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Options Pricing, Interest Rates, and Debt Issuance Strategies

by Essays
Words: 755
Pages: 3
Subject: Economics, Finance and Investment
Topics: Financial Questions Answered

Assignment Question

I’m working on a finance question and need the explanation and answer to help me learn. 1.A call option on the stock of Bedrock Boulders has a market price of $8. The stock sells for $28 a share, and the option has a strike price of $26 a share. Round your answers to the nearest dollar. What is the exercise value of the call option? What is the option’s time value? 2. Assume that you have been given the following information on Purcell Industries’ call options: Current stock price = $15 Strike price of option = $13 Time to maturity of option = 3 months Risk-free rate = 6% Variance of stock return = 0.11 d1 = 1.03630 N(d1) = 0.84997 d2 = 0.87047 N(d2) = 0.80798 According to the Black-Scholes option pricing model, what is the option’s value? Do not round intermediate calculations. Round your answer to the nearest cent. Use only the values provided in the problem statement for your calculations. 3. The current price of a stock is $34, and the annual risk-free rate is 3%. A call option with a strike price of $29 and with 1 year until expiration has a current value of $7.02. What is the value of a put option written on the stock with the same exercise price and expiration date as the call option? Do not round intermediate calculations. Round your answer to the nearest cent. 4. Use the Black-Scholes model to find the price for a call option with the following inputs: (1) current stock price is $29, (2) strike price is $36, (3) time to expiration is 6 months, (4) annualized risk-free rate is 5%, and (5) variance of stock return is 0.16. Do not round intermediate calculations. Round your answer to the nearest cent. 5. What is the implied interest rate on a Treasury bond ($100,000, 6% coupon, semiannual payment with 20 years to maturity) futures contract that settled at 100’16? Do not round intermediate calculations. Round your answer to two decimal places. If interest rates increased by 1%, what would be the contract’s new value? Do not round intermediate calculations. Round your answer to the nearest cent. 6. Carter Enterprises can issue floating-rate debt at LIBOR + 3% or fixed-rate debt at 9%. Brence Manufacturing can issue floating-rate debt at LIBOR + 2.0% or fixed-rate debt at 11%. Suppose Carter issues floating-rate debt and Brence issues fixed-rate debt. They are considering a swap in which Carter makes a fixed-rate payment of 8.00% to Brence and Brence makes a payment of LIBOR to Carter. What are the net payments of Carter and Brence if they engage in the swap? Round your answers to two decimal places. Use a minus sign to enter negative values, if any. Net payment of Carter: % Net payment of Brence: -(LIBOR + %) Would Carter be better off if it issued fixed-rate debt or if it issued floating-rate debt and engaged in the swap? The swap is good for Carter, if it issued -Select- fixed-rate debt floating-rate debt and engaged in the swap Item 3 . Would Brence be better off if it issued floating-rate debt or if it issued fixed-rate debt and engaged in the swap? The swap is good for Brence, if it issue what?

Answer

  • Exercise Value and Time Value of Call Option:
    • The exercise value of the call option is $2.
    • The time value of the call option is $6.
  • Option’s Value According to Black-Scholes Model:
    • The option’s value is approximately $3.05.
  • Value of Put Option:
    • The value of the put option is approximately $0.98.
  • Price for Call Option Using Black-Scholes Model:
    • The price for the call option is approximately $4.23.
  • Implied Interest Rate on Treasury Bond Futures:
    • The implied interest rate is approximately 5.84%.
    • If interest rates increased by 1%, the new contract value would be approximately $99,356.33.
  • Net Payments in Swap:
    • Net payment of Carter: -6.84%
    • Net payment of Brence: LIBOR + 6.84%

Carter would be better off if it issued floating-rate debt and engaged in the swap. Brence would be better off if it issued fixed-rate debt and engaged in the swap.

References

Black, F., & Scholes, M. (2023). The pricing of options and corporate liabilities. Journal of Political Economy, 81(3), 637-654.

Hull, J. C. (2019). Options, futures, and other derivatives. Pearson.

Fabozzi, F. J. (2018). Fixed Income Analysis (3rd ed.). Wiley.

FAQs

  1. What is the exercise value of a call option, and how is it calculated?
  2. Can you explain the Black-Scholes option pricing model and how it determines option values?
  3. How do implied interest rates affect Treasury bond futures contracts, and what happens if interest rates change?
  4. What are the key considerations when deciding between fixed-rate and floating-rate debt issuance strategies?
  5. How does a swap agreement benefit parties like Carter Enterprises and Brence Manufacturing in managing their debt?