Assume that an investor has $10,000 to invest. Stock can be purchased at $20 per share (500 shares can be purchased). Call options to purchase 100 shares at a price of $25 can be purchased for $500 (options to produce 2,000 shares can be purchased). Compare the change in the investor’s wealth from buying the stock and buying the options if the stock price at the expiration of the option is: $35. $24.

Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
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chapter 15 #7 Assume that an investor has $10,000 to invest. Stock can be purchased at $20 per share (500 shares can be purchased). Call options to purchase 100 shares at a price of $25 can be purchased for $500 (options to produce 2,000 shares can be purchased).

Compare the change in the investor’s wealth from buying the stock and buying the options if the stock price at the expiration of the option is:

  1. $35.
  2. $24.
# Problems in Warrant and Option Valuation

1. **Warrant Valuation:**
   - A warrant allows the holder to purchase a share of common stock at $20 per share within the next five years. The current stock price is $15, with no dividends expected, and an anticipated growth to $30. The time value of money is 12%.
     - a. **Minimum Value:** Determine the minimum value of the warrant.
     - b. **Maximum Value:** Calculate the maximum potential value.
     - c. **Present Value at Time 5:** Calculate the present value for a stock price of $30 at time 5.

2. **Warrant Valuation with Stock Price Increase:**
   - Assuming a belief that the stock price will increase to $40 in five years, assess the impact on the valuations in Problem 1.

3. **Zero Dividend Stock Valuation:**
   - With an expected stock price rise to $30 in five years and zero dividends:
     - a. Evaluate if an investor should purchase the warrant at $5 or the stock at $15.
     - b. Decision: Buy stock or three warrants?

4. **Impact of Dividend on Warrant Value:**
   - With a $1 anticipated dividend each year, evaluate the effect on buy-stock-versus-warrant decisions.

5. **Short-term Stock Price Increase:**
   - Assuming the warrant can be purchased for $5 and a stock price rise to $45 in near term:
     - Assess the impact on intrinsic present value and maximum price.

6. **Put Option Profitability:**
   - If the stock is currently $80, with a put option to sell at $75 costing $4 and stock dropping to $72 before expiry:
     - Determine the profitability of buying the put.

7. **Stock vs. Option Purchase:**
   - With $10,000 to invest and stock at $20 per share:
     - Compare buying 100 shares directly or using call options for 2,000 shares at $25, given stock prices of:
       - a. $35
       - b. $24

8. **Black-Scholes Model:**
   - Calculate an option’s value expiring in one year (T = 1) using:
     - Stock price (S): $45
     - Exercise price (K): $40
     - Interest rate (r): 1.20
     - Variance
Transcribed Image Text:# Problems in Warrant and Option Valuation 1. **Warrant Valuation:** - A warrant allows the holder to purchase a share of common stock at $20 per share within the next five years. The current stock price is $15, with no dividends expected, and an anticipated growth to $30. The time value of money is 12%. - a. **Minimum Value:** Determine the minimum value of the warrant. - b. **Maximum Value:** Calculate the maximum potential value. - c. **Present Value at Time 5:** Calculate the present value for a stock price of $30 at time 5. 2. **Warrant Valuation with Stock Price Increase:** - Assuming a belief that the stock price will increase to $40 in five years, assess the impact on the valuations in Problem 1. 3. **Zero Dividend Stock Valuation:** - With an expected stock price rise to $30 in five years and zero dividends: - a. Evaluate if an investor should purchase the warrant at $5 or the stock at $15. - b. Decision: Buy stock or three warrants? 4. **Impact of Dividend on Warrant Value:** - With a $1 anticipated dividend each year, evaluate the effect on buy-stock-versus-warrant decisions. 5. **Short-term Stock Price Increase:** - Assuming the warrant can be purchased for $5 and a stock price rise to $45 in near term: - Assess the impact on intrinsic present value and maximum price. 6. **Put Option Profitability:** - If the stock is currently $80, with a put option to sell at $75 costing $4 and stock dropping to $72 before expiry: - Determine the profitability of buying the put. 7. **Stock vs. Option Purchase:** - With $10,000 to invest and stock at $20 per share: - Compare buying 100 shares directly or using call options for 2,000 shares at $25, given stock prices of: - a. $35 - b. $24 8. **Black-Scholes Model:** - Calculate an option’s value expiring in one year (T = 1) using: - Stock price (S): $45 - Exercise price (K): $40 - Interest rate (r): 1.20 - Variance
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