Fight Finance

Courses  Tags  Random  All  Recent  Scores

Question 67  CFFA, interest tax shield

Here are the Net Income (NI) and Cash Flow From Assets (CFFA) equations:

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

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

What is the formula for calculating annual interest expense (IntExp) which is used in the equations above?

Select one of the following answers. Note that D is the value of debt which is constant through time, and ##r_D## is the cost of debt.



Question 68  WACC, CFFA, capital budgeting

A manufacturing company is considering a new project in the more risky services industry. The cash flows from assets (CFFA) are estimated for the new project, with interest expense excluded from the calculations. To get the levered value of the project, what should these unlevered cash flows be discounted by?

Assume that the manufacturing firm has a target debt-to-assets ratio that it sticks to.



Question 113  WACC, CFFA, capital budgeting

The US firm Google operates in the online advertising business. In 2011 Google bought Motorola Mobility which manufactures mobile phones.

Assume the following:

  • Google had a 10% after-tax weighted average cost of capital (WACC) before it bought Motorola.
  • Motorola had a 20% after-tax WACC before it merged with Google.
  • Google and Motorola have the same level of gearing.
  • Both companies operate in a classical tax system.

You are a manager at Motorola. You must value a project for making mobile phones. Which method(s) will give the correct valuation of the mobile phone manufacturing project? Select the most correct answer.

The mobile phone manufacturing project's:



Question 773  CFFA, WACC, interest tax shield, DDM

Use the below information to value a levered company with constant annual perpetual cash flows from assets. The next cash flow will be generated in one year from now, so a perpetuity can be used to value this firm. Both the operating and firm free cash flows are constant (but not equal to each other).

Data on a Levered Firm with Perpetual Cash Flows
Item abbreviation Value Item full name
##\text{OFCF}## $48.5m Operating free cash flow
##\text{FFCF or CFFA}## $50m Firm free cash flow or cash flow from assets
##g## 0% pa Growth rate of OFCF and FFCF
##\text{WACC}_\text{BeforeTax}## 10% pa Weighted average cost of capital before tax
##\text{WACC}_\text{AfterTax}## 9.7% pa Weighted average cost of capital after tax
##r_\text{D}## 5% pa Cost of debt
##r_\text{EL}## 11.25% pa Cost of levered equity
##D/V_L## 20% pa Debt to assets ratio, where the asset value includes tax shields
##t_c## 30% Corporate tax rate
 

 

What is the value of the levered firm including interest tax shields?



Question 457  PE ratio, Multiples valuation

Which firms tend to have low forward-looking price-earnings (PE) ratios? Only consider firms with positive PE ratios.



Question 165  DDM, PE ratio, payout ratio

For certain shares, the forward-looking Price-Earnings Ratio (##P_0/EPS_1##) is equal to the inverse of the share's total expected return (##1/r_\text{total}##). For what shares is this true?

Use the general accounting definition of 'payout ratio' which is dividends per share (DPS) divided by earnings per share (EPS) and assume that all cash flows, earnings and rates are real rather than nominal.

A company's forward-looking PE ratio will be the inverse of its total expected return on equity when it has a:



Question 341  Multiples valuation, PE ratio

Estimate Microsoft's (MSFT) share price using a price earnings (PE) multiples approach with the following assumptions and figures only:

  • Apple, Google and Microsoft are comparable companies,
  • Apple's (AAPL) share price is $526.24 and historical EPS is $40.32.
  • Google's (GOOG) share price is $1,215.65 and historical EPS is $36.23.
  • Micrsoft's (MSFT) historical earnings per share (EPS) is $2.71.

Source: Google Finance 28 Feb 2014.



Question 347  PE ratio, Multiples valuation

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



Question 348  PE ratio, Multiples valuation

Estimate the US bank JP Morgan's share price using a price earnings (PE) multiples approach with the following assumptions and figures only:

  • The major US banks JP Morgan Chase (JPM), Citi Group (C) and Wells Fargo (WFC) are comparable companies;
  • JP Morgan Chase's historical earnings per share (EPS) is $4.37;
  • Citi Group's share price is $50.05 and historical EPS is $4.26;
  • Wells Fargo's share price is $48.98 and historical EPS is $3.89.

Note: Figures sourced from Google Finance on 24 March 2014.



Question 354  PE ratio, Multiples valuation

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.



Question 357  PE ratio, Multiples valuation

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



Question 358  PE ratio, Multiples valuation

Estimate the Chinese bank ICBC's share price using a backward-looking price earnings (PE) multiples approach with the following assumptions and figures only. Note that the renminbi (RMB) is the Chinese currency, also known as the yuan (CNY).

  • The 4 major Chinese banks ICBC, China Construction Bank (CCB), Bank of China (BOC) and Agricultural Bank of China (ABC) are comparable companies;
  • ICBC 's historical earnings per share (EPS) is RMB 0.74;
  • CCB's backward-looking PE ratio is 4.59;
  • BOC 's backward-looking PE ratio is 4.78;
  • ABC's backward-looking PE ratio is also 4.78;

Note: Figures sourced from Google Finance on 25 March 2014. Share prices are from the Shanghai stock exchange.



Question 364  PE ratio, Multiples valuation

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



Question 402  PE ratio, no explanation

Which of the following companies is most suitable for valuation using PE multiples techniques?



Question 403  PE ratio, no explanation

Which of the following investable assets is the LEAST suitable for valuation using PE multiples techniques?



Question 414  PE ratio, pay back period, no explanation

A mature firm has constant expected future earnings and dividends. Both amounts are equal. So earnings and dividends are expected to be equal and unchanging.

Which of the following statements is NOT correct?



Question 463  PE ratio, Multiples valuation

Private equity firms are known to buy medium sized private companies operating in the same industry, merge them together into a larger company, and then sell it off in a public float (initial public offering, IPO).

If medium-sized private companies trade at PE ratios of 5 and larger listed companies trade at PE ratios of 15, what return can be achieved from this strategy?

Assume that:

  • The medium-sized companies can be bought, merged and sold in an IPO instantaneously.
  • There are no costs of finding, valuing, merging and restructuring the medium sized companies. Also, there is no competition to buy the medium-sized companies from other private equity firms.
  • The large merged firm's earnings are the sum of the medium firms' earnings.
  • The only reason for the difference in medium and large firm's PE ratios is due to the illiquidity of the medium firms' shares.
  • Return is defined as: ##r_{0→1} = (p_1-p_0+c_1)/p_0## , where time zero is just before the merger and time one is just after.



Question 468  PE ratio

A firm has 1 million shares which trade at a price of $30 each. The firm is expected to announce earnings of $3 million at the end of the year and pay an annual dividend of $1.50 per share.

What is the firm's (forward looking) price/earnings (PE) ratio?



Question 474  PE ratio

The below screenshot of Commonwealth Bank of Australia's (CBA) details were taken from the Google Finance website on 7 Nov 2014. Some information has been deliberately blanked out.

Image of CBA on Google finance on 7 Nov 2014

What was CBA's backwards-looking price-earnings ratio?



Question 483  PE ratio

The below screenshot of Microsoft's (MSFT) details were taken from the Google Finance website on 28 Nov 2014. Some information has been deliberately blanked out.

Image of MSFT on Google finance on 28 Nov 2014

What was MSFT's backwards-looking price-earnings ratio?



Question 493  PE ratio

A firm has 2m shares and a market capitalisation of equity of $30m. The firm just announced earnings of $5m and paid an annual dividend of $0.75 per share.

What is the firm's (backward looking) price/earnings (PE) ratio?



Question 537  PE ratio, Multiples valuation, no explanation

Estimate the French bank Societe Generale's share price using a backward-looking price earnings (PE) multiples approach with the following assumptions and figures only. Note that EUR is the euro, the European monetary union's currency.

  • The 4 major European banks Credit Agricole (ACA), Deutsche Bank AG (DBK), UniCredit (UCG) and Banco Santander (SAN) are comparable companies to Societe Generale (GLE);
  • Societe Generale's (GLE's) historical earnings per share (EPS) is EUR 2.92;
  • ACA's backward-looking PE ratio is 16.29 and historical EPS is EUR 0.84;
  • DBK's backward-looking PE ratio is 25.01 and historical EPS is EUR 1.26;
  • SAN's backward-looking PE ratio is 14.71 and historical EPS is EUR 0.47;
  • UCG's backward-looking PE ratio is 15.78 and historical EPS is EUR 0.40;

Note: Figures sourced from Google Finance on 27 March 2015.



Question 547  PE ratio, Multiples valuation, DDM, income and capital returns, no explanation

A firm pays out all of its earnings as dividends. Because of this, the firm has no real growth in earnings, dividends or stock price since there is no re-investment back into the firm to buy new assets and make higher earnings. The dividend discount model is suitable to value this company.

The firm's revenues and costs are expected to increase by inflation in the foreseeable future. The firm has no debt. It operates in the services industry and has few physical assets so there is negligible depreciation expense and negligible net working capital required.

Which of the following statements about this firm's PE ratio is NOT correct? The PE ratio should:

Note: The inverse of x is 1/x.



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?



Question 750  PE ratio, Multiples valuation

Itau Unibanco is a major listed bank in Brazil with a market capitalisation of equity equal to BRL 85.744 billion, EPS of BRL 3.96 and 2.97 billion shares on issue.

Banco Bradesco is another major bank with total earnings of BRL 8.77 billion and 2.52 billion shares on issue.

Estimate Banco Bradesco's current share price using a price-earnings multiples approach assuming that Itau Unibanco is a comparable firm.

Note that BRL is the Brazilian Real, their currency. Figures sourced from Google Finance on the market close of the BVMF on 24/7/15.



Question 905  market capitalisation of equity, PE ratio, payout ratio

The below graph shows the computer software company Microsoft's stock price (MSFT) at the market close on the NASDAQ on Friday 1 June 2018.

Based on the screenshot above, which of the following statements about MSFT is NOT correct? MSFT's:



Question 473  market capitalisation of equity

The below screenshot of Commonwealth Bank of Australia's (CBA) details were taken from the Google Finance website on 7 Nov 2014. Some information has been deliberately blanked out.

Image of CBA on Google finance on 7 Nov 2014

What was CBA's market capitalisation of equity?



Question 482  market capitalisation of equity

The below screenshot of Microsoft's (MSFT) details were taken from the Google Finance website on 28 Nov 2014. Some information has been deliberately blanked out.

Image of MSFT on Google finance on 28 Nov 2014

What was MSFT's market capitalisation of equity?



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 __________.



Question 349  CFFA, depreciation tax shield

Which one of the following will decrease net income (NI) but increase cash flow from assets (CFFA) in this year for a tax-paying firm, all else remaining constant?

Remember:

###NI = (Rev-COGS-FC-Depr-IntExp).(1-t_c )### ###CFFA=NI+Depr-CapEx - \Delta NWC+IntExp###



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?



Question 413  CFFA, interest tax shield, depreciation tax shield

There are many ways to calculate a firm's free cash flow (FFCF), also called cash flow from assets (CFFA).

One method is to use the following formulas to transform net income (NI) into FFCF including interest and depreciation tax shields:

###FFCF=NI + Depr - CapEx -ΔNWC + IntExp###

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

Another popular method is to use EBITDA rather than net income. EBITDA is defined as:

###EBITDA=Rev - COGS - FC###

One of the below formulas correctly calculates FFCF from EBITDA, including interest and depreciation tax shields, giving an identical answer to that above. Which formula is correct?



Question 857  Du Pont formula, accounting ratio

The Du Pont formula is:

###\dfrac{\text{Net Profit}}{\text{Sales}} \times \dfrac{\text{Sales}}{\text{Total Assets}} \times \dfrac{\text{Total Assets}}{\text{Owners' Equity}}###

Which of the following statements about the Du Pont formula is NOT correct?



