chapter 11 introduction to security valuation true… · chapter 11 introduction to security...

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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 economies and markets, 2) analysis of alternative industries and 3) analysis of industry influences.

(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, the

investor 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 performance

varies 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 return

on this investment. (f) 8 The required rate of return is determined by 1) the real risk free rate, 2) the

expected rate of inflation and 3) liquidity risk. (f) 9 The price of a bond can be calculated by discounting future coupons over the

bonds life by the yield to maturity. (f) 10 The growth rate of dividends and profit margin are the main determinants of the

P/E ratio. (t) 11 The dividend growth models are only meaningful for companies that have a

required 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 the

following 1) dividends, 2) Free cash flow or 3) coupons.

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(f) 14 In dividend discount models (DDM) with supernormal growth, supernormal growth may continue indefinitely. (t) 15 The real risk free rate depends on the real growth in the economy and for short period 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 not a consideration in the three-step valuation process?

a) Analysis of alternative economies b) Analysis of security markets c) Analysis of alternative industries d) Analysis of individual companies e) None of the above (that is, all are considerations in the three-step valuation

process)

(d) 2 Which of the following is not considered a basic economic force?

a) Fiscal policy b) Monetary policy c) Inflation d) P/E ratio e) 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 of

the 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 required

rate of return?

a) Low coupon bonds b) Junk bonds c) Common stocks d) Preferred stocks e) 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 investor’s required rate of return?

a) The economy’s real risk-free rate (RFR) b) The expected rate of inflation (I) c) A risk premium d) 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

6

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 current market. The firm's outstanding bond issue has 10 years remaining until maturity. The bonds were 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) $686.50 b) $699.00 c) $875.38 d) $868.50 e) $902.00

(e) 2 What will be the value of these securities in one year if the required return

declines to 6 percent?

a) $699.00 b) $802.50 c) $1259.05 d) $1012.17 e) $1137.54

USE THE FOLLOWING INFORMATION FOR THE NEXT TWO PROBLEMS

A major manufacturer is reevaluating its bonds since it is planning to issue a new bond in the current market. The firm's outstanding bond issue has 8 years remaining till maturity. The bonds 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) $796.11 b) $797.84 c) $826.73 d) $862.98 e) $904.00

(c) 4 What will be the value of these securities in one year if the required return


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a) $699.50 b) $885.50 c) $1000.00 d) $998.36 e) $936.72

USE THE FOLLOWING INFORMATION FOR THE NEXT TWO PROBLEMS A large grocery chain is reevaluating its bonds since it is planning to issue a new bond in the current market. The firm's outstanding bond issue has 6 years remaining until maturity. The bonds 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) $899.00 c) $822.70 d) $569.50 e) $962.00

(d) 6 What will be the value of these securities in one year if the required return


a) $899.43 b) $862.50 c) $869.88 d) $918.93 e) $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'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) $68.38 b) $65.35 c) $71.54 d) $61.87 e) $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 the company'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 receive your first dividend one year from now?

a) $26.67 b) $30.00 c) $31.54 d) $33.38 e) $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 the company'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) $44.98 b) $40.50 c) $41.44 d) $45.38 e) $44.10

(a) 10 In 1998, Drowny Inc. issued a $52 par value preferred stock that pays an 8

percent 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 receive your first dividend one year from now?

a) $37.82 b) $38.50 c) $39.44 d) $41.38 e) $44.10

(b) 11 Using the constant growth model, an increase in the required rate of return from

15 to 17 percent combined with an increase in the growth rate from 7 to 9 percent would 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%.



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 from


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.

USE THE FOLLOWING INFORMATION FOR THE NEXT TWO PROBLEMS Ridgemont Can Company's last dividend was $1.55 and the directors expect to maintain the historic 5 percent annual rate of growth. You plan to purchase the stock today because you feel that the growth rate will increase to 8 percent for the next three years and the stock will then reach $22.50 per share. (b) 16 How much should you be willing to pay for the stock if you require a 15 percent

return?

a) $16.97 b) $18.90 c) $21.32 d) $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) $18.90 b) $19.28 c) $22.14 d) $23.91 e) $25.46

USE THE FOLLOWING INFORMATION FOR THE NEXT TWO PROBLEMS 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 feel that 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 percent

return?


