Paying back your ship

[McPerth]

Let’s imagine your group has a MCr 24 ship (let’s make numbers easy) for which they still owe 30 years mortgage (so 360 months, at Cr 100000 per month, MCr 36). They have made a commercial venture that gives them a surplus of MCr 6, and they intend to use them to redeem part of their debt. How this is handled?

We all know that the money invested in paying back a mortgage gives you more benefit the sooner you pay it, as interests are also saved...

My idea is to multiply this money by 1 + (years remaining to pay x 2.5)/100 and subtract it from the total debt, recalculating the monthly payments from this new debt (total debt / months remaining to pay).

So, let’s imagine this MCr 24 worth ship, so your debt would be MCr 48, if you could pay MCr 24 in your first year, they would be worth 24 x 2, so your debt would be fully paid.

In the case shown above, the money will be worth 6 x (1 + (30 x 2.5)/100), so 6 x 1.75, and so MCr 10.5 would be subtracted from your MCr 36 debt, leaving you with a MCr 25.5 debt, which should be paid at a rate of MCr 25.5/360 a month, so MCr 0.0708333 (Cr 70834)/month for the next 360 months.

Thoughts?

 

[HG_B]

Thoughts?

When interest is amortized over the term of the loan (as in Trav) just use a online mortgage calculator for applying extra sums to the principle. It is tedious to calc this by hand.

 

[McPerth]

When interest is amortized over the term of the loan (as in Trav) just use a online mortgage calculator for applying extra sums to the principle. It is tedious to calc this by hand.

That's why I made this system to make it easy, without resorting to tedious or difficult calculations (you'd gess I'm not an economics expert...)

 

[CosmicGamer]

leaving you with a MCr 25.5 debt, which should be paid at a rate of MCr 25.5/360 a month, so MCr 0.0708333 (Cr 70834)/month for the next 360 months.

First, how can you have a 25.5 debt? That's more than the original loan. Probably just a wording issue. I think I get what you are saying.

Typically the monthly amount due is the monthly amount due. Payments are not recalculated just because you are paying extra against the principle. It usually just means that the ship loan would be payed off sooner.

I've never seen a ship last long enough that you'd need to worry about it. Just jot it down in case they trade the ship in or sell it or claim insurance and you can go online and figure it out if and when you need to.

Optionally, they could refinance and you just need to calculate the loan payoff and then determine the new loan parameters. Why not take it out to 40 years again instead of 30 and really lower the payments down or, if you can afford it, pay it off in 20 years or whatever. Just go online to figure it out.

 

[aramis]

Some loans come with a "cannot apply excess against principle" clause, but those usually note that excess loan payments reduce the end date of the note. I've seen a number of such loans done as private loan terms.

Note that such loan terms are excellent for long-term investing - the bank discourages buying it out outright. And, it's mentioned somewhere in canon that this is the way it works.

The recalculation method is pretty straightforward, but math intensive.

I'm cranking a spreadsheet... hold on.
Using a monthly recapitalization and monthly payment reducing principle prior to recapitalization, and no points... 12 payments per year, 13 months per year (to match imperial calendar) I get 5.15%.; using 12 months, it's 5.56%, and you can use real world calculators to do it easily.

 

[aramis]

12 months, 12 payments, MCr 1 financed, 20% down payment, end of each year.

Principle	Interest	paid	4167 12/12mo
795,803	3,688	50,004	1
789,910	3,661	100,008	2
783,682	3,632	150,012	3
777,099	3,602	200,016	4
770,139	3,569	250,020	5
762,782	3,535	300,024	6
755,007	3,499	350,028	7
746,787	3,461	400,032	8
738,098	3,421	450,036	9
728,914	3,378	500,040	10
719,205	3,333	550,044	11
708,944	3,286	600,048	12
698,097	3,236	650,052	13
686,630	3,182	700,056	14
674,509	3,126	750,060	15
661,697	3,067	800,064	16
648,153	3,004	850,068	17
633,836	2,938	900,072	18
618,703	2,868	950,076	19
602,707	2,793	1,000,080	20
585,797	2,715	1,050,084	21
567,921	2,632	1,100,088	22
549,027	2,545	1,150,092	23
529,056	2,452	1,200,096	24
507,944	2,354	1,250,100	25
485,627	2,251	1,300,104	26
462,038	2,141	1,350,108	27
437,102	2,026	1,400,112	28
410,744	1,904	1,450,116	29
382,882	1,775	1,500,120	30
353,430	1,638	1,550,124	31
322,298	1,494	1,600,128	32
289,388	1,341	1,650,132	33
254,602	1,180	1,700,136	34
217,829	1,010	1,750,140	35
178,960	829	1,800,144	36
137,872	639	1,850,148	37
94,440	438	1,900,152	38
48,529	225	1,950,156	39
-2	0	2,000,160	40

