividends but they are one-off and investors do not expect them to continue, unlike ordinary dividends which are expected to persist.

Question 443  corporate financial decision theory, investment decision, financing decision, working capital decision, payout policy

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

(a) Investment decision.

(b) Financing decision.

(c) Working capital decision.

(d) Payout policy decision.

(e) Capital or labour decision.

Question 447  payout policy, corporate financial decision theory

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

(a) Assets.

(b) Liabilities and owner's equity.

(c) Current assets and current liabilities.

(d) Dividends and buy backs.

(e) Net income, also known as earnings or net profit after tax.

Question 455  income and capital returns, payout policy, DDM, market efficiency

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.

(a) 2.7% pa.

(b) 3.0% pa.

(c) 3.5% pa.

(d) 3.3% pa.

(e) 3.8% pa.

Question 566  capital structure, capital raising, rights issue, on market repurchase, dividend, stock split, bonus issue

A company's share price fell by 20% and its number of shares rose by 25%. Assume that there are no taxes, no signalling effects and no transaction costs.

Which one of the following corporate events may have happened?

(a) $1 cash dividend when the pre-announcement stock price was $5.

(b) On-market buy-back of 20% of the company's outstanding stock.

(c) 5 for 4 stock split.

(d) 1 for 5 bonus issue.

(e) 1 for 4 rights issue at a subscription price of $3 when the pre-announcement stock price was $5.

Question 568  rights issue, capital raising, capital structure

A company conducts a 1 for 5 rights issue at a subscription price of $7 when the pre-announcement stock price was $10. What is the percentage change in the stock price and the number of shares outstanding? The answers are given in the same order. Ignore all taxes, transaction costs and signalling effects.

(a) -16.67%, 20%

(b) -5%, 20%

(c) 0%, 20%

(d) 7.14%, 20%

(e) 11.67%, 0%

Question 625  dividend re-investment plan, capital raising

Which of the following statements about dividend re-investment plans (DRP's) is NOT correct?

(a) DRP's are voluntary, shareholders only participate if they choose.

(b) DRP's increase the number of shares.

(c) The number of shares issued to a shareholder participating in a DRP is usually calculated as their total dividends owed, divided by the allocation share price which is usually close to the current market share price.

(d) DRP's do not incur brokerage costs for the shareholder. This is unlike the case where the shareholder uses the cash dividend to buy more shares herself.

(e) If all shareholders participated in a company's DRP, the company would not pay any dividends and the firm's share price would not fall due to the cash dividend or the DRP.

Question 666  rights issue, capital raising

A company conducts a 2 for 3 rights issue at a subscription price of $8 when the pre-announcement stock price was $9. Assume that all investors use their rights to buy those extra shares.

What is the percentage increase in the stock price and the number of shares outstanding? The answers are given in the same order.

(a) -60%,   150%

(b) -42.22%,   150%

(c) -40%,   66.67%

(d) -22.22%,   66.67%

(e) -4.44%,   66.67%

Question 407  income and capital returns, inflation, real and nominal returns and cash flows

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

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

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

(a) 11.100%, 4.000%, 7.100%.

(b) 11.140%, 4.040%, 7.100%.

(c) 4.902%, 0.000%, 4.902%.

(d) 9.140%, 4.040%, 5.100%.

(e) 9.140%, 4.040%, 7.100%.

Question 575  inflation, real and nominal returns and cash flows

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

(a) The nominal cash flow of $100 in 5 years is equivalent to a real cash flow of $86.2609 in 5 years. This means that $86.2609 will buy the same amount of goods and services now as $100 will buy in 5 years.

(b) The real discount rate of 10% pa is equivalent to a nominal discount rate of 13.3333% pa.

(c) The nominal price of goods and services will increase by 3% every year.

(d) The real price of goods and services will increase by 3% every year.

(e) The present value of your payment will increase by the nominal discount rate every year.

Question 728  inflation, real and nominal returns and cash flows, income and capital returns, no explanation

Which of the following statements about gold is NOT correct? Assume that the gold price increases by inflation. Gold has a:

(a) Nil income cash flow.

(b) Real total return of zero.

(c) Real capital return equal to the inflation rate.

(d) Real income return of zero.

(e) Nominal income return of zero.

