Question

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?

Answer 1

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))=$d(x)�e^{-(r*t(x))}$,where d(x)=$5 given

This is done so because dividends are paid out every 3 months.

PV(d(1))=5$e^{-(.1*(3/12))}$=4.8765

PV(d(2))=$5e^{-(.1*(6/12))}$=3.0326

PV(d(3))=$5e^{-(.1*(9/12))}$=2.3618

PV(d(4))=$5e^{-(.1*(12/12))}$=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.