- Miscellaneous
- Speech or Presentation
- May 23, 2018

Finance 09 June Problem Firm A Firm B Common Stock Price of Common Stock $46 $30 Cash Dividend 0 Convertible Bond

Principal

$1,000

$1,000

Conversion Price

$50

$33 1/3

20 shares

30 shares

Maturity

10 years

10 years

Coupon

7.5%

7.5%

Market Price

$1,100

$1, 100

1. Value of each bond in terms of stock:

Firm A: $46 x 20 shares = $920 shares

Firm B: $30 x 30 shares = $900 shares

2. Premium paid over each bond’s value as stock:

Firm A premium: $50 - 46 = $4 Premium percentage: ($4/46) x 100 = 8.69%

Firm B premium: $33.33-30-3.33 = 3.33 Premium percentage: ($3.33/30) x 100 = 11.10%

3. Each bonds income advantage over the stock into which the bond may be converted

Firm A: $75 – 46 = $29

Firm B: $75 – 30 = $45

4. Length of time when the income advantage will offset the premium determined

Firm A: 4 years

Years

Income Advantage

Premium

1

$29

$86.90

2

$58

$94.45

3

$87

$102.66

4

$116

$111.58

Firm B: 6 years

Years

Income Advantage

Premium

1

$45

$111

2

$74

$123

3

$103

$137

4

$132

$152

5

$161

$169

6

$190

$187

5. If after 4 years firm, As stock sells for $65 and the firm calls the bond, what is the holding period return and annual rate of return earned on investment in the stock or bond?

Firm A Holding Period of Return

Years

Capital ($)

Coupon Payment ($)

Return ($)

Rate of Return

1

1, 000

75

1075

7.5%

2

1, 000

150

1150

15%

3

1, 000

225

1225

22.5%

4

1, 300

300

1600

23.08%

5

1, 300

375

1675

28.85%

6

1,300

450

1750

34.62%

7

1, 300

525

1825

40.38%

8

1, 300

600

1900

46.15%

9

1, 300

675

1975

51.92%

10

1, 300

750

2050

57.69%

Firm A Annual Rate of Return

Years

Capital ($)

Coupon Payment ($)

Return ($)

Rate of Return

1-3

1, 000

75

1, 075

7.5%

4-10

1, 300

75

2, 075

5.76%

Problem 2

1. Many warrants were initially issued attached to bonds. They were subsequently detached and traded separately from the bonds. In some cases, the bond could be used in lieu of cash to exercise the warrant. Suppose a warrant is the option to buy stock at $ 10 a share ($ 1,000 for 100 shares). Currently the stock is selling for $ 13 ($ 1,300 for 100 shares), the bond is selling for $ 700, and the warrant to buy a share is selling for $ 4. What would you do and why would you do it?

Answer: Straddle option is a good investment strategy due to the fact that stock movement is not certain on which way to go. With the figures given, $1,000 will be paid for the option to buy stock and $400 to sell a share. The total cost is $1, 400. Writing the straddle, the writer will receive the total premium of $1,400. If the price of the stock drops, let’s say to $8, the call expires worthless but the puts are now in the money by $20 for a net value of $2,000. Therefore, there’ll still be a profit of $600 after subtracting the premiums for the options.

2. A put and a call have the following terms:

Call Options:

Strike Price

Term

Price

$30

3 months

$3

Put Options:

Strike Price

Term

Price

$30

3 months

$4

Price of the stock: $29

Illustrate how to use the call or the put to reduce your risk exposure.

a) What is the maximum possible profit on the position?

Answer: In order to have a maximum profit, the maximum stock price should fall at $37. Assuming there are 100 shares, the total net value will be $3, 700, having a total profit of $3,100 after deducting the premium.

b) What is the maximum possible loss on the position?

Answer: Maximum possible loss is $7 per share. Let’s say there are 100 shares, so the maximum loss is $700. It is the sum of put and call option, which is also the premium of the straddle.

c) What range of stock prices generates a profit?

Stock prices ranging from $23 to $37 will generate profit. You can calculate it by getting the upper and lower breakeven point.

Upper Break Even: $30 strike price + $7 net debit = $37

Lower Break Even: $30 strike price - $7 net debit = $23

d) What advantage does this position offer?

This position offer a smaller risk when the investor is confident that the market will move enough over the time the straddle is owned to make up for the premium invested. It would not take the whole stocks but only the premium paid.

3. Given the following:

Price of the stock $ 18

Price of a three- month call at $ 20 2

Price of a three- month call at $ 15 5

a) What is the profit (loss) at the expiration date of the options if the price of the stock is $ 14, $ 20, or $ 25 and if the investor buys the option with the $ 20 strike price and sells the other option?

For $14, the movement of the stock from $18 is -$4 which is equals to 2 ticks movement or $40 loss. If he will sell the stock for $14 which he bought for $20, he will incur loss of $6 plus $40 which is equals to $46 loss.

For $20, the movement of the stock from $18 is $2 which is equals to 1 tick movements or $20 profit. Buying of stocks at $20 and selling it at $20 result in no loss or profit. Total profit: $20.