Question 740  real and nominal returns and cash flows, DDM, inflation

Taking inflation into account when using the DDM can be hard. Which of the following formulas will NOT give a company's current stock price ##(P_0)##? Assume that the annual dividend was just paid ##(C_0)##, and the next dividend will be paid in one year ##(C_1)##.

(a) ##P_0=\dfrac{C_\text{1,nominal}}{r_\text{nominal} - g_\text{nominal}}##

(b) ##P_0 =\dfrac{C_0 (1+g_\text{nominal} )^1}{r_\text{nominal} - g_\text{nominal}}##

(c) ##P_0=\dfrac{C_\text{1,real}}{r_\text{real} - g_\text{real}}##

(d) ##P_0=\dfrac{C_0 (1+r_\text{real})^1}{r_\text{real} - g_\text{real}}##

(e) ##P_0=\dfrac{C_0(1+r_\text{nominal} )^1}{r_\text{nominal} - g_\text{nominal}} - C_0##

Question 749  Multiples valuation, PE ratio, price to revenue ratio, price to book ratio, NPV

A real estate agent says that the price of a house in Sydney Australia is approximately equal to the gross weekly rent times 1000.

What type of valuation method is the real estate agent using?

(a) Price to EBITDA multiple.

(b) Price to book multiple.

(c) Price to earnings multiple.

(d) Price to revenue multiple.

(e) Discounted cash flow (DCF).

Question 367  CFFA, interest tax shield

There are many ways to calculate a firm's free cash flow (FFCF), also called cash flow from assets (CFFA). Some include the annual interest tax shield in the cash flow and some do not.

Which of the below FFCF formulas include the interest tax shield in the cash flow?

###(1) \quad FFCF=NI + Depr - CapEx -ΔNWC + IntExp### ###(2) \quad FFCF=NI + Depr - CapEx -ΔNWC + IntExp.(1-t_c)### ###(3) \quad FFCF=EBIT.(1-t_c )+ Depr- CapEx -ΔNWC+IntExp.t_c### ###(4) \quad FFCF=EBIT.(1-t_c) + Depr- CapEx -ΔNWC### ###(5) \quad FFCF=EBITDA.(1-t_c )+Depr.t_c- CapEx -ΔNWC+IntExp.t_c### ###(6) \quad FFCF=EBITDA.(1-t_c )+Depr.t_c- CapEx -ΔNWC### ###(7) \quad FFCF=EBIT-Tax + Depr - CapEx -ΔNWC### ###(8) \quad FFCF=EBIT-Tax + Depr - CapEx -ΔNWC-IntExp.t_c### ###(9) \quad FFCF=EBITDA-Tax - CapEx -ΔNWC### ###(10) \quad FFCF=EBITDA-Tax - CapEx -ΔNWC-IntExp.t_c###

The formulas for net income (NI also called earnings), EBIT and EBITDA are given below. Assume that depreciation and amortisation are both represented by 'Depr' and that 'FC' represents fixed costs such as rent.

###NI=(Rev - COGS - Depr - FC - IntExp).(1-t_c )### ###EBIT=Rev - COGS - FC-Depr### ###EBITDA=Rev - COGS - FC### ###Tax =(Rev - COGS - Depr - FC - IntExp).t_c= \dfrac{NI.t_c}{1-t_c}###

(a) 1, 3, 5, 7, 9.

(b) 2, 4, 6, 8, 10.

(c) 1, 4, 6, 8, 10.

(d) 2, 3, 5, 7, 9.

(e) 1, 3, 5, 8, 10.

Question 801  negative gearing, leverage, capital structure

The following steps outline the process of ‘negative gearing’ an investment property in Australia. Which of these steps or statements is NOT correct? To successfully achieve negative gearing on an investment property:

(a) Buy an investment property with low expected future capital gains and high rental income, funded using a low proportion of debt (mortgage loan).

(b) Rent the investment property to a tenant;

(c) Negative gearing is achieved when the property investment’s annual taxable profit is negative, due to the loan’s interest expense being greater than the net rent (rental revenue less the renting expenses such as maintenance);

(d) Deduct the property’s income loss from the investor’s separate personal wage from labour. This means that the investor will pay less personal income tax than if they didn’t make the levered property investment;

(e) The investment property will be a positive-NPV investment if the capital gains are greater than the income losses on an after-tax, risk-adjusted, present-value basis.

