SECURITY VALUATION PRICIPLES

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CHAPTER 11

INTRODUCTION TO SECURITY VALUATION

TRUE/FALSE QUESTIONS

(f) 1 The three step valuation process consists of 1) analysis of alternative economiesand markets, 2) analysis of alternative industries and 3) analysis of industryinfluences.

(t) 2 The two components that are required in order to carry out asset valuation are 1)

the stream of expected cash flows and 2) the required rate of return.

(t) 3 The general economic influences would include inflation, political upheavals,monetary policy, and fiscal policy initiatives.

(f) 4 Given an optimistic economic and stock-market outlook for a country, theinvestor should underweight the allocation to this country in his/her portfolio.

(t) 5 The importance of an industry's performance on an individual stock's performancevaries across industries.

(t) 6 If the intrinsic value of an asset is greater than the market price, you would want

to buy the investment.

(t) 7 The most difficult part of valuing a bond is determining the required rate of returnon this investment.

(f) 8 The required rate of return is determined by 1) the real risk free rate, 2) theexpected rate of inflation and 3) liquidity risk.

(f) 9 The price of a bond can be calculated by discounting future coupons over thebonds life by the yield to maturity.

(f) 10 The growth rate of dividends and profit margin are the main determinants of theP/E ratio.

(t) 11 The dividend growth models are only meaningful for companies that have arequired rate of return that exceeds their dividend growth rate.

(t) 12 An example of a relative valuation technique is the Price/Cash Flow ratio.

(f) 13 Discounted cash flow techniques for equity valuation may use one of thefollowing 1) dividends, 2) Free cash flow or 3) coupons.


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(f) 14 In dividend discount models (DDM) with supernormal growth, supernormalgrowth may continue indefinitely.

(t) 15 The real risk free rate depends on the real growth in the economy and for shortperiod by temporary tightness or ease in capital markets.

(t) 16 The risk premium is impacted by business risk, financial risk, and liquidity risk.


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MULTIPLE CHOICE QUESTIONS

(e) 1 Which of the following is nota consideration in the three-step valuation process?

a) Analysis of alternative economiesb) Analysis of security marketsc) Analysis of alternative industriesd) Analysis of individual companiese) None of the above (that is, all are considerations in the three-step valuation

process)

(d) 2 Which of the following is notconsidered a basic economic force?

a)

Fiscal policyb) Monetary policyc)

Inflation

d) P/E ratioe) None of the above (that is, all are basic economic forces)

(d) 3 The process of fundamental valuation requires estimates of all the following

factors, except

a)

The time pattern of returns.b)

The economy's real risk-free rate.c) The risk premium for the asset.d) The times series of stock prices.e) The expected rate of inflation.

(e) 4 Which of the following 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) Choices b and c.e) Choices a and c.

(c) 5 The value of a corporate bond can be derived by calculating the present value ofthe interest payments and the present value of the face value at the bond's

a) Current yield.b)

Coupon rate.c) Required rate of return.


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d) Effective rate.e) Prime rate.

(d) 6 Which securities can be valued by dividing the annual dividend by the requiredrate of return?

a) Low coupon bondsb)

Junk bondsc) Common stocksd) Preferred stockse) Constant growth common stocks

(d) 7 According to the dividend growth model, if a company were to declare that it

would never pay dividends, its value would be

a)

Based on earnings.

b) Based on expectations regarding.c) Higher than similar firms since it could reinvest a greater amount in new

projects.d) Zero.

e) Based on the capital asset pricing model.

(d) 8 Dividend growth is a function of

a) Return on equity.b) The retention rate.

c) The payout ratio.d) a) and b).e) b) and c).

(c) 9 The real growth rate of an economy and condition in capital markets determine

the

a) Dividend payout ratio.b) Beta.c) Real risk free rate.d) Nominal risk free rate.e) Risk premium.

(d) 10 The growth rate of equity earnings without external financing is equal to


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a) Retention rate plus return on equity.b) Retention rate minus return on equity.c) Retention rate divided by return on equity.d)

Retention rate times return on equity.e) Return on equity divided by retention rate.

(d) 11 Which of the following factors influence an investors required rate of return?

a) The economys real risk-free rate (RFR)b) The expected rate of inflation (I)c) A risk premiumd) All of the above

e) None of the above

(e) 12 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) Choices a and b

e) All of the above


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MULTIPLE CHOICE PROBLEMS

USE THE FOLLOWING INFORMATION FOR THE NEXT TWO PROBLEMS

A major retailer is reevaluating its bonds since it is planning to issue a new bond in the currentmarket. The firm's outstanding bond issue has 10 years remaining until maturity. The bondswere issued with a 8 percent coupon rate (paid semiannually) and a par value of $1,000.Because of increased risk the required rate has risen to 10 percent.

(c) 1 What is the current value of these securities?

a) $686.50b) $699.00c) $875.38d)

$868.50e) $902.00

(e) 2 What will be the value of these securities in one year if the required returndeclines to 6 percent?

a) $699.00b) $802.50c) $1259.05d) $1012.17e)

$1137.54


A major manufacturer is reevaluating its bonds since it is planning to issue a new bond in thecurrent market. The firm's outstanding bond issue has 8 years remaining till maturity. Thebonds were issued with an 8 percent coupon rate (paid quarterly) and a par value of $1,000.Because of increased risk the required rate has risen to 12 percent.

(a) 3 What is the current value of these securities?

a) $796.11b) $797.84c) $826.73d)

$862.98e) $904.00

(c) 4 What will be the value of these securities in one year if the required returndeclines to 8 percent?


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a) $699.50b) $885.50c)

$1000.00d) $998.36e) $936.72


A large grocery chain is reevaluating its bonds since it is planning to issue a new bond in thecurrent market. The firm's outstanding bond issue has 6 years remaining until maturity. Thebonds were issued with a 6 percent coupon rate (paid semiannually) and a par value of $1,000.

Because of increased risk the required rate has risen to 10 percent.

(c) 5 What is the current value of these securities?

a)

$656.40

b) $899.00c) $822.70

d) $569.50e) $962.00

(d) 6 What will be the value of these securities in one year if the required returndeclines to 8 percent?

a) $899.43b) $862.50

c) $869.88d) $918.93e) $946.98

(d) 7 In 1998, Talbott Inc. issued a $110 par value preferred stock that pays a 9 percent

annual dividend. Due to changes in the overall economy and in the company'sfinancial condition investors are now requiring a 10 percent return. What pricewould you be willing to pay for a share of the preferred if you receive your firstdividend one year from now?

a) $68.38b) $65.35c) $71.54d) $61.87e) $78.37


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(a) 8 In 1998, Smitman Corp. issued a $50 par value preferred stock that pays a 8

percent annual dividend. Due to changes in the overall economy and in thecompany's financial condition investors are now requiring an 15 percent return.What price would you be willing to pay for a share of the preferred if you receiveyour first dividend one year from now?

a) $26.67b)

$30.00c) $31.54d) $33.38e) $38.37

(e) 9 In 1998, Green Leaf Co. issued a $63 par value preferred stock which pays a 7

percent annual dividend. Due to changes in the overall economy and in thecompany's financial condition investors are now requiring a 10 percent return.What price would you be willing to pay for a share of the preferred if you receive

your first dividend one year from now?

a) $44.98b) $40.50

c) $41.44d) $45.38

e) $44.10

(a) 10 In 1998, Drowny Inc. issued a $52 par value preferred stock that pays an 8percent annual dividend. Due to changes in the overall economy and in the

company's financial condition investors are now requiring an 11 percent return.What price would you be willing to pay for a share of the preferred if you receiveyour first dividend one year from now?

a) $37.82b) $38.50

c)

$39.44d) $41.38e) $44.10

(b) 11 Using the constant growth model, an increase in the required rate of return from15 to 17 percent combined with an increase in the growth rate from 7 to 9 percentwould cause the price to

a) Rise more than 2%.


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b) Rise less than 2%.c) Remain constant.d) Fall more than 2%.e)

Fall less than 2%.

(b) 12 Using the constant growth model, an increase in the required rate of return from16 to 19 percent combined with an increase in the growth rate from 8 to 11percent would cause the price to

a) Rise more than 3%b) Rise less than 3%.c) Remain constant.

d) Fall more than 3%.e)

Fall less than 3%.

(b) 13 Using the constant growth model, an increase in the required rate of return from

14 to 15 percent combined with an increase in the growth rate from 6 to 7 percentwould cause the price to

a) Rise more than 1%

b) Rise less than 1%.c) Remain constant.

d) Fall more than 1%.e)

Fall less than 1%.

(b) 14 Using the constant growth model, an increase in the required rate of return from17 to 20 percent combined with an increase in the growth rate from 8 to 11percent would cause the price to

a) Rise more than 3%b) Rise less than 3%.c) Remain constant.d) Fall more than 3%.

e)

Fall less than 3%.

(d) 15 Using the constant growth model, an increase in the required rate of return from14 to 18 percent combined with an increase in the growth rate from 8 to 12percent would cause the price to

a) Fall more than 4%b) Fall less than 4%.c) Rise more than 4%


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d) Rise less than 4%.e) Remain constant.