Question 987  interest tax shield, capital structure, debt terminology, no explanation

What creates interest tax shields for a company?



Question 855  cash cycle, accounting ratio

The below diagram shows a firm’s cash cycle.

Diagram

Which of the following statements about companies’ cash cycle is NOT correct?



Question 868  cash cycle

What is the Cash Conversion Cycle for a firm with a:

  • Payables period of 1 day;
  • Inventory period of 50 days; and
  • Receivables period of 30 days?

All answer options are in days:



Question 77  interest tax shield

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?



Question 206  CFFA, interest expense, interest tax shield

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:



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?



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?



Question 375  interest tax shield, CFFA

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

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



Question 88  WACC, CAPM

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.



Question 237  WACC, Miller and Modigliani, interest tax shield

Which of the following discount rates should be the highest for a levered company? Ignore the costs of financial distress.



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.



Question 766  CFFA, WACC, interest tax shield, DDM

Use the below information to value a levered company with constant annual perpetual cash flows from assets. The next cash flow will be generated in one year from now, so a perpetuity can be used to value this firm. Both the operating and firm free cash flows are constant (but not equal to each other).

Data on a Levered Firm with Perpetual Cash Flows
Item abbreviation Value Item full name
##\text{OFCF}## $100m Operating free cash flow
##\text{FFCF or CFFA}## $112m Firm free cash flow or cash flow from assets
##g## 0% pa Growth rate of OFCF and FFCF
##\text{WACC}_\text{BeforeTax}## 7% pa Weighted average cost of capital before tax
##\text{WACC}_\text{AfterTax}## 6.25% pa Weighted average cost of capital after tax
##r_\text{D}## 5% pa Cost of debt
##r_\text{EL}## 9% pa Cost of levered equity
##D/V_L## 50% pa Debt to assets ratio, where the asset value includes tax shields
##t_c## 30% Corporate tax rate
 

 

What is the value of the levered firm including interest tax shields?



Question 303  WACC, CAPM, CFFA

There are many different ways to value a firm's assets. Which of the following will NOT give the correct market value of a levered firm's assets ##(V_L)##? Assume that:

  • The firm is financed by listed common stock and vanilla annual fixed coupon bonds, which are both traded in a liquid market.
  • The bonds' yield is equal to the coupon rate, so the bonds are issued at par. The yield curve is flat and yields are not expected to change. When bonds mature they will be rolled over by issuing the same number of new bonds with the same expected yield and coupon rate, and so on forever.
  • Tax rates on the dividends and capital gains received by investors are equal, and capital gains tax is paid every year, even on unrealised gains regardless of when the asset is sold.
  • There is no re-investment of the firm's cash back into the business. All of the firm's excess cash flow is paid out as dividends so real growth is zero.
  • The firm operates in a mature industry with zero real growth.
  • All cash flows and rates in the below equations are real (not nominal) and are expected to be stable forever. Therefore the perpetuity equation with no growth is suitable for valuation.

Where:

###r_\text{WACC before tax} = r_D.\frac{D}{V_L} + r_{EL}.\frac{E_L}{V_L} = \text{Weighted average cost of capital before tax}### ###r_\text{WACC after tax} = r_D.(1-t_c).\frac{D}{V_L} + r_{EL}.\frac{E_L}{V_L} = \text{Weighted average cost of capital after tax}### ###NI_L=(Rev-COGS-FC-Depr-\mathbf{IntExp}).(1-t_c) = \text{Net Income Levered}### ###CFFA_L=NI_L+Depr-CapEx - \varDelta NWC+\mathbf{IntExp} = \text{Cash Flow From Assets Levered}### ###NI_U=(Rev-COGS-FC-Depr).(1-t_c) = \text{Net Income Unlevered}### ###CFFA_U=NI_U+Depr-CapEx - \varDelta NWC= \text{Cash Flow From Assets Unlevered}###

Question 772  interest tax shield, capital structure, leverage

A firm issues debt and uses the funds to buy back equity. Assume that there are no costs of financial distress or transactions costs. Which of the following statements about interest tax shields is NOT correct?



Question 804  CFFA, WACC, interest tax shield, DDM

Use the below information to value a levered company with annual perpetual cash flows from assets that grow. The next cash flow will be generated in one year from now. Note that ‘k’ means kilo or 1,000. So the $30k is $30,000.

Data on a Levered Firm with Perpetual Cash Flows
Item abbreviation Value Item full name
##\text{OFCF}## $30k Operating free cash flow
##g## 1.5% pa Growth rate of OFCF
##r_\text{D}## 4% pa Cost of debt
##r_\text{EL}## 16.3% pa Cost of levered equity
##D/V_L## 80% pa Debt to assets ratio, where the asset value includes tax shields
##t_c## 30% Corporate tax rate
##n_\text{shares}## 100k Number of shares
 

 

Which of the following statements is NOT correct?



Question 504  CFFA

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 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?



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?



Question 419  capital budgeting, NPV, interest tax shield, WACC, CFFA, CAPM, no explanation

Project Data
Project life 1 year
Initial investment in equipment $6m
Depreciation of equipment per year $6m
Expected sale price of equipment at end of project 0
Unit sales per year 9m
Sale price per unit $8
Variable cost per unit $6
Fixed costs per year, paid at the end of each year $1m
Interest expense in first year (at t=1) $0.53m
Tax rate 30%
Government treasury bond yield 5%
Bank loan debt yield 6%
Market portfolio return 10%
Covariance of levered equity returns with market 0.08
Variance of market portfolio returns 0.16
Firm's and project's debt-to-assets ratio 50%
 

Notes

  1. Due to the project, current assets will increase by $5m now (t=0) and fall by $5m at the end (t=1). Current liabilities will not be affected.

Assumptions

  • The debt-to-assets 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 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?



Question 89  WACC, CFFA, interest tax shield

A retail furniture company buys furniture wholesale and distributes it through its retail stores. The owner believes that she has some good ideas for making stylish new furniture. She is considering a project to buy a factory and employ workers to manufacture the new furniture she's designed. Furniture manufacturing has more systematic risk than furniture retailing.

Her furniture retailing firm's after-tax WACC is 20%. Furniture manufacturing firms have an after-tax WACC of 30%. Both firms are optimally geared. Assume a classical tax system.

Which method(s) will give the correct valuation of the new furniture-making project? Select the most correct answer.



Question 173  CFFA

Find Candys Corporation's Cash Flow From Assets (CFFA), also known as Free Cash Flow to the Firm (FCFF), over the year ending 30th June 2013.

Candys Corp
Income Statement for
year ending 30th June 2013
  $m
Sales 200
COGS 50
Operating expense 10
Depreciation 20
Interest expense 10
Income before tax 110
Tax at 30% 33
Net income 77
 
Candys Corp
Balance Sheet
as at 30th June 2013 2012
  $m $m
Assets
Current assets 220 180
PPE    
    Cost 300 340
    Accumul. depr. 60 40
    Carrying amount 240 300
Total assets 460 480
 
Liabilities
Current liabilities 175 190
Non-current liabilities 135 130
Owners' equity
Retained earnings 50 60
Contributed equity 100 100
Total L and OE 460 480
 

 

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



Question 176  CFFA

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

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



Question 188  CFFA

Find Trademark Corporation's Cash Flow From Assets (CFFA), also known as Free Cash Flow to the Firm (FCFF), over the year ending 30th June 2013.

Trademark Corp
Income Statement for
year ending 30th June 2013
  $m
Sales 100
COGS 25
Operating expense 5
Depreciation 20
Interest expense 20
Income before tax 30
Tax at 30% 9
Net income 21
 
Trademark Corp
Balance Sheet
as at 30th June 2013 2012
  $m $m
Assets
Current assets 120 80
PPE    
    Cost 150 140
    Accumul. depr. 60 40
    Carrying amount 90 100
Total assets 210 180
 
Liabilities
Current liabilities 75 65
Non-current liabilities 75 55
Owners' equity
Retained earnings 10 10
Contributed equity 50 50
Total L and OE 210 180
 

 

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



Question 208  CFFA

Find UniBar Corp's Cash Flow From Assets (CFFA), also known as Free Cash Flow to the Firm (FCFF), over the year ending 30th June 2013.

UniBar Corp
Income Statement for
year ending 30th June 2013
  $m
Sales 80
COGS 40
Operating expense 15
Depreciation 10
Interest expense 5
Income before tax 10
Tax at 30% 3
Net income 7
 
UniBar Corp
Balance Sheet
as at 30th June 2013 2012
  $m $m
Assets
Current assets 120 90
PPE    
    Cost 360 320
    Accumul. depr. 40 30
    Carrying amount 320 290
Total assets 440 380
 
Liabilities
Current liabilities 110 60
Non-current liabilities 190 180
Owners' equity
Retained earnings 95 95
Contributed equity 45 45
Total L and OE 440 380
 

 

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



Question 209  CFFA

Find Piano Bar's Cash Flow From Assets (CFFA), also known as Free Cash Flow to the Firm (FCFF), over the year ending 30th June 2013.

Piano Bar
Income Statement for
year ending 30th June 2013
  $m
Sales 310
COGS 185
Operating expense 20
Depreciation 15
Interest expense 10
Income before tax 80
Tax at 30% 24
Net income 56
 
Piano Bar
Balance Sheet
as at 30th June 2013 2012
  $m $m
Assets
Current assets 240 230
PPE    
    Cost 420 400
    Accumul. depr. 50 35
    Carrying amount 370 365
Total assets 610 595
 
Liabilities
Current liabilities 180 190
Non-current liabilities 290 265
Owners' equity
Retained earnings 90 90
Contributed equity 50 50
Total L and OE 610 595
 

 

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



Question 223  CFFA, interest tax shield

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



Question 224  CFFA

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



Question 225  CFFA

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.



Question 226  CFFA

Find World Bar's Cash Flow From Assets (CFFA), also known as Free Cash Flow to the Firm (FCFF), over the year ending 30th June 2013.

World Bar
Income Statement for
year ending 30th June 2013
  $m
Sales 300
COGS 150
Operating expense 50
Depreciation 40
Interest expense 10
Taxable income 50
Tax at 30% 15
Net income 35
 
World Bar
Balance Sheet
as at 30th June 2013 2012
  $m $m
Assets
Current assets 200 230
PPE    
    Cost 400 400
    Accumul. depr. 75 35
    Carrying amount 325 365
Total assets 525 595
 
Liabilities
Current liabilities 150 205
Non-current liabilities 235 250
Owners' equity
Retained earnings 100 100
Contributed equity 40 40
Total L and OE 525 595
 

 

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



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:



Question 273  CFFA, capital budgeting

Value the following business project to manufacture a new product.

Project Data
Project life 2 yrs
Initial investment in equipment $6m
Depreciation of equipment per year $3m
Expected sale price of equipment at end of project $0.6m
Unit sales per year 4m
Sale price per unit $8
Variable cost per unit $5
Fixed costs per year, paid at the end of each year $1m
Interest expense per year 0
Tax rate 30%
Weighted average cost of capital after tax per annum 10%
 

Notes

  1. The firm's current assets and current liabilities are $3m and $2m respectively right now. This net working capital will not be used in this project, it will be used in other unrelated projects.
    Due to the project, current assets (mostly inventory) will grow by $2m initially (at t = 0), and then by $0.2m at the end of the first year (t=1).
    Current liabilities (mostly trade creditors) will increase by $0.1m at the end of the first year (t=1).
    At the end of the project, the net working capital accumulated due to the project can be sold for the same price that it was bought.
  2. The project cost $0.5m to research which was incurred one year ago.