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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) $11.15 b) $14.44 c) $14.86 d) $18.90 e) $19.24

(e) 20 Ross Corporation paid dividends per share of $1.20 at the end of 1990. At the end

of 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 retention

rate 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 is

5.65%, and the long term average return on the S&P 500 is 11%. Calculate the required 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 three

years dividends will grow as follows, 5% next year, 15% in year two, and 25% in year 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 a multistage dividend discount model.

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

(a) 24 The P/E ratio for BMI Corporation 21, and the P/Sales ratio is 5.2. The industry

P/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 of

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

a) $2, $2.08, $2.16 b) $2, $2.05, $2.10 c) $2.16, $2.24, $2.32 d) $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) $113.40 b) $122.47 c) $132.27 d) $142.85 e) $154.35

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

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

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

a) $136.29 b) $133.03 c) $120.33 d) $123.43 e) $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 a normal 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, $2.05 b) $1.64, $1.78, $1.94 c) $1.64, $1.94, $2.24 d) $1.5, $2.40, $3.30 e) $2.07, $2.14, $2.21

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

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

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

a) $4.67

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b) $3.08 c) $5.67 d) $4.5 e) $1.53

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

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

(a) 33 Tayco Corporation has just paid dividends of $3 per share. The earnings per share

for the company was $4. If you believe that the appropriate discount rate is 15%, and the long term growth rate is 6%, then the firm’s P/E ratio is

a) 8.33 b) 33.33 c) 44.44 d) 11.11 e) None of the above

15

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

16

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 + 22.50 1.15 (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

17

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 15.11.15.

)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) = $2.16 Year 2 Dividends = 2(1 + .08)2 = $2.33 Year 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) = $3.087 P5 = 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) = $1.64 Year 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) = $2.037 P3 = 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

19

FIXED-INCOME ANALYSIS

TRUE/FALSE QUESTIONS (f) 1 The price of a bond is the presents value of

future coupons and face value discounted by the coupon rate.

(t) 2 The yield to maturity of a bond the interest

rates that equates the present value of all future coupons and face value to the current price of the bond.

(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 cash

flows are reinvested at the computed YTM. (t) 5 Yield to maturity and current yield are equal

when the bond is selling for exactly par value. (t) 6 The promised yield to call measures the

expected rate of return for a bond held to first call date.

(f) 7 The promised yield to maturity measures the

expected rate of return for a bond held for a minimum period of ten years.

(t) 8 Realized yield measures the expected rate of

return of a bond if the bond is sold prior to its maturity.

(t) 9 The fully taxable equivalent yield of a

nontaxable bond with a promised yield of 7 percent is 10.29 percent, assuming a tax rate of 32 percent.

(f) 10 The major problem facing a bond analyst valuing

a U.S. government bond is the ability to forecast the real risk-free rate of interest.

(t) 11 When investing in a foreign bond versus a

domestic bond, the additional risk factors you must consider are exchange rate risk and country risk.

(t) 12 The fundamental determinants of interest rates

are the real risk free rate, inflation, and the risk premium.

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(f) 13 According to the expectations hypothesis, a rising yield curve indicates that investors demand for long maturity bonds is expected to rise.

(t) 14 According to the segmented market hypothesis

yields for a particular maturity segment depend on supply and demand within the maturity segment.

(f) 15 For a given change in yield bond price

volatility is inversely related to term to maturity.

(t) 16 For a given change in yield bond price

volatility 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 bond’s

price-yield curve deviates from the linear approximation of that curve.

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MULTIPLE CHOICE QUESTIONS (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 generally

slope upward because

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

short 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 yield

curve indicates that

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

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

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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 demand for short-term bonds has risen.

e) None of the above. (c) 6 According to the segmented-market hypothesis a rising yield curve

indicates that

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

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

e) None of the above. (b) 7 According to the expectations hypothesis a rising yield curve indicates

that investors expect

a) Future short term rates to fall b) Future short term rates to rise c) Future long term rates to rise d) Future long term rates to fall e) None of the above

(e) 8 The annual interest paid on a bond relative to

its prevailing market price is called its .

a) Promised yield b) Yield to maturity c) Coupon rate d) Effective yield e) Current yield

(b) 9 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.

23

e) Credit quality, inflation and the risk free rate.

(d) 10 If the holding period is equal to the term to

maturity for a corporate bond the rate of discount represents the .

a) Coupon yield b) Effective yield c) Yield to call d) Yield to maturity e) 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 issues while lenders prefer to invest in long maturity issues.

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

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

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

(a) 12 The promised yield to maturity calculation

assumes that

a) All coupon interest payments are reinvested at the current market interest rate for the bond.

