Question Tag: Options

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  • 20 Marks

FM – May 2019 – L3 – Q5 – Portfolio Management

Evaluate whether an option price is fair for hedging Yaro Plc. shares, and explain how changes in volatility and the risk-free rate affect the value of a call option.

You are the portfolio manager of an asset management company based in Kano. Your company has in its portfolio 27,750,000 shares of Yaro Plc., a company listed on the Nigerian Stock Exchange. The shares are currently trading at N3.60 per share.

Your company plans to sell the shares in six months’ time to pay dividends, and you plan to hedge the risk of Yaro’s shares falling by more than 5% from their current market value. A decision has therefore been taken to buy an over-the-counter option to protect the shares. A merchant bank has offered to sell an appropriate six-month option to your company for N1,250,000.

Yaro’s share price has an annual standard deviation of 13%, and the risk-free rate is 4% per year.

Required:

a. Evaluate whether or not the price at which the merchant bank is willing to sell the option is a fair price.

b. Explain briefly (without any calculations) how a decrease in the value of each of the following variables is likely to change the value of a call option:
i. Volatility of the stock price
ii. Risk-free rate

(Total: 15 Marks)

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  • 3 Marks

FM – May 2022 – L3 – Q6b – Financial Risk Management

Calculate the number of put options needed to delta-hedge a short position.

In your personal investment portfolio, you have gone short (i.e., you have sold) 110,000 units of Big Bank plc. Call and put options exist on the bank’s shares. You decide to hedge your position using put options on the bank’s shares. For the relevant option, you know that:
N(d1) = 0.45

You are required to calculate how many put options you will need to buy or sell to delta-hedge. Be specific.

 

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  • 20 Marks

FM – Nov 2023 – L3 – SB – Q2 – Foreign Exchange Risk Management

Analyze hedging methods for foreign exchange risk involving a future CHF transaction.

About one year ago, you were employed by Tesco, an American company based in New York. You work online from home in Nigeria and are a member of the international treasury of Tesco.

Tesco supplies medical equipment to the USA and Europe and also buys some basic raw materials from Europe. It is currently 30 November 2024. On 31 May 2025, Tesco is due to receive CHF16.3 million from a Swiss customer and also to pay CHF4.0 million to a Swiss supplier.

Exchange rates (quoted as US$/CHF1):

  • Spot: 1.0292 – 1.0309
  • Three months forward: 1.0322 – 1.0341
  • Six months forward: 1.0356 – 1.0378

Annual interest rates available to Tesco:

  • Switzerland: 3.2% (investing), 4.4% (borrowing)
  • USA: 4.6% (investing), 5.8% (borrowing)

Currency futures (contract size CHF125,000, futures price quoted as US$ per CHF1):

  • Future price: December – 1.0306, March – 1.0336, June – 1.0369

Currency options (contract size CHF125,000; exercise price quotation US$ per CHF1, premium in US cents per CHF1):

Calls Puts
Dec Mar June Dec Mar June
1.0375 0.47 0.50 0.53 0.74 0.79 0.86

Required:

  • a. Calculate the net receipt if hedged using a forward contract. (4 Marks)
  • b. Calculate the net receipt if hedged using money market hedging. (8 Marks)
  • c. Calculate the net receipt if hedged using futures. (10 Marks)
  • d. Calculate the net receipt if hedged using options. (8 Marks)
    (Total: 30 Marks)

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  • 20 Marks

FR – Nov 2023 – L2 – Q4a & b – Earnings Per Share (IAS 33)

Discuss diluted EPS and calculate EPS measures for Ebonyi Limited.

IAS 33 requires publicly-traded companies to calculate a diluted Earning Per Share (EPS) in addition to their basic EPS for the current year (with a comparative diluted EPS for the previous year), allowing for the effect of all dilutive potential ordinary shares.

