Question

XYZ stock has a share price of $125 today. All rates of interest are 5% per year with continuous compounding. Finally, XYZ is scheduled to pay the following dividends per share over the next year: a dividend of $3.0 per share in three months and a dividend of $3.0 per share in six months. Derive today’s forward price of the stock for delivery in nine months.

Answer 1

Current stock price = S₀ = $125, Interest rate r = 5% with continuous compounding

First we will calculate present value of dividends

Dividend in 3 months = D1 = $3 , Time to dividend in 3 months = (3/12) years = t1 = 0.25 yeares

Dividend in 6 months = D2 = $6 , Time to dividend in 6 months = (6/12) = t2 = 0.50 years

We know that Present value of a cash flow = Future value x e^{-r x time to cash flow}

where r = per annum continuously compounded interest rate

Present value of dividends = PVD = D1 x e^-(r)(t1) + D2 x e^-(r)(t2) = 3 x e^-(5%)(0.25) + 3 x e^-(5%)(0.50) = 3 x e^-0.0125 + 3 x e^-0.025 = 3 x 0.98757780 + 3 x 0.97530991 = 2.967733 + 2.925929 = 5.888662

Time to delivery or maturity = (9/12) years = t = 0.75 years

Forward price = (S₀ - PVD) x e^rt = (125-5.888662) x e^(5%)(0.75) = 119.111338 x e^0.0375 = 119.111338 x 1.038211 = 123.6627

Hence Forward Price of stock for delivery in 9 months = $123.6627