Question 619  CFFA

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

(a) Net income, depreciation and interest expense.

(b) Depreciation and capital expenditure.

(c) Current assets, current liabilities and cost of goods sold (COGS).

(d) Current assets, current liabilities and capital expenditure.

(e) Current assets, current liabilities and depreciation expense.

Question 205  depreciation tax shield, CFFA

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?

(a) 'Straight line' or 'prime cost' depreciation, which allocates equal depreciation expenses over each year of the asset's life.

(b) 'Diminishing value' or 'reducing balance' depreciation, which allocates more depreciation expense at the start of the asset's life and less towards the end.

(c) No depreciation at all, so the asset is always kept on the books as being the same value that it was bought for. The asset will cause no depreciation expense in any year.

(d) Allocating all of the depreciation expense to the final year of the asset's life.

(e) Allocating all of the depreciation expense to the first year of the asset's life. Accountants would call this 'expensing' the asset, rather than 'capitalising' it and depreciating it slowly.

Question 368  interest tax shield, CFFA

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

###\begin{aligned} FFCF &= (Rev - COGS - Depr - FC - IntExp)(1-t_c) + \\ &\space\space\space+ Depr - CapEx -\Delta NWC + IntExp(1-t_c) \\ \end{aligned}###

Does this annual FFCF or the annual interest tax shield?

Question 371  interest tax shield, CFFA

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?

Question 841  gross domestic product, government spending

The government spends money on:

• Goods and services such as defence, police, schools, hospitals and roads; and
• Transfer payments (also called welfare) such as the pension, dole, disability support and student support.

When calculating GDP (=C+I+G+X-M), the ‘government spending’ component (G) is supposed to include:

(a) Gross government spending on goods and services only.

(b) Gross government spending on transfer payments only.

(c) Net government spending which is goods and services expenditure less tax revenue.

(d) Net government spending which is transfer payments expenditure less tax revenue.

(e) Net government spending which is total expenditure (goods and services plus transfer payments expenditure) less tax revenue.

Question 853  gross domestic product

Which form of production is included in the Gross Domestic Product (GDP) reported by the government statistics agency?

(a) Home-production such as Grandma babysitting her grand-children for free.

(b) Production in the under-ground economy such as work paid for in cash to evade the tax authorities.

(c) Production in the wild, such as when kangaroos multiply in the bush.

(d) Goods produced and exchanged in the barter economy that are not reported to the tax authorities.

(e) Inventory build-up such as goods produced in a factory that were sold to a wholesaler but have not yet been sold to a retailer or consumer.

Question 1034  duration, monetary policy, inflation, market efficiency

On 18 March 2022 the AFR's James Thomson wrote: "In a world where the bombs are still falling in Ukraine and the Fed is just getting started on what looks likely to be a year-long cycle of rising interest rates, it would take a certain amount of bravery to embrace the sort of high-tech, long duration plays that Wood favours" (Thomson, 2022).

Which of the following US macro-economic data releases is most likely to cause Cathie Wood's ARK ETF share price to fall?

(a) GDP growth meeting expectations.

(b) Surprisingly high inflation, above expectations

(c) Surprisingly high unemployment, above expectations.

(d) Surprisingly low consumption, investment and exports, below expectations.

(e) The surprise announcement of lower corporate tax rates.

Question 1045  payout policy, leverage, capital structure, beta

A levered firm has only 2 assets on its balance sheet with the below market values and CAPM betas. The risk free rate is 3% pa and the market risk premium is 5% pa. Assume that the CAPM is correct and all assets are fairly priced.

Balance Sheet Market Values and Betas
Balance sheet item	Market value ($m)	Beta
Cash asset	0.5	0
Truck assets	0.5	2
Loan liabilities	0.25	0.1
Equity funding	?	?

 

The firm then pays out all of its cash as a dividend. Assume that the beta and yield on the loan liability remain unchanged. Ignore taxes, transaction costs, signalling, information asymmetries and other frictions.

Which of the following statements is NOT correct? This event led to a:

(a) $0.5m decrease in equity to $0.25m and cash to zero.

(b) Asset beta of 1 and required return on assets (or WACC before tax) of 8% pa.

(c) $0.50 fall in the share price if there are 1 million shares.

