Chapter 24Problems 1-22

Input boxes in tanOutput boxes in yellowGiven data in blueCalculations in redAnswers in green

NOTE: Some functions used in these spreadsheets may require that the "Analysis ToolPak" or "Solver Add-in" be installed in Excel.To install these, click on "Tools|Add-Ins" and select "Analysis ToolPak" and "Solver Add-In."

NOTE: Some functions used in these spreadsheets may require that the "Analysis ToolPak" or "Solver Add-in" be installed in Excel.To install these, click on "Tools|Add-Ins" and select "Analysis ToolPak"

Chapter 24Question 1

Input Area:

T-bills 5.6%Share price $ 66 Price won't drop below $ 60

a. Exercise price on a call $ 55 b. Exercise price on a call $ 45 c. Exercise price on a put $ 55

Output Area:

a. Call value $ 13.92 Intrinsic value $ 11.00

b. Call value $ 23.39 Intrinsic value $ 21.00

c. Put value $ - There is no possiblity that the put will finish in the money. Intrinsic value = $0.

Chapter 24Question 2

Input Area:

CallsOption Strike Price Expiration Volume Last

RWJ85 80 Mar 230 2.8085 80 Apr 170 6.0085 80 Jul 139 8.0585 80 Oct 60 10.20

Output Area:

a. The calls are in the money. The intinsic value is

b. The puts are out of the money. The intrinsic value is

c. The Mar call and the Oct put are mispriced. The call is mispriced because it is selling for less than its intrinsic value. If the option expired today, the arbitrage would be to buy the call for $2.80,exercise it and pay $80 for a share of stock, and sell the stock for $85. Riskless profit of $2.20.The Oct put is mispriced because it sells for less than the July put. To take advantage of this,sell the July put for $3.90 and buy the October put for $3.65, for a cash inflow of $0.25. TheThe exposure of the short position is completely covered by the long position in the Octoberput, with a positive cash inflow today.

PutsVolume Last

160 0.80127 1.4043 3.9011 3.65

$5.00

$0.00

The Mar call and the Oct put are mispriced. The call is mispriced because it is selling for less than its intrinsic value. If the option expired today, the arbitrage would be to buy the call for $2.80,exercise it and pay $80 for a share of stock, and sell the stock for $85. Riskless profit of $2.20.The Oct put is mispriced because it sells for less than the July put. To take advantage of this,sell the July put for $3.90 and buy the October put for $3.65, for a cash inflow of $0.25. TheThe exposure of the short position is completely covered by the long position in the October

Chapter 24Question 3

Input Area:

CallsOption Strike Price Expiration Volume Last

Macrosoft119 120 Feb 85 3.23119 120 Mar 61 4.41119 120 May 22 6.97119 120 Aug 3 10.20

a. Contracts bought 10 Feb call $ 120

b. Share price $ 134 Share price $ 126

c. Contracts bought 10 Share price $ 109

d. Contracts sold 10 Share price $ 108 Share price $ 132

Output Area:

a. Price $ 3,230.00

b. $ 14,000 $ 6,000

c. Initial cost $ 9,100 Maximum gain $ 110,900 Terminal value $ 11,000 Net gain $ 1,900

d. Option payoff $ (12.00)Net profit $ (2,900)Option payoff $ - Net profit $ 9,100

ST

ST

Break-even $ 110.90 For terminal stock prices above $ 110.90 , the writer of the put option makes a net profit.

