Consider a stock expected to pay a dividend $5 per share in three months. The current stock price is $100, and the annualized interest rate is 10% . An investor tries to take a long position in a one-year forward contract on the stock. What is the forward price?
The equation to find forward price is
F=(S-D)(e^rt)
F-Forward price
S-current spot price of the asset=$100
e=2.7183
r-risk free rate=10%=.1
t-time period of contract=1 year
Here D=sum of dividends present value
=PV(d(1))+PV(d(2))+PV(d(3))+PV(d(4))
PV(d(x))=,where d(x)=$5 given
This is done so because dividends are paid out every 3 months.
PV(d(1))=5=4.8765
PV(d(2))==3.0326
PV(d(3))==2.3618
PV(d(4))==1.8393
Therefore Total dividends,D=4.8765+3.0326+2.3618+1.8393
=$12.11
F=(S-D)(e^rt)
S=$100,D=$12.11,r=.1,t=1 year
Therefore forward price F=(100-12.11)(e^(.1×1))
=$97.133.
Thank you for asking.
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