(d) Equity beta of 3.9 and required return of 22.5% pa.

(e) Debt-to-assets ratio of 50%.

Question 305  option, short selling, speculation

You believe that the price of a share will fall significantly very soon, but the rest of the market does not. The market thinks that the share price will remain the same. Assuming that your prediction will soon be true, which of the following trades is a bad idea? In other words, which trade will NOT make money or prevent losses?

(a) Sell all existing stock that you own.

(b) Short sell the stock.

(c) Buy put options on the stock.

(d) Sell put options on the stock.

(e) Sell call options on the stock.

Question 334  option

Which option position has the possibility of unlimited potential losses?

(a) Long call options.

(b) Short call options.

(c) Long put options.

(d) Short put options.

(e) No option positions have the possibility of unlimited potential losses.

Question 399  option, no explanation

A European call option will mature in ##T## years with a strike price of ##K## dollars. The underlying asset has a price of ##S## dollars.

What is an expression for the payoff at maturity ##(f_T)## in dollars from owning (being long) the call option?

(a) ##\max(S_T - K, 0)##.

(b) ##\max(S_T - K, K)##.

(c) ##\max(K-S_T, 0)##.

(d) ##\max(K-S_T, K)##.

(e) ##\min(K-S_T, 0)##.

Question 588  option

If trader A has sold the right that allows counterparty B to buy the underlying asset from him at maturity if counterparty B wants then trader A is:

(a) Long a call option.

(b) Long a put option.

(c) Short a call option.

(d) Short a put option.

(e) Neither long or short a call or a put option.

Question 680  option, no explanation

A trader buys one crude oil European style put option contract on the CME expiring in one year with an exercise price of $44 per barrel for a price of $6.64. The crude oil spot price is $40.33. If the trader doesn’t close out her contract before maturity, then at maturity she will have the:

(a) Obligation to sell the underlying oil at $44 per barrel.

(b) Right to buy the underlying oil at $44 per barrel if she wants.

(c) Right to sell the underlying oil at $44 per barrel if she wants.

(d) Obligation to buy the underlying oil $44 per barrel if the counterparty chooses to sell it.

(e) Obligation to sell the underlying oil at $44 per barrel if the counterparty chooses to buy it.

Question 687  option, no explanation

Which of the following statements about call options is NOT correct?

(a) Buyers of call options are required to pay an initial margin at the start.

(b) Call options are a zero-sum game in the sense that the winner gains at the expense of the loser.

(c) Buyers of call options have to pay the option price at the start.

(d) Buyers of call options do not care about the credit risk of the original call option seller since the contract is novated by the exchange.

(e) Speculators who sell call options hope that the underlying asset price falls.

Question 436  option, no explanation

Will the price of an out-of-the-money put option on equity or if the standard deviation of returns (risk) of the underlying shares becomes higher?

Question 584  option, option payoff at maturity, option profit

Which of the following statements about European call options on non-dividend paying stocks is NOT correct?

(a) A long call option's payoff at maturity is equal to the maximum of zero or the underlying asset price at maturity minus the exercise price. ##f_\text{T,LC} = max(S_T - K, 0)##

(b) A long call option's profit is equal to the payoff at maturity less the initial option price. ##\pi_\text{LC} = max(S_T - K, 0) - c_0##

(c) The breakeven price is the underlying asset price at which a long option contract gives zero profit. When ##max(S_T - K, 0) - c_0 = 0##, then ##S_T = K+c_0##.

(d) A call option's break-even price is always more than its strike price.

(e) Call options should only be exercised at maturity if the underlying asset price is above the break-even price.

Question 102  option, hedging

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:

(a) Only (i) is true.

(b) Only (ii) is true.

(c) Only (iii) is true.

(d) Only (i) and (ii) is true.

(e) All statements (i), (ii) and (iii) are true.

Question 423  takeover

Acquirer firm plans to launch a takeover of Target firm. The deal is expected to create a present value of synergies totaling $105 million. A 40% scrip and 60% cash offer will be made that pays the fair price for the target's shares plus 75% of the total synergy value. The cash will be paid out of the firm's cash holdings, no new debt or equity will be raised.

