(1) Time value of money. Shareholders aren't getting $13.65 today. If DELL traded at $13.65, I could short it and earn a risk-free yield on the short proceeds between now and when the payout is made.
(2) Merger risk. Did I say risk-free? I lied. Deals fall apart for reasons ranging from shareholder litigation to antitrust issues to Michael Dell getting pissed off because his socks got wet. The difference between the forward stock price (stock minus time value) and payout is the expected probability of the deal closing.
Disclaimer: I have an outstanding position in DELL.
I was illustrating, by negation, why a $13.65 buy-out shouldn't immediately lead to the stock rising to $13.65 (because it would produce an arbitrage opportunity).
Note that today the stock did get bid up to $13.48. If the deal takes {90, 180, 270, 360} days to pay out, you would be borrowing from the market at {5.2%, 2.6%, 1.7%, 1.3%}. Add to that the cost of a call (to protect you from a rival bidder or enhanced tender) and subtract the probability of the deal falling through and you have a cost of capital. This isn't risk-free since 13.48 != 13.65, but depending on your time horizon, break-up assumptions, and the asset you're buying with the financing, it could still be an attractive proposition.
(2) Merger risk. Did I say risk-free? I lied. Deals fall apart for reasons ranging from shareholder litigation to antitrust issues to Michael Dell getting pissed off because his socks got wet. The difference between the forward stock price (stock minus time value) and payout is the expected probability of the deal closing.
Disclaimer: I have an outstanding position in DELL.