Hi all, as I’ve indicated in other posts, the “wheelbarrow” I like to push is the effect of time value of money. One of my pet hates is seeing marketing hype from some lender or financial guru purporting to save us squillions of dollars in loan repayments if we just follow their magic formula (extra payments) to reduce the principal. The problem is that we must put in extra of today’s dollars in order to save lowly depreciated dollars that would have to be paid in 25 years time. The only sensible way to compare different loan repayment methods is to bring all payments back to Present Worth (at the start of the loan) using standard discount formulas.
Following on from RentMaster’s example in the “Interest Only Loans” post, and my examples of calculations of present worth, I’ve shown a few more combinations in the table below:
Number|Loan| Repayment|Total | Present
Months|Type| Amount |Repayments | Worth
|-- |
|
|
Tax Bracket: 0.0%
120 |IO | 1,166.67 | 340,000.00 | 258,990.57
120 |PI | 2,322.17 | 278,660.35 | 234,833.31
200 |IO | 1,166.67 | 433,333.33 | 288,298.17
200 |PI | 1,696.87 | 339,374.46 | 256,852.67
300 |IO | 1,166.67 | 550,000.00 | 316,521.35
300 |PI | 1,413.56 | 424,067.52 | 282,359.54
Tax Bracket: 48.5%
120 |IO | 1,166.67 | 272,100.00 | 201,769.72
120 |PI | 2,322.17 | 240,510.08 | 201,045.00
200 |IO | 1,166.67 | 320,166.67 | 202,648.95
200 |PI | 1,696.87 | 271,777.85 | 201,705.58
300 |IO | 1,166.67 | 380,250.00 | 203,495.64
300 |PI | 1,413.56 | 315,394.77 | 202,470.79
The formulas used are shown in that post, except this time I’ve done the calculations correctly for present worth of the P&I loan with tax deduction. There is probably a formula for doing this, but it was just as easy to write a database program that would refer each individual payment (reduced by the tax refund) back to present worth, iteratively. The computer can whip around 300 calculations in a microsecond so it doesn’t matter if it’s clumsy looking.
I know it looks a bit of a mess, but you can see (in the 0 tax bracket) that increasing P&I payments from $1413 to $1696 appears to save $84693 in total payments by shortening the loan from 300 to 200 months, but in reality, ie in today’s dollars, it will only save $25507. Interestingly the loan doesn’t really cost us much if the tax man helps at 48.5% and inflation does the rest.
RentMaster, I know the maths looks a bit messy, but it’s relatively straightforward to plug the formulas into a spreadsheet (I’m sure a lot of them are built in functions) or database. As you are a software programmer you would probably find the code easier to follow, so I’ll include my code below.(sorry about padding out the forum with geeky code) Sorry also that the pesky forum program is stripping off all my lovely indenting!
Jim.“Timevalu” is the name of my database table, and its fields are shown in square brackets. “;” denotes comments to the right. Upper case words are reserved words and words starting in lower case are variables. I’m sure you could massage the syntax into whatever program you use. POW(x,y) means x to the power y.
EDIT "timevalu"
SCAN
p = [Principal]
r = [Interest Rate]/1200 ; Converts % p/a to
;fraction per month.
i = [Inflation Rate]/1200 ; ditto
n = [N Periods]
TaxFactor = [tax bracket]/100
rFactor = POW((1+r),n)
iFactor = POW((1+i),n)
; Capital Recovery Factor {A/P} =
; (r*rFactor)/(rFactor-1)
; (r or i used as appropriate)
; Single Payment Present Worth Factor
; {P/F} = 1/iFactor
IF [Loan Type] = "IO" ; (Interest Only)
THEN [Repayment Amount] = p*r
afterTaxRepayment = [Repayment Amount] *
(1 - TaxFactor)
[Present Worth] = afterTaxRepayment/
((i*iFactor)/(iFactor-1))
+ P/iFactor
[total repayments] = n *
afterTaxRepayment + p
ELSE ; Principal & Interest loan
[Repayment Amount] = p*(r*rFactor)/
(rFactor-1)
; to calculate Present Worth of all
; repayments, first must
; deduct tax refund from each
;payment, and bring each payment
; back to present worth individually.
amountOwing = P
presentWorth = 0
totalPayments = 0
FOR counter FROM 1 TO n
interestPayable = amountOwing * r
amountOwing = amountOwing +
interestPayable
- [repayment amount]
afterTaxRepayment =
[repayment amount] -
interestPayable * TaxFactor
totalPayments = totalPayments +
afterTaxRepayment
presentWorth = presentWorth +
afterTaxRepayment /
POW((1+i),counter)
ENDFOR
[present worth] = presentWorth
[total repayments] = totalPayments
ENDIF
ENDSCAN
This is a great post. This is a fundamental technique in the valuation of stocks as well (except you should increase your discount rate to account for risk). I think that would make a nifty little app for someone to use that lets you compare loan savings of the discounted vs non discounted amounts..
