CIS September 2012 Exam Diet Examination Paper 1.2: Corporate Finance

CIS September 2012 Exam Diet

Examination Paper 1.2:

Corporate Finance

Equity Valuation and Analysis

Fixed Income Valuation and Analysis

Corporate Finance (1 - 33)

1.

Which of the following statements best describes the job of a financial manager?

A.

To ensure that dividends are paid to shareholders regularly.

B.

To ensure appropriate mix of debt and equity in the firm’s capital structure.

C.

To create value from the firm’s capital budgeting, financing and liquidity activities.

D.

To maintain adequate level of liquidity for the firm at all times.

2.

Which of the following statements is/are correct in respect of agency cost in companies?

I.

Agency costs are the costs of having an agent to make decisions on behalf of the principal.

II.

Agency costs are potentially lower in large companies than in small companies.

III.

Agency cost can also be described as value loss to shareholders resulting from the divergence of interest between the shareholders and the company’s management.

A.

I only.

B.

I and II only.

C.

I and III only.

D.

II and III only.

3.

One of the major problems with the payback period method of investment appraisal is that:

A.

It majorly employs the use of a discount factor that is arbitrarily fixed.

B.

It can only be used for costly projects with equal streams of cash flow.

C.

It does not consider the scrap value and working capital related to a project.

D.

It forces managers to have an artificially short-term orientation and take poor investment decisions.

4.

If a company has a beta of 1.36, the implication is that:

A.

It has higher risk, but lower required return, than the market.

B.

It has lower risk, but higher required return, than the market.

C.

It has higher risk, but higher required return, than the market.

D.

It has lower risk, but lower required return, than the market.

5.

Which of the following is not a consideration in the selection of an investment?

I.

Risk and safety of principal.

II.

Current income versus capital appreciation.

III.

Liquidity.

A.

I and II only.

B.

II and III only.

C.

III only.

D.

None of the above.

6.

The criterion which ranks projects according to the ratio of present value to initial investment is:

A.

The internal rate of return.

B.

The profitability index.

C.

The net present value.

D.

The payback period.

7.

Which of the following is not a characteristic of preference shares?

A.

They pay dividends like equity securities.

B.

They can exist in perpetuity.

C.

Dividends to investors are tax-deductible.

D.

They could be issued with warrants attached.

8.

The Modigliani-Miller dividend irrelevance theory enunciates that:

A.

Dividend payout ratio tends to decrease in years when earnings increase.

B.

Firms use funds to repurchase shares when investment choices are held constant.

C.

Except for tax and transaction cost considerations, dividend policy is irrelevant.

D.

Except for tax and investment policy, dividend policy is irrelevant.

9.

In order to enable Mr. Johnson withdraw N540,000 annually from an investment in a bank deposit with 12% rate of interest, how much must be set aside if the withdrawal starts from now to an indefinite time in the feature?

A.

N4,500,000

B.

N5,400,000

C.

N2,682,000

D.

N27,000,000

10.

A system in which companies are directed and managed in the best interest of the owners and investors is referred to as ______

A.

Corporate finance strategy.

B.

Corporate governance.

C.

Corporate stewardship.

D.

Corporate alliance.

11.

What is the cost of equity given the rate of return on risk-free securities and market portfolio to be 9% and 14% respectively and beta factor as 0.8?

A.

13%

B.

27.4%

C.

12%

D.

18%

12.

The percentage change in a security returns for one percentage change in market return is measured by ________

A.

Alpha.

B.

Beta.

C.

Marginal rate of return.

D.

Average rate of return.

13.

_________ is a privilege a shareholder has to maintain his stake in company ownership by purchasing a proportionate share of any new issue of ordinary shares.

A.

Divestment strategy.

B.

Pre-emptive right.

C.

Investment strategy.

D.

Voting for shares right.

14.

___________ amounts to converting a company’s reserves into share capital.

A.

Scrip issue.

B.

Right reserve.

C.

Floatation.

D.

Stock consolidation.

15.

Implicit costs which evolve out of mismanagement of a firm are referred to as:

A.

Intrinsic costs.

B.

Agency costs.

C.

Capital costs.

D.

Shareholders’ costs.

16.

The difference between a company’s asset beta and equity beta reflects the _____

A.

Business risk.

B.

Financial risk.

C.

Debt beta.

D.

