A $66 stock pays a dividend of $1.40 every 3 months, with the first dividend coming...

A $66 stock pays a dividend of $1.40 every 3 months, with the first dividend coming 3 months from today. The continuously compounded risk-free rate is 6%. What is the price of a prepaid forward contract that expires 6 months from today, immediately after the second dividend?

a. $65.19

b. $64.62

c. $63.26

d. $63.20

e. $63.37

Solutions

Expert Solution

Current stock price = Spot price S = $66, Dividend in three months = $1.40, Dividends in 6 months = $1.40

We know the price of prepaid forward contract is equal to spot price less present value of all future dividends till the expiration of contract.

Price of prepaid forward contract takes into consideration all dividends that are received by the holder of the stock till the expiration of contract.Since the contract expires after 6 months. immediately after second dividend so dividend in 6 months will be considered for calculation of price of prepaid forward contract

Continuously compounded risk free rate = r = 6%

Present value of dividend = Dividend x e^-^rT

For dividend in three months T = 3/12, For dividend in 6 months T = 6/12

Now we get

Price of prepaid forward contract = Spot price - Present value of dividend in 3 months - Present value of dividend in 6 months

= 66 - 1.40e^-6%(3/12) - 1.40e^-^6%(6/12) = 66 - 1.40e^-0.015 - 1.40e^-0.03 = 66 - 1.40 x 0.985111 - 1.40 x 0.970445 = 66 - 1.37915 - 1.35862 = 63.26223 = 63.26 (rounded to two decimal places)

Hence price of prepaid forward contract = 63.26

jeff jeffy answered 1 year ago

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