Assumptions

  • All cash flows occur at the start or end of the year as appropriate, not in the middle or throughout the year.
  • All rates and cash flows are real. The inflation rate is 3% pa.
  • All rates are given as effective annual rates.
  • The business considering the project is run as a 'sole tradership' (run by an individual without a company) and is therefore eligible for a 50% capital gains tax discount when the equipment is sold, as permitted by the Australian Tax Office.

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



Question 291  CFFA

Find Scubar Corporation's Cash Flow From Assets (CFFA), also known as Free Cash Flow to the Firm (FCFF), over the year ending 30th June 2013.

Scubar Corp
Income Statement for
year ending 30th June 2013
  $m
Sales 200
COGS 60
Depreciation 20
Rent expense 11
Interest expense 19
Taxable Income 90
Taxes at 30% 27
Net income 63
 
Scubar Corp
Balance Sheet
as at 30th June 2013 2012
  $m $m
Inventory 60 50
Trade debtors 19 6
Rent paid in advance 3 2
PPE 420 400
Total assets 502 458
 
Trade creditors 10 8
Bond liabilities 200 190
Contributed equity 130 130
Retained profits 162 130
Total L and OE 502 458
 

 

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

The cash flow from assets was:



Question 296  CFFA, interest tax shield

Which one of the following will decrease net income (NI) but increase cash flow from assets (CFFA) in this year for a tax-paying firm, all else remaining constant?

Remember:

###NI=(Rev-COGS-FC-Depr-IntExp).(1-t_c )### ###CFFA=NI+Depr-CapEx - ΔNWC+IntExp###



Question 342  CFFA, capital budgeting

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

Image of option graphs

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?



Question 343  CFFA, capital budgeting

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

Image of option graphs

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?



Question 344  CFFA, capital budgeting

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

Image of option graphs

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?



Question 350  CFFA

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
Cash 0 0
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:



Question 351  CFFA

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

  • Achieve firm free cash flow (FFCF or CFFA) of $1m.
  • Pay dividends of $1.8m
  • Complete a $1.3m share buy-back.
  • Spend $0.8m on new buildings without buying or selling any other fixed assets. This capital expenditure is included in the CFFA figure quoted above.

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 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?



Question 359  CFFA

Which one of the following will have no effect on net income (NI) but decrease cash flow from assets (CFFA or FFCF) in this year for a tax-paying firm, all else remaining constant?

Remember:

###NI=(Rev-COGS-FC-Depr-IntExp).(1-t_c )### ###CFFA=NI+Depr-CapEx - ΔNWC+IntExp###



Question 360  CFFA

Find Ching-A-Lings Corporation's Cash Flow From Assets (CFFA), also known as Free Cash Flow to the Firm (FCFF), over the year ending 30th June 2013.

Ching-A-Lings Corp
Income Statement for
year ending 30th June 2013
  $m
Sales 100
COGS 20
Depreciation 20
Rent expense 11
Interest expense 19
Taxable Income 30
Taxes at 30% 9
Net income 21
 
Ching-A-Lings Corp
Balance Sheet
as at 30th June 2013 2012
  $m $m
Inventory 49 38
Trade debtors 14 2
Rent paid in advance 5 5
PPE 400 400
Total assets 468 445
 
Trade creditors 4 10
Bond liabilities 200 190
Contributed equity 145 145
Retained profits 119 100
Total L and OE 468 445
 

 

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

The cash flow from assets was:



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?



Question 366  opportunity cost, NPV, CFFA

Your friend is trying to find the net present value of an investment which:

  • Costs $1 million initially (t=0); and
  • Pays a single positive cash flow of $1.1 million in one year (t=1).

The investment 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.

Method 1: ##-1m + \dfrac{1.1m}{(1+0.1)^1} ##

Method 2: ##-1m + 1.1m - 1m \times 0.1 ##

Method 3: ##-1m + \dfrac{1.1m}{(1+0.1)^1} - 1m \times 0.1 ##

Which of the above calculations give the correct NPV? Select the most correct answer.



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 369  interest tax shield, CFFA

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

###\begin{aligned} FFCF &= (EBIT)(1-t_c) + Depr - CapEx -\Delta NWC + IntExp.t_c \\ &= (Rev - COGS - Depr - FC)(1-t_c) + Depr - CapEx -\Delta NWC + IntExp.t_c \\ \end{aligned} \\###
Does this annual FFCF or the annual interest tax shield?


Question 511  capital budgeting, CFFA

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

One Year Mining Project Data
Project life 1 year
Initial investment in building mine and equipment $9m
Depreciation of mine and equipment over the year $8m
Kilograms of gold mined at end of year 1,000
Sale price per kilogram $0.05m
Variable cost per kilogram $0.03m
Before-tax cost of closing mine at end of year $4m
Tax rate 30%
 

Note 1: Due to the project, the firm also anticipates finding some rare diamonds which will give before-tax revenues of $1m at the end of the year.

Note 2: The land that will be mined actually has thermal springs and a family of koalas that could be sold to an eco-tourist resort for an after-tax amount of $3m right now. However, if the mine goes ahead then this natural beauty will be destroyed.

Note 3: The mining equipment will have a book value of $1m at the end of the year for tax purposes. However, the equipment is expected to fetch $2.5m when it is sold.

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



Question 512  capital budgeting, CFFA

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

Project Data
Project life 2 years
Initial investment in equipment $6m
Depreciation of equipment per year for tax purposes $1m
Unit sales per year 4m
Sale price per unit $8
Variable cost per unit $3
Fixed costs per year, paid at the end of each year $1.5m
Tax rate 30%
 

Note 1: The equipment will have a book value of $4m at the end of the project for tax purposes. However, the equipment is expected to fetch $0.9 million when it is sold at t=2.

Note 2: Due to the project, the firm will have to purchase $0.8m of inventory initially, which it will sell at t=1. The firm will buy another $0.8m at t=1 and sell it all again at t=2 with zero inventory left. The project will have no effect on the firm's current liabilities.

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



Question 555  capital budgeting, CFFA

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

Project Data
Project life 2 years
Initial investment in equipment $8m
Depreciation of equipment per year for tax purposes $3m
Unit sales per year 10m
Sale price per unit $9
Variable cost per unit $4
Fixed costs per year, paid at the end of each year $2m
Tax rate 30%
 

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

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

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

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



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.



Question 658  CFFA, income statement, balance sheet, no explanation

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.



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

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



Question 74  WACC, capital structure, CAPM

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



Question 78  WACC, capital structure

A company issues a large amount of bonds to raise money for new projects of similar risk to the company's existing projects. The net present value (NPV) of the new projects is positive but small. Assume a classical tax system. Which statement is NOT correct?



Question 91  WACC, capital structure

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?



Question 94  leverage, capital structure, real estate

Your friend just bought a house for $400,000. He financed it using a $320,000 mortgage loan and a deposit of $80,000.

In the context of residential housing and mortgages, the 'equity' tied up in the value of a person's house is the value of the house less the value of the mortgage. So the initial equity your friend has in his house is $80,000. Let this amount be E, let the value of the mortgage be D and the value of the house be V. So ##V=D+E##.

If house prices suddenly fall by 10%, what would be your friend's percentage change in equity (E)? Assume that the value of the mortgage is unchanged and that no income (rent) was received from the house during the short time over which house prices fell.

Remember:

### r_{0\rightarrow1}=\frac{p_1-p_0+c_1}{p_0} ###

where ##r_{0-1}## is the return (percentage change) of an asset with price ##p_0## initially, ##p_1## one period later, and paying a cash flow of ##c_1## at time ##t=1##.



Question 98  capital structure, CAPM

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

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



Question 99  capital structure, interest tax shield, Miller and Modigliani, trade off theory of capital structure

A firm changes its capital structure by issuing a large amount of debt and using the funds to repurchase shares. Its assets are unchanged.

Assume that:

  • The firm and individual investors can borrow at the same rate and have the same tax rates.
  • The firm's debt and shares are fairly priced and the shares are repurchased at the market price, not at a premium.
  • There are no market frictions relating to debt such as asymmetric information or transaction costs.
  • Shareholders wealth is measured in terms of utiliity. Shareholders are wealth-maximising and risk-averse. They have a preferred level of overall leverage. Before the firm's capital restructure all shareholders were optimally levered.

According to Miller and Modigliani's theory, which statement is correct?



Question 104  CAPM, payout policy, capital structure, Miller and Modigliani, risk

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:



Question 114  WACC, capital structure, risk

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



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?



Question 116  capital structure, CAPM

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?



Question 301  leverage, capital structure, real estate

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.



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?



Question 376  leverage, capital structure, no explanation

Interest expense on debt is tax-deductible, but dividend payments on equity are not. or ?


Question 377  leverage, capital structure

Issuing debt doesn't give away control of the firm because debt holders can't cast votes to determine the company's affairs, such as at the annual general meeting (AGM), and can't appoint directors to the board. or ?


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 379  leverage, capital structure, payout policy

Companies must pay interest and principal payments to debt-holders. They're compulsory. But companies are not forced to pay dividends to share holders. or ?


Question 380  leverage, capital structure

The "interest expense" on a company's annual income statement is equal to the cash interest payments (but not principal payments) made to debt holders during the year. or ?


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?



Question 398  financial distress, capital raising, leverage, capital structure, NPV

A levered firm has 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.

In one year the firm's assets will be worth:

  • $13.2m with probability 0.5 in the good state of the world, or
  • $6.6m with probability 0.5 in the bad state of the world.

A new project presents itself which requires an investment of $2m and will provide a certain cash flow of $3.3m in one year.

The firm doesn't have any excess cash to make the initial $2m investment, but the funds can be raised from shareholders through a fairly priced rights issue. Ignore all transaction costs.

Should shareholders vote to proceed with the project and equity raising? What will be the gain in shareholder wealth if they decide to proceed?



Question 409  NPV, capital structure, capital budgeting

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##



Question 411  WACC, capital structure

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?



Question 454  NPV, capital structure, capital budgeting

A mining firm has just discovered a new mine. So far the news has been kept a secret.

The net present value of digging the mine and selling the minerals is $250 million, but $500 million of new equity and $300 million of new 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 equity and bond raising to shareholders simultaneously in the same announcement. The shares and bonds will be issued shortly after.

Once the announcement is made and the new shares and bonds are issued, what is the expected increase in the value of the firm's assets ##(\Delta V)##, market capitalisation of debt ##(\Delta D)## and market cap of equity ##(\Delta E)##? Assume that markets are semi-strong form efficient.

The triangle symbol ##\Delta## 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: ##\Delta V = \Delta D+ \Delta E##



Question 524  risk, expected and historical returns, bankruptcy or insolvency, capital structure, corporate financial decision theory, limited liability

Which of the following statements is NOT correct?



Question 531  bankruptcy or insolvency, capital structure, risk, limited liability

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.



Question 536  idiom, bond pricing, capital structure, leverage

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

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



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?



Question 567  stock split, capital structure

A company conducts a 4 for 3 stock split. What is the percentage change in the stock price and the number of shares outstanding? The answers are given in the same order.



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.



Question 618  capital structure, no explanation

Who owns a company's shares? The:



Question 800  leverage, portfolio return, risk, portfolio risk, capital structure, no explanation

Which of the following assets would you expect to have the highest required rate of return? All values are current market values.



Question 801  negative gearing, leverage, capital structure, no explanation

The following steps set out 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:



Question 802  negative gearing, leverage, capital structure, no explanation

Which of the following statements about ‘negative gearing’ is NOT correct?



Question 241  Miller and Modigliani, leverage, payout policy, diversification, NPV

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

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

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

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

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

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

Which of the above statement(s) are true?