Portfolio risk.

17.

Using the NPV criterion, a project should be selected when:

A.

Its NPV is positive or zero.

B.

Its NPV is equal to zero.

C.

Its NPV is negative.

D.

Its outflows are greater than its inflows.

18.

Which of the following is not one of the qualities which make debt attractive to firms?

A.

The cost of debt is generally less than the cost of share capital.

B.

Debt interests only get paid when the company is making a profit.

C.

It reduces the amount of corporate tax payable by firms.

D.

The required return on debt is lower because, from the lender's point of view, debt is less risky than equity.

19.

If the total value of cash flow from a firm's projects was N1m this year, cash flow growth is expected to be 4% into perpetuity, and the firm's cost of capital is 9%, what would be the value of the firm?

A.

N20m

B.

N5m

C.

N25m

D.

N20.8m

20.

If the weighting of equity in total capital is 1/3, that of debt is 2/3, the return on equity is 15% that of debt is 10% and the corporate tax rate is 32%, what is the

Weighted Average Cost of Capital (WACC)?

A.

10.533%

B.

7.533%

C.

9.533%

D.

11.350%

21.

Which of the following does not make the firm more vulnerable to financial distress?

A.

High sensitivity of the company's revenues to the general level of economic activity.

B.

High proportion of fixed to variable costs.

C.

Physical capital assets which are relatively illiquid and difficult-to-market.

D.

The tax shield.

22.

Which of the following would not be financed from working capital?

A.

Cash float.

B.

Accounts receivable.

C.

Credit sales.

D.

A new personal computer for the office.

23.

What are home-made dividends and why would investors 'make' them?

A.

Home-made dividends represent sale of shares by relatively impatient investors.

B.

Home-made dividends represent purchase of shares by relatively impatient investors.

C.

Home-made dividends represent sale of shares by relatively patient investors.

D.

Home-made dividends represent purchase of shares by relatively patient investors.

24.

Tax shield is most appropriately described by which of the following?

A.

Tax shield is a benefit which accrues to companies which are able to channel their funds through tax havens.

B.

Tax shield is the benefit which accrues to firms which are located in special enterprise areas.

C.

Tax shield is the phenomenon whereby allowable expenses such as debt interest and depreciation reduce taxable profit.

D.

Tax shield allows initial capital expenditure to be offset against tax, when calculating taxable profit.

25.

Which of the following would be counted as part of incremental cash flow?

A.

Sunk cost.

B.

Depreciation.

C.

Fixed overhead cost.

D.

Change in working capital.

Use the information below to answer questions 26 and 27:

Your company is currently analyzing the launch of a new division, which is expected to generate the following cash flows:

Year

Cash flow

(N’000)

0

1

2

3

4

(750,000)

300,000

250,000

118,000

375,000

5

26.

If the required rate of return on this project is 11%, what is its NPV?

A.

N302,600

B.

N319,273

C.

N354,393

D.

N388,532

502,000

27.

What is the payback period of the project (to the nearest month)?

A.

3 years, 8 months.

B.

4 years, 3 months.

C.

4 years, 6 months.

D.

4 years, 10 months.

28.

The popularity of the return on capital employed (ROCE) for project appraisal among entrepreneurs is due to which of the following?

I.

Simplicity of usage.

II.

Ease of understanding.

III.

It factors in project risk.

A.

I and II only.

B.

I and III only.

C.

II and III only.

D.

All of the above.

29.

Which of the following is not a feature of debenture stocks?

A.

They pay fixed interest to investors.

B.

They do not confer voting rights on holders.

C.

The interest element is tax-deductible.

D.

They are collaterized.

30.

Which of the following will cause a company’s WACC to rise?

A.

A decrease in expected inflation.

B.

A decrease in tax rate.

C.

A decrease in interest rate.

D.

A decrease in dividend rate.

31.

Which of the following is not a feature of convertible bond?

A.

It is generally regarded as an hybrid between debt and equity.

B.

Holders usually participate in the decision making of the company.

C.

It is convertible into the equity of the issuer under agreed terms and conditions.

D.

It attracts a lower coupon rate than a non-convertible bond.

32.

Effective credit control policy requires careful consideration of which of the following?

I.

Credit period.

II.

Cost of cash discounts.

III.

Collection policy.

IV.

Earnings Retention policy.

A.

II, III and IV only.