Required: a. Explain the purpose of the dilutive measures and discuss THREE types of dilution. (8 Marks)

b. The statement of financial position (extracts) for Ebonyi Limited for the year ended December 31, 2022 is as follows:

Equity and Liabilities N’000
Ordinary shares (N1 each) 12,000
Retained earnings 36,000
Equity 48,000
Non-current liabilities:
5% convertible loan notes 4,000

Additional information: i. As at December 31, 2022, there has been no new issue of shares or loan notes for several years.
ii. The loan notes are convertible into ordinary shares in year 2023 or year 2024 at the following rates.
iii. At 30 shares for every N100 of loan notes if converted at December 31, 2023.
iv. At 25 shares for every N100 of loan notes if converted at December 31, 2024.
v. Company income tax rate is 30% on profit.

Required: Calculate the basic EPS and diluted EPS for year 2022. (8 Marks)

c. IAS 33 allows an entity to disclose an alternative measure of EPS in addition to the EPS calculated.

Required: Identify and explain TWO conditions that are required in accordance with IAS 33 to be complied with where an alternative measure of EPS is shown in the financial statements of an entity. (4 Marks)

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  • 7 Marks

FR – Nov 2022 – L2 – Q6b – Potential Ordinary Shares

Rank the types of potential ordinary shares and calculate the diluted EPS for Jumai Nigeria Limited.

The following information relates to Jumai Nigeria Limited for the year ended December 31, 2020.
Issued ordinary shares of 50k each N3,000,000
Profit for the year N18,000,000
Average market price of shares during the year was N70 per share. The potential financial instruments in existence in the company are detailed below:
i. 800,000 options with exercise price of N52.50.
ii. 5% convertible bond of N6,000,000. Each bond is convertible in year 2025 into ordinary shares at the rate of 30 new shares for every N100 bonds.
iii. 200,000 8% convertible preference shares at N10 per share. Each preference share is convertible in year 2024 at the rate of one ordinary share for every 25 preference shares held. The Company income tax rate is 30%. Assume that all the options are exercised.
Required:
Rank the potential ordinary shares and calculate the diluted EPS for the year ended December 31, 2020. (7 Marks)

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  • 7 Marks

FM – Nov 2020 – L2 – Q3b – Futures and hedging with futures | Hedging with options

Explain intrinsic value of an option and calculate the intrinsic value for USD/GH¢ call options over several months.

i) Explain the term intrinsic value of an option. (1 mark)

ii) DUU Ghana Ltd bought USD/GH¢ call options from KASA Ltd. The table below shows the various spot rates and strike prices for the various tenors.

Month Spot Rate USD/GH¢ Exercise Rate/Price USD/GH¢
1 5.1 4.8
2 5.3 5.0
3 5.5 5.4
4 5.8 5.8
5 5.7 6.0
6 6.0 6.4

Required:

Determine the intrinsic value of the option for each trading month and clearly indicate the months in which the option is in-the-money, at-the-money, or out-of-the-money. (6 marks)

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  • 10 Marks

FM – MAY 2019 – L2 – Q3b – Foreign exchange risk and currency risk management | Hedging with options

Calculate profit or loss from option contracts and advise on whether to exercise the options for Universal Plastics Ghana Ltd.

Universal Plastics Ghana Ltd imported raw materials from U.S.A. and Europe for the manufacture of plastic products. The company entered into option contracts with ZAA Bank Ghana Ltd to hedge its six months’ currency risk or exposure. The details of the option contracts are as follows:

Details Transaction Amount Strike Price/ Exchange Rate Spot Rate on Maturity Date Option Premium Paid to the Bank
OPTION A Bought Call option to buy USD against GH¢ US$10m USD/GH¢ 4.7 USD/GH¢ 4.5
OPTION B Bought Call option to buy EURO against GH¢ EUR 8m EUR/GH¢ 5.9 EUR/GH¢ 6.3

Required:

  1. Calculate the profit or loss of OPTION A and advise Universal Plastics Ghana Ltd whether to exercise or not. (4 marks)
  2. Calculate the profit or loss of OPTION B and advise Universal Plastics Ghana Ltd whether to exercise or not. (4 marks)
  3. Calculate the overall profit or loss on the decision to hedge based on (i) and (ii) above. (2 marks)

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  • 20 Marks

FM – May 2019 – L3 – Q5 – Portfolio Management

Evaluate whether an option price is fair for hedging Yaro Plc. shares, and explain how changes in volatility and the risk-free rate affect the value of a call option.

