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# DVC buy-in and amortization (a math snooze-fest)

Discussion in 'DVC-Mousecellaneous' started by dmunsil, Jun 18, 2013.

1. ### dmunsilDisney Uber-Nerd

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This is hoisted from another thread where we're deliberately trying to ruin a new DVC member's fun by doing financial analysis of DVC. So hopefully all the math nerds can come over here and we can get all numerical and stuff.

Anyway, it's bothered me for a while that lots of people calculate the "all in" cost of DVC by adding the dues cost to the buy-in divided by the number of years. That's not right. Money now is worth more than money later. If I am buying something that will get me a discount 40 years from now, I will not pay the same amount of money as if I'm getting a discount today.

(There's a related error where people calculate their "payoff point" in years by adding up all their discounts to see in what year they end up "paying off" their buy in. That's also not right - it takes more years than the simple analysis would suggest, because the money you are going to save in the future is worth less than the money you paid in the present.)

One way to spread a buy-in cost over a number of years is an amortization. This is the same calculation used to figure the payment on a mortgage of a certain amount, which makes sense, because in essence you're the bank - you give Disney a chunk of money, and they promise to "pay it back" by giving you discounts on rooms in future years. The cost to you for those discounted rooms in the future is the amortized cost.

In other words, of the discounts Disney is giving you, the amortized cost is just the payback of the money you paid in. That's the amount of money you could have gotten just putting the money in a mutual fund and slowly drawing money out until it was down to 0 somewhere in the future.

So for, say, Boardwalk, there are 29 years remaining. If I had to pay \$72 per point, how much per point per year, assuming that I could have put \$72 into a mutual fund earning 4.5% instead? The answer is \$4.49, which is much higher than the simple \$72/29, or \$2.48. So my all-in cost is \$4.49 every year, plus the dues cost, though to be a useful analysis I need to account for the rise on costs of dues over time.

However, that's not as useful a way of looking at it. For one thing, there's inflation. Amortization calculates a fixed payment in nominal dollars every period, because that's the way most people think about money. Calculating everything in "real" (i.e. inflation-adjusted) dollars is hard to work out. But not doing do makes things difficult to project far into the future. Near the end of the Boardwalk contract's life, my dues might have risen to \$11, but the amortized buy-in (using my previous calculation) is still \$4.49. Since the cost of everything else in the world has gone up, my cost per year has gone down in real dollars.

One way to get around this is to do inflation-adjusted amortization. A simple way of doing that is to pick what appears to be a reasonable inflation amount and subtract it from my implied interest rate that I could get for my money. So if I think I can get 4.5% from a mutual fund, but inflation is going to be 2%, then I calculate the amortization as 4.5% - 2% = 2.5%. Then I'm getting a "real dollar" amortization. Now my cost for my \$72 per point contract is \$3.52 per year in constant 2013 dollars. In fact that number in nominal dollars will go up by 2% every year, but it's the same value in real inflation-adjusted dollars.

Doing inflation adjustment on the buy-in means I need to do inflation adjustment on my dues increase as well. It means that a 3.5% dues increase per year is a 1.5% dues increase in real dollars. Again, accounting for all of this can make your head hurt. The key is to either do everything in real dollars or in nominal dollars and stick to it.

Ultimately whether you do a real dollar amortization or a nominal dollar amortization is a bit of a complicated decision, and it depends on the analysis you're trying to do. But either one is clearly a better way to go than just dividing the buy-in cost by the number of years. Doing that kind of simple division understates the cost of buying DVC, which to some extent is something that Disney exploits to make the purchase appear more attractive than it really is.

As it turns out, if you use your points to stay in DVC properties, the discounts are so large that it always pays off no matter what. If you do a slapdash analysis or a rigorous analysis, it's still a bargain. If you use your points to stay in rooms with the least payoff in cash value (which would be 1 bedrooms, for what it's worth), you still come out ahead. It just takes longer to come out ahead for certain rooms and times of year than for other rooms and times of year.

On the other hand, if you use your points for cruises and staying in Disney (non-DVC) hotels, doing the financial analysis correctly shows that you're losing money with every stay. The amortized cost of the buy-in plus the dues is less than the cash value of the room or cruise.