For $25, the movement of the stock from $18 is $7 which is equals to 3.5 ticks movements or $70 profit. If he will sell the stock for $25 which he bought for $18 will result a profit of $7 plus the $70 which is equals to $77 profit.

b) Compare the profit (loss) from this strategy with shorting the stock at $ 18. .3

For $14, the movement of the stock from $18 is -$4 which is equals to 13 and 1/3 ticks movement or $240 loss. If he will sell the stock for $14 which he bought for $20, he will incur loss of $6 plus $240 which is equals to $246 loss.

For $20, the movement of the stock from $18 is $2 which is equals to 6 and 1/3 tick movements or $124 profit. Buying of stocks at $20 and selling it at $20 result in no loss or profit. Total profit: $124.

For $25, the movement of the stock from $18 is $7 which is equals to 23and 1/3 ticks movements or $420 profit. If he will sell the stock for $25 which he bought for $18 will result a profit of $7 plus the $420 which is equals to $427 profit.

c) What is the profit (loss) at the expiration date of the options if the price of the stock is $ 14, $ 20, or $ 25 and if the investor buys the option with the $ 15 strike price and sells the other option?

For $14, the movement of the stock from $18 is -$4 which is equals to 2 ticks movement or $40 loss. If he will sell the stock for $14 which he bought for $15, he will incur $1 loss plus the $40 which is equals to $41 loss.

For $20, the movement of the stock from $18 is -$2 which is equals to 1 tick movement or $20 profit. If he will sell the stock for $20 which he bought for $15, he will incur $5 profit plus the $20 which is equals to $25.

For $25, the movement of the stock from $18 is $7 which is equals to 3.5 ticks movements or $70 profit. If he will sell the stock for $25 which he bought for $15 it will result for a profit of $10 plus the $70 which is equals to $80.

d) Compare the profit (loss) from this strategy with buying the stock at $ 18.

For $14, the movement of the stock from $18 is -$4 which is equals to 2 ticks movement or $40 loss. If he will buy the stock for $18 which he could sell for $14, he will incur $4 profit plus the $40 loss which is equals to $36 loss.

For $20, the movement of the stock from $18 is -$2 which is equals to 1 tick movement or $20 profit. If he will buy the stock for $18 which he could sell for $15, he will incur $3 loss plus the $20 which is equals to $17 profit.

For $25, the movement of the stock from $18 is $7 which is equals to 3.5 ticks movements or $70 profit. If he will buy the stock for $18 which he could sell for $25 it will result in a loss of $7 plus the $70 profit which is equals to $63.

Principal

$1,000

$1,000

Conversion Price

$50

$33 1/3

20 shares

30 shares

Maturity

10 years

10 years

Coupon

7.5%

7.5%

Market Price

$1,100

$1, 100

1. Value of each bond in terms of stock:

Firm A: $46 x 20 shares = $920 shares

Firm B: $30 x 30 shares = $900 shares

2. Premium paid over each bond’s value as stock:

Firm A premium: $50 - 46 = $4 Premium percentage: ($4/46) x 100 = 8.69%

Firm B premium: $33.33-30-3.33 = 3.33 Premium percentage: ($3.33/30) x 100 = 11.10%

3. Each bonds income advantage over the stock into which the bond may be converted

Firm A: $75 – 46 = $29

Firm B: $75 – 30 = $45

4. Length of time when the income advantage will offset the premium determined

Firm A: 4 years

Years

Income Advantage

Premium

1

$29

$86.90

2

$58

$94.45

3

$87

$102.66

4

$116

$111.58

Firm B: 6 years

Years

Income Advantage

Premium

1

$45

$111

2

$74

$123

3

$103

$137

4

$132

$152

5

$161

$169

6

$190

$187

5. If after 4 years firm, As stock sells for $65 and the firm calls the bond, what is the holding period return and annual rate of return earned on investment in the stock or bond?

Firm A Holding Period of Return

Years

Capital ($)

Coupon Payment ($)

Return ($)

Rate of Return

1

1, 000

75

1075

7.5%

2

1, 000

150

1150

15%

3

1, 000

225

1225

22.5%

4

1, 300

300

1600

23.08%

5

1, 300

375

1675

28.85%

6

1,300

450

1750

34.62%

7

1, 300

525

1825

40.38%

8

1, 300

600

1900

46.15%

9

1, 300

675

1975

51.92%

10

1, 300

750

2050

57.69%

Firm A Annual Rate of Return

Years

Capital ($)

Coupon Payment ($)

Return ($)

Rate of Return

1-3

1, 000

75

1, 075

7.5%

4-10

1, 300

75

2, 075

5.76%

Problem 2

1. Many warrants were initially issued attached to bonds. They were subsequently detached and traded separately from the bonds. In some cases, the bond could be used in lieu of cash to exercise the warrant. Suppose a warrant is the option to buy stock at $ 10 a share ($ 1,000 for 100 shares). Currently the stock is selling for $ 13 ($ 1,300 for 100 shares), the bond is selling for $ 700, and the warrant to buy a share is selling for $ 4. What would you do and why would you do it?