Firms Involved in the Takeover
	Acquirer	Target
Assets ($m)	6,000	700
Debt ($m)	4,800	400
Share price ($)	40	20
Number of shares (m)	30	15

Ignore transaction costs and fees. Assume that the firms' debt and equity are fairly priced, and that each firms' debts' risk, yield and values remain constant. The acquisition is planned to occur immediately, so ignore the time value of money.

Calculate the merged firm's share price and total number of shares after the takeover has been completed.

(a) $36.74 share price and 37.5m shares on issue.

(b) $37.925 share price and 30m shares on issue.

(c) $40.875 share price and 33.706422m shares on issue.

(d) $40.875 share price and 35.559633m shares on issue.

(e) $47.5556 share price and 33.75m shares on issue.

Question 421  takeover

Acquirer firm plans to launch a takeover of Target firm. The deal is expected to create a present value of synergies totaling $105 million. A scrip offer will be made that pays the fair price for the target's shares plus 75% of the total synergy value.

Firms Involved in the Takeover
	Acquirer	Target
Assets ($m)	6,000	700
Debt ($m)	4,800	400
Share price ($)	40	20
Number of shares (m)	30	15

Ignore transaction costs and fees. Assume that the firms' debt and equity are fairly priced, and that each firms' debts' risk, yield and values remain constant. The acquisition is planned to occur immediately, so ignore the time value of money.

Calculate the merged firm's share price and total number of shares after the takeover has been completed.

(a) $26.7778 share price and 45m shares on issue.

(b) $40.875 share price and 39.266055m shares on issue.

(c) $42.0639 share price and 38.15625m shares on issue.

(d) $42.8 share price and 37.5m shares on issue.

(e) $50.875 share price and 30m shares on issue.

Question 863  option, binomial option pricing

A one year European-style call option has a strike price of $4. The option's underlying stock pays no dividends and currently trades at $5. The risk-free interest rate is 10% pa continuously compounded. Use a single step binomial tree to calculate the option price, assuming that the price could rise to $8 ##(u = 1.6)## or fall to $3.125 ##(d = 1/1.6)## in one year. The call option price now is:

(a) 1.336851119

(b) 1.782468159

(c) 1.836881513

(d) 1.969931972

(e) 2.030068028

Question 795  option, Black-Scholes-Merton option pricing, option delta, no explanation

Which of the following quantities from the Black-Scholes-Merton option pricing formula gives the Delta of a European put option?

(a) ##N[d_1]##

(b) ##N[d_2]##

(c) ##−N[−d_1]##

(d) ##−N[−d_2]##

(e) ##N[−d_2]##

Question 797  option, Black-Scholes-Merton option pricing, option delta, no explanation

Which of the following quantities from the Black-Scholes-Merton option pricing formula gives the risk-neutral probability that a European put option will be exercised?

(a) ##N[d_1]##

(b) ##N[d_2]##

(c) ##−N[−d_1]##

(d) ##−N[−d_2]##

(e) ##N[−d_2]##

Question 903  option, Black-Scholes-Merton option pricing, option on stock index

A six month European-style call option on the S&P500 stock index has a strike price of 2800 points.

The underlying S&P500 stock index currently trades at 2700 points, has a continuously compounded dividend yield of 2% pa and a standard deviation of continuously compounded returns of 25% pa.

The risk-free interest rate is 5% pa continuously compounded.

Use the Black-Scholes-Merton formula to calculate the option price. The call option price now is:

(a) 162.83 points

(b) 220.56 points

(c) 226.43 points

(d) 230.91 points

(e) 317.45 points

Question 383  Merton model of corporate debt, real option, option

In the Merton model of corporate debt, buying a levered company's debt is equivalent to buying the company's assets and:

(a) Selling government bonds.

(b) Buying a call option on the company's assets.

(c) Buying a put option on the company's assets.

(d) Selling a call option on the company's assets.

(e) Selling a put option on the company's assets.

Question 385  Merton model of corporate debt, real option, option

A risky firm will last for one period only (t=0 to 1), then it will be liquidated. So it's assets will be sold and the debt holders and equity holders will be paid out in that order. The firm has the following quantities:

##V## = Market value of assets.

##E## = Market value of (levered) equity.

##D## = Market value of zero coupon bonds.

##F_1## = Total face value of zero coupon bonds which is promised to be paid in one year.

The levered equity graph above contains bold labels a to e. Which of the following statements about those labels is NOT correct?