Anyway, I want to be clear: no matter how you run the numbers, it's a good deal buying into DVC if you use it mostly to stay in DVC properties. It's such a good deal, in fact, that it's still saves most people money if they finance their purchase at 11% interest. That's accounting for the time value of money and everything. I still keep squinting at the numbers trying to figure out where I've gone wrong. It feels bizarre to me that Disney would make such a one-sided deal in some sense. Obviously Disney has plenty of financial analysts, so I trust that they're pretty happy with the payoff matrix. But it still feels strange. I've always been suspicious of a free lunch, and DVC seems too good to be true.

Now ELMC will tell me I should never use the phrase "free lunch" when talking about DVC.

3. ### agie65New Disney FanDVC Gold

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this conversation was way overdue. For many reasons, first for people who offer their points for sale 7-8 to understand those points cost more in their pocket, also for some lurker, who want to low ball.
Cost to own and maintain these points involves many different hidden cost and most of the time people just forget those cost, all they can see is MF.

4. ### ELMCDIS Veteran

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With all due respect, you've been on here a month. Are you sure you have the perspective necessary to determine that a conversation is overdue?

The face of the matter is that these types of analyses have come and gone, and every few months there is someone new to the DVC forums that comes on and thinks they have the next best analysis. In my opinion, it unnecessarily complicates matters.

5. ### RSWA2Mouseketeer

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Feb 10, 2013
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Great analysis, as usual. I always enjoy your posts.

I would say that the financial gain which others have pointed out in other threads that Disney gets with DVC is obviously not the stays, but the initial capital investment that they gain in the initial purchase of points, which helps pay the cost/debt from building the DVC, plus the years of tickets, merchandise, food, and others.

6. ### iluvthsgamMouseketeerDVC Gold

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This type of analysis might be too much detail for some, but for others I think this is how they want to think about their purchase. Not everyone thinks about the opportunity cost of their money, but some people do. Some people have a budget, some don't. So I think for those who like this level of detail and analysis this is great. For those that don't like to get that detailed in their financial life they can simply move along.

A question that I have while looking this over is that you calculate the real dollar buy-in cost of \$3.52 in your example. But that is only for this current year, correct? Or is the calculation giving you that it is \$3.52 in today's real dollars for each year left on the contract? (30 years left x \$3.52 per point = \$105.60 per point in today's real dollars ?)

7. ### dmunsilDisney Uber-Nerd

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I do think that having some kind of gut feeling of the time value of money, or at least that it exists, is important. Money tomorrow is worth less than the same amount of money today, and not because of inflation, because of interest. It's something people should incorporate into their worldview. But it's hard; it's not a natural or obvious way to look at things.

No, the value in todays real dollars is \$72. That's the point. Assuming I believe that I can get 4.5% interest on my money and inflation is going to be 2%, I should treat \$72 as being exactly as valuable as an annuity that pays \$4.49 per year for 29 years or a different annuity that pays \$3.52 the first year, increasing 2% per year every year thereafter for 29 years.

If you look at a table of payments in nominal dollars for the nominal amortization, it's just \$4.49 a year for 29 years. For the inflation adjusted one, the nominal payments are \$3.52, then \$3.59, then \$3.66, etc. Eventually the last payment is \$6.12, which I expect to have the same inflation-adjusted value 29 years from now as \$3.52 today.

The idea is that my perception of value of the DVC membership does not change radically from year to year. It lets me book essentially the same rooms every year for 29 years. So if I account for it in nominal dollars, I'm accounting for the annual cost with a number that's too high at the beginning and too low at the end. Using an inflation-adjusted amortization helps compensate for that effect.

And, of course, if I account for it by just doing a straight division of cost by years, I'm using a number that's too low at the beginning, and way too low at the end.

8. ### dmunsilDisney Uber-Nerd

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Thanks very much! It's nice to know someone is getting enjoyment from them.

Yes, it seems to be tied in with both the time value of money and the value of lowering risk. By selling the whole resort up front, they cover the construction cost and a healthy profit, and then the maintenance cost is covered for the whole contract period. Meanwhile, they have a captive audience of sorts who are likely to stay at WDW.