PutsVolume Last

40 3.7022 5.3011 7.303 9.10

, the writer of the put option makes a

Chapter 24Question 4

Input Area:

Low stock price $ 62 High stock price $ 86 T-bills 5%

a. Current price $ 70 Exercise price $ 65

b. Exercise price $ 75

Output Area:

a. $ 8.10

b. $ 5.02

C0

C0

Chapter 24Question 5

Input Area:

Low stock price $ 75 High stock price $ 95 T-bills 6%

a. Current price $ 85 Exercise price $ 65

b. Exercise price $ 70

Output Area:

a. $ 23.68

b. $ 17.81

C0

C0

Chapter 24Question 6

Input Area:

Call option price $ 1,300 Stock price $ 48 Stock price $ 67 Exercise price $ 60 Risk-free rate 8%

Output Area:

$ 13.00

$ 79.73

C0

S0

Chapter 24Question 7

Input Area:

Asset value $ 1,050 Asset value in 1 yr $ 1,000 Asset value in 1 yr $ 1,270 Risk-free rate 7%Debt FV $ 1,000

Output Area:

a. $ 115.42

b. $ 934.58 Interest rate 7.00%

c. The value of the equity will increase. The debt requires a higher return, thereforethe present value of the debt is less whilethe value of the firm does not change.

E0

D0

Chapter 24Question 8

Input Area:

Debt face value $ 1,000 a. Asset value $ 1,140

Asset value in 1 yr $ 920 Asset value in 1 yr $ 1,430 Risk-free rate 6%

b. Asset value in 1 yr $ 800 Asset value in 1 yr $ 1,600

Output Area:

a. $ 229.40

$ 910.60

b. $ 288.96 The stockholders will prefer the new asset structure because their potential gain increases while their maximum potentialloss remains unchanged.

E0

D0

E0

Chapter 24Question 9

Input Area:

Convertible debenture $ 1,000 Conversion price $ 35 Common stock price $ 46

Output Area:

Conversion ratio 28.57 Conversion value $ 1,314.29

Chapter 24Question 10

Input Area:

Conversion price $ 55 Coupon rate 5.2%Par value $ 1,000 Nonconvertible debenture % 7%Settlement date 01/01/08Maturity date 01/01/38Market price of stock $ 41

Output Area:

a. Straight bond value $ 775.50 Conversion ratio 18.18 Conversion value $ 745.45 The minimum value for this bond is the maximum of the straight bond price or theconversion value, in this case $ 775.50

b. The option embedded in the bond adds the extravalue.

Chapter 24Question 11

Input Area:

Settlement date 01/01/08Maturity date 01/01/38Coupon rate 7%Coupons per year 2 Par value $ 1,000 Conversion price $ 45 Market price of stock $ 39 Nonconvertible coupon rate 9%

Output Area:

a. Straight bond value $ 793.62 Conversion ratio 22.22 Conversion value $ 866.67 The minimum value for this bond is the maximum of the straight bond price or theconversion value, in this case $ 866.67

b. Conversion premium 15.38%

Chapter 24Question 12

Input Area:

Detachable warrants 25 Face value $ 1,000 Settlement date 01/01/08Maturity date 01/01/23Coupon $ 45 Yield 7%

Output Area:

Coupon rate 4.50%Bond value component $ 772.30 Warrant component $ 227.70 Price of one warrant $ 9.11

Chapter 24Question 13

Input Area:

New machine cash flow $ 320,000 Price $ 1,800,000 Pirce decline/year $ 120,000 Lowest price $ 1,200,000 Technology life 10 Required return 12%

Output Area:

Purchase in year: NPV 0 $ 8,071.37 1 $ 22,357.08 2 $ 23,632.59 3 $ 14,521.81 4 $ (2,764.29)5 $ (26,369.24)6 $ (115,536.32)

You should purchase when the NPV is the highest, which is $ 23,632.59

Chapter 24Question 14

Input Area:

Units sold per year 7,500 Net cash flow per unit $ 68 Life time 10 Annual operating cash flow $ 510,000 Initial investment $ 2,300,000 Discount rate 14%Abandonment value $ 1,500,000

Output Area:

a. NPV $ 360,218.98

b. Q 4,460 Abandon the project if Q < 4,460 because NPV(abandonment) > NPV(project CF's)

c. The abandonment value is the market value ofthe project. If you continue with the project in one year, you forego this cash that could have been used for something else.