Ridgemont Can Company's last dividend was $1.55 and the directors expect to maintain thehistoric 5 percent annual rate of growth. You plan to purchase the stock today because you feelthat the growth rate will increase to 8 percent for the next three years and the stock will thenreach $22.50 per share.

(b) 16 How much should you be willing to pay for the stock if you require a 15 percentreturn?

a)

$16.97

b) $18.90c) $21.32d)

$32.63

e) None of the above

(d) 17 How much should you be willing to pay for the stock if you feel that the 8 percent

growth rate can be maintained indefinitely and you require a 15 percent return?

a) $18.90b)

$19.28c)

$22.14

d) $23.91e) $25.46


The National Motor Company's last dividend was $1.25 and the directors expect to maintain the

historic 4 percent annual rate of growth. You plan to purchase the stock today because you feelthat the growth rate will increase to 7 percent for the next three years and the stock will then

reach $25.00 per share.

(d) 18 How much should you be willing to pay for the stock if you require a 16 percentreturn?

a) $17.34b) $18.90c)

$19.09d) $19.21e)

None of the above


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(c) 19 How much should you be willing to pay for the stock if you feel that the 7 percent

growth rate can be maintained indefinitely and you require a 16 percent return?

a) $11.15b) $14.44c) $14.86d) $18.90e)

$19.24

(e) 20 Ross Corporation paid dividends per share of $1.20 at the end of 1990. At the endof 2000 it paid dividends per share of $3.50. Calculate the compound annual

growth rate in dividends.

a) 52.17%b) 34.28%c)

23%

d) 19.17%e) 11.29%

(a) 21 Hunter Corporation had a dividend payout ratio of 63% in 1999. The retentionrate in 1999 was

a)

37%b)

63%

c) 50%d) 0%

e) 100%

(a) 22 The beta for the DAK Corporation is 1.25. If the yield on 30 year T-bonds is5.65%, and the long term average return on the S&P 500 is 11%. Calculate therequired rate of return for DAK Corporation.

a) 12.34%b) 7.06%c) 13.74%d) 5.35%e) 5.65%

(c) 23 Micro Corp. just paid dividends of $2 per share. Assume that over the next threeyears dividends will grow as follows, 5% next year, 15% in year two, and 25% inyear 3. After that growth is expected to level off to a constant growth rate of 10%


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per year. The required rate of return is 15%. Calculate the intrinsic value using amultistage dividend discount model.

a)

$5.56b) $66.4c) $49.31d) $43.66e) none of the above

(a) 24 The P/E ratio for BMI Corporation 21, and the P/Sales ratio is 5.2. The industryP/E ratio is 35 and the industry P/Sales ratio is 7.5. Based on relative valuation,BMI is

a)

Undervalued on the basis of relative P/E and relative P/S.

b) Overvalued on the basis of relative P/E and undervalued on the basis ofrelative P/S.

c)

Undervalued on the basis of relative P/E and overvalued on the basis of

relative P/S.d) Overvalued on the basis of relative P/E and relative P/S.

e) None of the above.

USE THE FOLLOWING INFORMATION FOR THE NEXT FOUR PROBLEMS

Consider a firm that has just paid a dividend of $2. An analyst expects dividends to grow at arate 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%.

(d) 25 The dividends for years 1, 2, and 3 are

a) $2, $2.08, $2.16b) $2, $2.05, $2.10c) $2.16, $2.24, $2.32d) $2.16, $2.33, $2.52

e)

$2.07, $2.14, $2.21

(e) 26 The future price of the stock in year 5 is

a) $113.40b) $122.47c) $132.27d) $142.85e) $154.35


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(b) 27 The present value today of dividends for years 1 to 5 is

a)

$4.06b) $10.28c) $12.40d) $8.19e) $6.11

(c) 28 The price of the stock today (P0) is

a) $136.29

b) $133.03c)

$120.33

d) $123.43e) $126.60

USE THE FOLLOWING INFORMATION FOR THE NEXT FOUR PROBLEMS

Consider a firm that has just paid a dividend of $1.5. An analyst expects dividends to grow at a

rate of 9% per year for the next three years. After that dividends are expected to grow at anormal rate of 5% per year. Assume that the appropriate discount rate is 7%.

(b) 29 The dividends for years 1, 2, and 3 are

a) $1.5, $2.0, $2.05b)

$1.64, $1.78, $1.94

c) $1.64, $1.94, $2.24d) $1.5, $2.40, $3.30e) $2.07, $2.14, $2.21

(d) 30 The future price of the stock in year 3 is

a)

$81.75b) $84.81c) $92.56d) $101.85e) $111.16

(a) 31 The present value today of dividends for years 1 to 3 is

a) $4.67


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b) $3.08c) $5.67d) $4.5e)

$1.53

(b) 32 The price of the stock today (P0) is

a)

$84.81b) $87.81c) $91.09d) $94.32e) $97.61

(a) 33 Tayco Corporation has just paid dividends of $3 per share. The earnings per sharefor the company was $4. If you believe that the appropriate discount rate is 15%,and the long term growth rate is 6%, then the firms P/E ratio is

a) 8.33

b) 33.33c) 44.44

d) 11.11e) None of the above


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CHAPTER 11

ANSWERS TO PROBLEMS

1 P =20

20

)05.1(

1000

05.

)05.1(

11

40

= $875.38

2 P =18

18

)03.1(

1000

03.

)03.1(

11

40

= $1137.54

3 P =32

32

)03.1(

1000

03.

)03.1(

11

20

= $796.11

4 P = 28

28

)02.1(

1000

02.

)02.1(

11

20

= $796.11

5 P =12

12

)05.1(

1000

05.

)05.1(

11

30

= $822.70

6 P =10

10

)04.1(

1000

04.

)04.1(11

30

= $918.93

7 Dividend = .09 x $110 = $9.90 Price = 9.90 0.16 = $61.87

8 Dividend = .08 x $50 = $4.00 Price = 4.00 0.15 = $26.67


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9 Dividend = .07 x $63 = $4.41 Price = 4.41 0.10 = $44.10

10 Dividend = .08 x $52 = $4.16 Price = 4.16 0.11 = $37.82

11 %= P2/P1= [(D0)(1 + g2)/(k2- g2)] [(D0)(1 + g1)/(k1- g1)] - 1

= [(D0)(1 + 0.09)/(0.17 - 0.09)] [(D0)(1 + 0.07)/(0.15 - 0.07)] 1

= (13.625 13.375) - 1 = 1.87% < 2%

12 %= P2/P1= [(D0)(1 + g2)/(k2- g2)] [(D0)(1 + g1)/(k1- g1)] - 1

= [(D0)(1 + 0.11)/(0.19 - 0.11)] [(D0)(1 + 0.08)/(0.16 - 0.08)] 1

= (13.875 13.50) - 1 = 2.78% < 3%

13 %= P2/P1= [(D0)(1 + g2)/(k2- g2)] [(D0)(1 + g1)/(k1- g1)] - 1

= [(D0)(1 + 0.07)/(0.15 - 0.07)] [(D0)(1 + 0.06)/(0.14 - 0.06)] 1

= (13.375 13.25) - 1 = 0.94% < 1%

14 %= P2/P1= [(D0)(1 + g2)/(k2- g2)] [(D0)(1 + g1)/(k1- g1)] - 1

= [(D0)(1 + 0.11)/(0.20 - 0.11)] [(D0)(1 + 0.08)/(0.17 - 0.08)] 1

= (12.33 12.00) - 1 = 2.75% < 3%

15 %= P2/P1= [(D0)(1 + g2)/(k2- g2)] [(D0)(1 + g1)/(k1- g1)] - 1

= [(D0)(1 + 0.12)/(0.18 - 0.12)] [(D0)(1 + 0.08)/(0.14 - 0.08)] 1

= (18.66 18.00) - 1 = 3.77% < 4%

16 P = 1.55(1.08) + 1.55(1.08)2+ 1.55(1.08)3 + 22.501.15 (1.15)2 (1.15)3 (1.15)3

= $1.456 + $1.367 + $1.284 + $14.794 = $18.90

17 P = (1.55 x 1.08) (0.15 - 0.08) = $23.91

18 P = 1.25(1.07) + 1.25(1.07)2+ 1.25(1.07)

3+ 25.00

1.16 (1.16)2 (1.16)3 (1.16)3

= $1.153 + $1.064 + $0.981 + $16.016 = $19.21

19 P = (1.25 x 1.07) (0.16 - 0.07) = $14.86


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20 g = (3.50/1.20)1/10 1 = 11.29%

21 retention rate = 1 - 0.63 = 37%

22 required return = .0565 + 1.25(.11 - .0565) = 12.34%

23 price =332 15.1

1.15.

