The Advanced Financial Management formulae sheet

Option pricing and real options

Arkwell Co's shares trade at $5.20. A European call option on one share has an exercise price of $5.00 and expires in nine months. The risk-free rate is 4% a year and the volatility of the share price is 30% a year. No dividend is paid before expiry. Take N(d1) = 0.6541 and N(d2) = 0.5543.

What is the value of the call option, in $ to two decimal places? (2 marks)

$

International investment

Linthwaite Co, whose home currency is the $, owns a subsidiary in Poland. The subsidiary's taxable profits will be PLN 12m in year 1, PLN 14m in year 2 and PLN 16m in year 3, taxed at 15% in Poland in the year they arise.

Linthwaite Co's home tax rate is 25%, charged on the subsidiary's taxable profits with double tax relief for the Polish tax, and paid in $ in the same year. The forecast exchange rates are PLN 4.32, 4.45 and 4.58 per $1 for years 1 to 3. Linthwaite Co discounts at 10%, with the present value table factors to three decimal places.

What is the present value of the extra home tax Linthwaite Co pays on the subsidiary's profits, in $000 to the nearest $000? (2 marks)

$

Valuing equity and debt

The assets of Rylstone Co have a market value of $200m and a volatility of 30% a year. Its only debt is a zero coupon loan with $160m repayable in three years. The risk-free rate is 5% a year.

Treat the equity as a European call option on the assets with the $160m as the exercise price. Take N(d1) = 0.8359 and N(d2) = 0.6766. The market value of the debt is the value of the assets less the value of the equity.

What annual yield, compounded once a year, do lenders earn if they buy the debt at its market value and are repaid $160m, as a percentage to two decimal places? (2 marks)

$