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

c) All coupon interest payments are reinvested at short 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 reinvested

during 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.

24

(c) 14 Consider a bond portfolio manager who expects interest rates to decline and has to choose between the following two bonds.

Bond A: 10 years to maturity, 5% coupon, 5% yield to maturity

Bond B: 10 years to maturity, 3% coupon, 4% yield to maturity

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

maturity. 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 of

return of a bond assuming that you sell it prior to its maturity.

a) Yield to maturity b) Current yield c) Realized yield d) Coupon rate e) None of the above

(a) 16 The yield to call is a more conservative yield

measure whenever the price of a callable bond is quoted at a value

a) Equal to or greater than par plus one year's

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

25


(c) 1 Assume that you purchase a 3-year $1,000 par

value bond, with a 15% coupon, and a yield of 8%. After you purchase the bond, one- year interest rates are as follow, year 1 = 8%, year 2 = 10%, year 3 = 14% (these are the reinvestment rates). Calculate the realized horizon yield if you hold the 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 par

value bond, with a 5% coupon, and a yield of 9%. Immediately after you purchase the bond, yields fall to 7% and remain at that level to maturity. Calculate the realized horizon yield, if you hold the bond for 5 years and then sell. Interest is paid 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 par

value bond, with a 4% coupon, and a yield of 7%. Immediately after you purchase the bond, yields rise to 8% and remain at that level to maturity. Calculate the realized horizon yield if you hold the 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.

26

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

a) $1579.46 b) $918.89 c) $789.29 d) $1000 e) $743.29

(b) 5 Calculate the Macaulay duration for the bond

a) 4.19 years b) 4.36 years c) 8.72 years d) 8.38 years e) 9.52 years

(a) 6 Calculate the modified duration for the bond


(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 is paid 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 yield to maturity of 8%. Interest is paid annually.

a) 6.44 years b) 5.25 years c) 4.44 years d) 2.50 years e) None of the above

(a) 9 A 15-year bond has a $1,000 par value bond, a 4% coupon

and a yield to maturity of 3.3%. Interest is paid annually. The bond's current yield is

27

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% coupon

and a yield to maturity of 8%. Interest is paid semiannually. The bond's price is


(b) 11 A 15-year bond, purchased 5 years ago, has a $1,000 par

value bond, a 10% coupon and a yield to maturity of 12%. Interest is paid annually. The bond's price is

a) $864 b) $887 c) $1152 d) $1123 e) None of the above

(d) 12 A 20-year, $1,000 par value bond has an 11% coupon and is

currently priced at par. Interest is paid semiannually. The bond's effective annual yield is

a) 5.50% b) 5.65% c) 11.00% d) 11.30% e) None of the above

USE THE FOLLOWING INFORMATION FOR THE NEXT TWO PROBLEMS Five years ago your firm issued $1,000 par, 20 year bonds with a 6% coupon rate and an 8% call premium. The price of these bonds now is $1103.80. Assume annual compounding. (b) 13 Calculate the yield to maturity of these bonds

today.

a) 6% b) 5% c) 8% d) 7.31%

28

e) 7.81% (b) 14 If these bonds are now called, what is the

actual yield to call for the investors who originally purchased them?

a) 6.83% b) 7.38% c) 7.81% d) 7.92% e) 8.47%

USE THE FOLLOWING INFORMATION FOR THE NEXT TWO PROBLEMS You purchase an 8% coupon, 25 year, $1,000 par, semiannual payment bond priced at $980 when it has 15 years remaining until maturity. (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 5

years 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, $1,000

par bond maturing in three years if the yield to

29

maturity is 10 percent and interest is paid semiannually.


(d) 19 Calculate the modified duration for a 10-year, 12 percent

bond with a yield to maturity of 10 percent and a Macaulay duration of 7.2 years. Assume semiannual compounding.