Answer: Straddle option is a good investment strategy due to the fact that stock movement is not certain on which way to go. With the figures given, $1,000 will be paid for the option to buy stock and $400 to sell a share. The total cost is $1, 400. Writing the straddle, the writer will receive the total premium of $1,400. If the price of the stock drops, let’s say to $8, the call expires worthless but the puts are now in the money by $20 for a net value of $2,000. Therefore, there’ll still be a profit of $600 after subtracting the premiums for the options.

2. A put and a call have the following terms:

Call Options:

Strike Price

Term

Price

$30

3 months

$3

Put Options:

Strike Price

Term

Price

$30

3 months

$4

Price of the stock: $29

Illustrate how to use the call or the put to reduce your risk exposure.

a) What is the maximum possible profit on the position?

Answer: In order to have a maximum profit, the maximum stock price should fall at $37. Assuming there are 100 shares, the total net value will be $3, 700, having a total profit of $3,100 after deducting the premium.

b) What is the maximum possible loss on the position?

Answer: Maximum possible loss is $7 per share. Let’s say there are 100 shares, so the maximum loss is $700. It is the sum of put and call option, which is also the premium of the straddle.

c) What range of stock prices generates a profit?

Stock prices ranging from $23 to $37 will generate profit. You can calculate it by getting the upper and lower breakeven point.

Upper Break Even: $30 strike price + $7 net debit = $37

Lower Break Even: $30 strike price - $7 net debit = $23

d) What advantage does this position offer?

This position offer a smaller risk when the investor is confident that the market will move enough over the time the straddle is owned to make up for the premium invested. It would not take the whole stocks but only the premium paid.

3. Given the following:

Price of the stock $ 18

Price of a three- month call at $ 20 2

Price of a three- month call at $ 15 5

a) What is the profit (loss) at the expiration date of the options if the price of the stock is $ 14, $ 20, or $ 25 and if the investor buys the option with the $ 20 strike price and sells the other option?

For $14, the movement of the stock from $18 is -$4 which is equals to 2 ticks movement or $40 loss. If he will sell the stock for $14 which he bought for $20, he will incur loss of $6 plus $40 which is equals to $46 loss.

For $20, the movement of the stock from $18 is $2 which is equals to 1 tick movements or $20 profit. Buying of stocks at $20 and selling it at $20 result in no loss or profit. Total profit: $20.

For $25, the movement of the stock from $18 is $7 which is equals to 3.5 ticks movements or $70 profit. If he will sell the stock for $25 which he bought for $18 will result a profit of $7 plus the $70 which is equals to $77 profit.

b) Compare the profit (loss) from this strategy with shorting the stock at $ 18. .3

For $14, the movement of the stock from $18 is -$4 which is equals to 13 and 1/3 ticks movement or $240 loss. If he will sell the stock for $14 which he bought for $20, he will incur loss of $6 plus $240 which is equals to $246 loss.

For $20, the movement of the stock from $18 is $2 which is equals to 6 and 1/3 tick movements or $124 profit. Buying of stocks at $20 and selling it at $20 result in no loss or profit. Total profit: $124.

For $25, the movement of the stock from $18 is $7 which is equals to 23and 1/3 ticks movements or $420 profit. If he will sell the stock for $25 which he bought for $18 will result a profit of $7 plus the $420 which is equals to $427 profit.

c) What is the profit (loss) at the expiration date of the options if the price of the stock is $ 14, $ 20, or $ 25 and if the investor buys the option with the $ 15 strike price and sells the other option?

For $14, the movement of the stock from $18 is -$4 which is equals to 2 ticks movement or $40 loss. If he will sell the stock for $14 which he bought for $15, he will incur $1 loss plus the $40 which is equals to $41 loss.

For $20, the movement of the stock from $18 is -$2 which is equals to 1 tick movement or $20 profit. If he will sell the stock for $20 which he bought for $15, he will incur $5 profit plus the $20 which is equals to $25.

For $25, the movement of the stock from $18 is $7 which is equals to 3.5 ticks movements or $70 profit. If he will sell the stock for $25 which he bought for $15 it will result for a profit of $10 plus the $70 which is equals to $80.

d) Compare the profit (loss) from this strategy with buying the stock at $ 18.

For $14, the movement of the stock from $18 is -$4 which is equals to 2 ticks movement or $40 loss. If he will buy the stock for $18 which he could sell for $14, he will incur $4 profit plus the $40 loss which is equals to $36 loss.

For $20, the movement of the stock from $18 is -$2 which is equals to 1 tick movement or $20 profit. If he will buy the stock for $18 which he could sell for $15, he will incur $3 loss plus the $20 which is equals to $17 profit.

For $25, the movement of the stock from $18 is $7 which is equals to 3.5 ticks movements or $70 profit. If he will buy the stock for $18 which he could sell for $25 it will result in a loss of $7 plus the $70 profit which is equals to $63.