B.

I, III and IV only.

C.

I, II and III only.

D.

All of the above.

33.

A N1,000 par value irredeemable bond selling for N500 in the market has a coupon rate of 15%. What is the required rate of return?

A.

2%

B.

20%

C.

30%

D.

50%

Equity Valuation and Analysis (34 - 67)

34.

Which of the following factors influence an investor’s required rate of return?

A.

The economy’s real risk-free rate.

B.

The expected rate of inflation.

C.

A risk premium.

D.

All of the above.

35.

Many stock analysts assume that a mispriced stock will:

A.

Immediately return to its intrinsic value.

B.

Gradually approach its intrinsic value over several years.

C.

Never return to its intrinsic value.

D.

Return to its intrinsic value within a few days.

36.

Which of the following comparative valuation models is not appropriate for valuing a company that is making losses?

I.

Price earnings ratio.

II.

Price to sales ratio.

III.

Price to book ratio.

A.

I only.

B.

I and II only.

C.

I and III only.

D.

II and III only.

37.

You wish to earn a return of 10% on each of two stocks, C and D. Each of the stocks is expected to pay a dividend of N2 in the upcoming year. The expected growth rate of dividends is 9% for stock C and 10% for stock D.

The intrinsic value of stock C ________

A.

Will be greater than the intrinsic value of stock D.

B.

Will be the same as the intrinsic value of stock D.

C.

Will be less than the intrinsic value of stock D.

D.

Cannot be calculated without knowing the rate of return on the market portfolio.

38.

A top down analysis of a firm starts with ____________

A.

The global economy.

B.

The relative value of the firm.

C.

The absolute value of the firm.

D.

The domestic economy.

39.

Which of the following is not considered a basic economic force?

A.

Fiscal policy.

B.

P/E ratio.

C.

Monetary policy.

D.

Inflation.

40.

Which of the following statements is correct?

A.

If intrinsic value > Market price, you should buy.

B.

If intrinsic value > Market price, you should sell.

C.

If intrinsic value < Market price, you should sell.

D.

(A) and (C) above.

41.

According to the dividend growth model, if a company were to declare that it would never pay dividends, its value would be:

A.

Zero.

B.

Based on earnings.

C.

Based on future expectations.

D.

Higher than similar firms since it could reinvest a greater amount in new projects.

42.

Dividend growth is a function of:

A.

Return on equity.

B.

The retention rate.

C.

The payout ratio.

D.

(A) and (B) above.

43.

The real growth rate of an economy and condition in the capital markets determine the:

A.

Dividend payout ratio.

B.

Beta.

C.

Real risk free rate.

D.

Risk premium.

44.

The P/E ratio is determined by:

A.

The required rate of return.

B.

The expected dividend payout ratio.

C.

The expected growth rate of dividends.

D.

All of the above.

45.

The beta for the XYZ Plc is 1.25. If the yield on 30 year T-bonds is 5.65%, and the long term average return on the All Share Index is 11%. Calculate the required rate of return for XYZ Plc.

A.

12.34%

B.

7.06%

C.

5.65%

D.

5.35%

46.

Consider a firm that has just paid a dividend of N2. An analyst expects dividends to grow at a rate of 8% per year for the next five years. After that dividends are expected to grow at a normal rate of 5% per year. Assume that the appropriate discount rate is 7%.

The dividends for years 1, 2 and 3 are:

A.

N2.16, N2.24, N2.32

B.

N2.16, N2.33, N2.52

C.

N2, N2.08, N2.16

D.

N2, N2.05, N2.10

47.

What should be the proper course of action for a corporation whose return on equity is greater than the return required from its stockholders?

A.

The company should reduce its dividends and plow more of its earnings back into its operation.

B.

The company should increase its dividends now that its profits are growing at a faster rate.

C.

Dividend policy is irrelevant when it comes to this matter.

D.

None of the above.

48.

Investors with the value investment style will select stocks with _____ dividend yields.

A.

High.

B.

Low.

C.

The value investment style is unrelated to dividend yield.

D.

Zero.

49.

The rights of equity shareholders do not include which of the following?

I.

Right to demand for dividend income annually.

II.

Residual right to earnings.

III.

Pre-emptive right to maintain proportion of ownership through rights issue.

IV.

Right of residual claim on the assets of the company.

A.

I only.

B.