)1.1)(25.1)(15.1)(05.1(2

15.1

)25.1)(15.1)(05.1(2

15.1

)15.1)(05.1(2

15.1

)05.1(2 = $49.31

24 Relative P/E = 21/35 = undervalued

Relative P/S = 5.2/7.5 = undervalued

25 Year 1 Dividends = 2(1 + .08) = $2.16Year 2 Dividends = 2(1 + .08)2= $2.33Year 3 Dividends = 2(1 + .08)3= $2.52

26 Future price of stock in year 5 = P5 = D6/(k g)where g is the normal growth rate = 5%D6 = 2(1 + .08)5(1 + .05) = $3.087P5 = 3.087/(.07 - .05) = $154.35

27 The present value today of dividends from years 1 to 5 =

2.16/(1.07) +2.33/(1.07)2+ 2.52/(1.07)3+ 2.72/(1.07)4 + 2.94/(1.07)5= $10.28

28 P0 = PV of dividends yr1 to yr5 + PV of P5

= 10.28 + 154.35/(1.07)5= $120.33

29 Year 1 Dividends = 1.5(1 + .09) = $1.64Year 2 Dividends = 1.5(1 + .09)2= $1.78

Year 3 Dividends = 1.5(1 + .09)3

= $1.94

30 Future price of stock in year 3 = P3 = D4/(k g)

where g is the normal growth rate = 5%D4 = 1.5(1 + .09)3(1 + .05) = $2.037P3 = 2.037/(.07 - .05) = $101.85

31 The present value today of dividends from years 1 to 3 =

1.64/(1.07) +1.78/(1.07)2+ 1.94/(1.07)3 = $4.67


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32 P0 = PV of dividends yr1 to yr5 + PV of P3

= 4.67 + 101.85/(1.07)3= $87.81

33 P/E =

06.15.

06.1(4

)06.1(3

= 8.33

CHAPTER 12


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FIXED-INCOME ANALYSIS


(f) 1 The price of a bond is the presents value offuture coupons and face value discounted by thecoupon rate.

(t) 2 The yield to maturity of a bond the interestrates that equates the present value of all futurecoupons and face value to the current price of thebond.

(f) 3 The current yield is the annual coupon payment

divided by the face value of the bond.

(t) 4 Yield to maturity assumes that all interim cashflows are reinvested at the computed YTM.

(t) 5 Yield to maturity and current yield are equalwhen the bond is selling for exactly par value.

(t) 6 The promised yield to call measures theexpected rate of return for a bond held to firstcall date.

(f) 7 The promised yield to maturity measures theexpected rate of return for a bond held for aminimum period of ten years.

(t) 8 Realized yield measures the expected rate ofreturn of a bond if the bond is sold prior to itsmaturity.

(t) 9 The fully taxable equivalent yield of anontaxable bond with a promised yield of 7 percentis 10.29 percent, assuming a tax rate of 32percent.

(f) 10 The major problem facing a bond analyst valuinga U.S. government bond is the ability to forecastthe real risk-free rate of interest.

(t) 11 When investing in a foreign bond versus adomestic bond, the additional risk factors you mustconsider are exchange rate risk and country risk.

(t) 12 The fundamental determinants of interest ratesare the real risk free rate, inflation, and therisk premium.


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(f) 13 According to the expectations hypothesis, arising yield curve indicates that investors demandfor long maturity bonds is expected to rise.

(t) 14 According to the segmented market hypothesisyields for a particular maturity segment depend onsupply and demand within the maturity segment.

(f) 15 For a given change in yield bond pricevolatility is inversely related to term tomaturity.

(t) 16 For a given change in yield bond pricevolatility is inversely related to coupon.

(t) 17 For a given change in yield bond price

volatility is directly related to duration.

(t) 18 Convexity is a measure of how much a bondsprice-yield curve deviates from the linearapproximation of that curve.


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(a) 1 If you expected interest rates to fall, you would prefer to own bonds with

a)

Long durations and high convexity.b)

Long durations and low convexity.c)

Short durations and high convexity.d)

Short durations and low convexity.e) None of the above.

(c) 2 If you expected interest rates to fall, you would prefer to own bonds with

a)

Short maturities and low coupons.b)Long maturities and high coupons .c)

Long maturities and low coupons.d)

Short maturities and high coupons.e)

None of the above.

(d) 3 If you expected interest rates to rise, you would prefer to own bonds with

a)Short maturities and low coupons.b)Long maturities and high coupons.c)

Long maturities and low coupons.

d)

Short maturities and high coupons.e) None of the above.

(a) 4 According to the liquidity preference hypothesis yield curves generallyslope upward because

a)

Investors prefer short maturity obligations to long maturity obligations.b)

Investors prefer long maturity obligations toshort maturity obligations.

c)

Investors prefer less volatile long maturity obligations.d)Investors prefer more volatile short maturity

obligations.e)None of the above.

(b) 5 According to the segmented-market hypothesis a downward sloping yieldcurve indicates that

a) Demand for long-term bonds has fallen and demand for short-termbonds has fallen.

b)

Demand for long-term bonds has risen and demandfor short-term bonds has fallen.


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c) Demand for long-term bonds has fallen and demand for short-termbonds has risen.

d)

Demand for long-term bonds has risen and demand

for short-term bonds has risen.e)

None of the above.

(c) 6 According to the segmented-market hypothesis a rising yield curveindicates that

a) Demand for long-term bonds has fallen and demand for short-termbonds has fallen.

b)Demand for long-term bonds has risen and demandfor short-term bonds has fallen.

c) Demand for long-term bonds has fallen and demand for short-term

bonds has risen.d)

Demand for long-term bonds has risen and demandfor short-term bonds has risen.

e) None of the above.

(b) 7 According to the expectations hypothesis a rising yield curve indicatesthat investors expect

a)

Future short term rates to fallb)Future short term rates to risec)Future long term rates to rise

d)

Future long term rates to falle)

None of the above

(e) 8 The annual interest paid on a bond relative toits prevailing market price is called its

.

a)Promised yieldb)

Yield to maturityc)Coupon rated)

Effective yielde)Current yield

(b) 9 For a domestic bond the risk premium isdetermined by

a)

Credit quality, term to maturity and exchangerate risk.

b)

Credit quality, term to maturity and callfeatures.

c)Call features, sinking fund provisions andcountry risk.

d)Term to maturity, call features and inflation.


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e)

Credit quality, inflation and the risk freerate.

(d) 10 If the holding period is equal to the term tomaturity for a corporate bond the rate of discountrepresents the .

a)Coupon yieldb)

Effective yieldc)Yield to calld)Yield to maturitye)Reinvestment rate

(d) 11 Which of the following could be an explanation

for a downward sloping yield curve

a)

Borrowers prefer to sell short maturity issueswhile lenders prefer to invest in long maturityissues.

b)

Demand for long term bonds has risen and demandfor short term bonds has fallen.

c)

Investors prefer short maturity obligations tolong maturity obligations.

d)a) and b).e)b) and c).

(a) 12 The promised yield to maturity calculationassumes that

a)

All coupon interest payments are reinvested atthe current market interest rate for the bond.

b)All coupon interest payments are reinvested atthe coupon interest rate for the bond.

c)All coupon interest payments are reinvested atshort tem money market interest rates.

d)All coupon interest payments are not reinvested.e)None of the above

(a) 13 If the coupon payments are not reinvestedduring the life of the issue then the

a)

Promised yield is greater than realized yield.b)

Promised yield is less than realized yield.c)

Nominal yield declines.d)Nominal yield is greater than promised yield.e)

Current yield equals the yield to maturity.


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(c) 14 Consider a bond portfolio manager who expectsinterest rates to decline and has to choose betweenthe following two bonds.

Bond A: 10 years to maturity, 5% coupon, 5% yieldto maturityBond B: 10 years to maturity, 3% coupon, 4% yieldto maturity

a)Bond A because it has a higher coupon rate.b)

Bond A because it has a higher yield tomaturity.

c)Bond B because it has a lower coupon rate.d)Bond A or Bond B because the maturities are the

same.e)

None of the above.

(c) 15 measures the expected rate ofreturn of a bond assuming that you sell it prior toits maturity.

a)

Yield to maturityb)Current yieldc)

Realized yieldd)Coupon ratee)None of the above

(a) 16 The yield to call is a more conservative yieldmeasure whenever the price of a callable bond isquoted at a value

a)

Equal to or greater than par plus one year'sinterest.

b)Equal to par.c)

Equal to par less one year's interest.d)Less than par.e)Five percent over par.


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(c) 1 Assume that you purchase a 3-year $1,000 parvalue bond, with a 15% coupon, and a yield of 8%.After you purchase the bond, one- year interestrates are as follow, year 1 = 8%, year 2 = 10%,year 3 = 14% (these are the reinvestment rates).Calculate the realized horizon yield if you holdthe bond to maturity. Interest is paid annually.

a)9.37%b)7.28%c)

8.53%d)10.67%

e)

14.0%

(e) 2 Assume that you purchase a 10-year $1,000 parvalue bond, with a 5% coupon, and a yield of 9%.Immediately after you purchase the bond, yieldsfall to 7% and remain at that level to maturity.Calculate the realized horizon yield, if you holdthe bond for 5 years and then sell. Interest ispaid annually.

a)16.25%b)

12.15%c)

7.75%d)

9.05%e)

10.15%

(b) 3 Assume that you purchase a 10-year $1,000 parvalue bond, with a 4% coupon, and a yield of 7%.Immediately after you purchase the bond, yieldsrise to 8% and remain at that level to maturity.Calculate the realized horizon yield if you holdthe bond to maturity. Interest is paid annually.

a)

7.0%b)

7.18%c)

8.0%d)

15.25%e)

8.18%

THE FOLLOWING INFORMATION IS FOR THE NEXT FOUR PROBLEMS

A $1000 par value bond with 5 years to maturity and a 6% coupon has a yield to maturity of 8%.Interest is paid semiannually.