(a) 20 A 12-year, 8 percent bond with a YTM of 12 percent has a

Macaulay duration of 9.5 years. If interest rates decline by 50 basis points, what will be the percent change in price for this bond? Assume semiannual compounding.

a) +4.48% b) +4.61% c) +8.48% d) +8.96% e) +17.92%

30

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

2 The purchase price is = $743.29 =

10

10

09.1

1000

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

The realized horizon yield = 10.15% =

31

129.743

53.12055/1

3 The purchase price is = $789.29 =

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

The realized horizon yield = 7.18% =

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%

32

8 The price of the bond = $920.15 =

5

5

08.1

1000

08.08.1

11

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 9 The price of the bond = $1081.78 =

15

15

033.1

1000

033.033.1

11

40

Current yield = 40/1081.78 = 3.7% 10 The price of the bond = $1162.22 =

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 to maturity is 11% or 5.5% semiannual. Effective annual yield = (1 + .055)2 - 1 = 11.30%

33

13 1103.80 = 15

15

)1(

1000)1(

11

60ytmytm

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

40ytmytm

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%

34

18 Macaulay Duration = PV of weighted cash flows/Current price = 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 yield to 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 %ΔP = -Dmod x Δi = -(8.96) x (-0.005) = 0.0448 = 4.48% increase

35

CHAPTER 17

AN INTRODUCTION TO DERIVATIVE INSTRUMENTS

TRUE/FALSE QUESTIONS (t) 1 A cash or spot contract is an agreement for the

immediate delivery of an asset such as the purchase of 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 or

sell an asset, but not the obligation to do it, the best instrument is an option rather than a futures contract.

(f) 4 Investment costs are generally higher in the

derivative markets than in the corresponding cash markets.

(t) 5 Forward contracts are traded over-the-counter and

are generally not standardized. (t) 6 The forward currency market has low liquidity

relative to the currency futures market. (f) 7 A futures contract is an agreement between a trader

and the clearinghouse of the exchange for delivery of an asset in the future.

(t) 8 A primary function of futures markets is to allow

investors to transfer risk. (f) 9 The futures market is a dealer market where all the

details of the transactions are negotiated. (t) 10 For futures, the initial margin requirement is

quivalent 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 clearinghouse

experiences major swings in their net balances to ensure stability for the investors.

(t) 13 If you have entered into a currency futures hedge

for the Japanese yen in connection with buying Japanese equipment, if the yen goes from 110 yen/$1 to 100 yen/$1, you will lose in the spot market but have an offsetting gain in the futures market.

36

(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, Stock

Price – Exercise Price] (f) 17 Options that can be exercised at any up to and

including the expiration day are called European Options.

(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 a

price of $5.50 will be in the money if the price of the underlying stock is $50.

(f) 20 A put option with an exercise price of $60 and a

price of $0.50 will be in the money if the price of the underlying stock is $70.

37

MULTIPLE CHOICE QUESTIONS (a) 1 Which of the following is a reason for the

existence of derivatives?

a) They help shift risk from risk-averse investors to 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 to

purchase an asset at a specified price at a future specified 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 against

inflation 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 a

given number of shares in a specific common stock at a set price; a put obliges the investor

38

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

b) both give the investor the opportunity to participate in stock market dealings without the risk of actual stock ownership.

c) a call option gives the investor the right to purchase a given number of shares of a specified stock at a set price; a put option gives the investor the right to sell a given number of shares of a stock at a set price.

d) a put option has risk, since leverage is not as great 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 exceeds the exercise price.

b) A call option in which the exercise price exceeds the stock price.

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

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

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

(d) 7 If you were to sell a June call option with an

exercise price of 50 for $8 and simultaneously buy a 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 expiration

is (where V is the underlying asset's market price and 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]

39

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

a) The same expiration date and strike price. b) The same expiration date but different strike

price. c) A different expiration date but same strike

price. d) A different expiration date and different strike

price. e) Options in different markets.

(b) 10 According to put/call parity

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

b) Stock price + Put Price = Call Price + Risk Free Bond Price

c) Put price + Call Price = Stock Price + Risk Free Bond Price

d) Stock price - Put Price = Call Price + Risk Free Bond Price

e) Stock price + Call Price = Put Price - Risk Free Bond Price

(b) 11 Which of the following statements does not apply to

a put option?

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

b) To protect against a decline in prices of a stock you own, you could sell a put option against your position.

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

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

e) If you hedge a long profit position and the stock continues to increase in price, your put option will expire worthless.

(a) 12 You own a stock which has risen from $10 per share

to $32 per share. You wish to delay taking the profit but you are troubled about the short run behavior of the stock market. An effective action on your part would be to

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

40

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 with

an exercise price of $50 for $8 and simultaneously sell an October call option with an exercise price of $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 call

options in the same stock with

a) The same expiration date and strike price. b) The same expiration date but different strike

price. c) A different expiration date but same strike

price. d) A different expiration date and different strike

price. e) Options in different markets.

