Delivery companies offer same-day delivery (SDD) in more and more cities. SDD defines a business model in which a customer order is fulfilled the same day it is issued. To gain a competitive advantage, companies start offering increasingly narrower delivery deadlines of a few hours length. Currently, many companies struggle to cost-efficiently maintain a network of depots and vehicles to deliver the orders within the promised delivery deadlines. In this paper, we quantify the impact of delivery deadlines on the delivery costs in a simulation study. We further analyze the impact of delivery deadlines to the design of the delivery network. To this end, we extend an existing dynamic routing method from the literature. In our computational case study of the Iowa City area, we show that the costs and the network-layout for SDD significantly depend on the delivery deadlines and that an extension of the deadline by only one hour may reduce delivery costs substantially.