 

[aramis]

13 months, 12 payments (skip a month for annual maintenance)

Principle	Interest	paid	4167 12/13mo
791,916	3,401	50,004	1
786,084	3,376	100,008	2
779,919	3,350	150,012	3
773,401	3,322	200,016	4
766,510	3,292	250,020	5
759,223	3,261	300,024	6
751,520	3,228	350,028	7
743,372	3,193	400,032	8
734,761	3,156	450,036	9
725,656	3,117	500,040	10
716,028	3,075	550,044	11
705,849	3,031	600,048	12
695,085	2,985	650,052	13
683,707	2,936	700,056	14
671,676	2,885	750,060	15
658,957	2,830	800,064	16
645,509	2,772	850,068	17
631,288	2,711	900,072	18
616,254	2,647	950,076	19
600,360	2,578	1,000,080	20
583,551	2,506	1,050,084	21
565,782	2,430	1,100,088	22
546,994	2,349	1,150,092	23
527,130	2,264	1,200,096	24
506,129	2,174	1,250,100	25
483,925	2,078	1,300,104	26
460,446	1,977	1,350,108	27
435,624	1,871	1,400,112	28
409,378	1,758	1,450,116	29
381,631	1,639	1,500,120	30
352,291	1,513	1,550,124	31
321,273	1,380	1,600,128	32
288,478	1,239	1,650,132	33
253,802	1,090	1,700,136	34
217,142	933	1,750,140	35
178,383	766	1,800,144	36
137,401	590	1,850,148	37
94,071	404	1,900,152	38
48,259	207	1,950,156	39
-179	-1	2,000,160	40

 

[rancke]

Or you could make it payments on every day of the year that is divisible by 30.


Hans

 

[BlackBat242]

I take it this is for the Traveller "game-within-a-game" called Accountants and Architects?

 

[Icosahedron]

I'd look at it like this:

Initial calc:
Ship cost = 30M
Down Payment = 20% = 6M
Loan Amount = 24M
Repayment = 1/240*24M = 0.1M/mo
Initial debt = 0.1M*480mo = 48M

10 yrs later:
120*0.1M = 12M paid, outstanding debt = 48-12 = 36M

If you pay off 6M, there are two low maths methods depending on the nature of the Mortgage contract (ie whether your payments are made from the sum owing at the time or from the sum loaned. Method 1 should be illegal because you are paying out money for a loan that you no longer have):

Method 1.
Current debt is 36M to be paid over 360mo = 0.1M/mo
New debt is 30M to be paid over 360mo = 0.08333/mo

Method 2.
New Nominal Debt = 24-6 = 18M
Repayment = 1/240*18 = 0.075M/mo
New debt = 0.075*360mo = 27M

 

[McPerth]

First, how can you have a 25.5 debt? That's more than the original loan. Probably just a wording issue. I think I get what you are saying.

Due to interests and bank financing. The MCr 36 (before you redeem MCr 6) or 25.5 (after redeeming) come from what you will pay in all your remaining montly payments, not from what principal you still owe.

Typically the monthly amount due is the monthly amount due. Payments are not recalculated just because you are paying extra against the principle. It usually just means that the ship loan would be payed off sooner.

For what I've seen from mortgages, you can refinance them each year (or twice a year). Of course other mortgages may work differently...

I've never seen a ship last long enough that you'd need to worry about it. Just jot it down in case they trade the ship in or sell it or claim insurance and you can go online and figure it out if and when you need to.

But you surely have seen ships with some years paid (e.g. a Merchant rolling 3 times a ship in mustering out, so having 20 years paid)

Optionally, they could refinance and you just need to calculate the loan payoff and then determine the new loan parameters. Why not take it out to 40 years again instead of 30 and really lower the payments down or, if you can afford it, pay it off in 20 years or whatever. Just go online to figure it out.