However, the ancillary benefits of getting people to stay at WDW and buy tickets and so forth can't be the whole answer, or they wouldn't have built Aulani. The resort ultimately has to pay for itself to make sense.

9. ### marynvinceDIS Veteran

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There are some of us that figured out Disney was a good deal without the formal analysis. Others could care less and yet to others, no analysis will yield a positive reason to buy DVC. However you get here, if you decided to buy, and if you are happy that you did and remain happy that you did, no analysis can change that. Whether you financed so that you could take your children before they were no longer children or paid cash because you could, it doesn't matter. The joy you bring yourself, and likely the magic you bring a child makes it more than worthwhile in my opinion. None of us are guaranteed our next vacation, we need to make the best of this vacation.

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dmunsil, I have been following your now numerous detailed posts that provide an abundance of information that must take a long time to gather and go through for each post, and I believe you are either overly compulsive or certifiably insane to devote so much time to this, and either way I consider you an excellent addition to these boards.

As to "value" of DVC, I always kept my thinking to a more base level. I bought because I always wanted to be able to get a 1BR or 2BR on site and thus avoid doing what we had been doing, renting two connecting rooms at a deluxe resort (that is definitely a comparison where DVC wins the value issue). To Disney this has always been a multiple money maker so there should be no crying for it. It gets the sale price. It turns over most of the cost of keeping the resort up to the members. It has a dues structure based on costs but which guarantees it a profit annually as the managing agent: the management fee item in the dues is a set fee of about 12% of the total dues (except taxes) and thus rises annually as dues rise. That amount essentially covers central MS operations with what ever is left over (likely a lot) going to Disney. Particular resort administration, front desk, maintenance, all resort employees, etc costs are all additional items of the dues. It also keeps some % of rooms rent and gains more by trade outs and breakage units. Moreover, it gets a mass of devoted Disney philes who will come annually and spend money on Disney. So it definitely wins coming and going.

11. ### iluvthsgamMouseketeerDVC Gold

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So the value per point is \$72 in today's real dollars.
Then you have two amortizations. The first is nominal which is \$4.49 a year for 29 years per point = a total of \$130.21. The second is inflation adjusted which starts at \$3.52 per year per point and ends up at \$6.12 per year point, adding up those values over 29 years = a total of \$136.55.

\$72 today at an inflation rate of 2% is equal to \$127.86 in 29 years. That is why the total payments in your analysis will be a total of more than \$72, correct?

12. ### YokukuEarning My Ears

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With all due respect, why are you jumping on new members like that? Just because the join date is new, doesn't mean they may or may not have been lurking the forums for years and have some insight as to the regular discussions occurring.

Yes, there's always the latest and greatest analysis/spreadsheet/numerology thread going on to justify someone's past or future DVC purchase. Nothing wrong with it - numbers change over time (just look at resale values the past 6 months), and people have a new situation that may or may not fit the current thread. While a lot are similar, someone's slightly new insight or twist may be just the thing someone else was looking for to justify (or remove) their want for DVC. Some don't need a spreadsheet and slide rule - they'll do a basic look at costs of DVC vs what they've currently been spending at Disney and decide it is worth it (or not). Others want to look at it a little more carefully and use some spreadsheets to get some more detail, since it is a long-term purchase commitment. And others just love math and are closet accounting geeks.

Anyway, sorry for the post if it offended anyone, hate to see newbies anywhere being jumped on for no real reason; and congrats on finally giving me an excuse to de-lurk after three years.

13. ### ELMCDIS Veteran

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It's quite possible that they have been on here for years, but I only know what I see based on the join date. I don't think I jumped on anyone. Someone who has been on this forum for two months made a comment about something being a long time coming. I addressed it. It's fair game, and nobody jumped on anybody until you decided to finally contribute and defend someone who doesn't need defending. While your motives are noble, your actions are a bit unnecessary. If you post something in these forums, you should expect that your statements could be challenged. Not attacked, not jumped on, but challenged. That's the key to productive discourse. Sorry if it ruffled your feathers.

