Forward price of dividend stream, with a 'special dividend'

[cac2008]

Hi all,

I'm having a problem with a question involving calculating the forward price of a stock.

"A 3-month forward contact is issued at t=0 on a stock with price of £150 per share. Dividends are received continuously and reinvested to give a dividend yield of 3% pa. In addition (and this is the bit that is throwing me) a special dividend of £30 per share is paid at t=\( \frac{2}{12} \). Assuming no arbitrage and a risk free \(\delta\) = 5% pa, determine the forward price per share."

Simple says I. The forward price of a normal continuously payable dividend is \( S_{0} e^{(\delta-D)T} \) and the price of the asset at t=0 should be reduced by the present value of the special dividend to represent income paid, so the final price is \((150 - 30e^{-(\frac{2(0.05)}{12})})e^{\frac{3(0.05-0.03)}{12}} = £120.85\).

The solution says £120.70 (so not a million miles off) but does something I don't understand. It says that to work out the special dividend, we work out 'the holding at t=\(\frac{2}{12}\) by applying the dividend yield, so they do:
$$ 30(e^{-0.03 \times \frac{3}{12}} \times e^{0.05 \times \frac{2}{12}} )= 30e^{-0.03 \times \frac{1}{12}} $$

Then they accumulate this to \(t=\frac{3}{12}\), and subtract it from the accumulated value of the dividend stream.

Can anyone shed any light on why this was done? Its a topic I definately need to revisit, but once I get my head around this method i'm sure I can grasp it.

 

[Oxymoron]

Hi all,

I'm having a problem with a question involving calculating the forward price of a stock.

"A 3-month forward contact is issued at t=0 on a stock with price of £150 per share. Dividends are received continuously and reinvested to give a dividend yield of 3% pa. In addition (and this is the bit that is throwing me) a special dividend of £30 per share is paid at t=\( \frac{2}{12} \). Assuming no arbitrage and a risk free \(\delta\) = 5% pa, determine the forward price per share."

Simple says I. The forward price of a normal continuously payable dividend is \( S_{0} e^{(\delta-D)T} \) and the price of the asset at t=0 should be reduced by the present value of the special dividend to represent income paid, so the final price is \((150 - 30e^{-(\frac{2(0.05)}{12})})e^{\frac{3(0.05-0.03)}{12}} = £120.85\).

The solution says £120.70 (so not a million miles off) but does something I don't understand. It says that to work out the special dividend, we work out 'the holding at t=\(\frac{2}{12}\) by applying the dividend yield, so they do:
$$ 30(e^{-0.03 \times \frac{3}{12}} \times e^{0.05 \times \frac{2}{12}} )= 30e^{-0.03 \times \frac{1}{12}} $$

Then they accumulate this to \(t=\frac{3}{12}\), and subtract it from the accumulated value of the dividend stream.

Can anyone shed any light on why this was done? Its a topic I definately need to revisit, but once I get my head around this method i'm sure I can grasp it.

When a company pays out dividend, it's stock prices reduces by the value of the dividend (ex-dividend). Forward prices will need to be adjusted to reflect this fall.

 

[John Lee]

Please bear in mind that this question is a nightmare becuase the examiners made a mistake in the question. They actually meant to say a special dividend for every shareholder (rather than per share). Which makes it much nicer!