Question 406  leverage, WACC, margin loan, portfolio return

One year ago you bought $100,000 of shares partly funded using a margin loan. The margin loan size was $70,000 and the other $30,000 was your own wealth or 'equity' in the share assets.

The interest rate on the margin loan was 7.84% pa.

Over the year, the shares produced a dividend yield of 4% pa and a capital gain of 5% pa.

What was the total return on your wealth? Ignore taxes, assume that all cash flows (interest payments and dividends) were paid and received at the end of the year, and all rates above are effective annual rates.

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 936  CAPM, WACC, IRR

You work for XYZ company and you’ve been asked to evaluate a new project which has double the systematic risk of the company’s other projects.

You use the Capital Asset Pricing Model (CAPM) formula and input the treasury yield ##(r_f )##, market risk premium ##(r_m-r_f )## and the company’s asset beta risk factor ##(\beta_{XYZ} )## into the CAPM formula which outputs a return.

This return that you’ve just found is:



Question 408  leverage, portfolio beta, portfolio risk, real estate, CAPM

You just bought a house worth $1,000,000. You financed it with an $800,000 mortgage loan and a deposit of $200,000.

You estimate that:

  • The house has a beta of 1;
  • The mortgage loan has a beta of 0.2.

What is the beta of the equity (the $200,000 deposit) that you have in your house?

Also, if the risk free rate is 5% pa and the market portfolio's return is 10% pa, what is the expected return on equity in your house? Ignore taxes, assume that all cash flows (interest payments and rent) were paid and received at the end of the year, and all rates are effective annual rates.



Question 506  leverage, accounting ratio

A firm has a debt-to-equity ratio of 25%. What is its debt-to-assets ratio?



Question 507  leverage, accounting ratio

A firm has a debt-to-equity ratio of 60%. What is its debt-to-assets ratio?



Question 663  leverage, accounting ratio

A firm has a debt-to-assets ratio of 20%. What is its debt-to-equity ratio?



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?

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 799  LVR, leverage, accounting ratio

In the home loan market, the acronym LVR stands for Loan to Valuation Ratio. If you bought a house worth one million dollars, partly funded by an $800,000 home loan, then your LVR was 80%. The LVR is equivalent to which of the following ratios?



Question 85  WACC, CAPM

A company has:

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

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



Question 97  WACC, no explanation

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.



Question 117  WACC

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

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

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

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



Question 302  WACC, CAPM

Which of the following statements about the weighted average cost of capital (WACC) is NOT correct?



Question 118  WACC

A company has:

  • 100 million ordinary shares outstanding which are trading at a price of $5 each. Market analysts estimated that the company's ordinary stock has a beta of 1.5. The risk-free rate is 5% and the market return is 10%.
  • 1 million preferred shares which have a face (or par) value of $100 and pay a constant annual dividend of 9% of par. The next dividend will be paid in one year. Assume that all preference dividends will be paid when promised. They currently trade at a price of $90 each.
  • Debentures that have a total face value of $200 million and a yield to maturity of 6% per annum. They are publicly traded and their market price is equal to 110% of their face value.

The corporate tax rate is 30%. All returns and yields are given as effective annual rates.

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



Question 983  corporate financial decision theory, Du Pont formula, accounting ratio

A company manager is thinking about the firm's book assets-to-equity ratio, also called the 'equity multiplier' in the Du Pont formula:

###\text{Equity multiplier} = \dfrac{\text{Total Assets}}{\text{Owners' Equity}}###

What's the name of the decision that the manager is thinking about? In other words, the assets-to-equity ratio is the main subject of what decision?

Note: Du Pont formula for analysing book return on equity:

###\begin{aligned} \text{ROE} &= \dfrac{\text{Net Profit}}{\text{Sales}} \times \dfrac{\text{Sales}}{\text{Total Assets}} \times \dfrac{\text{Total Assets}}{\text{Owners' Equity}} \\ &= \text{Net profit margin} \times \text{Total asset turnover} \times \text{Equity multiplier} \\ \end{aligned}###

Question 470  accounting ratio, no explanation

Which of the following statements is NOT correct?



Question 471  risk, accounting ratio

High risk firms in danger of bankruptcy tend to have:



Question 472  quick ratio, accounting ratio

A firm has current assets totaling $1.5b of which cash is $0.25b and inventories is $0.5b. Current liabilities total $2b of which accounts payable is $1b.

What is the firm's quick ratio, also known as the acid test ratio?



Question 490  expected and historical returns, accounting ratio

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



Question 495  risk, accounting ratio, no explanation

High risk firms in danger of bankruptcy tend to have:



Question 845  accounting ratio, no explanation

Safe firms with low chances of bankruptcy will tend to have:



Question 345  capital budgeting, break even, NPV

Project Data
Project life 10 yrs
Initial investment in factory $10m
Depreciation of factory per year $1m
Expected scrap value of factory at end of project $0
Sale price per unit $10
Variable cost per unit $6
Fixed costs per year, paid at the end of each year $2m
Interest expense per year 0
Tax rate 30%
Cost of capital per annum 10%
 

Notes

  1. The firm's current liabilities are forecast to stay at $0.5m. The firm's current assets (mostly inventory) is currently $1m, but is forecast to grow by $0.1m at the end of each year due to the project.
    At the end of the project, the current assets accumulated due to the project can be sold for the same price that they were bought.
  2. A marketing survey was used to forecast sales. It cost $1.4m which was just paid. The cost has been capitalised by the accountants and is tax-deductible over the life of the project, regardless of whether the project goes ahead or not. This amortisation expense is not included in the depreciation expense listed in the table above.

Assumptions

  • All cash flows occur at the start or end of the year as appropriate, not in the middle or throughout the year.
  • All rates and cash flows are real. The inflation rate is 3% pa.
  • All rates are given as effective annual rates.

Find the break even unit production (Q) per year to achieve a zero Net Income (NI) and Net Present Value (NPV), respectively. The answers below are listed in the same order.



Question 410  CAPM, capital budgeting

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##?



Question 458  capital budgeting, no explanation

Which of the following is NOT a valid method to estimate future revenues or costs in a pro-forma income statement when trying to value a company?



Question 485  capital budgeting, opportunity cost, sunk cost

A young lady is trying to decide if she should attend university or not.

The young lady's parents say that she must attend university because otherwise all of her hard work studying and attending school during her childhood was a waste.

What's the correct way to classify this item from a capital budgeting perspective when trying to decide whether to attend university?

The hard work studying at school in her childhood should be classified as:



Question 486  capital budgeting, opportunity cost, sunk cost

A young lady is trying to decide if she should attend university. Her friends say that she should go to university because she is more likely to meet a clever young man than if she begins full time work straight away.

What's the correct way to classify this item from a capital budgeting perspective when trying to find the Net Present Value of going to university rather than working?

The opportunity to meet a desirable future spouse should be classified as:



Question 487  capital budgeting, opportunity cost, sunk cost

A young lady is trying to decide if she should attend university or begin working straight away in her home town.

The young lady's grandma says that she should not go to university because she is less likely to marry the local village boy whom she likes because she will spend less time with him if she attends university.

What's the correct way to classify this item from a capital budgeting perspective when trying to decide whether to attend university?

The cost of not marrying the local village boy should be classified as:



Question 491  capital budgeting, opportunity cost, sunk cost

A man is thinking about taking a day off from his casual painting job to relax.

He just woke up early in the morning and he's about to call his boss to say that he won't be coming in to work.

But he's thinking about the hours that he could work today (in the future) which are:



Question 492  capital budgeting, opportunity cost, sunk cost

A man has taken a day off from his casual painting job to relax.

It's the end of the day and he's thinking about the hours that he could have spent working (in the past) which are now:



Question 655  capital budgeting, opportunity cost, sunk cost

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



Question 768  accounting terminology, book and market values, no explanation

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

Which of the following groups of items are NOT synonyms?



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

Which of the following statements is NOT correct?



Question 401  capital budgeting, CFFA

The hardest and most important aspect of business project valuation is the estimation of the:



Question 179  bond pricing, capital raising

A firm wishes to raise $20 million now. They will issue 8% pa semi-annual coupon bonds that will mature in 5 years and have a face value of $100 each. Bond yields are 6% pa, given as an APR compounding every 6 months, and the yield curve is flat.

How many bonds should the firm issue?



Question 194  bond pricing, capital raising

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

How many bonds should the firm issue?



Question 230  bond pricing, capital raising

A firm wishes to raise $10 million now. They will issue 6% pa semi-annual coupon bonds that will mature in 8 years and have a face value of $1,000 each. Bond yields are 10% pa, given as an APR compounding every 6 months, and the yield curve is flat.

How many bonds should the firm issue?



Question 544  bond pricing, capital raising, no explanation

A firm wishes to raise $10 million now. They will issue 6% pa semi-annual coupon bonds that will mature in 3 years and have a face value of $100 each. Bond yields are 5% pa, given as an APR compounding every 6 months, and the yield curve is flat.

How many bonds should the firm issue?



Question 625  dividend re-investment plan, capital raising

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



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.



Question 755  bond pricing, capital raising, no explanation

A firm wishes to raise $50 million now. They will issue 7% pa semi-annual coupon bonds that will mature in 6 years and have a face value of $100 each. Bond yields are 5% pa, given as an APR compounding every 6 months, and the yield curve is flat.

How many bonds should the firm issue?



Question 756  bond pricing, capital raising, no explanation

A firm wishes to raise $50 million now. They will issue 5% pa semi-annual coupon bonds that will mature in 3 years and have a face value of $100 each. Bond yields are 6% pa, given as an APR compounding every 6 months, and the yield curve is flat.

How many bonds should the firm issue?



Question 757  bond pricing, capital raising, no explanation

A firm wishes to raise $50 million now. They will issue 5% pa semi-annual coupon bonds that will mature in 10 years and have a face value of $100 each. Bond yields are 5% pa, given as an APR compounding every 6 months, and the yield curve is flat.

How many bonds should the firm issue?



Question 788  rights issue, capital raising

A firm wishes to raise $100 million now. The firm's current market value of equity is $300m and the market price per share is $5. They estimate that they'll be able to issue shares in a rights issue at a subscription price of $4. All answers are rounded to 6 decimal places. Ignore the time value of money and assume that all shareholders exercise their rights. Which of the following statements is NOT correct?



Question 789  rights issue, capital raising

A firm wishes to raise $30 million now. The firm's current market value of equity is $60m and the market price per share is $20. They estimate that they'll be able to issue shares in a rights issue at a subscription price of $15. Ignore the time value of money and assume that all shareholders exercise their rights. Which of the following statements is NOT correct?



Question 803  capital raising, rights issue, initial public offering, on market repurchase, no explanation

Which one of the following capital raisings or payouts involve the sale of shares to existing shareholders only?



Question 986  initial public offering, capital raising, no explanation

In an initial public offering (IPO):



Question 808  Markowitz portfolio theory, portfolio return

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.

Which of the following statements about this graph and Markowitz portfolio theory is NOT correct?

Image of CML graph



Question 809  Markowitz portfolio theory, CAPM, Jensens alpha, CML, systematic and idiosyncratic risk

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

Image of CML graph

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



Question 217  NPV, DDM, multi stage growth model

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 498  NPV, Annuity, perpetuity with growth, multi stage growth model

A business project is expected to cost $100 now (t=0), then pay $10 at the end of the third (t=3), fourth, fifth and sixth years, and then grow by 5% pa every year forever. So the cash flow will be $10.5 at the end of the seventh year (t=7), then $11.025 at the end of the eighth year (t=8) and so on perpetually. The total required return is 10℅ pa.

Which of the following formulas will NOT give the correct net present value of the project?