(b) 15 A stock currently sells for $75 per share. A call option on the stock with an exercise price $70 currently sells for $5.50. The call 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 call option on the stock with an exercise price $155 currently sells for $2.50. The call option is


41

(c) 17 A stock currently sells for $75 per share. A put option on the stock with an exercise price $70 currently sells for $0.50. The put option is


(a) 18 A stock currently sells for $15 per share. A put option on the stock with an exercise price $15 currently sells for $1.50. The put option is


(b) 19 A stock currently sells for $15 per share. A put option on the stock with an exercise price $20 currently sells for $6.50. The put option is


42

MULTIPLE CHOICE PROBLEMS (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 January put option.

a) $11 b) $24 c) $19 d) $30 e) $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) $120 b) $15 c) $105 d) $116 e) $104

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

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

a) $10 b) -$4 c) $5 d) $6 e) $15 (c) 4 Assume that you purchased shares of a stock at a price of $35 per share. At this time you purchased a put option with a $35 strike price for $3. The stock currently trades at $40. Calculate the dollar return on this option strategy.

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

43

(c) 5 Assume that you purchased shares of a stock at a price of $35 per share. At this time you wrote a call option with a $35 strike and received a call price of $2. The stock currently trades at $70. Calculate the dollar return on this option strategy.

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

(b) 6 A stock currently trades at $110. June call options on the stock with a strike price of $105 are priced at $4. Calculate the arbitrage profit that you can earn

a) $0 b) $1 c) $5 d) $4 e) None of the above (c) 7 Datacorp stock currently trades at $50. August call options on the stock with a strike price of $55 are priced at $5.75. October call options with a strike price of $55 are priced at $6.25. Calculate the value of the time premium between the August and October options.

a) -$0.50 b) $0 c) $0.50 d) $5 e) -$5 (a) 8 A stock currently trades at $110. June put options on the stock with a strike price of $115 are priced at $5.25. Calculate the dollar return on one put contract.

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

44

(d) 9 A stock currently trades at $110. June call options on the stock with a strike price of $105 are priced at $5.75. Calculate the dollar return on one call contract.

a) -$50 b) $500 c) $575 d) -$75 e) $0 (e) 10 Consider a stock that is currently trading at $50. Calculate the intrinsic value for a put option that has an exercise price of $55. a) $0 b) $50 c) $55 d) $105 e) $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) $0 b) $50 c) $35 d) $15 e) $85 (e) 12 Consider a stock that is currently trading at $25. Calculate the intrinsic value for a call option that has an exercise price of $35. a) $25 b) $35 c) $10 d) -$10 e) $0 (c) 13 Consider a stock that is currently trading at $25. Calculate the intrinsic value for a call option that has an exercise price of $15. a) $25 b) $35

45

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

USE THE FOLLOWING INFORMATION FOR THE NEXT THREE PROBLEMS December futures on the S&P 500 stock index trade at 250 times the index value of 1187.70. Your broker requires an initial margin of 10% percent on futures contracts. The current value of the S&P 500 stock index is 1178. (c) 14 How much must you deposit in a margin account if you wish to purchase one contract?

a) $267,232.5 b) $29,450 c) $29,692.50 d) $30,000 e) $265,050

(c) 15 Suppose at expiration the futures contract price is 250 times the index value of 1170. Disregarding transaction costs, what is your 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 the

S&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

USE THE FOLLOWING INFORMATION FOR THE NEXT THREE PROBLEMS A futures contract on Treasury bond futures with a December

expiration 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%.

46

(c) 17 Calculate the current value of one contract

a) $100,000 b) $103,600.5 c) $103,187.5 d) $102,306.3 e) $104,293.5

(c) 18 Calculate the initial margin deposit

a) $10,000 b) $10,360.50 c) $10,318.75 d) $10,230.63 e) $10,429.35

(b) 19 If the futures contract is quoted at 105:08 at expiration 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 (or 83 15/32) against this position. Because you feel interest rates will rise you sell 10 bond futures at 81:15 (or 81 15/32) against this position. Two months later you decide to close your position. The bonds have fallen to 78 and the futures contracts are at 75:16 (75 16/32). Disregarding margin and transaction costs, what is your gain or loss?

a) $5,000 loss b) $500 loss c) Breakeven d) $500 gain e) $5,000 gain

USE THE FOLLOWING INFORMATION FOR THE NEXT TWO PROBLEMS On the last day of October, you are considering the purchase of 100 shares of Trivia Corporation common stock selling at $32 3/8 per share and also considering one Trivia option contract.