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(b) 4 Calculate the current price of the bond.

a)

$1579.46

b)

$918.89c)

$789.29d)

$1000e)

$743.29

(b) 5 Calculate the Macaulay duration for the bond

a)4.19 yearsb)4.36 yearsc)8.72 yearsd)

8.38 yearse)9.52 years

(a) 6 Calculate the modified duration for the bond

a)

4.19 yearsb)

4.36 yearsc)8.72 yearsd)


(a) 7 Estimate the percentage price change for this 5-year $1,000

par value bond, with a 6% coupon, if the yield rises from 8% to 8.5%. Interest ispaid semiannually.

a)

2.1%b)2.1%c)4.4%d)4.4%e)None of the above

(c) 8 Calculate the Macaulay duration for a 5-year$1,000 par value bond, with a 6% coupon and a yieldto maturity of 8%. Interest is paid annually.

a)6.44 yearsb)

5.25 yearsc)4.44 yearsd)

2.50 yearse)None of the above

(a) 9 A 15-year bond has a $1,000 par value bond, a 4% couponand a yield to maturity of 3.3%. Interest is paid annually. The bond's currentyield is


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a)

3.7%b)4.0%c)

3.3%

d)

7.3%e)

None of the above

(d) 10 A 5-year bond has a $1,000 par value bond, a 12% couponand a yield to maturity of 8%. Interest is paid semiannually. The bond's price is

a)$864.65b)

$1081.78c)$852.80d)$1162.22e)None of the above

(b) 11 A 15-year bond, purchased 5 years ago, has a $1,000 parvalue bond, a 10% coupon and a yield to maturity of 12%. Interest is paid

annually. The bond's price is

a)

$864b)$887c)

$1152d)

$1123e)

None of the above

(d) 12 A 20-year, $1,000 par value bond has an 11% coupon and iscurrently priced at par. Interest is paid semiannually. The bond's effective annualyield is

a)

5.50%b)

5.65%c)

11.00%d)11.30%e)

None of the above


Five years ago your firm issued $1,000 par, 20 year bonds with a6% coupon rate and an 8% call premium. The price of these bondsnow is $1103.80. Assume annual compounding.

(b) 13 Calculate the yield to maturity of these bondstoday.

a)

6%b)5%c)

8%d)7.31%


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e)

7.81%

(b) 14 If these bonds are now called, what is theactual yield to call for the investors whooriginally purchased them?

a)

6.83%b)7.38%c)

7.81%d)7.92%e)8.47%


You purchase an 8% coupon, 25 year, $1,000 par, semiannualpayment bond priced at $980 when it has 15 years remaining untilmaturity.

(c) 15 What is its yield to maturity?

a)4.12%b)

4.66%c)8.24%d)9.32%e)14.82%

(d) 16 What is the yield to call if the bond is called 5years from today with a 5% premium?

a)

4.12%b)

4.66%c)8.24%d)

9.32%e)14.82%

(b) 17 The current market price of MCB Corporation's bond is

$1122.50. A 12% coupon interest rate is paid annually, and the par value is equal

to $1,000. What is the yield to maurity if the bond matures ten years from today?

a)

9%b)10%c)

12%d)13%e)14%

(d) 18 Calculate the duration of a 6 percent, $1,000par bond maturing in three years if the yield to


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maturity is 10 percent and interest is paidsemiannually.

a)

1.35 yearsb)

1.78 yearsc)

2.50 yearsd)

2.78 yearse)

2.95 years

(d) 19 Calculate the modified duration for a 10-year, 12 percentbond with a yield to maturity of 10 percent and a Macaulay duration of 7.2 years.Assume semiannual compounding.

a)

6.43 years

b)

6.55 yearsc)

6.79 yearsd)


(a) 20 A 12-year, 8 percent bond with a YTM of 12 percent has aMacaulay duration of 9.5 years. If interest rates decline by 50 basis points, whatwill be the percent change in price for this bond? Assume semiannualcompounding.

a)

+4.48%b)

+4.61%c)

+8.48%d)+8.96%e)

+17.92%


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CHAPTER 12

ANSWERS TO MULTIPLE CHOICE PROBLEMS

1 The purchase price is = $1180.40 =

3

3

08.1

1000

08.

08.1

11

150

The terminal value of cash flows = $1509.10 =

150(1.1)(1.14) + 150(1.14) + 150 + 1000

The realized horizon yield = 8.53% =

140.1180

10.15093/1


10

10

09.11000

09.09.1

11

50

The selling price after 5 years is = $918 =

5

5

07.1

1000

07.

07.1

11

50

The terminal value of cash flows at year 5 = $1205.53 =

07.

107.150

5

+ 918



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129.743

53.12055/1


10

10

07.1

1000

07.

07.1

11

40

The terminal value of cash flows at year 10 = $1579.46 =

08.

108.140

10

+ 1000


129.789

46.157910/1

4 The price of the bond = $918.89 =

10

10

04.1

1000

04.

04.1

11

30

5 The present value of the weighted cash flows = $8015.41 =

30/(1.04) + 60/(1.04)2 + 90/(1.04)3 +120/(1.04)4+150/(1.04)5

180/(1.04)6+ 210/(1.04)7+ 240/(1.04)8+ 270/(1.04)9+

10300/(1.04)10

Macaulay duration = 8015.41/918.89 = 8.72

Or 8.72/2 = 4.36 years

6 Modified duration = 4.36/(1 + .04) = 4.19 years.

7 %price change = -(4.19 x 0.5) = -2.1%


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5

5

08.1

1000

08.

08.111

60

The present value of the weighted cash flows = $4084.82 =

60/(1.08) + 120/(1.08)2 + 180/(1.08)3

+ 240/(1.08)4 + 5300/(1.08)5

Macaulay duration = 4084.41/920.15 = 4.44 years


15

15

033.1

1000

033.

033.1

11

40

Current yield = 40/1081.78 = 3.7%


10

10

04.1

1000

04.

04.1

11

60

11 The price of the bond = $887 =

10

10

12.1

1000

12.

12.1

11

100

12 Since the bond is priced at par the yield tomaturity is 11% or 5.5% semiannual.

Effective annual yield = (1 + .055)2- 1 = 11.30%


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13 1103.80 =15

15

)1(

1000)1(

1

160

ytmytm

ytm

annual ytm = 0.05 or 5%

14 1000 =5

5

)1(

1000)1(

11

60ytcytc

ytc

ytc = 7.38% nominal yield

15 980 =30

30

)1(

1000)1(

11

40

ytmytm

ytm

annual ytm = 0.0412 x 2 or 8.24%

16 980 =10

10

)1(

1050)1(

11

40ytcytc

ytc

annual ytc = 0.0466 x 2 = 0.0932 or 9.32%

17 1122.50 =10

10

)1(

1000)1(

11

120ytmytm

ytm

annual ytm = 0.10 or 10%


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18 Macaulay Duration = PV of weighted cash flows/Currentprice = 5552.25/1000

= 5.55225 six month periods or 2.77613 years.

PV of weighted cash flows =

654321 05.1

61030

05.1

530

05.1

430

05.1

330

05.1

230

05.1

130 xxxxxx = 5552.25

Current price =$1000 since coupon rate is equal to yieldto maturity.

19 Dmod= 7.2/(1 + .10/2)

= 7.2/1.05 = 6.86 years

20 Dmod= 9.5/(1 + .12/2)

= 9.5/1.06 = 8.96 years

%P = -Dmodx i

= -(8.96) x (-0.005) = 0.0448

= 4.48% increase


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CHAPTER 17

AN INTRODUCTION TO DERIVATIVE INSTRUMENTS


(t) 1 A cash or spot contract is an agreement for theimmediate delivery of an asset such as the purchaseof stock on the NYSE.

(t) 2 Forward and futures contracts, as well as options,are types of derivative securities.

(t) 3 If an investor wants to acquire the right to buy orsell an asset, but not the obligation to do it, the

best instrument is an option rather than a futurescontract.

(f) 4 Investment costs are generally higher in thederivative markets than in the corresponding cashmarkets.

(t) 5 Forward contracts are traded over-the-counter andare generally not standardized.

(t) 6 The forward currency market has low liquidityrelative to the currency futures market.

(f) 7 A futures contract is an agreement between a traderand the clearinghouse of the exchange for deliveryof an asset in the future.

(t) 8 A primary function of futures markets is to allowinvestors to transfer risk.

(f) 9 The futures market is a dealer market where all thedetails of the transactions are negotiated.

(t) 10 For futures, the initial margin requirement isquivalent to 3-6 percent of the contract's value.

(t) 11 Since futures contracts are "marked-to-market"daily, the gains and losses are settled daily.

(f) 12 Due to daily marking-to-market, the clearinghouseexperiences major swings in their net balances toensure stability for the investors.

