A stock is expected to pay a dividend of $1 per share in three months and anothe

Question

A stock is expected to pay a dividend of $1 per share in three months and another dividend of $1 per share in nine months. The stock price is $50 today, and the risk-free rate of interest is 5% per annum with continuous compounding for all maturities. Today, an investor takes a long position in a one-year forward contract on the stock.

Today, what are the forward price and the initial value of the forward contract?

Five months from today, assume that the price of the stock will be $55 and that the risk-free rate of interest will still be 5% per annum. What will be the forward price and the value of the long position in the forward contract written at the initial price determined in a)?

Explanation / Answer

(part-a)

step-1: convert risk free interest rate per annum to per month.

per annum interest rate=5%

so, per month interest rate=5/12=.417%

Step -2: present value of all dividend to be received.

(a) present value of $1 dividend to be received in 3 months from now=1/(1+.417%)3=$0.988

(b) present value of $1 dividend to be received in 9 months from now=1/(1+.417%)9=$0.963

Total (a)+(b)=$1.951

Step -3:

Forward price=(Current price-present value of all future benefit)*(1+r)n

   =($50-$1.951)*(1.05)1

=$ 50.45

r-risk free rate

n-no. of years

thus, today the forward price is $ 50.45

(part-b)

present value of dividend to be received after 4 months from 5 months after now=1/(1+.417)4

   =$.983

forward price=($55-$.983)*(1+5%*7/12)

=$55.59

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