You are the portfolio manager of an asset management company based in Kano. Your company has in its portfolio 27,750,000 shares of Yaro Plc., a company listed on the Nigerian Stock Exchange. The shares are currently trading at N3.60 per share.

Your company plans to sell the shares in six months’ time to pay dividends, and you plan to hedge the risk of Yaro’s shares falling by more than 5% from their current market value. A decision has therefore been taken to buy an over-the-counter option to protect the shares. A merchant bank has offered to sell an appropriate six-month option to your company for N1,250,000.

Yaro’s share price has an annual standard deviation of 13%, and the risk-free rate is 4% per year.

Required:

a. Evaluate whether or not the price at which the merchant bank is willing to sell the option is a fair price.

b. Explain briefly (without any calculations) how a decrease in the value of each of the following variables is likely to change the value of a call option:
i. Volatility of the stock price
ii. Risk-free rate

(Total: 15 Marks)

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  • 3 Marks

FM – May 2022 – L3 – Q6b – Financial Risk Management

Calculate the number of put options needed to delta-hedge a short position.

In your personal investment portfolio, you have gone short (i.e., you have sold) 110,000 units of Big Bank plc. Call and put options exist on the bank’s shares. You decide to hedge your position using put options on the bank’s shares. For the relevant option, you know that:
N(d1) = 0.45

You are required to calculate how many put options you will need to buy or sell to delta-hedge. Be specific.

 

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  • 20 Marks

FM – Nov 2023 – L3 – SB – Q2 – Foreign Exchange Risk Management

Analyze hedging methods for foreign exchange risk involving a future CHF transaction.

About one year ago, you were employed by Tesco, an American company based in New York. You work online from home in Nigeria and are a member of the international treasury of Tesco.

Tesco supplies medical equipment to the USA and Europe and also buys some basic raw materials from Europe. It is currently 30 November 2024. On 31 May 2025, Tesco is due to receive CHF16.3 million from a Swiss customer and also to pay CHF4.0 million to a Swiss supplier.

Exchange rates (quoted as US$/CHF1):

  • Spot: 1.0292 – 1.0309
  • Three months forward: 1.0322 – 1.0341
  • Six months forward: 1.0356 – 1.0378

Annual interest rates available to Tesco:

  • Switzerland: 3.2% (investing), 4.4% (borrowing)
  • USA: 4.6% (investing), 5.8% (borrowing)

Currency futures (contract size CHF125,000, futures price quoted as US$ per CHF1):

  • Future price: December – 1.0306, March – 1.0336, June – 1.0369

Currency options (contract size CHF125,000; exercise price quotation US$ per CHF1, premium in US cents per CHF1):

Calls Puts
Dec Mar June Dec Mar June
1.0375 0.47 0.50 0.53 0.74 0.79 0.86

Required:

  • a. Calculate the net receipt if hedged using a forward contract. (4 Marks)
  • b. Calculate the net receipt if hedged using money market hedging. (8 Marks)
  • c. Calculate the net receipt if hedged using futures. (10 Marks)
  • d. Calculate the net receipt if hedged using options. (8 Marks)
    (Total: 30 Marks)

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  • 20 Marks

FR – Nov 2023 – L2 – Q4a & b – Earnings Per Share (IAS 33)

Discuss diluted EPS and calculate EPS measures for Ebonyi Limited.

IAS 33 requires publicly-traded companies to calculate a diluted Earning Per Share (EPS) in addition to their basic EPS for the current year (with a comparative diluted EPS for the previous year), allowing for the effect of all dilutive potential ordinary shares.