I and II only.

C.

II and III only.

D.

I, II and IV only.

50.

The rate of return of the stock market moves faster than that of stock X when the market is trending upward. Stock X is most likely to have:

A.

Beta of zero.

B.

Beta of 1.

C.

Beta greater than 1.

D.

Beta lower than 1.

51.

When you observe relatively very low price-earnings ratio and low price to book ratio, the market is most likely:

A.

Bullish.

B.

Bearish.

C.

Recovering.

D.

Uncertain.

52.

Which of the following ratios will be most helpful when analysing equity investments aimed at generating dividend income in the next few years?

I.

Return on equity.

II.

Dividend payout ratio.

III.

Liquidity ratio.

IV.

Stock turnover.

A.

I and II only.

B.

I and IV only.

C.

II and IV only.

D.

I, III and IV only.

53.

Which of the following factors can affect stock prices?

A.

The national economy.

B.

The political situation in the country.

C.

Global macroeconomic factors.

D.

All of the above.

54.

What is the most appropriate discount rate to use when applying a Free Cash Flow to

Equity valuation model?

A.

Weighted Average Cost of Capital.

B.

Equity investors’ required rate of return.

C.

Risk-free rate.

D.

General interest rate in the economy.

55.

The present value of all future cash proceeds to the investor in a stock is referred to as_________

A.

Dividend payout ratio.

B.

Market capitalization rate.

C.

Plowback ratio.

D.

Intrinsic value.

56.

Which of the following best describes capital gains?

A.

Profit resulting between the purchase and sale of securities.

B.

Taxable profit that occurs when a company decides to capitalize some of its accumulated reserves.

C.

When a company decides on an upward revaluation its fixed assets.

D.

Total dividends shareholders receive in the duration of his share holding.

57.

A stock split, such as 4 for 1, means:

I.

An investor will have four times as many shares as he currently has.

II.

The value of each share after the stock split remains as before.

III.

Total par value of stocks increases.

A.

I only.

B.

I and II only.

C.

I and III only.

D.

All of the above.

58.

An increase in which of the following variables is most likely to increase the value of a company?

A.

Long term sustainable growth rate.

B.

Investors’ required return.

C.

Dividend yield.

D.

Interest rate.

59.

Which of the following statements is not true about the Gordon’s model?

A.

It is valid only when g is less than k.

B.

It is valid only when k is less than g.

C.

It assumes constant growth of dividends.

D.

Its variables need to be carefully estimated.

60.

Which of the following is not a characteristic of an investment company?

A.

It allows investors’ holdings to remain liquid.

B.

It allows investors to make their own specific investment choices.

C.

It allows investors to diversify their holdings, regardless of size.

D.

It gives investors professional management of their holdings.

Use the information below to answer questions 61 to 63:

Sure Tool Limited is expected to pay a dividend of N2 in the upcoming year. The riskfree rate of return is 4% and the expected return on the market portfolio is 14%.

Analysts expect the price of Sure Tool Limited’s shares to be N22 a year from now. The beta of Sure Tool Company's stock is 1.25

61.

What is the market's required rate of return on Sure Tool's stock?

A.

14.0%

B.

17.5%

C.

16.5%

D.

15.25%

62.

What is the intrinsic value of Sure Tool’s stock today?

A.

N20.60

B.

N20.00

C.

N12.12

D.

N22.00

63.

If Sure Tool's intrinsic value is N21.00 today, what must be its growth rate?

A.

10%

B.

4%

C.

6%

D.

7%

Use the information below to answer questions 64 and 65:

You are given the following information from the financial statements of ABC Limited.

Sales

Operating cost

Depreciation

Interest expenses

Increase in working capital

Investment in fixed assets

Applicable taxes (30% tax rate)

N'000

5,500

1,000

3,300

300

250

2,500

270

64.

What is the Gross (Operating) Cash flow of ABC Limited?

A.

N630

B.

N900

C.

N930

D.

N3,930

65.

What is the Free Cash flow to Equity of ABC Limited?

A.

N930

B.

N1,180

C.

N1,430

D.

N3,930

66.

Samba had a Free Cash Flow to Equity of N1.6 million last year and has 3.2 million shares outstanding. Samba's required return on equity is 12% and WACC is 9.8%.

If Free Cash Flow to Equity is expected to grow at 9% forever, what is the intrinsic value of Samba's shares?