(t) 13 If you have entered into a currency futures hedgefor the Japanese yen in connection with buyingJapanese equipment, if the yen goes from 110 yen/$1to 100 yen/$1, you will lose in the spot market buthave an offsetting gain in the futures market.


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(f) 14 According to put call parity:

Call Price + Put Price = Stock Price + Risk Free

Bond Price

(f) 15 The intrinsic value of a call option is Max[0,Exercise Price Stock Price]

(f) 16 The intrinsic value of a put option is Max[0, StockPrice Exercise Price]

(f) 17 Options that can be exercised at any up to andincluding the expiration day are called EuropeanOptions.

(f) 18 Options that can only be exercised on the

expiration day are called American Options.

(t) 19 A call option with an exercise price of $45 and aprice of $5.50 will be in the money if the price ofthe underlying stock is $50.

(f) 20 A put option with an exercise price of $60 and aprice of $0.50 will be in the money if the price ofthe underlying stock is $70.


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(a) 1 Which of the following is a reason for the

existence of derivatives?

a)

They help shift risk from risk-averse investorsto risk-takers.

b)

They help shift risk from risk-takers to risk-averse investors.

c)

They allow investors to speculate.d)They allow investors to purchase assets with

less risk.e)They allow investors to earn above average

returns.

(b) 2 If you enter into a forward contract agreeing topurchase an asset at a specified price at a futurespecified date

a)

You would be short forward.b)

You would be long forward.c)You would be long futures.d)

You would be short futures.e)None of the above.

(b) 3 Futures differ from forward contracts because

a)

Forwards have less liquidity risk.b)

Futures have less credit risk.c)

Futures have less maturity risk.d)

Forwards are marked to market.e)

Forwards have less credit risk.

(e) 4 Future contracts can be used by portfolio managers to?

a)Protect the investment portfolio againstinflation in the economy.

b)Seek protection against the increasing

volatility of interest rates.c)

Adjust asset allocation.d)

a) and b).e)

b) and c)

(c) 5 A call option differs from a put option in that

a)

a call option obliges the investor to purchase agiven number of shares in a specific commonstock at a set price; a put obliges the investor


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to sell a certain number of shares in a commonstock at a set price.

b)

both give the investor the opportunity to

participate in stock market dealings without therisk of actual stock ownership.

c)

a call option gives the investor the right topurchase a given number of shares of a specifiedstock at a set price; a put option gives theinvestor the right to sell a given number ofshares of a stock at a set price.

d)a put option has risk, since leverage is not asgreat as with a call.

e)None of the above

(b) 6 Which of the following statements is a true

definition of an out-of-the-money option?

a)

A call option in which the stock price exceedsthe exercise price.

b)

A call option in which the exercise priceexceeds the stock price.

c)A call option in which the exercise priceexceeds the stock price.

d)A put option in which the exercise price exceedsthe stock price.

e)A call option in which the call premium exceedsthe stock price.

(d) 7 If you were to sell a June call option with anexercise price of 50 for $8 and simultaneously buya June call option with an exercise price of 60 for$3, you would be

a) Bullish and taking a high risk.b) Bullish and conservative.c) Bearish and taking a high risk.d) Bearish and conservative.e) Neutral.

(a) 8 The value of a call option just prior to expirationis (where V is the underlying asset's market priceand X is the option's exercise price)

a)

Max [0, V - X]b)

Max [0, X - V]c)Min [0, V - X]d)

Min [0, X - V]e)Max [0, V > X]


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(c) 9 A horizontal spread involves buying and sellingcall options in the same stock with

a)

The same expiration date and strike price.b)

The same expiration date but different strikeprice.

c)

A different expiration date but same strikeprice.

d)A different expiration date and different strikeprice.

e)Options in different markets.

(b) 10 According to put/call parity

a)Stock price + Call Price = Put Price + Risk Free

Bond Priceb)

Stock price + Put Price = Call Price + Risk FreeBond Price

c)

Put price + Call Price = Stock Price + Risk FreeBond Price

d)

Stock price - Put Price = Call Price + Risk FreeBond Price

e)

Stock price + Call Price = Put Price - Risk FreeBond Price

(b) 11 Which of the following statements does notapply toa put option?

a)

You can sell a put option as a means to buy astock at a price below the current market price.

b)

To protect against a decline in prices of astock you own, you could sell a put optionagainst your position.

c)You would buy a put option for a volatile stockyou want to buy with good long-term prospectsbut uncertain near term prospects.

d)You would sell an option on a stock you expectto increase in price to earn extra income.

e)

If you hedge a long profit position and thestock continues to increase in price, your putoption will expire worthless.

(a) 12 You own a stock which has risen from $10 per shareto $32 per share. You wish to delay taking theprofit but you are troubled about the short runbehavior of the stock market. An effective actionon your part would be to

a)Purchase a put.b)Purchase a call.


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c)

Purchase an index option.d)Utilize a bearish spread.e)

Utilize a bullish spread.

(b) 13 If you were to purchase an October call option withan exercise price of $50 for $8 and simultaneouslysell an October call option with an exercise priceof $60 for $2, you would be

a)Bullish and taking a high risk.b)Bullish and conservative.c)Bearish and taking a high risk.d)Bearish and conservative.e)

Neutral.

(b) 14 A vertical spread involves buying and selling calloptions in the same stock with

a)

The same expiration date and strike price.b)

The same expiration date but different strikeprice.

c)

A different expiration date but same strikeprice.

d)A different expiration date and different strikeprice.

e)Options in different markets.

(b) 15 A stock currently sells for $75 per share. A calloption on the stock with an

exercise price $70 currently sells for $5.50. Thecall option is

a)

At-the-money.b)In-the-money.c)Out-of-the-money.d)At breakeven.e)None of the above.

(c) 16 A stock currently sells for $150 per share. A calloption on the stock with an

exercise price $155 currently sells for $2.50. Thecall option is

a)

At-the-money.b)In-the-money.c)

Out-of-the-money.d)At breakeven.e)None of the above.


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(c) 17 A stock currently sells for $75 per share. A putoption on the stock with an

exercise price $70 currently sells for $0.50. The

put option is

a)

At-the-money.b)

In-the-money.c)

Out-of-the-money.d)At breakeven.e)

None of the above.

(a) 18 A stock currently sells for $15 per share. A putoption on the stock with an

exercise price $15 currently sells for $1.50. Theput option is

a)

At-the-money.b)

In-the-money.c)

Out-of-the-money.d)

At breakeven.e)

None of the above.

(b) 19 A stock currently sells for $15 per share. A putoption on the stock with an

exercise price $20 currently sells for $6.50. Theput option is

a)

At-the-money.b)

In-the-money.c)

Out-of-the-money.d)

At breakeven.e)

None of the above.


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(a) 1 A stock currently trades for $25. January call

options with a strike price of$20 sell for $6. The appropriate risk free bond has

a price of $30. Calculate the price of the Januaryput option.

a)$11b)

$24c)$19d)$30e)$25

(e) 2 A stock currently trades for $115. January call

options with a strike price of $100 sell for $16,and January put options a strike price of $100 sell for $5.

Estimate the price of a risk free bond.

a)

$120b)

$15c)$105d)

$116e)$104

(d) 3 Assume that you have purchased a call option with astrike price $60 for $5.

At the same time you purchase a put option on thesame stock with a strike price of $60 for $4. Ifthe stock is currently selling for $75 per share,calculate the dollar return on this optionstrategy.

a) $10b) -$4c) $5d) $6e) $15

(c) 4 Assume that you purchased shares of a stock at aprice of $35 per share. At

this time you purchased a put option with a $35strike price for $3. The stock currently trades at$40. Calculate the dollar return on this option

strategy.

a)

$3b)-$2c)$2d)-$3e)$0


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(c) 5 Assume that you purchased shares of a stock at a

price of $35 per share. Atthis time you wrote a call option with a $35 strike

and received a call price of $2. The stockcurrently trades at $70. Calculate the dollar return on this

option strategy.

a)

$25b)-$2c)$2d)-$25e)$0

(b) 6 A stock currently trades at $110. June call optionson the stock with a strike

price of $105 are priced at $4. Calculate thearbitrage profit that you can earn

a) $0b) $1c) $5d) $4e) None of the above

(c) 7 Datacorp stock currently trades at $50. August calloptions on the stock

with a strike price of $55 are priced at $5.75.October call options with a strike price of $55 arepriced at $6.25. Calculate the value of the time

premium between the August and October options.

a) -$0.50b) $0c) $0.50d) $5e) -$5

(a) 8 A stock currently trades at $110. June put optionson the stock with a strike

price of $115 are priced at $5.25. Calculate thedollar return on one put contract.

a) -$25b) $500c) $0d) -$75e) $525


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(d) 9 A stock currently trades at $110. June call optionson the stock with a strike

price of $105 are priced at $5.75. Calculate the

dollar return on one call contract.

a) -$50b) $500c) $575d) -$75e) $0

(e) 10 Consider a stock that is currently trading at $50.Calculate the intrinsic

value for a put option that has an exercise priceof $55.

a) $0b) $50c) $55d) $105e) $5

(a) 11 Consider a stock that is currently trading at $50.Calculate the intrinsic value

for a put option that has an exercise price of $35.

a) $0b) $50c) $35d) $15e) $85

(e) 12 Consider a stock that is currently trading at $25.Calculate the intrinsic

value for a call option that has an exercise priceof $35.

a) $25

b) $35c) $10d) -$10e) $0

(c) 13 Consider a stock that is currently trading at $25.Calculate the intrinsic

value for a call option that has an exercise priceof $15.

a) $25b) $35


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c) $10d) $60e) $0

USE THE FOLLOWING INFORMATION FOR THE NEXT THREE PROBLEMS

December futures on the S&P 500 stock index trade at 250 timesthe index value of 1187.70. Your broker requires an initialmargin of 10% percent on futures contracts. The current value ofthe S&P 500 stock index is 1178.