Required: a. Explain the purpose of the dilutive measures and discuss THREE types of dilution. (8 Marks)

b. The statement of financial position (extracts) for Ebonyi Limited for the year ended December 31, 2022 is as follows:

Equity and Liabilities N’000
Ordinary shares (N1 each) 12,000
Retained earnings 36,000
Equity 48,000
Non-current liabilities:
5% convertible loan notes 4,000

Additional information: i. As at December 31, 2022, there has been no new issue of shares or loan notes for several years.
ii. The loan notes are convertible into ordinary shares in year 2023 or year 2024 at the following rates.
iii. At 30 shares for every N100 of loan notes if converted at December 31, 2023.
iv. At 25 shares for every N100 of loan notes if converted at December 31, 2024.
v. Company income tax rate is 30% on profit.

Required: Calculate the basic EPS and diluted EPS for year 2022. (8 Marks)

c. IAS 33 allows an entity to disclose an alternative measure of EPS in addition to the EPS calculated.

Required: Identify and explain TWO conditions that are required in accordance with IAS 33 to be complied with where an alternative measure of EPS is shown in the financial statements of an entity. (4 Marks)

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  • 7 Marks

FR – Nov 2022 – L2 – Q6b – Potential Ordinary Shares

Rank the types of potential ordinary shares and calculate the diluted EPS for Jumai Nigeria Limited.

The following information relates to Jumai Nigeria Limited for the year ended December 31, 2020.
Issued ordinary shares of 50k each N3,000,000
Profit for the year N18,000,000
Average market price of shares during the year was N70 per share. The potential financial instruments in existence in the company are detailed below:
i. 800,000 options with exercise price of N52.50.
ii. 5% convertible bond of N6,000,000. Each bond is convertible in year 2025 into ordinary shares at the rate of 30 new shares for every N100 bonds.
iii. 200,000 8% convertible preference shares at N10 per share. Each preference share is convertible in year 2024 at the rate of one ordinary share for every 25 preference shares held. The Company income tax rate is 30%. Assume that all the options are exercised.
Required:
Rank the potential ordinary shares and calculate the diluted EPS for the year ended December 31, 2020. (7 Marks)

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  • 7 Marks

FM – Nov 2020 – L2 – Q3b – Futures and hedging with futures | Hedging with options

Explain intrinsic value of an option and calculate the intrinsic value for USD/GH¢ call options over several months.

i) Explain the term intrinsic value of an option. (1 mark)

ii) DUU Ghana Ltd bought USD/GH¢ call options from KASA Ltd. The table below shows the various spot rates and strike prices for the various tenors.

Month Spot Rate USD/GH¢ Exercise Rate/Price USD/GH¢
1 5.1 4.8
2 5.3 5.0
3 5.5 5.4
4 5.8 5.8
5 5.7 6.0
6 6.0 6.4

Required:

Determine the intrinsic value of the option for each trading month and clearly indicate the months in which the option is in-the-money, at-the-money, or out-of-the-money. (6 marks)

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  • 10 Marks

FM – MAY 2019 – L2 – Q3b – Foreign exchange risk and currency risk management | Hedging with options

Calculate profit or loss from option contracts and advise on whether to exercise the options for Universal Plastics Ghana Ltd.

Universal Plastics Ghana Ltd imported raw materials from U.S.A. and Europe for the manufacture of plastic products. The company entered into option contracts with ZAA Bank Ghana Ltd to hedge its six months’ currency risk or exposure. The details of the option contracts are as follows:

Details Transaction Amount Strike Price/ Exchange Rate Spot Rate on Maturity Date Option Premium Paid to the Bank
OPTION A Bought Call option to buy USD against GH¢ US$10m USD/GH¢ 4.7 USD/GH¢ 4.5
OPTION B Bought Call option to buy EURO against GH¢ EUR 8m EUR/GH¢ 5.9 EUR/GH¢ 6.3

Required:

  1. Calculate the profit or loss of OPTION A and advise Universal Plastics Ghana Ltd whether to exercise or not. (4 marks)
  2. Calculate the profit or loss of OPTION B and advise Universal Plastics Ghana Ltd whether to exercise or not. (4 marks)
  3. Calculate the overall profit or loss on the decision to hedge based on (i) and (ii) above. (2 marks)

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