Question

Assume that you own a dividend-paying stock currently worth $150. You plan to sell the stock in 250 days. In order to hedge against a possible price decline, you wish to take a short position in a forward contract that expires in 250 days. The risk-free rate is 5.25% per annum (discretely compounding). Over the next 250 days, the stock will pay dividends according to the following schedule:

Days to Next Dividend	Dividends per Share ($)
30	1.25
120	1.25
210	1.25

(a) Calculate the forward price of a contract established today and expiring in 250 days.

(b) It is now 100 days since you entered the forward contract. The stock price is $115. Calculate the value of the forward contract at this point.

c) At expiration, the price of the stock is $130. Calculate the value ot the forward contract at expiration

About this question, if we have a continuos interest what is the solution ?

Answer 1

		Future Value (PV) of Cash Flow:
		(Cash Flow)*((1+i)^N)
		i=Interest Rate=5.25%=0.0525
		N=Number of years in the future
		Since forward contracts needs to be settled in future date,
		Forward Price will be equal to future value of Cash flows
		A	B=250-A	C=B/360	D	E=D*(1.0525^C)
		Number of days	Number of days to 250	Years to250days	Cash flow	Future value
		0	250	0.694444	$150	155.4258589
		30	220	0.611111	($1.25)	-1.289704419
		120	130	0.361111	($1.25)	-1.273311501
		210	40	0.111111	($1.25)	-1.257126947
					SUM	151.6057161
	(a)	Forward Price of Contract	$151.61
	(b)	Forward Price after 100 days
		A	B=150-A	C=B/360	D	E=D*(1.0525^C)
		Number of days	Number of days to 250	Years to250days	Cash flow	Future value
		0	150	0.416667	$115	117.478137
		20	130	0.361111	($1.25)	-1.273311501
		110	40	0.111111	($1.25)	-1.257126947
					SUM	114.9476985
		Forward Price of Contract	$114.95
	.(c)	Forward Price	$151.61
		Price at expiration (Settlement)	$130
		Value of Forward Contract at expiration	$21.61	(151.61-130)
		If we have a continuous interest :
		Future value =Present value*(e^(0.0525*N)
		N=number of Years in to the Future
		There willnot be much difference as calculation below shows
		A	B=250-A	C=B/360	D	E=D*(e^(0.0525*C))
		Number of days	Number of days to 250	Years to250days	Cash flow	Future value
		0	250	0.694444	$150	155.56966
		30	220	0.611111	($1.25)	($1.290754)
		120	130	0.361111	($1.25)	($1.273924)
		210	40	0.111111	($1.25)	($1.257313)
					SUM	151.747672
		Forward Price of Contract	$151.75