Question

A stock is currently priced at 200. the continuously compounded risk-free rate of interest if r%. the two-year forward price of the stock is 208. the stock pays a dividend of 1 at the end of each year. at the end of the second year, the dividend is paid before delivery of the two-year forward. determine r, rounded to at least three decimal places.

Answer 1

Spot price of stock / Present value (S) = 200

Forward price of stock (Future value) = 208

Dividend each year = 1

Time (T) = 2 years

Dividend yield (dy) = Dividend / Stock price = 1/200 = 0.5%

We have to calculate the risk- free rate (r%). We can do that by the following formula of valuation of forward contracts with continuous dividends,

Forward Price (FP) =

Putting values in the above equation we get,

Solving for r we get,

r = 3.816%