7. A BCD stock pays an 8% continuous dividend. The current price is $50 and the...

7. A BCD stock pays an 8% continuous dividend. The current price is $50 and the continuously compounded risk-free rate is 6%. What is the price of a prepaid forward contract that expires 1 year from today? What is the price of a forward contract that expires at the same time?

Solutions

Expert Solution

Spot Price = $50 | Risk-free rate = 6% | Continous Dividend = 8% | Time to expiry = 1 year

Price of Prepaid Forward contract is price paid today for a contract where stocks would be received at the end of Year 1. It is essentially Spot price - Dividends missed out.

Therefore, Price of Prepaid Forward Contract formula = Spot Price * e^{-Dividend Yield * T}

Price of a Prepaid Forward Contract = 50 * e^{-8% * 1} ----------------------(Continuous dividend of 8%)

Price of a Prepaid Forward Contract = 50 * 0.92312

Price of a Prepaid Forward Contract for ABCD stock expiring in 1 year = $ 46.16

The Price of a Forward contract is the price of the stock continuously compounded at risk-free rate minus the Dividends missed out.

Therefore, Price of a Forward Contract formula = Spot Price * e^{Risk-free rate} ^{-Dividend Yield * T}

Price of a Forward Contract = 50 * e⁽^{6% - 8%) *
1}

Price of a Forward Contract = 50 * e^-2%

Price of a Forward Contract = 50 * 0.98020

Price of a Forward Contract for ABCD stock expiring in 1 year = $ 49.01

Hence, Price of a Prepaid Forward Contract is $ 46.16 and Price of a Forward contract is $ 49.01

jeff jeffy answered 1 year ago

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