The only thing is (and I haven’t followed previous threads and thus may be a dumb question), what does the POW formula do?
ie POW((1+r),n)
EZ-Rent. The free tax and cashflow simulator for Australian property investors.
http://www.ez-rent.comWay above my head, unfortunately : ( but I like the general idea.
Put a one-off $5k payment into a P&I loan, save maybe $20k (future dollars) in interest and shorten the term of the loan 5 years.
Spending 5k today to get $20k more equity over (say) 20 years is not that bad (7% pa) for an unleveraged risk-free investment like paying off a loan. Even if the 20k future saving is worth less than $20k today.
As I see it the main disadvantage is that the 5k put into the loan reduces what you can buy today. If you think the property could grow in value or returns CF+ then that could be seen as a disadvantage assuming you’re willing to bear the increased debt.
Peter
The only thing is (and I haven’t followed previous threads and thus may be a dumb question), what does the POW formula do?
ie POW((1+r),n)
Thanks for your response EZ. The formula above is just (1+r) to the nth power. Its just how it’s expressed in the database language (Paradox Application Language). It’s just what happens when you compound interest, ie if you’ve got 7% interest, then the loan will increase at 1.07 X 1.07 X 1.07 after 3 years, ie (1 + .07) to the power 3, except for the part you pay off.
It’s difficult to display the formulas in this text only forum, and difficult to display code when it strips off leading spaces. Hopefully you can see how the code is bracketed.
A good website reference for the discount formulas can be found at http://www.eng.ufl.edu/home/env5075/envdocs/econfac.htm It displays them properly with superscripts etc.
I’m sure it’s not over your head Peter, its just compound interest as I’ve shown above. You don’t really need to know exactly how the formulas are derived anyway. All financial calculators and spreadsheets have most of them built in. All bank (etc) websites have calculators to derive repayments. I’m just highlighting the effect when you bring all payments back to present worth, and mainly the fact that the loan doesn’t really cost you much in real terms if it’s tax deductible at 48.5%. Silly as it sounds, paying principal back in this situation doesn’t actually change your net worth much in real terms, as it is only a 3 to 4% investment after tax, and that is negated by inflation.
I guess it’s all about risk. You can pay down your principal to reduce your exposure to increased interest rates, or park it in an offset account which does the same thing, or put into an investment that pays at least 7% after tax.
I guess I’ve compromised with 30 year loans, because (a) paying principal “feels” better and (b) I managed to buy 4 properties, all negatively geared that I could only just afford at the time. It would have been easier with IO loans.Sorry to ramble on. Hopefully some food for thought.
Jim.thanks doogs, that was very interesting, gives me all the more reason not to pay loans off quicker.
i’ve always used any extra money to buy another property.
thanks for reminding me i was doing the right thing.[^]
Just don’t get overcommited Investron! A lot of us are going to have egg on our face if interest rates hike back up to 17% again. That 5 year fixed rate of 6.5% is starting to look a bit tempting, because I don’t have much leeway in my cash flow. It’s getting easier every year though. Lucky I’ve been putting a bit away in the form of principal
]All looks gd. I dont think you should worry about interest rates going back over 10 the econnemy cant afford it i think if you budget up to about 8.5 you should be pretty safe (this is only my opinion) all my calculations are based on 8.5% interest if i cant afford it with all my loans at 8.5% i wont buy it or i will find a bigger deposit.
brettSorry to bump this post up again everyone, but I’ve just discovered the “code” button, and I thought I might try it on the code I wrote in this post. This is a useful button if you are trying to line up columns in a table or trying to show indentation (bracketing) in code etc, ie it keeps the font non-proportional (eg courier) and doesn’t eat up the leading spaces.
Jim
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