Cost Justify: new ntwk or band-aide?

I have a customer that is looking at overhauling an outdated network. The IT Manager an CFO are leaning towards the overhaul while the IT Director wants to patch and band-aide the network together. Does anyone have documentation supporting “Doing it right” (redesigning the network. I am especially interested in cost justification white papers showing that temporary band-aide solutions cost more time/money/support in the long-term.