Question

A $50 each pays $1 dividend every 3 months, with the first dividend coming 3 months from today. The continuously compounded risk-free rate is 6%. a. What is the price of a prepaid forward contract that expires 1 year from today, immediately after the fourth-quarter dividend? b. What is the price of a forward contract that expires at the same time?

Answer 1

(a) Prepaid Forward contract price equals the value that the forward contract buyer would have paid in case the payment for the contract was being made today. In cases of non-benefit accruing assets, the prepaid forward price equals the underlying asset's spot price. In cases of assets that accrue benefits over the forward contract's tenure, the prepaid forward price equals the current spot price less the present value of the benefits.

Current Spot Price = $ 50, Quarterly Dividends = $ 1, Forward Tenure = 1year or 4 quarters and Risk-Free Rate = 6 %

Therefore, Prepaid Forward Price = Fp = 50 - [1/e^(0.06 x 0.25)] -[1/e^(0.06 x 0.5)] - [1/e^(0.06 x 0.75)] - [1/e^(0.06 x 1)] = $ 46.14668 ~ $ 46.15

(b) Normal Forward Price (Payable at Forward Expiry) = Fp x e^(0.06 x 1) = 46.15 x e^(0.06 x 1) = $ 49.0002 ~ $ 49