Question 763  multi stage growth model, DDM

A stock is expected to pay its first dividend of $20 in 3 years (t=3), which it will continue to pay for the next nine years, so there will be ten $20 payments altogether with the last payment in year 12 (t=12).

From the thirteenth year onward, the dividend is expected to be 4% more than the previous year, forever. So the dividend in the thirteenth year (t=13) will be $20.80, then $21.632 in year 14, and so on forever. The required return of the stock is 10% pa. All rates are effective annual rates. Calculate the current (t=0) stock price.



Question 935  real estate, NPV, perpetuity with growth, multi stage growth model, DDM

You're thinking of buying an investment property that costs $1,000,000. The property's rent revenue over the next year is expected to be $50,000 pa and rent expenses are $20,000 pa, so net rent cash flow is $30,000. Assume that net rent is paid annually in arrears, so this next expected net rent cash flow of $30,000 is paid one year from now.

The year after, net rent is expected to fall by 2% pa. So net rent at year 2 is expected to be $29,400 (=30,000*(1-0.02)^1).

The year after that, net rent is expected to rise by 1% pa. So net rent at year 3 is expected to be $29,694 (=30,000*(1-0.02)^1*(1+0.01)^1).

From year 3 onwards, net rent is expected to rise at 2.5% pa forever. So net rent at year 4 is expected to be $30,436.35 (=30,000*(1-0.02)^1*(1+0.01)^1*(1+0.025)^1).

Assume that the total required return on your investment property is 6% pa. Ignore taxes. All returns are given as effective annual rates.

What is the net present value (NPV) of buying the investment property?



Question 75  WACC, CAPM

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.



Question 66  CAPM, SML

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



Question 71  CAPM, risk

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



Question 72  CAPM, portfolio beta, portfolio risk

Portfolio Details
Stock Expected
return
Standard
deviation
Correlation Beta Dollars
invested
A 0.2 0.4 0.12 0.5 40
B 0.3 0.8 1.5 80
 

What is the beta of the above portfolio?



Question 76  CAPM, SML

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



Question 79  CAPM, risk

Which statement is the most correct?



Question 80  CAPM, risk, diversification

Diversification is achieved by investing in a large amount of stocks. What type of risk is reduced by diversification?



Question 86  CAPM

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



Question 90  CAPM, risk

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



Question 92  CAPM, SML, CML

Which statement(s) are correct?

(i) All stocks that plot on the Security Market Line (SML) are fairly priced.

(ii) All stocks that plot above the Security Market Line (SML) are overpriced.

(iii) All fairly priced stocks that plot on the Capital Market Line (CML) have zero idiosyncratic risk.

Select the most correct response:



Question 93  correlation, CAPM, systematic risk

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?



Question 106  CAPM

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



Question 110  CAPM, SML, NPV

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

Investment projects that plot above the SML would have:



Question 112  CAPM, risk

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



Question 231  CAPM

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



Question 232  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 5% pa and the market portfolio's expected return is 10% pa. All returns are effective annual rates.

What is the price of the stock now?



Question 235  SML, NPV, CAPM, risk

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

Investment projects that plot on the SML would have:



Question 244  CAPM, SML, NPV, risk

Examine the following graph which shows stocks' betas ##(\beta)## and expected returns ##(\mu)##:

Image of CAPM SML graph

Assume that the CAPM holds and that future expectations of stocks' returns and betas are correctly measured. Which statement is NOT correct?



Question 248  CAPM, DDM, income and capital returns

The total return of any asset can be broken down in different ways. One possible way is to use the dividend discount model (or Gordon growth model):

###p_0 = \frac{c_1}{r_\text{total}-r_\text{capital}}###

Which, since ##c_1/p_0## is the income return (##r_\text{income}##), can be expressed as:

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

So the total return of an asset is the income component plus the capital or price growth component.

Another way to break up total return is to use the Capital Asset Pricing Model:

###r_\text{total}=r_\text{f}+β(r_\text{m}- r_\text{f})###

###r_\text{total}=r_\text{time value}+r_\text{risk premium}###

So the risk free rate is the time value of money and the term ##β(r_\text{m}- r_\text{f})## is the compensation for taking on systematic risk.

Using the above theory and your general knowledge, which of the below equations, if any, are correct?

(I) ##r_\text{income}=r_\text{time value}##

(II) ##r_\text{income}=r_\text{risk premium}##

(III) ##r_\text{capital}=r_\text{time value}##

(IV) ##r_\text{capital}=r_\text{risk premium}##

(V) ##r_\text{income}+r_\text{capital}=r_\text{time value}+r_\text{risk premium}##

Which of the equations are correct?



Question 271  CAPM, option, risk, systematic risk, systematic and idiosyncratic risk

All things remaining equal, according to the capital asset pricing model, if the systematic variance of an asset increases, its required return will increase and its price will decrease.
If the idiosyncratic variance of an asset increases, its price will be unchanged.

What is the relationship between the price of a call or put option and the total, systematic and idiosyncratic variance of the underlying asset that the option is based on? Select the most correct answer.

Call and put option prices increase when the:



Question 326  CAPM

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



Question 617  systematic and idiosyncratic risk, risk, CAPM

A stock's required total return will increase when its:



Question 450  CAPM, risk, portfolio risk, no explanation

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?



Question 627  CAPM, SML, NPV, Jensens alpha

Image of CML SML graph

Assets A, B, M and ##r_f## are shown on the graphs above. Asset M is the market portfolio and ##r_f## is the risk free yield on government bonds. Which of the below statements is NOT correct?



Question 628  CAPM, SML, risk

Image of CML SML graph

Assets A, B, M and ##r_f## are shown on the graphs above. Asset M is the market portfolio and ##r_f## is the risk free yield on government bonds. Assume that investors can borrow and lend at the risk free rate. Which of the below statements is NOT correct?



Question 657  systematic and idiosyncratic risk, CAPM, no explanation

A stock's required total return will decrease when its:



Question 661  systematic and idiosyncratic risk, CAPM

A stock's total standard deviation of returns is 20% pa. The market portfolio's total standard deviation of returns is 15% pa. The beta of the stock is 0.8.

What is the stock's diversifiable standard deviation?



Question 669  beta, CAPM, risk

Which of the following is NOT a valid method for estimating the beta of a company's stock? Assume that markets are efficient, a long history of past data is available, the stock possesses idiosyncratic and market risk. The variances and standard deviations below denote total risks.



Question 672  CAPM, beta

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

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



Question 673  CAPM, beta, expected and historical returns

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

In the last 5 minutes, bad economic news was released showing a higher chance of recession. Over this time the share market fell by 1%. The risk free rate was unchanged.

What do you think was the stock's historical return over the last 5 minutes, given as an effective 5 minute rate?



Question 674  CAPM, beta, expected and historical returns

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

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

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



Question 777  CAPM, beta

The market's expected total return is 10% pa and the risk free rate is 5% pa, both given as effective annual rates.

A stock has a beta of 0.5.

In the last 5 minutes, the federal government unexpectedly raised taxes. Over this time the share market fell by 3%. The risk free rate was unchanged.

What do you think was the stock's historical return over the last 5 minutes, given as an effective 5 minute rate?



Question 778  CML, systematic and idiosyncratic risk, portfolio risk, CAPM, no explanation

The capital market line (CML) is shown in the graph below. The total standard deviation is denoted by σ and the expected return is μ. Assume that markets are efficient so all assets are fairly priced.

Image of CML graph

Which of the below statements is NOT correct?



Question 810  CAPM, systematic and idiosyncratic risk, market efficiency

Examine the graphs below. Assume that asset A is a single stock. Which of the following statements is NOT correct? Asset A:

Image of CML graph



Question 873  Sharpe ratio, Treynor ratio, Jensens alpha, SML, CAPM

Which of the following statements is NOT correct? Fairly-priced assets should:



Question 920  SML, CAPM, Sharpe ratio, Treynor ratio, Jensens alpha, no explanation

Over-priced assets should NOT:



Question 937  CAPM, SML

The market's expected total return is 10% pa and the risk free rate is 5% pa, both given as effective annual rates.

A stock has a beta of 0.7.

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



Question 938  CAPM, SML

The market's expected total return is 10% pa and the risk free rate is 5% pa, both given as effective annual rates.

A stock has a beta of 0.7.

In the last 5 minutes, bad economic news was released showing a higher chance of recession. Over this time the share market fell by 2%. The risk free rate was unchanged. What do you think was the stock's historical return over the last 5 minutes, given as an effective 5 minute rate?



Question 939  CAPM, systematic and idiosyncratic risk

A common phrase heard in financial markets is that ‘high risk investments deserve high returns’. To make this statement consistent with the Capital Asset Pricing Model (CAPM), a high amount of what specific type of risk deserves a high return?

Investors deserve high returns when they buy assets with high:



Question 940  CAPM, DDM

A stock has a beta of 1.2. Its next dividend is expected to be $20, paid one year from now.

Dividends are expected to be paid annually and grow by 1.5% pa forever.

Treasury bonds yield 3% pa and the market portfolio's expected return is 7% pa. All returns are effective annual rates.

What is the price of the stock now?



Question 923  omitted variable bias, CAPM, single factor model, single index model, no explanation

Capital Asset Pricing Model (CAPM) and the Single Index Model (SIM) are single factor models whose only risk factor is the market portfolio’s return. Say a Taxi company and an Umbrella company are influenced by two factors, the market portfolio return and rainfall. When it rains, both the Taxi and Umbrella companies’ stock prices do well. When there’s no rain, both do poorly. Assume that rainfall risk is a systematic risk that cannot be diversified and that rainfall has zero correlation with the market portfolio’s returns.

Which of the following statements about these two stocks is NOT correct?

The CAPM and SIM:



Question 875  omitted variable bias, systematic and idiosyncratic risk, CAPM, single factor model, two factor model

The Capital Asset Pricing Model (CAPM) and the Single Index Model (SIM) are single factor models whose only risk factor is the market portfolio’s return. Say a Solar electricity generator company and a Beach bathing chair renting company are influenced by two factors, the market portfolio return and cloud cover in the sky. When it's sunny and not cloudy, both the Solar and Beach companies’ stock prices do well. When there’s dense cloud cover and no sun, both do poorly. Assume that cloud coverage risk is a systematic risk that cannot be diversified and that cloud cover has zero correlation with the market portfolio’s returns.

Which of the following statements about these two stocks is NOT correct?

The CAPM and SIM:



Question 807  market efficiency, expected and historical returns, CAPM, beta, systematic risk, no explanation

You work in Asia and just woke up. It looked like a nice day but then you read the news and found out that last night the American share market fell by 10% while you were asleep due to surprisingly poor macro-economic world news. You own a portfolio of liquid stocks listed in Asia with a beta of 1.6. When the Asian equity markets open, what do you expect to happen to your share portfolio? Assume that the capital asset pricing model (CAPM) is correct and that the market portfolio contains all shares in the world, of which American shares are a big part. Your portfolio beta is measured against this world market portfolio.

When the Asian equity market opens for trade, you would expect your portfolio value to:



Question 416  real estate, market efficiency, income and capital returns, DDM, CAPM

A residential real estate investor believes that house prices will grow at a rate of 5% pa and that rents will grow by 2% pa forever.

All rates are given as nominal effective annual returns. Assume that:

  • His forecast is true.
  • Real estate is and always will be fairly priced and the capital asset pricing model (CAPM) is true.
  • Ignore all costs such as taxes, agent fees, maintenance and so on.
  • All rental income cash flow is paid out to the owner, so there is no re-investment and therefore no additions or improvements made to the property.
  • The non-monetary benefits of owning real estate and renting remain constant.

Which one of the following statements is NOT correct? Over time:



Question 338  market efficiency, CAPM, opportunity cost, technical analysis

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.