14. ### dbs1228DIS Veteran

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All I know is I spent about 35000.00 over 14 years on accommodations only staying 10 nights at the cabins - 1 bdrm 1 bath! In that time we did do the dvc tour in 2006, I think, and we walked away from it. All they were selling was SSR and it just did not appeal to me I really wanted MK area. In the meantime we were fortunate enough to have money put away in the stock market, boy we would have been much better off buying an older property back then (I did not know it was possible or we probably would have since we liked the idea) we lost more money in the stock market then we would have paid for a 2 bedroom villa for 10 nights each year by buying into dvc! I know you cannot look at it in hind sight but people keep talking about "if you were to invest your money instead of buying you would make a certain %" well that can go the other way also!

Bottom line for us is we have had many many great vacations at the Ft and my kids (adults) still miss staying there so I know we made the right choice at the time for us. I am thrilled to have bought into dvc and love sharing Disney with DD's friends, our friends and family. I hope by the time I retire we will have close to 1000 points so we can go several times a year!

15. ### lawboy2001Soon to be DVCer

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I wish I had read this thread two weeks ago - I had wracked my brain trying to figure out how to cost the DVC purchase decision.

I did ultimately decide on an opportunity cost type of analysis similar to what is set out in this thread - wherein I consider the foregone income on the money used to purchase DVC, as part of the cost. So for example, if I spend 25k on points, I calculate an opportunity cost of \$2,500 per year: i.e. a 10% ROI. Optimistic probably. Less tax, the cost to me is only about \$1,400. That, plus the maintenance costs of approximately \$1,100, gives an annual cost (in year one at least!) of \$2,500, which is well below the market price of the dvc accommodations I would occupy with my points. And then I make some assumptions for subsequent years, that my costs (maintenance and opportunity cost) will rise with inflation, but then so would the market price of booking Disney resorts normally.

Since I think I would re-sell my stake in 15-20 years, I would probably get back a good chunk of the investment, so I don't think an amortization schedule would work for my costing analysis, but otherwise, if you believe your investment is spent, you would need to account for that and incorporate that cost into the analysis as well.

Someone mentioned a free lunch. There definitely still is none. When you run the numbers rationally, you are getting a good deal on the accommodations, but on the flip side, you are also committing to staying at Disney resorts for decades. That takes away some of your freedom of choice, and it also guarantees Disney a great deal of income. Over the years of your contract, you will spend tons of money on all things Disney. And but for DVC, you would have spent a lot of that money somewhere other than Disney resorts.

16. ### GalunEarning My Ears

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IMO there is an easier way to calculate this.

Take your most inefficient BWV 1BR which cost 43 points for a Fri/Sat, with rack rate of \$645. Your implied value per point is \$645 / 43 = \$15. MF = \$5.84 for net value of \$9.16 per point.

Plug this into excel. PV = \$72. FV = \$0. N = 29. PMT = \$9.16. Solve for RATE = 12.28%. That's your internal rate of return. As long as it beats your cost of capital (to buy DVC), you should buy.

17. ### dmunsilDisney Uber-Nerd

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Thanks much. I know all this detail isn't everyone's cup of tea, but I figure we're all nerds here of one kind or another. I can't be the only one thinking about this stuff. And it's nice to have validation that DVC is a good deal from someone who's run the numbers differently than you have.

I agree with your analysis, though on that last point I'm not sure how big a factor it is. It doesn't explain Hilton Head, Vero Beach, and Aulani. There's no park nearby to make money on, so the resort itself must make money. The only money they get is from maintenance fees, miscellaneous fees like extra towels and daily cleaning service, the store revenue, and onsite restaurants. It seems at first glance like that would be a lower revenue than you'd get from a hotel, but I guess with a hotel you have a bunch of risk, and a bunch of periods where you have to work at it to fill the hotel. With a timeshare, the whole year is paid for in advance. I guess the management fee turns out to be a nice tidy profit, and guaranteed year after year. It's just that the management fees are so much less income than they'd get by filling up the hotel even if they averaged half of rack rate. Maybe they really can't fill up a hotel for an average of half of rack rate.