In this case, you're not refinancing your mortgage, you're just redeeming part of your principle. Those are two different things.

Using a monthly recapitalization and monthly payment reducing principle prior to recapitalization, and no points... 12 payments per year, 13 months per year (to match imperial calendar) I get 5.15%.; using 12 months, it's 5.56%, and you can use real world calculators to do it easily.

Traveller talks about paying for 480 months (see quote below), not 40 years. So, as many reference are made to those 40 years, I assume there are 12 payments a year, either by paying each day divisible by 30 (as hans suggests, and so having 5 "free" days a year) or by skipping one month a year (probably the one for maintenance).

If you make 13 payments a year (to match Imperial calendar) you'll pay your ship in a little less of 37 years, not matching with the many references to 40 years.

I'd look at it like this:

Initial calc:
Ship cost = 30M
Down Payment = 20% = 6M
Loan Amount = 24M
Repayment = 1/240*24M = 0.1M/mo
Initial debt = 0.1M*480mo = 48M

10 yrs later:
120*0.1M = 12M paid, outstanding debt = 48-12 = 36M

I'm afraid you calculated it wrong. The 20% down payment isn't subtracted from the price of the ship when calculating financing, so that you end paying 220% of the ship's cost

From Bk2, page 7 (or TTB page 52):

after a down payment of 20% of the cash price of the starship <snip> Standard termsi nvolve the payment of 1/240th of the cash price each month for 480 months. In effect, interest and bank financing cost a simple 120% of the final cost of the ship, and the total financed price equals 220% ofthe cash purchase price

BTW, I guess Will's tables have the same error, as they begin (as I understand them) with a principle of MCr 0.8 for a MCr 1 loan.

If you pay off 6M, there are two low maths methods depending on the nature of the Mortgage contract (ie whether your payments are made from the sum owing at the time or from the sum loaned. Method 1 should be illegal because you are paying out money for a loan that you no longer have):

Method 1.
Current debt is 36M to be paid over 360mo = 0.1M/mo
New debt is 30M to be paid over 360mo = 0.08333/mo

Method 2.
New Nominal Debt = 24-6 = 18M
Repayment = 1/240*18 = 0.075M/mo
New debt = 0.075*360mo = 27M

This ignores that for the initial payments you're paying mostly interests, and few principle (see Will's tables, above), so, the same 1/6 of the remaining debt at the begining of your mortgage will be worth more than at the end of it.

In 10 years, you have paid MCr 12 and have 36 to pay, as we both calculated, but that does not mean you've paid 1/4 of your principle. In fact, according to Will's tables you whould have only paid about 10% of it.

 

[Icosahedron]

I'm afraid you calculated it wrong. The 20% down payment isn't subtracted from the price of the ship when calculating financing, so that you end paying 220% of the ship's cost

BTW, I guess Will's tables have the same error, as they begin (as I understand them) with a principle of MCr 0.8 for a MCr 1 loan.

I'm not so sure. The rule is a little ambiguous, but by your interpretation that 20% isn't a down payment at all, it's a fee. By my method you end up paying 220% of the sum you've been loaned.

This ignores that for the initial payments you're paying mostly interests, and few principle (see Will's tables, above), so, the same 1/6 of the remaining debt at the begining of your mortgage will be worth more than at the end of it.

In 10 years, you have paid MCr 12 and have 36 to pay, as we both calculated, but that does not mean you've paid 1/4 of your principle. In fact, according to Will's tables you whould have only paid about 10% of it.

Depends on how much maths you want to do. The method I outlined suffices for MTU. I'd rather play Traveller than Accountants and Architects, but of course you can add as much complexity as you want.

 

[McPerth]

I'm not so sure. The rule is a little ambiguous, but by your interpretation that 20% isn't a down payment at all, it's a fee. By my method you end up paying 220% of the sum you've been loaned.

As I read it (of course I can be wrong) in your method you end paying MCr 6 (Down payment) + 48 (along the years, for a total of MCr 54, and that is a total of 180% of the MCr 30 ship cost.

While I agree the rule is ambiguous (as it says 1/240 of the cash price, not the full cash price), the fact it specifies the total cost is 220%, IMHO, seems to hint the down payment is,in fact, a fee.

Depends on how much maths you want to do. The method I outlined suffices for MTU. I'd rather play Traveller than Accountants and Architects, but of course you can add as much complexity as you want.