Question 729  book and market values, balance sheet, no explanation

If a firm makes a profit and pays no dividends, which of the firm’s accounts will increase?



Question 737  financial statement, balance sheet, income statement

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



Question 738  financial statement, balance sheet, income statement

Where can a private firm's market value of equity be found? It can be sourced from the company's:



Question 73  portfolio risk, standard deviation

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.



Question 111  portfolio risk, correlation

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



Question 83  portfolio risk, standard deviation

Portfolio Details
Stock Expected
return
Standard
deviation
Correlation ##(\rho_{A,B})## Dollars
invested
A 0.1 0.4 0.5 60
B 0.2 0.6 140
 

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



Question 293  covariance, correlation, portfolio risk

All things remaining equal, the higher the correlation of returns between two stocks:



Question 283  portfolio risk, correlation, needs refinement

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.



Question 285  covariance, portfolio risk

Two risky stocks A and B comprise an equal-weighted portfolio. The correlation between the stocks' returns is 70%.

If the variance of stock A increases but the:

  • Prices and expected returns of each stock stays the same,
  • Variance of stock B's returns stays the same,
  • Correlation of returns between the stocks stays the same.

Which of the following statements is NOT correct?



Question 556  portfolio risk, portfolio return, standard deviation

An investor wants to make a portfolio of two stocks A and B with a target expected portfolio return of 12% pa.

  • Stock A has an expected return of 10% pa and a standard deviation of 20% pa.
  • Stock B has an expected return of 15% pa and a standard deviation of 30% pa.

The correlation coefficient between stock A and B's expected returns is 70%.

What will be the annual standard deviation of the portfolio with this 12% pa target return?



Question 718  arithmetic and geometric averages

The symbol ##\text{GDR}_{0\rightarrow 1}## represents a stock's gross discrete return per annum over the first year. ##\text{GDR}_{0\rightarrow 1} = P_1/P_0##. The subscript indicates the time period that the return is mentioned over. So for example, ##\text{AAGDR}_{1 \rightarrow 3}## is the arithmetic average GDR measured over the two year period from years 1 to 3, but it is expressed as a per annum rate.

Which of the below statements about the arithmetic and geometric average GDR is NOT correct?



Question 719  mean and median returns, return distribution, arithmetic and geometric averages, continuously compounding rate

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



Question 720  mean and median returns, return distribution, arithmetic and geometric averages, continuously compounding rate

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.



Question 921  utility, return distribution, log-normal distribution, arithmetic and geometric averages, no explanation

Who was the first theorist to propose the idea of ‘expected utility’?



Question 721  mean and median returns, return distribution, arithmetic and geometric averages, continuously compounding rate

Fred owns some Commonwealth Bank (CBA) shares. He has calculated CBA’s monthly returns for each month in the past 20 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 1% per month using this formula:

###\bar{r}_\text{monthly}= \dfrac{ \displaystyle\sum\limits_{t=1}^T{\left( r_\text{t monthly} \right)} }{T} =0.01=1\% \text{ per month}###

He also found the standard deviation of these monthly returns which was 5% 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} =0.05=5\%\text{ per month}###

Which of the below statements about Fred’s CBA shares is NOT correct? Assume that the past historical average return is the true population average of future expected returns.



Question 46  NPV, annuity due

The phone company Telstra have 2 mobile service plans on offer which both have the same amount of phone call, text message and internet data credit. Both plans have a contract length of 24 months and the monthly cost is payable in advance. The only difference between the two plans is that one is a:

  • 'Bring Your Own' (BYO) mobile service plan, costing $50 per month. There is no phone included in this plan. The other plan is a:
  • 'Bundled' mobile service plan that comes with the latest smart phone, costing $71 per month. This plan includes the latest smart phone.

Neither plan has any additional payments at the start or end.

The only difference between the plans is the phone, so what is the implied cost of the phone as a present value?

Assume that the discount rate is 2% per month given as an effective monthly rate, the same high interest rate on credit cards.



Question 145  NPV, APR, annuity due

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

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



Question 346  NPV, annuity due

Your poor friend asks to borrow some money from you. He would like $1,000 now (t=0) and every year for the next 5 years, so there will be 6 payments of $1,000 from t=0 to t=5 inclusive. In return he will pay you $10,000 in seven years from now (t=7).

What is the net present value (NPV) of lending to your friend?

Assume that your friend will definitely pay you back so the loan is risk-free, and that the yield on risk-free government debt is 10% pa, given as an effective annual rate.



Question 530  Annuity, annuity due, no explanation

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

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



Question 761  NPV, annuity due, no explanation

The phone company Optus have 2 mobile service plans on offer which both have the same amount of phone call, text message and internet data credit. Both plans have a contract length of 24 months and the monthly cost is payable in advance. The only difference between the two plans is that one is a:

  • 'Bring Your Own' (BYO) mobile service plan, costing $80 per month. There is no phone included in this plan. The other plan is a:
  • 'Bundled' mobile service plan that comes with the latest smart phone, costing $100 per month. This plan includes the latest smart phone.

Neither plan has any additional payments at the start or end. Assume that the discount rate is 1% per month given as an effective monthly rate.

The only difference between the plans is the phone, so what is the implied cost of the phone as a present value? Given that the latest smart phone actually costs $600 to purchase outright from another retailer, should you commit to the BYO plan or the bundled plan?



Question 984  principal agent problem, moral hazard, asymmetric information, no explanation

When does the ‘principal-agent problem’ occur? Is it when:

I. The principal has conflicting incentives (moral hazard);

II. The agent has conflicting incentives (moral hazard);

III. The principal has incomplete information about the agent (asymmetric information); or

IV. The agent has incomplete information about the principal (asymmetric information)?

The principal-agent problem occurs when statements:



Question 65  annuity with growth, needs refinement

Which of the below formulas gives the present value of an annuity with growth?


Hint: The equation of a perpetuity without growth is: ###V_\text{0, perp without growth} = \frac{C_\text{1}}{r}###

The formula for the present value of an annuity without growth is derived from the formula for a perpetuity without growth.

The idea is than an annuity with T payments from t=1 to T inclusive is equivalent to a perpetuity starting at t=1 with fixed positive cash flows, plus a perpetuity starting T periods later (t=T+1) with fixed negative cash flows. The positive and negative cash flows after time period T cancel each other out, leaving the positive cash flows between t=1 to T, which is the annuity.

###\begin{aligned} V_\text{0, annuity} &= V_\text{0, perp without growth from t=1} - V_\text{0, perp without growth from t=T+1} \\ &= \dfrac{C_\text{1}}{r} - \dfrac{ \left( \dfrac{C_\text{T+1}}{r} \right) }{(1+r)^T} \\ &= \dfrac{C_\text{1}}{r} - \dfrac{ \left( \dfrac{C_\text{1}}{r} \right) }{(1+r)^T} \\ &= \dfrac{C_\text{1}}{r}\left(1 - \dfrac{1}{(1+r)^T}\right) \\ \end{aligned}###

The equation of a perpetuity with growth is:

###V_\text{0, perp with growth} = \dfrac{C_\text{1}}{r-g}###

Question 893  balance of payments, current account

This question is about the Balance of Payments. Australia's current account as a percent of nominal gross domestic product (GDP) per annum is shown in the graph below.

Assume that all foreign and domestic assets are either debt which makes interest income or equity which makes dividend income, and vice versa for liabilities which cost interest and dividend payments, respectively.

Which of the following statements is NOT correct?



Question 776  market efficiency, systematic and idiosyncratic risk, beta, income and capital returns

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



Question 412  enterprise value, no explanation

A large proportion of a levered firm's assets is cash held at the bank. The firm is financed with half equity and half debt.

Which of the following statements about this firm's enterprise value (EV) and total asset value (V) is NOT correct?



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?



Question 445  financing decision, corporate financial decision theory

The financing decision primarily affects which part of a business?



Question 95  interest tax shield

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##



Question 240  negative gearing, interest tax shield

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

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

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



Question 771  debt terminology, interest expense, interest tax shield, credit risk, no explanation

You deposit money into a bank account. Which of the following statements about this deposit is NOT correct?



Question 127  interest expense

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?



Question 43  pay back period

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?



Question 52  IRR, pay back period

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



Question 60  pay back period

The required return of a project is 10%, given as an effective annual rate.

What is the payback period of the project in years?

Assume that the cash flows shown in the table are received smoothly over the year. So the $121 at time 2 is actually earned smoothly from t=1 to t=2.

Project Cash Flows
Time (yrs) Cash flow ($)
0 -100
1 11
2 121
 



Question 175  pay back period, no explanation

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?



Question 182  NPV, IRR, pay back period

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



Question 190  pay back period

A project has the following cash flows:

Project Cash Flows
Time (yrs) Cash flow ($)
0 -400
1 0
2 500
 

What is the payback period of the project in years?

Normally cash flows are assumed to happen at the given time. But here, assume that the cash flows are received smoothly over the year. So the $500 at time 2 is actually earned smoothly from t=1 to t=2.



Question 191  NPV, IRR, profitability index, pay back period

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



Question 220  pay back period, no explanation

A project has the following cash flows. Normally cash flows are assumed to happen at the given time. But here, assume that the cash flows are received smoothly over the year. So the $105 at time 2 is actually earned smoothly from t=1 to t=2:

Project Cash Flows
Time (yrs) Cash flow ($)
0 -90
1 30
2 105
 

What is the payback period of the project in years?



Question 489  NPV, IRR, pay back period, DDM

A firm is considering a business project which costs $11m now and is expected to pay a constant $1m at the end of every year forever.

Assume that the initial $11m cost is funded using the firm's existing cash so no new equity or debt will be raised. The cost of capital is 10% pa.

Which of the following statements about net present value (NPV), internal rate of return (IRR) and payback period is NOT correct?



Question 496  NPV, IRR, pay back period

A firm is considering a business project which costs $10m now and is expected to pay a single cash flow of $12.1m in two years.

Assume that the initial $10m cost is funded using the firm's existing cash so no new equity or debt will be raised. The cost of capital is 10% pa.

Which of the following statements about net present value (NPV), internal rate of return (IRR) and payback period is NOT correct?



Question 501  NPV, IRR, pay back period

The below graph shows a project's net present value (NPV) against its annual discount rate.

Which of the following statements is NOT correct?



Question 781  NPV, IRR, pay back period

You're considering a business project which costs $11m now and is expected to pay a single cash flow of $11m in one year. So you pay $11m now, then one year later you receive $11m.

Assume that the initial $11m cost is funded using the your firm's existing cash so no new equity or debt will be raised. The cost of capital is 10% pa.

Which of the following statements about the net present value (NPV), internal rate of return (IRR) and payback period is NOT correct?



Question 746  pay back period

A stock is expected to pay a dividend of $1 in one year. Its future annual dividends are expected to grow by 10% pa. So the first dividend of $1 is in one year, and the year after that the dividend will be $1.1 (=1*(1+0.1)^1), and a year later $1.21 (=1*(1+0.1)^2) and so on forever.

Its required total return is 30% pa. The total required return and growth rate of dividends are given as effective annual rates. The stock is fairly priced.

Calculate the pay back period of buying the stock and holding onto it forever, assuming that the dividends are received as at each time, not smoothly over each year.



Question 475  payout ratio, dividend, no explanation

The below screenshot of Commonwealth Bank of Australia's (CBA) details were taken from the Google Finance website on 7 Nov 2014. Some information has been deliberately blanked out.

Image of CBA on Google finance on 7 Nov 2014

What was CBA's approximate payout ratio over the 2014 financial year?

Note that the firm's interim and final dividends were $1.83 and $2.18 respectively over the 2014 financial year.



