Forward price with dividends

[Richard_07]

Hi everyone,

I don't think I would ever come up with the solution to the question 6 from September 2005 exam under exam conditions on my own.

I'm just wondering if there is any alternative explanation? I was thinking of using the formula K=(S0-PVd)*e^(rt), where PVd is the present value of future dividends. The PV of dividends will be 0.03*e^(-0.07/12)+0.03e^(-0.07*7/12)+etc.
But my final answer for the fair forward price is different to $9.98 from the solutions...

Thanks

 

[withoutapaddle]

your formula is sound but the dividend payments are not $0.03 each they are 3% of the share price i.e 0.03*St ~$0.3 (St changes)

if you used 0.3 as your 'dividend payments' it give a forward price of $9.96

so what is the share price? it the risk neural price, i.e. St=So*e^(rt) but now r is different from 7% since the the total expected return is 7% which includes the dividends

i.e r = ln{e^(.07)/1.03^2}

 

[Richard_07]

Thanks for your answer.

If I change the question so that dividends are now paid continuously at a constant rate 0.03 per annum, what would be the fair price of forward?

Is it F=10*e^((0.07+0.03)*20/12) ?

 

[withoutapaddle]

the investor can get hold of the St in two ways

1. buy So * exp(-qt) now - after reinvesting it will be worth St guaranteed (as dividends are guaranteed!)
2. enter into a forward contract for strike price K @ time t, to guarantee this payoff the present day value of this is K * exp(-rt) needs to be set aside (i.e. we ignore credit risk)

but these have equivalent payoffs of St hence 1. = 2.

i.e. K * exp(-rt) = So * exp(-qt)

K = So* exp({r-q}t)