Yes - by using simple math!
TIW gives a 20% discount and adds an 18% gratuity. The cost is $150 for one card. Tax on food is 6.5% (exception: all star resorts).
We can calculate the savings by first taking your normal spend (S) and normal gratiuty percentage (G) which gives us your cost of a meal (C)
Code:
C = (1.065 * S) + (G * S)
We can then calculate the discounted cost of a meal
Code:
(Cd) Cd = (1.065 * (.8S)) + (.18S)
[Note: TIW gratuity is added on the pre-discount total but taxes apply to the post-discount total and tips are not taxed (for you)].
Your savings ($s) is
which simplifies to
Your break-even is found when $s is equal to the cost of TIW. If you want to know how much that is, plug in your personal gratuity percentage and solve for S.
As an example, let's assume that you already tip the TIW amount of 18%, which is expressed as 0.18. We can then solve for 150 = .18S + 0.033S, which simplified to 150 = 0.213S and results in a required spend S of $704.23 before you break even.
Alternatively, you can calculate your savings with 1 - (Cd / C) which looks like
Code:
1 - (((1.065 * (.8S)) + (.18S)) / ((1.065 * S) + (G * S)))
With our example of a standard 18% tip, your savings is 1-0.828916 or 17%.
If you typically tip below 18%, your break even point will be higher. If you typically tip above 18%, you'll either have a lower break-even point if you accept the standard tip or a higher break-even point if you add additional gratuity.
E: Someone correct me if I did that math wrong. I'm bored at lunch and did this on a napkin.
E2: You also get free valet parking and theme park entrance with TIW. We could get more complicated by averaging your spend per visit and calculating the added savings of X free parkings, but that might make the math a bit harder to read and I don't think most people think that way. Just assume the breakpoint is a bit lower than above if you make trips just to eat. You also get some cool events which may add some value that is more difficult to quantify.