That's why I suggested this, again IMHO, simple method, as neither I want to include too much maths on the game (yet I had to read the rules of A&A before giving my opinion on it )

 

[Icosahedron]

Heh, looks like you're right - yet another 30-year assumption shot down. What can I say? IMTU mortgages are a little cheaper and a down payment doesn't need to be paid twice.

It seems that, by the actual rule, the bank is charging you interest on money they haven't lent you. I'd be a bit miffed if my bank charged me interest on the 20% down payment I'd made from my own pocket...

I suppose it could be argued that their rates are actually higher on the loan they have made and that the rate simply happens to be equivalent to 220% of the total cost, but it seems a bit contrived to me.

Anyhow, answering your original question, whichever way you work the mortgage, you can still see from the above what my method for paying off a lump sum would be.

 

[aramis]

Heh, looks like you're right - yet another 30-year assumption shot down. What can I say? IMTU mortgages are a little cheaper and a down payment doesn't need to be paid twice.

It seems that, by the actual rule, the bank is charging you interest on money they haven't lent you. I'd be a bit miffed if my bank charged me interest on the 20% down payment I'd made from my own pocket...

I suppose it could be argued that their rates are actually higher on the loan they have made and that the rate simply happens to be equivalent to 220% of the total cost, but it seems a bit contrived to me.

Anyhow, answering your original question, whichever way you work the mortgage, you can still see from the above what my method for paying off a lump sum would be.

it's actually 1/240 of the purchase value, or 1/192 of the financed amount. Works out the same either way. 5.5%-ish on the 80% borrowed. Which means, yes, you're paying around some 20%+(2.5x80%) paid = 220% of purchase price.

Note that most house loans put the entire house's value as the collateral on the (typically) 90% financed loan. Many real world fishing vessel loans require not just the ship but also some non-mobile real property be listed as collateral.

 

[Darkwing]

Keeping it simple, I assume a 40-year fixed rate mortgage. If you make an extra payment, just like a house payment, then it's handled one of two ways. If you just pay MCr 6, then knock MCr 6 off the total debt, meaning it is now a 24-year mortgage remaining. Players will usually find that good enough, because they don't own a house, and don't think that much about it.
If they do own a house, they're gonna say "what! wait aminute, here, I marked it 'principal only', dagnabbit!"
At that point, it's now a MCr18 debt, and has to be reamortized. Do the same basic math, and now that Cr100k becomes ~CR 75K.
Or have them roll to refinance. If they get a good roll, they might get a slightly better interest rate, and then they can multiply the above amounts by 0.9 to 0.99 to get a total monthly payment around CR 68k - CR74 K.

 

[Fritz_Brown]

There are 3 (RL) ways to handle this, and most of them have been touched on - but I'm not sure everyone is seeing the different concepts at work.

First, I have a car loan that is a set amount. They figured the interest, then applied it, and that is the amount I owe. Period. As I pay slightly more than the required amount each month, the minimum monthly payment slips down a little bit each time - keeping the original payoff date. The 'value' of this loan decreases linearly over time, assuming a steady payment. This loan works exactly (well, it's not 40 years long and doesn't have me paying 220% of the purchase price) like a canonical starship loan, based on what Aramis and others are saying.

I also have a mortgage that calculates the interest monthly (I think), based upon outstanding principal. If I pay extra against the principal, the interest recalculates. The total amount required to pay off this loan changes constantly as the principal changes - and it changes in a more geometric progression, accelerating toward the end of the loan period. This is not a canonical way to do starship loans. This method would be overly complicated given that the actual value of the ship (much like a car) decreases over the life of the loan, rather than increasing (as with a home in a healthy economy) - there would be depreciation to figure in for the bank, and they don't want to hold paper on something that doesn't have at least the same value as the loan.

The third method is the re-fi (refinancing). This would involve going back to the bank and requesting a new loan (with the same or better terms) for a lesser amount or a new loan period. If you have a simple loan (the first example) this doesn't benefit you as much, since you have to re-fi the interest already built into the first loan. If you re-fi the other type, you aren't having to re-fi any of the interest that hasn't yet accumulated. This re-fi can be independent of any extra payments - it becomes attractive if you have a lump sum because you can reduce the amount you are financing.

