This is what your senior managers are often most concerned about.
The way I see it you need to figure out how much it costs the business if function X breaks. If the network fails, how much does the business lose per day.
Let's not forget there is an additional cost if the usual staff cannot do their work, time lost to restore backups etc.
Now factor the cost of getting some adhoc help via an external company in case of emergency. Eventually the network will fail and if you alone cannot fix it you'll need help.
Hopefully you now have some *realistic* and yet scary figures. You need to figure out what sort of resiliency the network has and what is the likelihood of a total catastrophic failure. The less redundant the setup, the higher the chance.
Bring this information to the relevant people and demonstrate how these risks are lowered with additional headcount/equipment.
If you have more than 5 minutes to think about this I'm sure you'll expand on this line of thought and come up with something even more polished.