# Question: Suppose IBM pays a dividend D on their shares S at time τ. Show that S(τ+) = S(τ−) − D. Actually, to be precise, τ should be what is called the ex-dividend date. You should again argue your solution from the assumption of no arbitrage. S(τ+) means the value of S just after τ, and S(τ−) the value just before. – Free Chegg Question Answer

Suppose IBM pays a dividend D on their shares S at time τ. Show that S(τ+) = S(τ−) − D. Actually, to be precise, τ should be what is called the ex-dividend date. You should again argue your solution from the assumption of no arbitrage. S(τ+) means the value of S just after τ, and S(τ−) the value just before.

`Transcribed text From Image: `

`Answer:`

We know, the change of the stock price (S) after declaring a dividend (D) is calculated as:

………….(1)

= tax rate payable on dividend

= tax rate payable on capital gain

In case of no-arbitrage possibility there will be no tax payable, i.e.,

and

So from (1)

But

= price before dividend paid (value before ex-dividend)- price after dividend paid (value after ex-dividend)

So

So