This is really a simple math problem.
Make a table of the costs of each scenario.
Insurance for one year ($100)
Cost of replacing iPhone ($300)
Cost of not replacing iPhone ($0)
Assign some utility scores to these outcomes on a scale from 1 to 10.
Buying insurance. 3
Replacing iPhone without insurance. 0
Nothing bad happening to it. 10
Costs*Probabilities will give you your expected value. Then you can compare these to a certainty equivalent to determine how much you really feel comfortable paying for insurance.
Insurance expected value.
($50) * 1.00 = ($50)
Take an educated guess on your past experience the odds of needing to replace the phone.
($300) * 0.20 + ($0) * 0.80 = ($60)
Now use your happiness numbers. That, is assuming money and happiness are not related linearly for you. Some people might say winning $10 million dollars would make them X happy, but winning $20 million probably would make them between 1X and 2X happy, not 2.00X happy exactly.
Just tweak the numbers around like the cost of insurance, replacing phone, and probability of needing a replacement. If you are risk neutral, go with the better expected value.
If the other guy only had to pay $200, you would have to expect the probability of needing an iphone replaced is around 25%, or a lesser percentage if having the coverage really gives you a greater sense of safety and security.