I mean, if the revenue from maintenance fees for a DVC resort are similar to the revenue they get from rooms at a deluxe resort, that implies a lot of heavy discounts and a lot of empty rooms. I kinda thought Disney was pretty good at filling up rooms, so it still feels like a head-scratcher.

18. ### dmunsilDisney Uber-Nerd

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You can't just add up all the numbers and get a useful quantity. Time value of money - that's the point.

Time value of money is the concept that because you could get interest on your money, via a mutual fund, bond, or other investment, money in hand today is equivalent to a larger amount of money in the future. Or alternatively, in order to get a sum of money in the future, you should be willing to only spend a smaller sum today, because it has to be measured against the amount you could get from a bond or mutual fund. It actually has nothing specifically to do with inflation.

Here's another way to look at it: If you take either one of those lists of payments, and calculate the present value of each year's payment using the same interest rate (4.5%) that was used to calculate it, and add up all those present values, you get back the same number we started with originally (\$72). This is true for the inflation-adjusted one as well as the flat amortization.

It's tempting to take a stream of payments or costs and just add them up, but it's not correct. It's not ever correct. It leads to incorrect valuation of time-based money flows.

For example, which is worth more: a payment stream that starts at \$20 the first year, and goes down by \$1 per year for 20 years then ends, or one that starts at \$1 and goes up by \$1 every year for 20 years then ends? Or one that is a constant \$10.50 per year for 20 years?

A simple addition of the amounts tells you they're the same, and they're all worth \$210. But that's wrong; they're not the same and none of them is worth \$210. The first one is worth \$155, the second one is worth \$118, and the third is worth \$137, assuming the same 4.5% interest rate.

For lots of simple, short, time payments of less than 10 years, calculating an amortization just doesn't make enough difference to be worthwhile. With stuff like DVC where the time horizons are 29+ years, amortization produces some really significant effects.

No. It's just time value of money. The money you will get 29 years from now is worth a lot less today than the money you get this year. In order to spend \$72 today on an annuity, I need to get back more than \$72 over time to account for interest. This is all in nominal dollars; inflation is a separate issue that you can calculate separately if you want.

19. ### dmunsilDisney Uber-Nerd

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This doesn't really work, because the dues and cash rates go up over time. And they've gone up faster than inflation, and not necessarily at the same rate. So your payment will not actually be \$9.16 continuously; it'll be steadily increasing, which makes the internal rate of return higher than you've calculated, by approximately the long term average rate of dues and cash increase (assuming they go up together at about the same rate). So if they go up at 3.5% the IRR ends up being about 15.78%.

I'm not sure most people know what their long term cost of capital is, though.

20. ### DeanDIS Veteran<br><a href="http://www.wdwinfo.com/dis

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I'm not going to get into specific numbers as much as you clearly intend to (though I'm happy to see it unfold) but I did want to add a couple of points. One, that I look at DVC as you would a high risk investment, because that's what it really is. Not only would I consider the time value of money, I'd want a return (ROI) over a shorter period than the RTU, I use 10 years plus I want a 20% return or savings based on real costs, not rack rates. The other issue, and one of the reasons I'm not going to do minutia math, is that I feel the psychology of timeshares ends up being far more important than just the numbers. Put another way, DVC likely saves almost no one any money in the long run though it MIGHT or might not provide additional value. Put an even different way, someone who has the bug is usually going to find a way to convince themselves to buy and quickly fall into the "don't confuse me with facts" group.

21. ### GalunEarning My Ears

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Sure, for simplicity's sake I just assumed a constant spread and I got 12.28% from rate function of a financial calculator, which would be the real rate of return if you assume the spread grows in line with inflation. You can make further assumptions about differential growth rate among inflation, MF and rack rate, which you did.

But I agree with Dean. The calculation is garbage in garbage out and can justify whatever conclusion you want. What if 12.28% or inflation adjusted 15.78% return is not good enough? Well, go for the deluxe view standard studio, \$459 rack rate for 19 points, implied value of \$24.16 per point, for a spread of \$18.32, and IRR of about 27%. On the other hand, when Disney runs a 30% special on their rack rate, your rate of return is only 7.5%, which is quite poor for the amount of risk you take on.