Chapter 24Question 15

Input Area:

Units per year if successful 9,500 Units per year if unsuccessful 4,000 Net cash flow per unit $ 68 Successful operating cash flow $ 646,000 Initial operating cash flow $ 510,000 Initial investment $ 2,300,000 Life time 10 Discount rate 14%Abandonment value $ 1,500,000

Output Area:

a. Success:PV future CF's $3,195,356.21

Failure: (Calculation assumes that if the project is unsuccessful it will be abandoned.)From #14, Q < 4,460 so you will abandon, PV = $ 1,500,000 Year 1 expected value $ 2,857,678.10 NPV $ 206,735.18

b. No abandonment, PV future CF's $1,345,413.14 Gain from option to abandonment $ 154,586.86 Option is 50% likely to occur:Value = $ 67,801.25

Chapter 24Question 16

Input Area:

Units per year if successful 9,500 Units per year if unsuccessful 4,000 Net cash flow per unit $ 68 Annual operating cash flow $ 646,000 Initial operating cash flow $ 510,000 Initial investment $ 2,300,000 Life time 10 Discount rate 14%Abandonment value $ 1,500,000 Projected sales after expansion 19,000

Output Area:

Success: PV future CF's $6,390,712.41 Failure: (Calculation assumes that if the project is unsuccessful it will be abandoned.)From #14, Q < 4,460 abandon the project, PV = $ 1,500,000 Year 1 expected value $ 4,455,356.21 NPV $ 1,608,207.20 Gain from option to expand, PV future CF's $3,195,356.21 Option is 50% likely to happen $ 1,597,678.10 Present value of option CF's $ 1,401,472.02

Chapter 24Question 17

Input Area:

Stock price today $ 65 Risk-free 5%Low price in one year $ 75 High price in one year $ 85

a. Exercise price $ 75

Output Area:

a. $ - The option isn't worth anything.

b. The stock price is too low for the option to finish in the money. The minimumreturn on the stock required to get the option in the money is 15.38%which is much higher than the risk-freerate of interest.

C0

Chapter 24Question 18

Input Area:

A BOffering price of bond $ 800 $ 1,000 Bond value $ 800 $ 950 Conversion value $ 1,000 $ 900

Output Area:

B is the more typical; A presents an arbitrage opportunity.Buy the bond for $800 and immediately convert it into stockthat can be sold for $1,000. A riskless $200 profit result.

Chapter 24Question 19

Input Area:

Face value $ 1,000 Current price $ 960 Conversion ratio 22 Coupon rate 6%Nonconvertible yield 9%Settlement date 01/01/08Maturity date 01/01/28Stock price $ 35

Output Area:

a. Conversion ratio 22.00 Conversion price $ 45.45 Conversion premium 29.87%

b. Straight bond value $ 723.98 Conversion value $ 770.00

c. Stock price $ 32.91

d. There are actually two option values to consider with a convertible bond. The conversion option value, defined as the market value less the floor value, and the speculative option value, defined as the floorvalue less the straight bond value. When the conversion is less than the straight-bondvalue, the speculative option is worth zero.Conversion value $ 190.00 Speculative option value $ 46.02 Total option value $ 236.02

Chapter 24Question 20

Input area:

Annual OCF $ 18,000,000 Project life 8 Discount rate 14%Initial investment $ 75,000,000 Aftertax salvage value in Year 1 $ 30,000,000

Output area:

a. NPV $ 8,499,550.09

b. Minimum cash flow $ 6,995,771.32

Chapter 24Question 21

Input Area:

Face value $ 1,000 Settlement date 01/01/05Maturity date 01/01/30Coupon 5.4%Conversion price $ 150 Current price $ 41.40 Growth rate 11%Callable value $ 1,200 Price when called $ 1,300 Required return 9%

Output Area:

Straight bond value $ 646.39 Conversion value $ 276.00 # of years 14.85 The bond will be called in 14.85 years, forcing conversion.Bond value $ 794.68