(c) 14 How much must you deposit in a margin account ifyou wish to purchase

one contract?

a)

$267,232.5b)

$29,450c)

$29,692.50d)

$30,000e)

$265,050

(c) 15 Suppose at expiration the futures contract price is250 times the index value

of 1170. Disregarding transaction costs, what isyour percentage return?

a)

1.87%b)

-0.68%c)

-14.90%d)

10.36%e)

None of the above

(b) 16 Calculate the return on a cash investment in theS&P 500 stock index over

the same time period

a)

1.87%

b)

-0.68%c)

-14.90%d)

10.36%e)

None of the above


A futures contract on Treasury bond futures with a Decemberexpiration date currently trade at

103:06. The face value of a Treasury bond futures contract is$100,000. Your broker requires an

initial margin of 10%.


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(c) 17 Calculate the current value of one contract

a)

$100,000b)

$103,600.5c)

$103,187.5d)

$102,306.3e)

$104,293.5

(c) 18 Calculate the initial margin deposit

a)$10,000b)

$10,360.50c)$10,318.75

d)

$10,230.63e)

$10,429.35

(b) 19 If the futures contract is quoted at 105:08 atexpiration calculate the

percentage return

a)1.99%b)19.99%c)20.62%d)25.37%e)

-13.65%

(e) 20 In your portfolio you have $1 million of 20 year,8 5/8 percent bonds which are selling at 83.15 (or83 15/32) against this position. Because you feelinterest rates will rise you sell 10 bond futuresat 81:15 (or 81 15/32) against this position. Twomonths later you decide to close your position.The bonds have fallen to 78 and the futurescontracts are at 75:16 (75 16/32). Disregardingmargin and transaction costs, what is your gain orloss?

a)

$5,000 lossb)

$500 lossc)

Breakevend)

$500 gaine)

$5,000 gain


On the last day of October, you are considering the purchase of100 shares of Trivia Corporation common stock selling at $32 3/8per share and also considering one Trivia option contract.


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Calls Puts

Price December March December

March30 3 3/4 5 1 1/42

35 2 1/2 3 1/2 4 1/2 4 3/4

(d) 21 If you decide to buy a March call option with anexercise price of 30, what is your dollar gain(loss) if you close the position when the stock isselling at 38 7/8?

a)$187.50 gainb)

$225.00 gainc)$287.50 gain

d)

$387.50 gaine)

$427.50 gain

(b) 22 If Bruce buys a March put option with an exerciseprice of 35, what is his dollar gain (loss) if hecloses his position when the stock is at 38 7/8?

a)$600.00 lossb)$475.00 lossc)$387.50 lossd)$25.00 losse)

He has a gain


John Shamrock is considering the following alternatives forinvesting in Clover Industries, which is now selling for $27 pershare:

1) Buy 100 shares,2) Buy 100 shares with a 60 percent margin depositand3) Buy a six month call option with a strike price

of $25 for $500.

(d) 23 Assuming no commissions or taxes what is theannualized percentage gain if the stock reaches $32in four months and was purchased on margin?

a)18.56%b)

30.86%c)46.30%d)92.59%e)128.90%


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(b) 24 Assuming no commissions or taxes what is the

annualized percentage gain if the stock reaches $32

in four months and a call was purchased?

a)

40%b)

120%c)

180%d)300%e)

360%


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CHAPTER 17


1 P = 6 + 30 25 = $11

2 Bond price = 115 + 5 16 = $104

3 Profit on call = (75 60) 5 = 10Profit on put = -4Total = $6

4 Profit on stock = 40 35 = 5Profit on put = -3Total = $2

5 Profit on stock = 70 35 = 25Profit on call = 35 70 + 2 = -23Total = $2

6 Arbitrage profit = 110 105 4 = $1

7 Time premium = 6.25 5.75 = $0.50

8 Dollar return = (115 110 5.25)(100) = -$25

9 Dollar return = (110 105 5.75)(100) = -$75

10 Put = Max[55 50, 0] = $5

11 Put = Max[35 50, 0] = $0

12 Call = Max[25 35, 0] = $0

13 Call = Max[25 15, 0] = $10

14 Margin = 0.10 x 250 x 1187.70 = $29,692.50

15 Purchase December contract250 x 1187.7 = $296,925

Sell December contract250 x 1170 = $292,500

Loss in futures = $292,500 - $296,925 = -$4425

Rate of return = -$4425/29,692.50 = -.1490 or -14.9%

16 Return on cash investment in the index = (1170 1178)/1178 = -0.0068 or 0.68%


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17 Current price is 103 6/32 percent of face value of$100,000

= 1.031875 x 100,000 = $103,187.50

18 Margin deposit = 0.10 x 103,187.5 = $10,318.75

19 Purchase December contract103 6/32 percent of 100,000 = $103,187.50

Sell December contract105 8/32 percent of $100,000 = $105,250

Gain in futures = $105,250 - $103,187.50 = $2,062.50

Rate of return = 2062.5/10318.75 = 0.1999 or 19.9%

20 BondsValue of portfolio (now) $834,687.50Value of portfolio (2 mo.) 780,000.00

Loss in value $54,687.50

FuturesSell 10 bond futures (now) $814,687.50

Buy 10 bond futures (2 mo.) 755,000.00

Gain in futures $59,687.50

Net gain = Gain in futures - loss in bond value= $59,687.50 - $54,687.50= $5,000

21 Max[0, 38 7/8 - 30] - 5 = $3 7/8 per share or $387.50 per 100 shares

22 Max[0, 35 - 38 7/8] - 4 3/4 = -4 3/4 per share or $475 lossper 100 shares

23 Margin = .60 x ($27 x 100 shares) = $1,620

Rate of return = (3200 2700)/1620 = 30.86%

Annualized rate of return = 30.86% x 12/4 = 92.59%


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24 Max[0,32 - 25] - 5 = $2 per share or $200 per contract

Rate of return = $200/$500 = 40%

Annualized rate of return = 40% x 12/4 = 120%


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CHAPTER 18

DERIVATIVES: ANALYSIS AND VALUATION


(f) 1 The owner of a call option on a futures contracthas the obligation to buy the futures contract at apredetermined strike price during a specified timeperiod.

(f) 2 Options on futures expire at the same time thefutures contract expires.

(t) 3 A warrant is an option to buy a stated number ofshares of common stock at a specified price at anytime during the life of the warrant.

(f) 4 A major difference between a call option and awarrant is that call options are issued by thecompany so that any proceeds from the sale of stockgo to the issuing firm.

(f) 5 According to the cost of carry model the futuresprice is the present value of the spot pricediscounted at the risk free rate.

(t) 6 In the cost of carry model the inclusion of storagecosts will increase the futures price.

(f) 7 The inclusion of dividends in the cost of carrymodel will increase the futures price.

(t) 8 The basis (Bt,T) at time t between the spot price(St) and a futures contract expiring at time T(Ft,T) is: St- Ft,T.

(f) 9 A riskless stock index arbitrage profit is possibleif the following condition holds: F0,T= S0(1 + rf

d)

T

, where spot price now is S0, value now of afutures contract expiring at time T is (F0,T), rfisthe risk free rate and d is the dividend.

(f) 10 One S&P 500 stock index futures option contract ispriced at $500 times the premium.

(f) 11 The underlying stock price and the value of the putoption are factors that impact the value of anAmerican call option.

(t) 12 The cost of carry is the foregone interest frominvesting in a risk free asset.


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(t) 13 The binomial option pricing model approximates the

price of an option obtained using the Black-Scholes

option pricing model as the number of subintervalsincreases.

(f) 14 Callable bonds allow the issuer the option sellingthe bonds a fixed price.

(f) 15 The intrinsic value of a warrant = (Market price ofcommon stock + Warrant exercise price) x Number ofshares specified by warrant.

(t) 16 By attaching a convertible feature to a bond issuea firm can often get a lower rate of interest onits debt.

(t) 17 The investment value of a convertible bonds is theprice which it would be expected to sell as astraight debt instrument.

(f) 18 The conversion parity price is equal to the parvalue of a convertible bond divided by the numberof shares into which it can be converted.