47

Calls Puts Price December March December

March 30 3 3/4 5 1 1/4

2 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 an

exercise price of 30, what is your dollar gain (loss) if you close the position when the stock is selling at 38 7/8?

a) $187.50 gain b) $225.00 gain c) $287.50 gain d) $387.50 gain e) $427.50 gain

(b) 22 If Bruce buys a March put option with an exercise

price of 35, what is his dollar gain (loss) if he closes his position when the stock is at 38 7/8?

a) $600.00 loss b) $475.00 loss c) $387.50 loss d) $25.00 loss e) He has a gain

USE THE FOLLOWING INFORMATION FOR THE NEXT TWO PROBLEMS John Shamrock is considering the following alternatives for investing in Clover Industries, which is now selling for $27 per share: 1) Buy 100 shares, 2) Buy 100 shares with a 60 percent margin deposit

and 3) Buy a six month call option with a strike price

of $25 for $500. (d) 23 Assuming no commissions or taxes what is the

annualized percentage gain if the stock reaches $32 in four months and was purchased on margin?

a) 18.56% b) 30.86% c) 46.30% d) 92.59% e) 128.90%

48

(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%

49

CHAPTER 17

ANSWERS TO MULTIPLE CHOICE PROBLEMS 1 P = 6 + 30 –25 = $11 2 Bond price = 115 + 5 – 16 = $104 3 Profit on call = (75 – 60) – 5 = 10 Profit on put = -4 Total = $6 4 Profit on stock = 40 – 35 = 5 Profit on put = -3 Total = $2 5 Profit on stock = 70 – 35 = 25 Profit on call = 35 – 70 + 2 = -23 Total = $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 contract 250 x 1187.7 = $296,925 Sell December contract 250 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%

50

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 contract 103 6/32 percent of 100,000 = $103,187.50 Sell December contract 105 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 Bonds Value of portfolio (now) $834,687.50 Value of portfolio (2 mo.) 780,000.00 Loss in value $54,687.50 Futures Sell 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 loss

per 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%

51

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%

52

CHAPTER 18

DERIVATIVES: ANALYSIS AND VALUATION

TRUE/FALSE QUESTIONS (f) 1 The owner of a call option on a futures contract

has the obligation to buy the futures contract at a predetermined strike price during a specified time period.

(f) 2 Options on futures expire at the same time the

futures contract expires. (t) 3 A warrant is an option to buy a stated number of

shares of common stock at a specified price at any time during the life of the warrant.

(f) 4 A major difference between a call option and a

warrant is that call options are issued by the company so that any proceeds from the sale of stock go to the issuing firm.

(f) 5 According to the cost of carry model the futures

price is the present value of the spot price discounted at the risk free rate.

(t) 6 In the cost of carry model the inclusion of storage

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

model 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 possible

if the following condition holds: F0,T = S0(1 + rf – d)T, where spot price now is S0, value now of a futures contract expiring at time T is (F0,T), rf is the risk free rate and d is the dividend.

(f) 10 One S&P 500 stock index futures option contract is

priced at $500 times the premium. (f) 11 The underlying stock price and the value of the put

option are factors that impact the value of an American call option.

(t) 12 The cost of carry is the foregone interest from

investing in a risk free asset.

53

(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 subintervals increases.

(f) 14 Callable bonds allow the issuer the option selling

the bonds a fixed price. (f) 15 The intrinsic value of a warrant = (Market price of

common stock + Warrant exercise price) x Number of shares specified by warrant.

(t) 16 By attaching a convertible feature to a bond issue

a firm can often get a lower rate of interest on its debt.

(t) 17 The investment value of a convertible bonds is the

price which it would be expected to sell as a straight debt instrument.

(f) 18 The conversion parity price is equal to the par

value of a convertible bond divided by the number of shares into which it can be converted.

