Refundable or Non-Refundable Deposit: A mathematical approach

[JFCruise]

I think this might be one of the most common questions "Is the Refundable Deposit Worth It"? And I was curious to see how "worth it" it was, using math and probabilities. So I fired up Excel and tried to figure out when it's worth it. Let's start with a couple of disclaimers:

1. Deposit amounts change per sailing, depending on the number of nights and the number of people in the stateroom. There's no way I'm going through every single possibility, but I'm putting the framework so that anyone can verify using their specific sailings.

2. This is mostly an experiment out of curiosity and for fun. I may have some things wrong.

Now - the first thing we need to define is something I call Expected Cost (XC for short going forward), which is nothing but the 'deposit' cost that we should expect. For example, if you  are going on a Cruise and the NRD is $500 - then your XC would be $500. Your XC for the RD on the same sailing - assuming a 250/room would be $750, in a 100% odds of going to the cruise, but $0 if the odds of going is 0% (why even do this, though?).

When it gets intersting is everything in between. The idea here is to minimize the risk of overspending. So for each probability, we need to multiply the XC of the RD. The XC for the NRD is always going to be 100% because, if you don't take the cruise, you lose that money. Always.

Let's assume a 2 person, 8 night cruise. The NRD per person is $250 and the RD is $250/room (or $125/person). The XC of the NRD is $500

If the odds of not canceling are 0%, the XC of the RD is $750. Or a loss of $250

If the odds are 50%, the XC-RD = $375, or a "win" of $125

The break point is at about 35%. Which means that if the chances of you canceling this specific cruise is about 35%, you should probable take the Refundable Deposit. I did the same with a 5 night cruise where the NRD was $100/person and the RD was $104/room and the results were the same. When it changes, is when you add more people to the room. On the same 5N, but adding a third person, the NRD goes up by $100, bt the RD stays the same. In this case, the break point is closer to 25%.

I've attached a table showing what I've done. Now feel free to roast me if anything seems wrong.

 

[instaGator]

Great idea trying to remove the guess work, but I am afraid that there are just too many options available to make an analytical model for the RD/NRD decision.  Here are just three more (of many) variables for you to consider.  First, most people who book NRD will have their losses capped at $100 per person, which is the change fee to move the cruise that they cannot go on to a different date when they can cruise.  Second, if the cruise fares stay constant over time (or go down), then many people will initially book RD and then change the booking to NRD just before the final payment date.  Third, since cruise prices seem to be continually rising now, the RD gives people the chance to lock in today’s price, which including the RD premium, will likely less money than if they waited until they were more certain that they would be able to sail. Keep at it @JFCruise!  I want you to succeed with your project!!

[JFCruise]

@instaGator - I tried to keep it as simple as possible, to be fair. Because there are way too many variables to actually have a very speciifc approach. And especially because I did it mostly for the fun of it. The idea was just comparing NRD vs RD in a straight up "yeah I'm not gonna go" scenario, not involving changes or anything like that. I would have to have a way more complex XC to include all the possibilities but that's way beyond my knowledge.

 

Quote

Third, since cruise prices seem to be continually rising now, the RD gives people the chance to lock in today’s price, which including the RD premium, will likely less money than if they waited until they were more certain that they would be able to sail.

I think this IS baked into the model, though. Since you might book the RD without being 100% convinced of going. It's just a matter of how sure you are.

[KaosFactor]

For me the biggest decision into going to non refundable was it was only 10 days until final payment anyway. Not to mention the difference between an NRD GTY and a regular room in our category was $1800 for the three of us.

[TXcruzer]

Am I missing something?  I have never seen differing deposits amounts for RD and NRD

[smokeybandit]

 

[steverk]

I think I'm missing something in the math.  It seems to me the real question is the reward (i.e. the reduced fare amount) vs. the cost (i.e. amount of the deposit you might lose) multiplied by the probability of cancelling.

This may seem picky, but I don't see the amount of the reduced fare in the calculation.

I've seen rare cases where there's no difference between refundable and non-refundable fares.  That's a no brainer. Go with the refundable.

I've also seen cases where the difference was over $1000.  I haven't tried to quantify that, but it is hard to swallow spending an extra $1000 to protect a $500 deposit unless there's almost no chance of taking the cruise.  Of course, why would you book the cruise if you didn't at least think it was a possibility?

Most of the time, the fares are somewhere in the middle.  Go NRD and you save $2-300.  That's more debatable, especially if you're booking years in advance.