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(a) 1 According to the cost of carry model therelationship between the spot (S0) and futuresprice (F0,T) is

a)

S0= F0,T/(1 + rf)T

b)S0= F0,T(1 + rf)T

c)

S0+ F0,T= (1 + rf)T

d)S0= F0,T+ (1 + rf)T

e)S0- F0,T= (1 + rf)T

(b) 2 The inclusion of the following in the cost of carrymodel will increase the

futures price

a)

Dividendsb)

Storage costsc)

Interest rated)

a) and b)e)None of the above

(b) 3 The basis (Bt,T) at time t between the spot price(St) and a futures contract expiring at time T(Ft,T) is

a)

Bt,T= St+ Ft,Tb)

Bt,T= St- Ft,Tc)

Bt,T= Stx Ft,Td)

Bt,T= St/ Ft,Te)

None of the above

(d) 4 A riskless stock index arbitrage profit is possibleif the following condition

holds:a)F0,T= S0(1 + rf d)

Tb)

F0,T> S0(1 + rf d)T

c)

F0,T< S0(1 + rf d)

T

d)

a) and b)e)

b) and c)

(d) 5 The value of a call option is positively relatedto:

a)

Underlying stock price.b)Time to expirationc)Exercise price.d)a) and b)e)b) and c)


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(c) 6 The value of a call option is inversely related to:

a)

Underlying stock price.b)

Time to expirationc)

Exercise price.d)

a) and b)e)b) and c)

(b) 7 The intrinsic value of a warrant is calculated as:

a)(Market price of common stock + Warrant exerciseprice) x Number of shares specified by warrant.

b)(Market price of common stock - Warrant exercise

price) x Number of shares specified by warrant.c)

(Market price of common stock + Warrant exerciseprice) / Number of shares specified by warrant.

d)

(Market price of common stock - Warrant exerciseprice) / Number of shares specified by warrant.

e)

None of the above.

(e) 8 An advantage of convertible bonds is

a)Investors get the upside potential of a bond.b)Investors get the upside potential of a stock.c)

Issuing firms can get a lower rate of intereston its debt.

d)

a) and b).e)

b) and c).

(d) 9 Warrants differ from options in a number of ways.Which of the following statements about warrantsand options is false?

a)When originally issued, the life of a warrant isusually much longer than that of a call option.

b)

Warrants are usually issued by the company on

whose stock the warrant is written.c)

Warrants are often used by companies assweeteners to make new issues of debt or equitymore attractive.

d)

Warrant holders have voting rights while optionholders do not.

e)

None of the above (that is, all statements aretrue)

(b) 10 If the hedge ratio is 0.50, this indicates that theportfolio should hold


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a.

Two shares of stock for every call optionwritten.

b.

One share of stock for every two call options

written.c.

Two shares of stock for every call optionpurchased.

d.

One share of stock for every two call optionspurchased.

e.Two call options for every put option written.

(a) 11 All of the following are normal characteristics ofa convertible bond, except

a)Conversion at the option of the issuer.b)

Conversion into a fixed number of shares ofcommon stock.

c)

A conversion price initially above the marketprice of the common stock.

d)

An interest rate lower than that on straightdebentures.

e)

Subordination.

(b) 12 The minimum price of a convertible bond is

a)

Min (Bond Value, Conversion Value).b)Max (Bond Value, Conversion Value).c)

Min (Stock Value, Conversion Value).d)Max (Stock Value, Conversion Value).

e)

None of the above.

(d) 13 The conversion premium for a convertible bond iscalculated as:

a)

(Market Price + Minimum Value) / Minimum Value.b)

(Market Price / Minimum Value) x Minimum Value.c)

(Market Price + Minimum Value) x Minimum Value.d)(Market Price - Minimum Value) / Minimum Value.e)

(Market Price x Minimum Value) / Minimum Value.

(a) 14 The conversion price parity for a convertible bondis defined as:

a)Market Price of Convertible Bond / ConversionRation.

b)

Market Price of Convertible Bond x ConversionRation.

c)

Market Price of Convertible Bond - ConversionRation.

d)

Market Price of Convertible Bond + ConversionRation.

e)

None of the above.


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THE following INFORMATION IS FOR THE NEXT TWO PROBLEMS

A stock currently trades for $120 per share. Options on the stock are available with a strike price

of $125. The options expire in 30 days. The risk free rate is 3% over this time period, and the

expected volatility is 0.35.

(d) 1 Use the Black-Scholes option pricing model tocalculate the price of a call option.

a)

$5.935b)$4.935c)

$3.935d)$2.935e)

None of the above

(a) 2 Calculate the price of the put option.

a)$7.623b)

$8.623c)$9.623

a)

$10.623b)None of the above

THE following INFORMATION IS FOR THE NEXT THREE PROBLEMS

A 3-month T-bond futures contract (maturity 20 years, coupon 6%, face $100,000) currently

trades at $98,781.25 (implied yield 6.11%). A 3-month T-note futures contract (maturity 20

years, coupon 6%, face $100,000) currently trades at $101,468.80 (implied yield 5.80%).

(b) 3 If you expected the yield curve to steepen, theappropriate NOB futures spread strategy would be

a)Go long the T-bond and short the T-noteb)Go short the T-bond and long the T-notec)Go long the T-bond and long the T-noted)

Go short the T-bond and short the T-notee)None of the above


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(a) 4 If you expected the yield curve to flatten, theappropriate NOB futures spread strategy would be

a)

Go long the T-bond and short the T-noteb)

Go short the T-bond and long the T-notec)

Go long the T-bond and long the T-noted)

Go short the T-bond and short the T-noteA)NONE OF THE ABOVE

(c) 5 Suppose the yield curve did flatten so the that theyield on the T-bond contract fell to 5.95% and theyield on the T-note rose to 5.85%. Calculate theProfit on the NOB futures spread. (Assume couponsare paid annually)

a)

-$5850.92b)-$2144.17c)

$2144.17b)$5850.92c)

None of the above

THE following INFORMATION IS FOR THE NEXT FOUR PROBLEMS

The S&P 500 stock index is at 1106.59. The annualized interest rate is 5% and the annualized

dividend is 2%.

(b) 6 Calculate the price now of a one year futurescontract .

a)

1106.59b)

1112.12c)

1139.79d)

1123.19e)None of the above

(b) 7 If the futures contract was currently available for1250, indicate the appropriate strategy that wouldearn an arbitrage profit.

a)Long futures, and short the index.b)

Short futures and long the index.c)Long futures and long the index.d)

Short futures and short the index.e)None of the above.


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(a) 8 If the futures contract was currently available for1050, indicate the appropriate strategy that wouldearn an arbitrage profit.

a)

Long futures, and short the index.b)

Short futures and long the index.c)

Long futures and long the index.a)

Short futures and short the index.b)None of the above.

(d) 9 If the futures contract was currently available for1250, calculate the arbitrage profit.

a)0b)143.41

c)

143.41d)137.84e)

-137.84

The following information is for the next FIVE problems

A coffee dealer expects to purchase 120,000 pounds of coffee in three months. To hedge theprice of coffee he plans to take a long position in a 3-month coffee futures contract prices at$0.5595 per pound. Each coffee futures contract is for 37,500 pounds and therefore the dealerpurchases 3 contracts. The current spot price for coffee is $0.485 per pound. Assume that threemonths from now the spot and futures prices are both $0.60 per pound.

(d) 10 Calculate the number of pounds, of the planned120,000 pound purchase, that is unhedged

a)45000b)

75000c)5000d)7500e)

4000

(b) 11 Calculate the basis now.

a)

$0b)

-$0.0745c)

$0.0745d)-$0.0405e)

$0.115

(a) 12 Calculate the basis three months from now.

a)

$0b)-$0.0745


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c)

$0.0745d)-$0.0405e)

$0.115

(e) 13 Calculate the profit or loss on the futuresposition at the end of three months.

a)$0b)

-$4500.25c)$4500.25d)-$4556.25e)$4556.25

(c) 14 Calculate the effective price at which the dealer

purchased the coffee.

a)

$0.5595b)

$0.485c)

$0.562d)

-$0.60e)$0.5223

(e) 15 Consider an asset that has a spot price of $650.The asset has a monthly dividend yield of 0.15%.Storage and insurance cost are 0.3% per month andthe monthly T-bill rate is 0.67%. Transaction costsare 0.45%. Calculate the non arbitrage price rangefor a 6 month futures contract.

a)

$683.54 and $705.63b)

$679.57 and $715.13c)$650.00 and $685.71d)

$650.00 and $679.57e)$679.57 and $685.71

(c) 16 Consider an asset that has a spot price of $650.The asset has a monthly dividend yield of 0.15%.

Storage and insurance cost are 0.3% per month andthe monthly T-bill rate is 0.67%. Calculate thefutures price for a 9-month contract.

a) $705.63b) $715.13c) $699.57d) $680.58e) $665.75

(a) 17 Three-month corn futures contracts currently sellfor 510 cents per bushel. Storage and insurance


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cost are 0.3% per month. The three-month T-billrate is 2% over this three month period. Calculatethe spot price for corn.

a) $5.3515b) $5.2323c) $6.2515d) $6.2323e) $5.1015

(d) 18 The spot price of a commodity is $1200. If the T-bill rate is 9% annualized, calculate the price fora 9-month futures contract on the commodity.

a) $2606.27

b) $1312.56c) $1227.20d) $1283.47e) $1200.00

USE THE FOLLOWING INFORMATION TO ANSWER THE NEXT THREE QUESTIONS

The information provided is relevant in the context of a oneperiod (one year) binomial option pricing model. A stockcurrently trades at $50 per share, a call option on the stock hasan exercise price of $45. The stock is equally likely to rise by

25% or fall by 25%. The one-year risk free rate is 2%.

