Similar issues happen for justifying security. But if you've got a price tag, then just do expected utility. What's the odds that you'll need a backup? 1%? 0.1%? Per year? And what's the value of that backup price tag during that time? $10m? 0.1% per year * 10m = 10k per year.
Give the price tag when missing. The argument is we need to fix this in order to insure against this catastrophic event.
Or take the price tag when missing multiply by the probability of needing it over the course of one year. This is a more accurate estimate for the annual cost of not creating the backup.