[JFCruise]

48 minutes ago, TXcruzer said:

Am I missing something?  I have never seen differing deposits amounts for RD and NRD

The NRD is basically minimum initial deposit you have to pay. In case of cancellation, Royal Caribbean does not return that deposit - but would return any extra payments you might have done before Final Payment. That quantity is per peson and is dependent on the number of nights. The RD is basically an insurance policy where, if you cancel your cruise, you don't lose that initial deposit. In the two cruises I checked, it was per stateroom.

[JFCruise]

41 minutes ago, steverk said:

I think I'm missing something in the math.  It seems to me the real question is the reward (i.e. the reduced fare amount) vs. the cost (i.e. amount of the deposit you might lose) multiplied by the probability of cancelling.

This may seem picky, but I don't see the amount of the reduced fare in the calculation.

I've seen rare cases where there's no difference between refundable and non-refundable fares.  That's a no brainer. Go with the refundable.

I've also seen cases where the difference was over $1000.  I haven't tried to quantify that, but it is hard to swallow spending an extra $1000 to protect a $500 deposit unless there's almost no chance of taking the cruise.  Of course, why would you book the cruise if you didn't at least think it was a possibility?

Most of the time, the fares are somewhere in the middle.  Go NRD and you save $2-300.  That's more debatable, especially if you're booking years in advance.

Yes. By multiplying the cost x the probability of cancelling, it gives you an 'Expected' cost. In this case, 'Expected' is more of a probabilistic term than a 'real' one.

And - it's not picky at all, but what is the amount of the reduced fare you are talking about?

In the few cruised I looked for these, plus the past few I've booked - from experience - I've never really seen no difference between NRD and RD. That would obviously be a no brainer because the XC of the refundable is 0 in any case.

[AshleyDillo]

6 hours ago, JFCruise said:

In the few cruised I looked for these, plus the past few I've booked - from experience - I've never really seen no difference between NRD and RD. That would obviously be a no brainer because the XC of the refundable is 0 in any case.

The fare delta between refundable and non-refundable tends to get less as it gets closer to final payment date. 

You can book very early when bookings go up and land a refundable fare that ends up being less than a non-refundable fare six months out from the sail date. Royal loves to make pricing on everything as dynamic as possible.

I would be interested to track the initial release date refundable fare price against the non-refundable price at different lengths of time from final payment date to see when the initial locked in refundable fare ends being less than the current refundable fares. Not interested enough to track it myself, mind you.

[twangster]

The delta varies by cabin type.

Interior tends to have a small delta, ocean view slightly more, balcony much more.  

It also seems to vary by other factors such as region.  

[ChessE4]

While I enjoy the math, I am more concerned with final price. We book in advance, and if refundable is a fair/good price, we get it. Sometimes our TA gives us a good nonrefundable rate, and we take it, too. Example: a balcony room at base price of 100 per night per person rather than 150 is a good deal for us. This is a smaller ship but has the itinerary we want.

[steverk]

14 hours ago, JFCruise said:

Yes. By multiplying the cost x the probability of cancelling, it gives you an 'Expected' cost. In this case, 'Expected' is more of a probabilistic term than a 'real' one.

And - it's not picky at all, but what is the amount of the reduced fare you are talking about?

In the few cruised I looked for these, plus the past few I've booked - from experience - I've never really seen no difference between NRD and RD. That would obviously be a no brainer because the XC of the refundable is 0 in any case.

I think an example would help.  Picking a cruise, more or less at random, let’s look at the 8 Night Caribbean & Perfect Day cruise departing June 21, 2024 from Orlando with a category 2N ocean view cabin on Adventure of the Seas.

Non-refundable fare for this cabin, including all taxes and fees for 2 people is $4727.28. The non-refundable deposit is $500.

Refundable fare for this cabin, including all taxes and fees for 2 people is $5361.28. The deposit is $500.

As you can see, booking non-refundable does not reduce your deposit.  However, the fare is $634 lower than the refundable fare.

BTW: I really did pick this cruise at random.  The difference between the fare is usually not that great.

[TXcruzer]

16 hours ago, JFCruise said:

The NRD is basically minimum initial deposit you have to pay. In case of cancellation, Royal Caribbean does not return that deposit - but would return any extra payments you might have done before Final Payment. That quantity is per peson and is dependent on the number of nights. The RD is basically an insurance policy where, if you cancel your cruise, you don't lose that initial deposit. In the two cruises I checked, it was per stateroom.

Understood. Thank you for the clarity. 

[JFCruise]

3 hours ago, steverk said:

As you can see, booking non-refundable does not reduce your deposit.  However, the fare is $634 lower than the refundable fare.

