A stock is expected to pay a dividend of €2 per share in 9 months. The...

A stock is expected to pay a dividend of €2 per share in 9 months. The stock price is €20, and the risk-free rate of interest is 5% per annum with continuous compounding for all maturities. An investor has just taken a long position in a 12-month forward contract on the stock. What is the Forward price (K)?

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Expert Solution

Share Price as on Today: €20 per share

Expected dividend: €2 per share in 9 months

Risk-free rate of interest: 5% per annum with continuous compounding.

Price of the forward contract: Future value of the share price + Future value of the dividend paid in 9th month

Price of the forward contract: (€20 * e^0.05*12/12 ) + (€2 * e^0.05*3/12 )

We know that the value of e = 2.71828 and will calculate dirty power for calculating value.

Price of the forward contract: (€20 * 1.05127) + (€2 * 1.01257)

Price of the forward contract: € 21.02 + € 2.02

Price of the forward contract: € 23.04

Hence, the Forward price is € 23.04

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