Chapter 24Question 22

Input Area:

Initial investment $ 12,000,000 Net working capital $ 900,000 Pretax revenue $ 9,100,000 Pretax operating costs $ 3,700,000 # of years 4 Tax rate 38%Discount rate 13%

Salvage value Year 1 $ 8,200,000 Year 2 $ 6,100,000 Year 3 $ 4,700,000 Year 4 $ -

Output Area:

Assuming the project lasts four years, the NPV is calculated as follows:Year 0 1Sales $ 9,100,000 Operating costs 3,700,000 Depreciation 3,000,000 EBT $ 2,400,000 Tax 912,000 Net income $ 1,488,000 +Depreciation ### 3,000,000 Operating CF $ 4,488,000

Change in NWC $ (900,000) 0Capital spending $ (12,000,000) 0Total cash flow $ (12,900,000)### $ 4,488,000

Net present value $ 1,001,414.16

Abandoned after one year:

Year 0 1Sales $ 9,100,000 Operating costs 3,700,000 Depreciation 3,000,000 EBT $ 2,400,000 Tax 912,000 Net income $ 1,488,000 +Depreciation 3,000,000 Operating CF $ 4,488,000

Change in NWC $ (900,000) $ 900,000 Capital spending $ (12,000,000) $ 8,504,000 Total cash flow $ (12,900,000) $ 13,892,000

Book value of equipment $ 9,000,000 Taxes on sale $ 304,000 Salvage value $ 8,504,000

Net present value $ (606,194.69)

Abandoned after two years:Year 0 1Sales $ 9,100,000 Operating costs 3,700,000 Depreciation 3,000,000 EBT $ 2,400,000 Tax 912,000 Net income $ 1,488,000 +Depreciation ### 3,000,000 Operating CF $ 4,488,000

Change in NWC $ (900,000) 0Capital spending $ (12,000,000) 0Total cash flow $ (12,900,000) $ 4,488,000

Book value of equipment $ 6,000,000 Taxes on sale $ (38,000)Salvage value $ 6,062,000

Net present value $ 38,710.94

Abandoned after three years:Year 0 1 Sales $ 9,100,000 Operating costs 3,700,000 Depreciation 3,000,000 EBT $ 2,400,000 Tax 912,000 Net income $ 1,488,000 +Depreciation ### 3,000,000 Operating CF $ 4,488,000

Change in NWC $ (900,000) 0Capital spending $ (12,000,000) 0Total cash flow $ (12,900,000) $ 4,488,000

Book value of equipment $ 3,000,000 Taxes on sale $ (646,000)Salvage value $ 4,054,000

Net present value $ 1,130,223.36

Assuming the project lasts four years, the NPV is calculated as follows:2 3 4

$ 9,100,000 $ 9,100,000 $ 9,100,000 3,700,000 3,700,000 3,700,000 3,000,000 3,000,000 3,000,000 $ 2,400,000 $ 2,400,000 $ 2,400,000 912,000 912,000 912,000 $ 1,488,000 $ 1,488,000 $ 1,488,000 3,000,000 3,000,000 3,000,000 $ 4,488,000 $ 4,488,000 $ 4,488,000

0 0 $ 900,000 0 0 0

$ 4,488,000 $ 4,488,000 $ 5,388,000

2 $ 9,100,000 3,700,000 3,000,000 $ 2,400,000 912,000 $ 1,488,000 3,000,000 $ 4,488,000

$ 900,000 $ 6,062,000 $ 11,450,000

2 3 $ 9,100,000 $ 9,100,000 3,700,000 3,700,000 3,000,000 3,000,000 $ 2,400,000 $ 2,400,000 912,000 912,000 $ 1,488,000 $ 1,488,000 3,000,000 3,000,000 $ 4,488,000 $ 4,488,000

0 $ 900,000 0 $ 4,054,000

$ 4,488,000 $ 9,442,000