In this case, the Refundable deposit (or at least what I'm using as such) is that $634. You are paying the other $4727.28 regardless. So the only concern is if you should pay the extra $634 to "protect" your $500 deposit. If your decision is a true cointoss (50-50 odds you go/no go) then the XC for the refundable deposit is $317. So you are probably better off taking the gamble on the RD.

[JFCruise]

4 hours ago, ChessE4 said:

While I enjoy the math, I am more concerned with final price. We book in advance, and if refundable is a fair/good price, we get it. Sometimes our TA gives us a good nonrefundable rate, and we take it, too. Example: a balcony room at base price of 100 per night per person rather than 150 is a good deal for us. This is a smaller ship but has the itinerary we want.

Totall! This is more of a hyopthetical experiment of when a refundable deposit is is worth it vs not, depending on the odds of going. However, I think that if you are sure you are going - except for an emergency - you should probably take the NRD since it will always be cheaper.

[steverk]

50 minutes ago, JFCruise said:

In this case, the Refundable deposit (or at least what I'm using as such) is that $634. You are paying the other $4727.28 regardless. So the only concern is if you should pay the extra $634 to "protect" your $500 deposit. If your decision is a true cointoss (50-50 odds you go/no go) then the XC for the refundable deposit is $317. So you are probably better off taking the gamble on the RD.

This has been an interesting thought experiment and I thank you for suggesting it.

That said, I don’t think you’re looking at this correctly. This isn’t insurance, where you pay a premium and you may or may not get a return.  Rather it is two different pricing structures, with 2 different expected costs. Further, the $500 is the deposit.  I say this not to be picky, but to avoid confusion. It  is referred to as a deposit by Royal and on the website.

Since you mentioned a coin toss, let’s go with that for the odds of going on this cruise and the example cruise I priced this morning.

If you booked the refundable deposit, you would expect to pay $5361.28 for the cruise if you go and $0 if you cancel before final payment date. If I remember my college statistics, that gives you an expected return of $2680.64 [ (cost of not going X probability of not going) + (cost of going X probability of going) which in this case is ($0 X .5) + ($5261.28 X 0.5) ]. Note, this isn’t what you expect to pay.  Rather, if you were faced with this exact decision a bunch of times, it is what you would expect for the average cost across the whole dataset.

If you booked non-refundable, you would give an expected return of $2613.64  [ ($500 X 0.5) + ($4727.28 X 0.5) ]. I’m ignoring the possibility of applying some of the non-refundable deposit on a later cruise for simplicity.

As you can see, on this particular example you’d be better off, from a statistical perspective, to go non-refundable.

In the real world, the pricing and refundable premium ($634 in this example) changes constantly. If we were considering a cruise with a $200 premium, then refundable would have worked out better. Further, the chances that you’ll cancel prior to final payment varies based on your ever changing circumstances.  Therefore, this calculation will vary constantly. Further, people react emotionally to losing money for any reason. So, by all means, do what feels best to you.

Like I said, it has been interesting. If I get a little bit of time, I’ll throw together a spreadsheet to make the calculation easy.  Thanks again for bringing it up!

[JFCruise]

21 minutes ago, steverk said:

That said, I don’t think you’re looking at this correctly. This isn’t insurance, where you pay a premium and you may or may not get a return.  Rather it is two different pricing structures, with 2 different expected costs. Further, the $500 is the deposit.  I say this not to be picky, but to avoid confusion. It  is referred to as a deposit by Royal and on the website.

But isn't having the refundable "deposit" (or however you want to call it) exactly that, a premium for which you may or may not get a return (the $500 NRD)?

I think we are saying the same thing and coming up with the same conclusion, just with a different perspective. I removed the whole non-deposit part of the fare for simplicity's sake - because you are paying the $4727.28 regardless of what type of fare you chose. You could do the same calculations you did without that part of the equation and get the same result.

26 minutes ago, steverk said:

If we were considering a cruise with a $200 premium, then refundable would have worked out better. Further, the chances that you’ll cancel prior to final payment varies based on your ever changing circumstances.  Therefore, this calculation will vary constantly. Further, people react emotionally to losing money for any reason. So, by all means, do what feels best to you.

For the first part - yes this is true, the delta will change. Sadly we can't have a one-size-fit-all algorythm - you need 2 inputs: the deposit amount and the premium for a refundable rate. And as you say they change all the time. My algorythm is assuming you are taking the decision now - because we don't know how those amounts will change on the future. Plus the whole fare increase makes the exercise moot. You can pay for the refundable fare today, and in a month, it's cheaper than the non-refundable.