54

MULTIPLE CHOICE QUESTIONS (a) 1 According to the cost of carry model the

relationship between the spot (S0) and futures price (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 carry model will increase the futures price

a) Dividends b) Storage costs c) Interest rate d) 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,T b) Bt,T = St - Ft,T c) Bt,T = St x Ft,T d) Bt,T = St / Ft,T e) None of the above

(d) 4 A riskless stock index arbitrage profit is possible if the following condition holds:

a) F0,T = S0(1 + rf – d)T b) 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 related to:

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

55

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

a) Underlying stock price. b) Time to expiration c) 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 exercise price) 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 exercise price) / Number of shares specified by warrant.

d) (Market price of common stock - Warrant exercise price) / 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 interest

on 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 warrants and options is false?

a) When originally issued, the life of a warrant is

usually 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 as

sweeteners to make new issues of debt or equity more attractive.

d) Warrant holders have voting rights while option holders do not.

e) None of the above (that is, all statements are true)

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

portfolio should hold

56

a. Two shares of stock for every call option written.

b. One share of stock for every two call options written.

c. Two shares of stock for every call option purchased.

d. One share of stock for every two call options purchased.

e. Two call options for every put option written. (a) 11 All of the following are normal characteristics of

a convertible bond, except

a) Conversion at the option of the issuer. b) Conversion into a fixed number of shares of

common stock. c) A conversion price initially above the market

price of the common stock. d) An interest rate lower than that on straight

debentures. 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 is calculated 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 bond is defined as:

a) Market Price of Convertible Bond / Conversion Ration.

b) Market Price of Convertible Bond x Conversion Ration.

c) Market Price of Convertible Bond - Conversion Ration.

d) Market Price of Convertible Bond + Conversion Ration.

e) None of the above.

57


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 to

calculate the price of a call option.


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

a) $7.623 b) $8.623 c) $9.623 a) $10.623 b) 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, the

appropriate NOB futures spread strategy would be

a) Go long the T-bond and short the T-note b) Go short the T-bond and long the T-note c) Go long the T-bond and long the T-note d) Go short the T-bond and short the T-note e) None of the above

58

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

a) Go long the T-bond and short the T-note b) Go short the T-bond and long the T-note c) Go long the T-bond and long the T-note d) Go short the T-bond and short the T-note A) NONE OF THE ABOVE

(c) 5 Suppose the yield curve did flatten so the that the

yield on the T-bond contract fell to 5.95% and the yield on the T-note rose to 5.85%. Calculate the Profit on the NOB futures spread. (Assume coupons are paid annually)

a) -$5850.92 b) -$2144.17 c) $2144.17 b) $5850.92 c) 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 futures

contract .

a) 1106.59 b) 1112.12 c) 1139.79 d) 1123.19 e) None of the above

(b) 7 If the futures contract was currently available for

1250, indicate the appropriate strategy that would earn 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.

59

(a) 8 If the futures contract was currently available for 1050, indicate the appropriate strategy that would earn 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 for

1250, calculate the arbitrage profit.

a) 0 b) 143.41 c) –143.41 d) 137.84 e) -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 the price 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 dealer purchases 3 contracts. The current spot price for coffee is $0.485 per pound. Assume that three months from now the spot and futures prices are both $0.60 per pound. (d) 10 Calculate the number of pounds, of the planned

120,000 pound purchase, that is unhedged

a) 45000 b) 75000 c) 5000 d) 7500 e) 4000

(b) 11 Calculate the basis now.

a) $0 b) -$0.0745 c) $0.0745 d) -$0.0405 e) $0.115

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

a) $0 b) -$0.0745

60

c) $0.0745 d) -$0.0405 e) $0.115

(e) 13 Calculate the profit or loss on the futures

position at the end of three months.

a) $0 b) -$4500.25 c) $4500.25 d) -$4556.25 e) $4556.25

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

purchased the coffee.

a) $0.5595 b) $0.485 c) $0.562 d) -$0.60 e) $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 and the monthly T-bill rate is 0.67%. Transaction costs are 0.45%. Calculate the non arbitrage price range for a 6 month futures contract.

a) $683.54 and $705.63 b) $679.57 and $715.13 c) $650.00 and $685.71 d) $650.00 and $679.57 e) $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 and the monthly T-bill rate is 0.67%. Calculate the futures price for a 9-month contract.

a) $705.63 b) $715.13 c) $699.57 d) $680.58 e) $665.75 (a) 17 Three-month corn futures contracts currently sell

for 510 cents per bushel. Storage and insurance

61

cost are 0.3% per month. The three-month T-bill rate is 2% over this three month period. Calculate the spot price for corn.

a) $5.3515 b) $5.2323 c) $6.2515 d) $6.2323 e) $5.1015 (d) 18 The spot price of a commodity is $1200. If the T-

bill rate is 9% annualized, calculate the price for a 9-month futures contract on the commodity.