Having said all that, the question is how much work you want to do - playing Accountants and Architects as Icosahedron said. The canonical method is the simplest. Paying more early would simply decrease the outstanding value of the loan, and the payments would be recalculated to last over the life of the loan, or the loan period would reduce. If your players want to be extra wise (not always a good aspiration, mind you!) they would put the 6MCr into a bond account, earning some interest, and simply make their ongoing loan payments out of that.

-- For a canonical starship (24MCr) loan, you pay 100kCr every month on a total of 48MCr owed. If you make a lump sum additional payment of 6MCr at the 6th month of the loan (in addition to your normal 100kCr), and they re-amortize over the remaining 474 months, the new payments are 87.3kCr.
-- If they don't re-amortize, you end up paying the loan off 60 months early (and continue paying 100kCr/month).
-- If you invest the 6MCr in a bond that pays 3% annually (180kCr), and you add that annual interest to your payment (never touching the 6MCr principal), beginning at the end of the first year of investing (month 18 of the loan), and don't re-amortize, you end up paying the loan off 61 months early, with final payment of only 80kCr.

In short, re-amortizing is good for reducing your expenses each month (definitely a win for the Trader struggling to make his payment), not re-amortizing is good for paying off early (but still outside the temporal scope of most campaigns). Investing and not re-amortizing pays off even earlier, and you still have 6MCr in the bank at the end.*

(BTW, for all those suggesting using an online calculator: some of them won't accept the large amounts needed to finance a starship. )


*If you drop that 6MCr onto the loan right at the end, you pay the whole thing off in 367 months - almost 10 years early!!!

 

[McPerth]

But on most mortgages, even without refinancing them, if you make early pays against the principle, they are worth more than if you make them latter, due to interest savings.

If you have a morgage to buy your home (I guess the best comparison with the ship's financing in Traveller, both due to time span and ammounts) and on the first year of it you win a loto prize that allows you to pay for the full mortgage, you can redeem it paying only a little more that its face value, so ending up paying just a little more in interests.

If this same loto prize comes to you when only 5 years mortgage remains, you can still redeem your mortgage, but in the end you'd paid much more due to interests, so this money being "worth" less.

That is what I tried to represent with my method, without resorting to complex calcultaions (IMHO the numbers are made quite easy), so making early payments worth to be done.

 

[Carlobrand]

Let’s imagine your group has a MCr 24 ship (let’s make numbers easy) for which they still owe 30 years mortgage (so 360 months, at Cr 100000 per month, MCr 36). They have made a commercial venture that gives them a surplus of MCr 6, and they intend to use them to redeem part of their debt. How this is handled?

We all know that the money invested in paying back a mortgage gives you more benefit the sooner you pay it, as interests are also saved...

My idea is to multiply this money by 1 + (years remaining to pay x 2.5)/100 and subtract it from the total debt, recalculating the monthly payments from this new debt (total debt / months remaining to pay).

So, let’s imagine this MCr 24 worth ship, so your debt would be MCr 48, if you could pay MCr 24 in your first year, they would be worth 24 x 2, so your debt would be fully paid.

In the case shown above, the money will be worth 6 x (1 + (30 x 2.5)/100), so 6 x 1.75, and so MCr 10.5 would be subtracted from your MCr 36 debt, leaving you with a MCr 25.5 debt, which should be paid at a rate of MCr 25.5/360 a month, so MCr 0.0708333 (Cr 70834)/month for the next 360 months.

Thoughts?

If you're gonna go the math route, have you considered investing rather than paying down your loan? Your loan's costing you, what, MCr 1.2 a year? Anything with a return over 5% per annum gives you enough to pay your annual payments with a bit of profit left over for yourself - and keeps paying out after the loan's paid off, giving you a nice sum for retirement. There'll be ups and downs, but a diversified portfolio on a big stable world like Mora or Trin ought to be both safe and profitable.

We older players tend to think about such things.

 

[Fritz_Brown]

If you have a morgage to buy your home (I guess the best comparison with the ship's financing in Traveller, both due to time span and ammounts) and on the first year of it you win a loto prize that allows you to pay for the full mortgage, you can redeem it paying only a little more that its face value, so ending up paying just a little more in interests.

You keep going to the compounding interest home mortgage to compare with the starship mortgage, and that's not canonical. As I mention above, the canonical mortgage is more like my simple loan on the car - all the interest is calculated, then added, and that's the total you owe.

If you use the compounding interest mortgage, then it *does* make sense to pay that windfall against the principal.