For your second part, it's a big part of it. And sadly for the algorythm, we can't easily put a definition to 30% odds of taking a cruise.

30 minutes ago, steverk said:

Like I said, it has been interesting. If I get a little bit of time, I’ll throw together a spreadsheet to make the calculation easy.  Thanks again for bringing it up!

No worries, and I like doing this sort of excecises and expanding on them, so if you have a spreadsheet by all means, do share.

[teddy]

I’m gonna be honest, I can tear an engine down to its individual parts and rebuild it, but this thread has me scratching my head. I’m very impressed (and confused) with the calculations and….well….math that’s in it.   
 

We do nrd because it’s always been cheaper overall, especially when booking onboard. The third party annual travel insurance plan we buy will reimburse our non refundable deposits, payments , etc for the covered reasons up to our limit.  

[steverk]

2 hours ago, JFCruise said:

But isn't having the refundable "deposit" (or however you want to call it) exactly that, a premium for which you may or may not get a return (the $500 NRD)?

Not really.  An insurance premium is paid in advance and is gone regardless of what happens. If you collect on the policy, it can be a good deal, but more often than not, you don't collect so the insurance company makes money and stays in business.

A cruise deposit is a portion of the fare you pay in advance to show you are serious about the cruise.  This is similar to earnest money on a real estate transaction.

Just like earnest money, it may or may not be refunded if you back out of the deal.  

A "refundable deposit" rate is one where you are given the deposit back if you back out before final payment date. However, you pay a higher fare if you go through with the cruise.

A similar thing has been happening with airfares for decades.  Most people buy non-refundable airline tickets because they are much cheaper. But you can buy a much more expensive ticket that can be refunded if you change your mind.  It isn't quite perfect, but it is a similar concept.

2 hours ago, JFCruise said:

For the first part - yes this is true, the delta will change. Sadly we can't have a one-size-fit-all algorythm - you need 2 inputs: the deposit amount and the premium for a refundable rate. And as you say they change all the time. My algorythm is assuming you are taking the decision now - because we don't know how those amounts will change on the future. Plus the whole fare increase makes the exercise moot. You can pay for the refundable fare today, and in a month, it's cheaper than the non-refundable.

Actually, you need 3. The amount of the deposit, the difference between the refundable and non-refundable fare (i.e. the delta) and the probability that you'll want to back out of the cruise before final payment date.  Note, it is only relevant if you back out before final payment date since different rules apply after.

The first two of these items is pretty easy to get.  Do a mock booking with both refundable and non-refundable fares and you've got them. 

The probability is much more nebulous. It depends on personal circumstances at the time of booking. I assume most people booking a cruise and putting down a deposit expect to take it. Therefore, most people would put the odds at somewhere around 90% on any given cruise.

2 hours ago, JFCruise said:

if you have a spreadsheet by all means, do share.

I don't have one at the moment, but this thread inspires me to put one together.  I'll see what I can do.

[JFCruise]

26 minutes ago, steverk said:

A "refundable deposit" rate is one where you are given the deposit back if you back out before final payment date. However, you pay a higher fare if you go through with the cruise.

So when you choose the "refundable deposit", you are charged an additional amount. The only difference between doing this and going straight with the NRD is that if you back out, you get your NRD back. I can easily see how that difference could be consituted as insuring the NRD, in a way. If you back out, you collect your NRD. If you go through with your cruise, you 'lose' that premium.

29 minutes ago, steverk said:

Actually, you need 3. The amount of the deposit, the difference between the refundable and non-refundable fare (i.e. the delta) and the probability that you'll want to back out of the cruise before final payment date. 

If you look at my original post, I pasted a screenshot with these 3 variables.

[steverk]

Here's my attempt at a spreadsheet to put numbers to the question.

I hope many people find it helpful!

refundable v nonrefundable fare optimizer.xlsx

[CruisingNewb]

You guys are all missing the true motive behind @JFCruise's experiment.  Its obvious he/she is trying to grab the attention of RCCL in order for RCCL to hire him/her as an analyst.  

Seriously though, the math was thought provoking and much appreciated.  Not gonna pretend that I understand it or will spend the time to understand it, but it looks fancy enough to convince me to go the non-refundable route.

[JFCruise]

15 minutes ago, CruisingNewb said:

Its obvious he/she is trying to grab the attention of RCCL in order for RCCL to hire him/her as an analyst.  

Do I get to cruise for free? Cause I'm in.