a) $2606.27 b) $1312.56 c) $1227.20 d) $1283.47 e) $1200.00 USE THE FOLLOWING INFORMATION TO ANSWER THE NEXT THREE QUESTIONS The information provided is relevant in the context of a one period (one year) binomial option pricing model. A stock currently trades at $50 per share, a call option on the stock has an 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 year

from 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) -1.4286 b) -2.9286 c) -2.8571 d) -2.5714 e) -1.1111

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

a) $7.56

62

b) $17.48 c) $9.26 d) $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 two period (two six month periods) binomial option pricing model. A stock currently trades at $60 per share, a call option on the stock has an exercise price of $65. The stock is equally likely to rise by 15% or fall by 15% during each six month period. The one-year risk free rate is 3%. (c) 22 Calculate the possible prices of the stock at the

end of one year

a) $69, $51, $79.35 b) $51, $79.35, $58.65 c) $79.35, $58.65, $43.35 d) $58.65, $43.35, $14.35 e) None of the above

(a) 23 Calculate the price of the call option after the

stock price has already moved up in value once (Cu)

a) $7.77 b) $14.35 c) $0 d) $4.21 e) $6.44

(c) 24 Calculate the price of the call option after the

stock price has already moved down in value once (Cd)

a) $7.77 b) $14.35 c) $0 d) $4.21 e) $6.44

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

a) $7.77 b) $14.35 c) $0 d) $4.21 e) $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. Each warrant entitles you to purchase one share of ABC Corporation. Calculate your rate of return assuming the warrant premium drops by 50 percent and 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%

USE THE FOLLOWING INFORMATION FOR THE NEXT THREE PROBLEMS BioTech Industries has debentures outstanding (par value $1,000) convertible into the company's common stock at $30. The coupon rate is 11 percent payable semiannually and they mature in 10 years. (d) 27 Calculate the conversion value of the bond if the

stock price is $27.00 per share. a) $ 600.00 b) $ 700.00 c) $ 800.00 d) $ 900.00 e) $1,000.00 (c) 28 Calculate the straight-bond value assuming that

bonds of equivalent risk and maturity are yielding 13 percent per year compounded semiannually.

a) $757.37 b) $796.83 c) $889.82 d) $902.65 e) $942.65 (d) 29 At present, what would be the minimum value of the

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

65

CHAPTER 18

ANSWERS TO MULTIPLE CHOICE PROBLEMS 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) = 0.3712 N(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, the

appropriate NOB futures spread strategy would be go short the T-bond and long the T-note

4 If you expected the yield curve to flatten, the appropriate NOB futures spread strategy would

be 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 it’s

theoretical value the appropriate strategy would be to short the futures contract and go long the index.

8 Since the futures contract is trading below it’s

theoretical value the appropriate strategy would be to go long 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 the

index at $1106.59. Hold for 60 days, then collect dividends and repay loan.

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

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

66

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 is 650(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 = $50 Exercise price = $45 Risk free rate = 2% Price in one year if stock rises = 50(1.25) = $62.50 Price 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] = $17.50 Intrinsic 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 held

long plus some number of call options written. Value of hedge portfolio if stock rises = Value of hedge portfolio 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)

67

C0 = $9.26 22 Current stock price = $60 Price in one year if stock rises 15% per six month period=

60(1.15)(1.15) = $$79.35 Price in one year if stock rises 15%, then falls 15% =

60(1.15)(0.85) = $58.65 Price in one year if stock declines 15% per period =

60(0.85)(0.85) = $43.35 23 Current stock price = $60 Exercise price = $65 Risk free rate = 3% or 1.49% per six month period = (1.03)0.5

– 1 = 0.0149 Price in six months if stock rises 15% = 60(1.15) = $69 Price in six month if stock falls 15% = 60(0.85) = $51 Price in one year if stock rises 15% per six month period=

60(1.15)(1.15) = $$79.35 Price in one year if stock rises 15%, then falls 15% =

60(1.15)(0.85) = $58.65 Price 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] = $0 Intrinsic value of call option if stock falls to $43.35 =

Max[0, 43.35 – 65] = $0 Estimate the number calls needed by constructing a hedge

portfolio. The hedge portfolio will consist of one share of stock held

long 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

68

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

25 To solve for the value of the call today (C0), first

determine the number of calls by constructing a hedge portfolio where:

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

since $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 greater

of the two values, the straight-debt value or the conversion value. In this case,

the minimum value is $900.00

69

(its conversion value).

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