Question 484  payout ratio, dividend, no explanation

The below screenshot of Microsoft's (MSFT) details were taken from the Google Finance website on 28 Nov 2014. Some information has been deliberately blanked out.

Image of MSFT on Google finance on 28 Nov 2014

What was MSFT's approximate payout ratio over the last year?

Note that MSFT's past four quarterly dividends were $0.31, $0.28, $0.28 and $0.28.



Question 488  income and capital returns, payout policy, payout ratio, DDM

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?



Question 212  rights issue

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.

  • 17/06/2009. Shares trade ex-rights. Rights trading commences.

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.



Question 214  rights issue

In late 2003 the listed bank ANZ announced a 2-for-11 rights issue to fund the takeover of New Zealand bank NBNZ. Below is the chronology of events:

  • 23/10/2003. Share price closes at $18.30.

  • 24/10/2003. 2-for-11 rights issue announced at a subscription price of $13. The proceeds of the rights issue will be used to acquire New Zealand bank NBNZ. Trading halt announced in morning before market opens.

  • 28/10/2003. Trading halt lifted. Last (and only) day that shares trade cum-rights. Share price opens at $18.00 and closes at $18.14.

  • 29/10/2003. Shares trade ex-rights.

All things remaining equal, what would you expect ANZ's stock price to open at on the first day that it trades ex-rights (29/10/2003)? Ignore the time value of money since time is negligibly short. Also ignore taxes.



Question 513  stock split, reverse stock split, stock dividend, bonus issue, rights issue

Which of the following statements is NOT correct?



Question 812  rights issue

A firm is about to conduct a 2-for-7 rights issue with a subscription price of $10 per share. They haven’t announced the capital raising to the market yet and the share price is currently $13 per share. Assume that every shareholder will exercise their rights, the cash raised will simply be put in the bank, and the rights issue is completed so quickly that the time value of money can be ignored. Disregard signalling, taxes and agency-related effects.

Which of the following statements about the rights issue is NOT correct? After the rights issue is completed:



Question 461  book and market values, ROE, ROA, market efficiency

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.



Question 289  DDM, expected and historical returns, ROE

In the dividend discount model:

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

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



Question 896  comparative advantage in trade, production possibilities curve, no explanation

Adam and Bella are the only people on a remote island. Their production possibility curves are shown in the graph.

Which of the following statements is NOT correct?



Question 735  debt terminology

You deposit money into a bank. Which of the following statements is NOT correct? You:



Question 736  debt terminology

You bought a house, primarily funded using a home loan from a bank. Which of the following statements is NOT correct?



Question 910  money market

Which of the following is NOT a money market security?



Question 858  indirect security, intermediated finance, no explanation

Which of the following transactions involves an ‘indirect security’ using a ‘financial intermediary’?



Question 467  book and market values

Which of the following statements about book and market equity is NOT correct?



Question 879  margin loan, Basel accord

The risk-weight on "Margin lending against listed instruments on recognised exchanges" is 20% according to APRA's interpretation of the Basel 3 Accord in 'Prudential Standard APS 112 Capital Adequacy: Standardised Approach to Credit Risk, Attachment A: Risk-weights for on-balance sheet assets'.

A bank is considering lending a $100,000 margin loan secured by an ASX-listed stock. How much regulatory capital will the bank require to grant this loan under the Basel 3 Accord? Ignore the capital conservation buffer and the off-balance sheet exposure.



Question 900  Basel accord

Which of the following statements about the Basel 3 minimum capital requirements is NOT correct? Common equity tier 1 (CET1) comprises the highest quality components of capital that fully satisfy all of the following characteristics:



Question 901  Basel accord

The below graph from the RBA shows the phase-in of the Basel 3 minimum regulatory capital requirements under the Basel Committee on Banking Supervision (BCBS) on the left panel and in Australia under the Australian Prudential Regulatory Authority (APRA) on the right panel.

Which of the following statements about the Basel 3 minimum regulatory capital requirements as at 2019 is NOT correct? All minimum amounts exclude the 2.5% counter-cyclical buffer.

The Basel 3 minimum regulatory capital requirement as a percent of Risk Weighted Assets (RWA) is:



Question 902  Basel accord

Below is a table of the 'Risk-weights for residential mortgages' as shown in APRA Basel 3 Prudential Standard APS 112 Capital Adequacy: Standardised Approach to Credit Risk January 2013.

LVR (%)

Standard eligible mortgages

Non-standard eligible mortgages

 

Risk-weight (no mortgage insurance)

%

Risk-weight (with at least 40% of the mortgage insured by an acceptable LMI)

%

Risk-weight (no mortgage insurance)

%

Risk-weight (with at least 40% of the mortgage insured by an acceptable LMI)

%

0 – 60

35

35

50

35

60.01 – 80

35

35

75

50

80.01 – 90

50

35

100

75

90.01 – 100

75

50

100

75

> 100.01

100

75

100

100

A bank is considering granting a home loan to a man to buy a house worth $1.25 million using his own funds and the loan. The loan would be standard with no lenders mortgage insurance (LMI) and an LVR of 80%.

What is the minimum regulatory capital that the bank requires to grant the home loan under the Basel 3 Accord? Ignore the capital conservation buffer.



Question 981  margin loan, Basel accord, credit conversion factor

Margin loans secured by listed stock have a Basel III risk weight of 20%.

For margin loans that cannot be immediately cancelled by banks and asked to be repaid, the credit conversion factor (CCF) is 20%.

Suppose you have a stock portfolio worth $500,000, financed by:

  • $300,000 of your own money; and
  • $200,000 of the bank’s funds in the form of a margin loan which can only be cancelled by the bank after 5 days notice. The margin loan’s maximum LVR is 70%.

How much regulatory capital must the bank hold due to your margin loan? Assume that the bank wishes to pay dividends to its shareholders, so include the 2.5% capital conservation buffer in your calculations.



Question 942  dividend date, ex dividend date

To receive the dividend you must own the stock when the market closes on which date?



Question 943  dividend date, ex dividend date

On which date would the stock price increase if the dividend and earnings are higher than expected?



Question 856  credit terms, no explanation

Your supplier’s credit terms are "1/10 net 30". Which of the following statements about these credit terms is NOT correct?

If you intend to buy an item from your supplier for a tag price of $100 and you:



Question 448  franking credit, personal tax on dividends, imputation 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 Australian imputation tax system applies because the company generates all of its income in Australia and pays corporate tax to the Australian Tax Office. Therefore all of the company's dividends are fully franked. The sole shareholder is an Australian for tax purposes and can therefore use the franking credits to offset his personal income tax liability.

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



Question 469  franking credit, personal tax on dividends, imputation tax system, no explanation

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

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



Question 494  franking credit, personal tax on dividends, imputation tax system

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?



Question 624  franking credit, personal tax on dividends, imputation tax system, no explanation

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



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?



Question 309  stock pricing, ex dividend date

A company announces that it will pay a dividend, as the market expected. The company's shares trade on the stock exchange which is open from 10am in the morning to 4pm in the afternoon each weekday. When would the share price be expected to fall by the amount of the dividend? Ignore taxes.

The share price is expected to fall during the:



Question 497  income and capital returns, DDM, ex dividend date

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?



Question 748  income and capital returns, DDM, ex dividend date

A stock will pay you a dividend of $2 tonight if you buy it today.

Thereafter the annual dividend is expected to grow by 3% pa, so the next dividend after the $2 one tonight will be $2.06 in one year, then in two years it will be $2.1218 and so on. The stock's required return is 8% pa.

What is the stock price today and what do you expect the stock price to be tomorrow, approximately?



Question 944  stock split, bonus issue, stock dividend

A 2-for-1 stock split is equivalent to a 1-for-1 bonus issue or a 100% stock dividend. or ?


Question 945  stock split, bonus issue, stock dividend

A 3-for-2 stock split is equivalent to a 1-for-2 bonus issue or a 200% stock dividend. or ?


Question 946  stock split, bonus issue, stock dividend

A 1-for-4 bonus issue is equivalent to a 4-for-1 stock split or a 25% stock dividend. or ?


Question 961  stock split, bonus issue

Which one of the following statements is NOT correct? A 1-for-4 bonus issue:



Question 109  credit rating, credit risk

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



Question 120  credit risk, payout policy

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

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



Question 197  credit risk

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?



Question 221  credit risk

You're considering making an investment in a particular company. They have preference shares, ordinary shares, senior debt and junior debt.

Which is the safest investment? Which will give the highest returns?



Question 798  idiom, diversification, market efficiency, sunk cost, no explanation

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



Question 822  option, sunk cost, no explanation

When does a European option's last-traded market price become a sunk cost?



Question 503  DDM, NPV, stock pricing

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

The total required return is 10% pa.

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



Question 50  DDM, stock pricing, inflation, real and nominal returns and cash flows

Most listed Australian companies pay dividends twice per year, the 'interim' and 'final' dividends, which are roughly 6 months apart.

You are an equities analyst trying to value the company BHP. You decide to use the Dividend Discount Model (DDM) as a starting point, so you study BHP's dividend history and you find that BHP tends to pay the same interim and final dividend each year, and that both grow by the same rate.

You expect BHP will pay a $0.55 interim dividend in six months and a $0.55 final dividend in one year. You expect each to grow by 4% next year and forever, so the interim and final dividends next year will be $0.572 each, and so on in perpetuity.

Assume BHP's cost of equity is 8% pa. All rates are quoted as nominal effective rates. The dividends are nominal cash flows and the inflation rate is 2.5% pa.

What is the current price of a BHP share?



Question 355  DDM, stock pricing

Stocks in the United States usually pay quarterly dividends. For example, the retailer Wal-Mart Stores paid a $0.47 dividend every quarter over the 2013 calendar year and plans to pay a $0.48 dividend every quarter over the 2014 calendar year.

Using the dividend discount model and net present value techniques, calculate the stock price of Wal-Mart Stores assuming that:

  • The time now is the beginning of January 2014. The next dividend of $0.48 will be received in 3 months (end of March 2014), with another 3 quarterly payments of $0.48 after this (end of June, September and December 2014).
  • The quarterly dividend will increase by 2% every year, but each quarterly dividend over the year will be equal. So each quarterly dividend paid in 2015 will be $0.4896 (##=0.48×(1+0.02)^1##), with the first at the end of March 2015 and the last at the end of December 2015. In 2016 each quarterly dividend will be $0.499392 (##=0.48×(1+0.02)^2##), with the first at the end of March 2016 and the last at the end of December 2016, and so on forever.
  • The total required return on equity is 6% pa.
  • The required return and growth rate are given as effective annual rates.
  • All cash flows and rates are nominal. Inflation is 3% pa.
  • Dividend payment dates and ex-dividend dates are at the same time.
  • Remember that there are 4 quarters in a year and 3 months in a quarter.

What is the current stock price?



Question 365  DDM, stock pricing

Stocks in the United States usually pay quarterly dividends. For example, the software giant Microsoft paid a $0.23 dividend every quarter over the 2013 financial year and plans to pay a $0.28 dividend every quarter over the 2014 financial year.

Using the dividend discount model and net present value techniques, calculate the stock price of Microsoft assuming that:

  • The time now is the beginning of July 2014. The next dividend of $0.28 will be received in 3 months (end of September 2014), with another 3 quarterly payments of $0.28 after this (end of December 2014, March 2015 and June 2015).
  • The quarterly dividend will increase by 2.5% every year, but each quarterly dividend over the year will be equal. So each quarterly dividend paid in the financial year beginning in September 2015 will be $ 0.287 ##(=0.28×(1+0.025)^1)##, with the last at the end of June 2016. In the next financial year beginning in September 2016 each quarterly dividend will be $0.294175 ##(=0.28×(1+0.025)^2)##, with the last at the end of June 2017, and so on forever.
  • The total required return on equity is 6% pa.
  • The required return and growth rate are given as effective annual rates.
  • Dividend payment dates and ex-dividend dates are at the same time.
  • Remember that there are 4 quarters in a year and 3 months in a quarter.

What is the current stock price?



Question 960  DDM, stock pricing

You are an equities analyst trying to value the equity of the Australian supermarket conglomerate Woolworths, with ticker WOW. In Australia, listed companies like Woolworths tend to pay dividends every 6 months. The payment around September is the final dividend and the payment around March is called the interim dividend. Both occur annually.

  • Today is mid-November 2018.
  • WOW's last final dividend of $0.50 was two months ago in mid-September 2018.
  • WOW's last interim dividend of $0.43 was eight months ago in mid-March 2018.
  • Judging by the dividend history and WOW's prospects, you judge that the growth rate in the dividends will be 3% pa forever.
  • Assume that WOW's total cost of equity is 6.5% pa. All rates are quoted as nominal effective rates.
  • The dividends are nominal cash flows and the inflation rate is 2.5% pa.

What should be the current share price of WOW?



Question 535  DDM, real and nominal returns and cash flows, stock pricing

You are an equities analyst trying to value the equity of the Australian telecoms company Telstra, with ticker TLS. In Australia, listed companies like Telstra tend to pay dividends every 6 months. The payment around August is called the final dividend and the payment around February is called the interim dividend. Both occur annually.

  • Today is mid-March 2015.
  • TLS's last interim dividend of $0.15 was one month ago in mid-February 2015.
  • TLS's last final dividend of $0.15 was seven months ago in mid-August 2014.

Judging by TLS's dividend history and prospects, you estimate that the nominal dividend growth rate will be 1% pa. Assume that TLS's total nominal cost of equity is 6% pa. The dividends are nominal cash flows and the inflation rate is 2.5% pa. All rates are quoted as nominal effective annual rates. Assume that each month is exactly one twelfth (1/12) of a year, so you can ignore the number of days in each month.

Calculate the current TLS share price.



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.



Question 988  variance, covariance, beta, CAPM, risk, no explanation

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?



Question 989  PE ratio, Multiples valuation, leverage, accounting ratio

A firm has 20 million shares, earnings (or net income) of $100 million per annum and a 60% debt-to-equity ratio where both the debt and asset values are market values rather than book values. Similar firms have a PE ratio of 12.

Which of the below statements is NOT correct based on a PE multiples valuation?



Question 990  Multiples valuation, EV to EBITDA ratio, enterprise value

A firm has:

2 million shares;

$200 million EBITDA expected over the next year;

$100 million in cash (not included in EV);

1/3 market debt-to-assets ratio is (market assets = EV + cash);

4% pa expected dividend yield over the next year, paid annually with the next dividend expected in one year;

2% pa expected dividend growth rate;

40% expected payout ratio over the next year;

10 times EV/EBITDA ratio.

30% corporate tax rate.

The stock can be valued using the EV/EBITDA multiple, dividend discount model, Gordon growth model or PE multiple. Which of the below statements is NOT correct based on an EV/EBITDA multiple valuation?



Question 49  inflation, real and nominal returns and cash flows, APR, effective rate

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?



Question 58  NPV, inflation, real and nominal returns and cash flows, Annuity

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

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

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

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

The Net Present Value is:



Question 64  inflation, real and nominal returns and cash flows, APR, effective rate

In Germany, nominal yields on semi-annual coupon paying Government Bonds with 2 years until maturity are currently 0.04% pa.

The inflation rate is currently 1.4% pa, given as an APR compounding per quarter. The inflation rate is not expected to change over the next 2 years.

What is the real yield on these bonds, given as an APR compounding every 6 months?



Question 155  inflation, real and nominal returns and cash flows, Loan, effective rate conversion

You are a banker about to grant a 2 year loan to a customer. The loan's principal and interest will be repaid in a single payment at maturity, sometimes called a zero-coupon loan, discount loan or bullet loan.

You require a real return of 6% pa over the two years, given as an effective annual rate. Inflation is expected to be 2% this year and 4% next year, both given as effective annual rates.

You judge that the customer can afford to pay back $1,000,000 in 2 years, given as a nominal cash flow. How much should you lend to her right now?



Question 180  equivalent annual cash flow, inflation, real and nominal returns and cash flows

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.



Question 210  real estate, inflation, real and nominal returns and cash flows, income and capital returns

Assume that the Gordon Growth Model (same as the dividend discount model or perpetuity with growth formula) is an appropriate method to value real estate.

The rule of thumb in the real estate industry is that properties should yield a 5% pa rental return. Many investors also regard property to be as risky as the stock market, therefore property is thought to have a required total return of 9% pa which is the average total return on the stock market including dividends.

Assume that all returns are effective annual rates and they are nominal (not reduced by inflation). Inflation is expected to be 2% pa.

You're considering purchasing an investment property which has a rental yield of 5% pa and you expect it to have the same risk as the stock market. Select the most correct statement about this property.



Question 239  income and capital returns, inflation, real and nominal returns and cash flows, interest only loan

A bank grants a borrower an interest-only residential mortgage loan with a very large 50% deposit and a nominal interest rate of 6% that is not expected to change. Assume that inflation is expected to be a constant 2% pa over the life of the loan. Ignore credit risk.

From the bank's point of view, what is the long term expected nominal capital return of the loan asset?



Question 278  inflation, real and nominal returns and cash flows

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

After one year, would you be able to buy , exactly the as or than today with the money in this account?


Question 295  inflation, real and nominal returns and cash flows, NPV

When valuing assets using discounted cash flow (net present value) methods, it is important to consider inflation. To properly deal with inflation:

(I) Discount nominal cash flows by nominal discount rates.

(II) Discount nominal cash flows by real discount rates.

(III) Discount real cash flows by nominal discount rates.

(IV) Discount real cash flows by real discount rates.

Which of the above statements is or are correct?



Question 353  income and capital returns, inflation, real and nominal returns and cash flows, real estate

A residential investment property has an expected nominal total return of 6% pa and nominal capital return of 3% pa.

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

What are the property's expected real total, capital and income returns? The answer choices below are given in the same order.



Question 363  income and capital returns, inflation, real and nominal returns and cash flows, real estate

A residential investment property has an expected nominal total return of 8% pa and nominal capital return of 3% pa.

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

What are the property's expected real total, capital and income returns? The answer choices below are given in the same order.



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.



Question 522  income and capital returns, real and nominal returns and cash flows, inflation, real estate

A residential investment property has an expected nominal total return of 6% pa and nominal capital return of 2.5% pa. Inflation is expected to be 2.5% pa.

All of the above are effective nominal rates and investors believe that they will stay the same in perpetuity.

What are the property's expected real total, capital and income returns?

The answer choices below are given in the same order.



Question 523  income and capital returns, real and nominal returns and cash flows, inflation

A low-growth mature stock has an expected nominal total return of 6% pa and nominal capital return of 2% pa. Inflation is expected to be 3% pa.

All of the above are effective nominal rates and investors believe that they will stay the same in perpetuity.

What are the stock's expected real total, capital and income returns?

The answer choices below are given in the same order.



Question 525  income and capital returns, real and nominal returns and cash flows, inflation

Which of the following statements about cash in the form of notes and coins is NOT correct? Assume that inflation is positive.

Notes and coins:



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?



Question 529  DDM, real and nominal returns and cash flows, inflation, real estate, no explanation

If housing rents are constrained from growing more than the maximum target inflation rate, and houses can be priced as a perpetuity of growing net rental cash flows, then what is the implication for house prices, all things remaining equal? Select the most correct answer.

Background: Since 1990, many central banks across the world have become 'inflation targeters'. They have adopted a policy of trying to keep inflation in a predictable narrow range, with the hope of encouraging long-term lending to fund more investment and maintain higher GDP growth.

Australia's central bank, the Reserve Bank of Australia (RBA), has specifically stated their inflation target range is between 2 and 3% pa.

Some Australian residential property market commentators suggest that because rental costs comprise a large part of the Australian consumer price index (CPI), rent costs across the nation cannot significantly exceed the maximum inflation target range of 3% pa without the prices of other goods growing by less than the target range for long periods, which is unlikely.


Question 554  inflation, real and nominal returns and cash flows

On his 20th birthday, a man makes a resolution. He will put $30 cash under his bed at the end of every month starting from today. His birthday today is the first day of the month. So the first addition to his cash stash will be in one month. He will write in his will that when he dies the cash under the bed should be given to charity.

If the man lives for another 60 years, how much money will be under his bed if he dies just after making his last (720th) addition?

Also, what will be the real value of that cash in today's prices if inflation is expected to 2.5% pa? Assume that the inflation rate is an effective annual rate and is not expected to change.

The answers are given in the same order, the amount of money under his bed in 60 years, and the real value of that money in today's prices.



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.



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?



Question 576  inflation, real and nominal returns and cash flows

What is the present value of a nominal payment of $1,000 in 4 years? The nominal discount rate is 8% pa and the inflation rate is 2% pa.



Question 577  inflation, real and nominal returns and cash flows

What is the present value of a real payment of $500 in 2 years? The nominal discount rate is 7% pa and the inflation rate is 4% pa.



Question 578  inflation, real and nominal returns and cash flows

Which of the following statements about inflation is NOT correct?



Question 604  inflation, real and nominal returns and cash flows

Apples and oranges currently cost $1 each. Inflation is 5% pa, and apples and oranges are equally affected by this inflation rate. Note that when payments are not specified as real, as in this question, they're conventionally assumed to be nominal.

Which of the following statements is NOT correct?



Question 664  real and nominal returns and cash flows, inflation, no explanation

What is the present value of real payments of $100 every year forever, with the first payment in one year? The nominal discount rate is 7% pa and the inflation rate is 4% pa.



Question 727  inflation, real and nominal returns and cash flows

The Australian Federal Government lends money to domestic students to pay for their university education. This is known as the Higher Education Contribution Scheme (HECS). The nominal interest rate on the HECS loan is set equal to the consumer price index (CPI) inflation rate. The interest is capitalised every year, which means that the interest is added to the principal. The interest and principal does not need to be repaid by students until they finish study and begin working.

Which of the following statements about HECS loans is NOT correct?



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:



Question 732  real and nominal returns and cash flows, inflation, income and capital returns

An investor bought a bond for $100 (at t=0) and one year later it paid its annual coupon of $1 (at t=1). Just after the coupon was paid, the bond price was $100.50 (at t=1). Inflation over the past year (from t=0 to t=1) was 3% pa, given as an effective annual rate.

Which of the following statements is NOT correct? The bond investment produced a:



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:



Question 739  real and nominal returns and cash flows, inflation

There are a number of different formulas involving real and nominal returns and cash flows. Which one of the following formulas is NOT correct? All returns are effective annual rates. Note that the symbol ##\approx## means 'approximately equal to'.



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)##.



Question 744  income and capital returns, real and nominal returns and cash flows, inflation

If someone says "my shares rose by 10% last year", what do you assume that they mean?



Question 745  real and nominal returns and cash flows, inflation, income and capital returns

If the nominal gold price is expected to increase at the same rate as inflation which is 3% pa, which of the following statements is NOT correct?



Question 284  covariance, correlation

The following table shows a sample of historical total returns of shares in two different companies A and B.

Stock Returns
Total effective annual returns
Year ##r_A## ##r_B##
2007 0.2 0.4
2008 0.04 -0.2
2009 -0.1 -0.3
2010 0.18 0.5
 

What is the historical sample covariance (##\hat{\sigma}_{A,B}##) and correlation (##\rho_{A,B}##) of stock A and B's total effective annual returns?