(b) 19 Calculate the possible prices of the stock one yearfrom today

a)

$37.50 or $17.50.b)

$62.50 or $37.50.c)

$62.50 or $17.50.d)

$50 or $45.e)

None of the above.

(a) 20 Estimate n, the number of call options that must be

written

a)-1.4286b)

-2.9286c)-2.8571d)

-2.5714e)

-1.1111

(c) 21 Calculate the price of the call option today (C0)

a)$7.56


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b)

$17.48c)$9.26d)

$5.0

e)

$17.15

USE THE FOLLOWING INFORMATION TO ANSWER THE NEXT FOUR QUESTIONS

The following information is provided in the context of a twoperiod (two six month periods) binomial option pricing model. Astock currently trades at $60 per share, a call option on thestock has an exercise price of $65. The stock is equally likelyto rise by 15% or fall by 15% during each six month period. Theone-year risk free rate is 3%.

(c) 22 Calculate the possible prices of the stock at the

end of one year

a)$69, $51, $79.35b)$51, $79.35, $58.65c)

$79.35, $58.65, $43.35d)$58.65, $43.35, $14.35e)

None of the above

(a) 23 Calculate the price of the call option after thestock price has already moved up in value once (Cu)

a)$7.77

b)

$14.35c)$0d)$4.21e)

$6.44

(c) 24 Calculate the price of the call option after thestock price has already moved down in value once(Cd)

a)

$7.77b)$14.35c)

$0

d)

$4.21e)$6.44

(d) 25 Calculate the price of the call option today (C0)

a)

$7.77b)

$14.35c)

$0d)

$4.21e)$6.44


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(d) 26 The exercise price of warrants for the stock of ABC

Corporation is $17. You purchase the warrants for

$4 each when ABC's stock price is $20 a share. Eachwarrant entitles you to purchase one share of ABCCorporation. Calculate your rate of returnassuming the warrant premium drops by 50 percentand you sell your warrants when the stock reaches$30 per share.

a) 37.5%b) 87.5%c) 137.5%d) 237.5%e) 337.5%


BioTech Industries has debentures outstanding (par value $1,000)convertible into the company's common stock at $30. The couponrate is 11 percent payable semiannually and they mature in 10years.

(d) 27 Calculate the conversion value of the bond if thestock price is $27.00 per share.

a) $ 600.00b) $ 700.00c) $ 800.00d) $ 900.00e) $1,000.00

(c) 28 Calculate the straight-bond value assuming thatbonds of equivalent risk and maturity are yielding13 percent per year compounded semiannually.

a) $757.37b) $796.83

c) $889.82d) $902.65e) $942.65

(d) 29 At present, what would be the minimum value of thebond?

a) $600.00b) $796.83c) $889.82d) $900.00e) $1000.00


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CHAPTER 18


1 Price using the B-S option pricing model

d1 = ln(120/125) + [(.03 + 5(.352))(.0833)]/(.35(.0833.5))= -0.3288

d2 = -0.3288 - (.35(.0833.5)) = -0.4298

N(d1) = 0.3712N(d2) = 0.3337

Call price = Pc = 120[0.3712 125(e-.03(.0833))(0.3337]

= $2.935

2 Put price = 2.935 + 125(e-.03(.0833)) 120 = $7.623

3 If you expected the yield curve to steepen, theappropriate NOB futures spread strategy would be go shortthe T-bond and long the T-note

4 If you expected the yield curve to flatten, the appropriate NOB futures spread strategy wouldbe go long the T-bond and short the T-note

5 First calculate the new prices of the T-bond and T-notes contracts using bond valuations

formulas with annual compounding. T-bond price = $100,580.21. T-note price =$101,123.59.

NOB profit = (100580.21 98781.25) + (101468.80 101123.59) = $2144.17

6 F(0, T) = 1106.59 + 1106.59(.00833 - .0033) = 1112.12

7 Since the futures contract is trading above itstheoretical value the appropriate strategy would be toshort the futures contract and go long the index.

8 Since the futures contract is trading below itstheoretical value the appropriate strategy would be to golong the futures contract and short the index.

9 You should short futures at $1250. Borrow at the rate of 0.833% (5%/(360/60)) to buy theindex at $1106.59. Hold for 60 days, then collect dividends and repayloan.

The net profit =1250 1106.59 1106.59(.00833 - .0033) = $137.84

10 Number of unhedged pounds = 120,000 3(37,500) = 7500


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11 Basis now = 0.485 0.5595 = -$0.0745

12 Basis three months from now = 0.60 0.60 = $0

13 Profit on the futures contract= (0.60 0.5595)(3)(37,500) = $4556.25

14 Effective price = [(120,000)(0.60) 4556.25]/120,000= $67,443.75/120,000 = $0.5620

15 The price range is650(1 0.0045)(1 + 0.0067 + 0.003 0.0015)6 =

$679.57

650(1 + 0.0045)(1 + 0.0067 + 0.003 0.0015)6 =$685.71

16 F(0, 9)) = 650( 1 + 0.0067 + 0.003 0.0015)9= $699.57

17 S(0) = 550/(1 + 0.0067 + 0.003)3= $5.3515

18 F(0, 9) = 1200(1 + 0.0075)9= $1283.47

19 If the stock rises the price one year for now will be =50(1 + 0.25) = $62.50

If the stock falls the price one year for now will be =50(1 - 0.25) = $37.50

20 Current stock price = $50Exercise price = $45Risk free rate = 2%Price in one year if stock rises = 50(1.25) = $62.50Price in one year if stock declines = 50(1.25) = $37.50

Intrinsic value of call option if stock rises to $62.50 =Max[0, 62.50 45] = $17.50Intrinsic value of call option if stock falls to $37.50 =Max[0, 37.50 45] = $0

Estimate the number calls needed by setting:The hedge portfolio will consist of one share of stock heldlong plus some number of call options written.Value of hedge portfolio if stock rises = Value of hedgeportfolio if stock falls

62.50 + (17.5)(n) = 37.50 + (0)(n)

n = -1.4286

21 Value of hedge portfolio today = 50 (1.4286)(C0) =37.5/(1.02)


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C0 = $9.26

22 Current stock price = $60Price in one year if stock rises 15% per six month period=60(1.15)(1.15) = $$79.35Price in one year if stock rises 15%, then falls 15% =60(1.15)(0.85) = $58.65Price in one year if stock declines 15% per period =60(0.85)(0.85) = $43.35

23 Current stock price = $60Exercise price = $65Risk free rate = 3% or 1.49% per six month period = (1.03)0.5

1 = 0.0149Price in six months if stock rises 15% = 60(1.15) = $69Price in six month if stock falls 15% = 60(0.85) = $51Price in one year if stock rises 15% per six month period=60(1.15)(1.15) = $$79.35Price in one year if stock rises 15%, then falls 15% =60(1.15)(0.85) = $58.65Price in one year if stock declines 15% per period =60(0.85)(0.85) = $43.35

Intrinsic value of call option if stock rises to $79.35 =Max[0, 79.35 65] = $14.35

Intrinsic value of call option if stock falls to $58.65=Max[0, 58.65 65] = $0Intrinsic value of call option if stock falls to $43.35 =Max[0, 43.35 65] = $0

Estimate the number calls needed by constructing a hedgeportfolio.The hedge portfolio will consist of one share of stock heldlong plus some number of call options written.

At the end of the first six month period:Value of hedge portfolio if stock rises = Value of hedge

portfolio if stock falls

79.35 + (14.35)(n) = 58.65 + (0)(n)

n = -1.44251

Value of hedge portfolio at the end of first six months = 69 (1.44251)(Cu) = 58.65/(1.0149)

Cu = $7.7719


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24 Cd= 0. Since the ending stock prices of $58.65 and $43.35are both below the exercise price.

25 To solve for the value of the call today (C0), firstdetermine the number of calls by constructing a hedgeportfolio where:

Right now:Value of hedge portfolio if stock rises = Value of hedgeportfolio if stock falls

69 + (7.7719)(n) = 51 + (0)(n)

n = -2.31603

Value of hedge portfolio now = 60 (2.31603)(C0) =51/(1.0149)

C0 = $4.2092

26 Intrinsic value = $20.00 - $17.00 = $3.00, therefore

Speculative value = $4.00 - $3.00 = $1.00

New intrinsic value = $30 - $17.00 = $13.00

Warrant price = $13.00 + $0.50 = $13.50

Rate of return = (13.50 - 4)/4 = 237.5%

27 The bond is convertible into 33.333 shares of common stocksince $1000/$30 = 33.333

shares.

The conversion value is 33.333 x $27 = $900.00

28 Price =20

20

)065.1(

1000

065.0

)065.1(

11

55

= $889.82

29 The minimum value of the bond would be at least the greaterof the two values, the

straight-debt value or the conversion value. In this case,the minimum value is $900.00


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(its conversion value).

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