A.

N14.76

B.

N18.67

C.

N26.35

D.

N68.13

67.

Which of the following is not a weakness of the price earnings ratio as a model for valuing a company?

A.

Earnings are generally unstable.

B.

Earnings can be easily manipulated.

C.

Earnings are subject to inflexible accounting standards and policies.

D.

None of the above.

Fixed Income Valuation and Analysis (68 - 100)

68.

The coupon rate of a bond is:

A.

The amount the issuer agrees to repay the bondholder by the maturity date.

B.

The number of years over which the issuer has promised to meet the conditions of the obligation.

C.

The interest rate that the issuer agrees to pay each year.

D.

Equivalent to the par value of a bond.

69.

The cash flows promised to the owner of a N250,000 par value bond with 5 years to maturity, paying an 8% coupon rate in semi-annual payments, are:

A.

Five annual payments of N80 plus one final payment of N1,000

B.

Ten semi-annual payments of N20,000 plus one final payment of N150,000

C.

Ten semi-annual payments of N10,000 plus one final payment of N250,00

D.

Five annual payments of N20,000 and a final payment equal to the market value at maturity.

Use the information below to answer questions 70 and 71:

N1,000 par value, 15% coupon bond of Global Resources Limited, redeemable at par, has

3 years to maturity. Investors’ required rate of return on equivalent bonds is 12%.

70.

What is the price of Global Resources Bond?

A.

N1,000

B.

N1,072.05

C.

N1,115.29

D.

N1,224.33

71.

What is the duration of the Global Resources Bond?

A.

2.36 years.

B.

2.48 years.

C.

2.64 years.

D.

2.93 years.

72.

Which of the following is not a component of call risk for a bond investor?

A.

The cash flow pattern of a callable bond is not known with certainty.

B.

When the issuer calls a bond, the investor is exposed to reinvestment risk.

C.

The value of a callable bond drops when expected interest-rate volatility decreases.

D.

The capital appreciation potential of a callable bond is lower than a noncallable bond.

73.

Which of the following bonds has the longest duration?

A.

5-year maturity, 6% coupon.

B.

5-year maturity, 12% coupon.

C.

10-year maturity, 6% coupon.

D.

10-year maturity, 12% coupon.

74.

Bonds which are unsecured obligations of the company are called:

A.

Indentures.

B.

Debentures.

C.

Bearers.

D.

Floating rate bonds.

75.

Which of the following would be classified as an affirmative financial covenant?

A.

Do not violate the lender's restriction on dividend payments.

B.

Provide audited financial statements on a timely basis.

C.

Use the loan for the agreed-upon purpose.

D.

Maintain a satisfactory working capital ratio (or current ratio).

76.

Preference in position among creditors when it comes to repayment is called:

A.

Creditor priority.

B.

Seniority.

C.

Liquidation preference.

D.

Repayment option.

77.

Bond price sensitivity is most related to which of the following?

A.

Maturity date.

B.

Market interest rates.

C.

Coupon rates.

D.

Duration of the bond.

78.

The interest rate risk of a bond normally is:

A.

Greater for shorter maturities.

B.

Lower for longer duration.

C.

Lower for higher coupons.

D.

None of the above.

79.

In general, the credit spread:

A.

Widens during economic expansions.

B.

Widens during economic contractions.

C.

Remains stable over time.

D.

All of the above.

80.

According to the liquidity-preference theory the forward rate is:

A.

Less than the expected future spot rate.

B.

Greater than the expected future spot rate.

C.

Equal to the expected future spot rate.

D.

None of the above.

81.

The difference in yield between debt issued by Zenith Bank Plc and debt issued by

Unilever Nigeria Plc would be referred to as:

A.

The inter-market yield spread.

B.

The on-the run yield spread.

C.

The intra-market yield spread.

D.

Credit spread.

82.

Responsibilities of a corporate trustee with regard to a bond's trust indenture do not include:

A.

Checking compliance.

B.

Authenticating the bonds issued.

C.

Negotiating the terms.

D.

Declaring defaults.

83.

Inflation risk arises because of the variation in the value of:

A.

Cash flows from a security due to excess supply.

B.

Net income from a security due to inflation.

C.

Cash flows from a security due to inflation.

D.

All of the above.

84.

Which of the following is not an explanation of the relationship between a bond's interest rate and its term to maturity?