(a) Label a represents the market value of equity ##(E)## at t=0 on the red curved line or t=1 on the blue crooked line.

(b) Label b represents the market value of equity now ##(E_0)##.

(c) Label c represents the market value of equity if the assets were liquidated right now.

(d) Label d represents the face value of debt at maturity ##(F_1)##.

(e) Label e represents the market value of debt ##(D)## at t=0 on the red curved line or t=1 on the blue crooked line.

Question 386  Merton model of corporate debt, real option, option

A risky firm will last for one period only (t=0 to 1), then it will be liquidated. So it's assets will be sold and the debt holders and equity holders will be paid out in that order. The firm has the following quantities:

##V## = Market value of assets.

##E## = Market value of (levered) equity.

##D## = Market value of zero coupon bonds.

##F_1## = Total face value of zero coupon bonds which is promised to be paid in one year.

The risky corporate debt graph above contains bold labels a to e. Which of the following statements about those labels is NOT correct?

(a) Label a represents the market value of equity ##(E)## at t=0 on the red curved line or t=1 on the blue crooked line.

(b) Label b represents the face value of debt at maturity ##(F_1)##.

(c) Label c represents the market value of debt now ##(D_0)##.

(d) Label d represents the face value of debt at maturity ##(F_1)##.

(e) Label e represents the market value of assets ##(V)## at t=0 on the red curved line or t=1 on the blue crooked line.

Question 434  Merton model of corporate debt, real option, option

A risky firm will last for one period only (t=0 to 1), then it will be liquidated. So it's assets will be sold and the debt holders and equity holders will be paid out in that order. The firm has the following quantities:

##V## = Market value of assets.

##E## = Market value of (levered) equity.

##D## = Market value of zero coupon bonds.

##F_1## = Total face value of zero coupon bonds which is promised to be paid in one year.

What is the payoff to debt holders at maturity, assuming that they keep their debt until maturity?

(a) ##\max(V_1 - F_1,0)##.

(b) ##\max(F_1, V_1)##.

(c) ##\max(F_1, 0)##.

(d) ##\min(F_1, V_1)##.

(e) ##\min(V_1-F_1, F_1)##.

Question 389  real option, option

You're thinking of starting a new cafe business, but you're not sure if it will be profitable.

You have to decide what type of cups, mugs and glasses you wish to buy. You can pay to have your cafe's name printed on them, or just buy the plain un-marked ones. For marketing reasons it's better to have the cafe name printed. But the plain un-marked cups, mugs and glasses maximise your:

(a) Expansion option.

(b) Abandonment option.

(c) Timing (or delaying) option.

(d) Production (or switching) option.

(e) Underlying asset.

Question 393  real option, option

A timing option is best modeled as a or option?

Question 395  real option, option

The cheapest mobile phones available tend to be those that are 'locked' into a cell phone operator's network. Locked phones can not be used with other cell phone operators' networks.

Locked mobile phones are cheaper than unlocked phones because the locked-in network operator helps create a monopoly by:

(a) Destroying customers' expansion option.

(b) Destroying customers' abandonment option.

(c) Destroying customers' timing (or delaying) option.

(d) Destroying customers' production (or switching) option.

(e) Growing customers' binomial tree.

Question 124  option, hedging

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:

(a) Buy calls on grain, buy calls on cattle livestock.

(b) Buy calls on grain, buy puts on cattle livestock.

(c) Buy puts on grain, buy calls on cattle livestock.

(d) Buy puts on grain, buy puts on cattle livestock.

(e) Statements (a) and (d) are both correct.

Question 839  option, put call parity

A stock, a call, a put and a bond are available to trade. The call and put options' underlying asset is the stock they and have the same strike prices, ##K_T##.

You are currently long the stock. You want to hedge your long stock position without actually trading the stock. How would you do this?

(a) Long call, long put and long bond.

(b) Long call, long put and short bond.

(c) Long call, short put and short bond.

(d) Short call, short put and short bond.

(e) Short call, long put and short bond.

Question 397  financial distress, leverage, capital structure, NPV

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) $2.5m, so they should vote yes.

(b) $2.045455m, so they should vote yes.

(c) $0.9m, so they should vote no.

(d) $0, so they should vote no.

(e) -$0.9m, so they should vote no.