Question

Stock ABC currently trades at a price of S0 = 100 and is scheduled to pay the following dividends:

(i) At time 0.2, a cash dividend of $8 per share will be paid.

(ii) From time 0.25 to time 0.75, dividends are paid continuously at a rate proportional to its price. The dividend yield is 6%.

(iii) At time 0.8, a cash dividend of $6 per share will be paid.

(iv) The continuously compounded risk-free interest rate is 5%.

Find the price of a one-year prepaid forward contract on stock ABC

Answer 1

price of S0 = 100

(i) At time 0.2, a cash dividend of $8 per share will be paid.

Rate= $8/$100= 8%

So= $100

time = 0.2

Theoritical price of forward contract = So * e^rt

= $100 * e ^0.08*0.02

= $100 * e^0.016

= $101.6

(ii) From time 0.25 to time 0.75, dividends are paid continuously at a rate proportional to its price. The dividend yield is 6%.

Theoritical price of forward contract = So * e^rt

=$100 * e^0.25*0.06

=$100 * e^0.015

=$101.5

Theoritical price of forward contract = So * e^rt

=$100 * e^0.75*0.06

=$100 * e^0.75*0.06

=$100 * e^0.045

=$104.5

(iii) At time 0.8, a cash dividend of $6 per share will be paid.

Theoritical price of forward contract = So * e^rt

=$100 * e^0.8*0.06

=$100 * e^0.8*0.06

=$100 * e^0.048

=$104.8

(iv) The continuously compounded risk-free interest rate is 5%.

Theoritical price of forward contract = So * e^rt

=$100 * e^0.8*0.05

=$100 * e^0.8*0.05

=$100 * e^0.04

=$104