A.

Default risk hypothesis.

B.

Expectations hypothesis.

C.

Liquidity preference hypothesis.

D.

Market segmentation hypothesis.

85.

For a domestic bond the risk premium is determined by:

A.

Credit quality, term to maturity and exchange rate risk.

B.

Credit quality, term to maturity and call features.

C.

Call features, sinking fund provisions and country risk.

D.

Term to maturity, call features and inflation.

86.

Step-up notes are:

A.

Bonds that have coupon payments that reset periodically according to some reference rate.

B.

Bonds that have no coupon payment for a deferred period.

C.

Securities that have a coupon rate that increases over time.

D.

Bonds that cannot experience a fall in market value.

87.

A call provision is:

A.

The right of the underlying borrowers in a pool of loan to repay an amount in excess of the scheduled principal repayment.

B.

The right of the underlying borrowers in a pool of loan to repay an amount that represents a deficit in relation to the scheduled principal repayment.

C.

The right of the issuer to retire the issue prior to the stated maturity date.

D.

The right of the issuer to call on the borrower to pay a premium on the bond at an agreed date in future.

88.

Bonds that are said to have a bullet maturity are:

A.

Those where the issuer is not required to make any principal repayments prior to the maturity date.

B.

Those where the issuer is not required to make any principal repayments after the maturity date.

C.

Those where the issuer is required to make principal repayments prior to the maturity date.

D.

None of the above.

89.

The current yield on a bond is equal to ________

A.

Annual interest divided by the current market price.

B.

The yield to maturity.

C.

Annual interest divided by the par value.

D.

The internal rate of return.

90.

To earn a high rating from the bond rating agencies, a firm should have:

A.

A low times interest earned ratio.

B.

A low debt to equity ratio.

C.

A high quick ratio.

D.

(B) and (C) above.

91.

All other things being equal, the price and yield on a bond are:

A.

Negatively related.

B.

Positively related.

C.

Sometimes positively and sometimes negatively related.

D.

Not related.

92.

Which of the following credit ratings, issued by Standard & Poor’s is considered to be investment grade rating?

I.

AAA

II.

AA

III.

A

IV.

BBB

A.

I and II only.

B.

III and IV only.

C.

I, II and III only.

D.

All of the above.

93.

Which of the following statements about zero-coupon bonds is correct?

A.

Interest is paid every six months.

B.

They have very stable resale price.

C.

They have no reinvestment risk.

D.

They have lower duration compared with coupon bonds.

94.

Which of the following is a characteristic of revenue bond?

A.

It is backed by the full faith and credit of the issuer.

B.

It is paid from the income generated by a specific project.

C.

It involves competitive underwriting.

D.

All of the above.

95.

Sinking funds are most likely to:

A.

Increase liquidity risk.

B.

Negatively affect bond rating.

C.

Increase prepayment risk.

D.

Reduce default risk.

96.

’’The sale of a security with the commitment by the seller to buy the same security back at a specified price at a designated future date’’, best describes:

A.

Commitment bond.

B.

Repurchase agreement.

C.

An adjustable price issue.

D.

Inverse floater.

97.

A short term unsecured promissory note that is issued in the open market and represents the obligation of the issuing company is called:

A.

Commercial paper.

B.

Bankers’ acceptance.

C.

Treasury note.

D.

Collateralized debt obligation.

98.

The minimum value of a convertible bond is:

A.

Its conversion value.

B.

Its straight value.

C.

The greater of its conversion value and its straight value.

D.

The lower of its conversion value and its straight value.

99.

Which of the following statement about warrants is not correct?

A.

A warrant could be used as sweetener to a bond issue.

B.

When warrants are exercised the balance sheet of the issuer is affected.

C.

Warrants are similar to call options in some respects.

D.

None of the above.

100.

Consider the following data of a bond of BYY Limited:

Par value:

Coupon rate:

N3,000

15%

Years to maturity: 2

If the required rate of return is 10%, then the value of the bond is:

A.

N3,000

B.

N3,034.93

C.

N3,260.33

D.

N3,900

Total = 100 marks

END OF PAPER

FORMULAE

Levered/unlevered beta:

Annuities:

Yield to maturity of a bond:

Valuation of perpetual bonds:

Price change approximated with duration:

Portfolio duration:

Macaulay duration: