Mortgage and investment choice.

[Andy]

Hello guys! I am new to forum hopefully going to stay for long since finance is my passion. However I faced an issue during my case study, which made me confuse a bit, can you please check my logic?

Small excursus - I have a case where I need to propose a financial plan to a client. My client is a family with some savings, house, mortgage loan and good living income.

:arrow:So they own a house which market value is 2 600 000 SEK(Swedish Kronor, Hej Hej from north!) their equity in it is 650 000 SEK and mortgage loan outstanding is 1 950 000 SEK. They have a variable mortgage rate, which they dont know(lol), but they pay only interest on it, which is 6000 SEK monthly. Therefore I need to calculate mortgage rate. So I do it like this (6000*12)/1 950 000 = 3.6923%. As far as I understand it is AAR, which equals EAR because we don't pay no principal here, thus no compounding effect. However if I divide it by 12 to find monthly rate will it be monthly AAR or EAR, or again both? In addition if for instance my client going to pay more than interest payment, can I use that 3.6923%/12 as a monthly rate, which now would include compounding in it?

:arrow:Second question that made me confused is - house price appreciation rate here is 4,4%. So the house price in ten years going to be 2 600 000*1.044^10 = 3 999 247 SEK, if to assume that house price appreciation rate would remain same. Hence if my client will pay only interest payments, his equity will rise from 650 000 SEK to 3 999 247 - 1 950 000 = 2 049 248 SEK, which gives him 12,16% rate of return with annual compounding on his initial equity of 650 000 SEK. However if he uses his 250 000SEK from saving account(0,4% interest) to repay part of mortgage tomorrow that would increase his equity to 900 000 SEK, but then rate of return drops to 8,57%. So the mortgage here can be used as leverage? Is my logic and assumptions correct? Does mortgage grow with house's price or stays same?

:arrow:Third issue(holds if my assumptions about mortgage correct) arises because he has several options to invest in. First is to repay mortgage, second is bank safe deposit account of 2.2% with AAR, third is to invest into green/ethical venture capital fund(crazy about ecology) with rate of return of X. So what I have thought. He should put money into repaying mortgage because he would get anything from as high as 12,16% to 4,4% return, or kinda return reflected in house price appreciation, this is supreme option in comparison with bank deposit since 2,2%<4,4%. Is that correct? Then if X>4,4% he should invest in fund, or if X<4,4% not invest, or do 50/50 solution to diversify a bit, or even 80/20 since he is really risk averse but still fulfill his aim to contribute to green technologies. Is this correct guys, I mean fact that he shall choose repaying mortgage over bank and fund if it's below 4,4%?

:arrow:The last question for someone with advanced knowledge. How can I emulate situation to find out at what interest rate he needs to switch from variable to fixed rate? I don't know fixed rate that bank offers, my teacher advised me to take a yield curve and assume that it's the fixed rate. So I have build a curve and it starts with 1.035% today and steadily goes up to 2.816% in 30 years. That makes me think that he definitely need to switch asap, because 2.816% is lower than his current 3.69231%. Unfortunately I don't believe that bank would allow him to do so, because right now he has no fixed mortgage term and can pay interest forever without paying principal. But if he want to switch to fixed one can he still have infinitive term? Would then the fixed rate be calculated using perpetuity formula? Like i = payment/loan? If yes than it's his current variable rate, which doesn't make sense. Also maybe someone knows how to calculate approximate fixed rate from variable rate or central bank repo/int rate, or is it subjective up to bank to decide?

Thank for your time guys! I am very grateful if you would express your thought upon my post and show me my faults if there are some. Have a wonderful day!

Cheers,
Andy.

 

[Andy]

Thanks for the answers Denis! I appreciate it a lot!

does not take in consideration that all along, 6,000 per month is paid....
The other stuff is just as iffy; keep in mind you need something
that the customer will understand...get my drift?

...and don't worry; if I'm wrong, Jeff or Dr Phil will jump in

Yes that's what I thought today when I've reviewed my calculations, I need to add those 6000 $. As a result calculated in excel using annuity formula I get much lower rate. I get like 5.58% when include 6000 into calculations.

Who is Jeff and Dr Phil? Are they mastodon of this forum? Super smart guys? I would love to meet them!

 

[JeffM]

Andy, my initial reaction: FORGET IT!!
As example, your 12.15% is just a gross calculation;
like, does not take in consideration that all along, 6,000 per month is paid....
The other stuff is just as iffy; keep in mind you need something
that the customer will understand...get my drift?

I suggest presenting the situation "as it is":
equity: 650,000
sale proceeds in 10 years: 4,000,000 - 1,950,000 = 2,050,000
monthly outlay to achieve above: 6,000

So now we have the same as someone opening a savings account,
initial deposit of 650,000 with deposits of 6,000 monthly over 10 years;
this works out to a rate of 5.30% annual compounded monthly,
and what happens is easy enough to see in bank statement format:

MONTH     DEPOSIT     INTEREST       BALANCE
0                                    650,000
1        6,000.00        2,870       658,870
2        6,000.00        2,910       667,780
...
119      6,000.00        8,920     2,035,020
120      6,000.00        8,980     2,050,000

Btw, the rate calculation in this instance cannot be made directly;
numeric method required.
...and don't worry; if I'm wrong, Jeff or Dr Phil will jump in

Actually Jeff might jump in even if denis was right. It's what mastodons do, particularly if they are not super-bright mastodons.

 

[Andy]

Actually Jeff might jump in even if denis was right. It's what mastodons do, particularly if they are not super-bright mastodons.

Heheh, look who's here! Hello there! Thanks for double check! Didn't mean no offense saying mastodon, sorry if that made you feel bad. I use it as a metaphor to someone wise and heavy-weight in some field. Same as bonza, shark or just keen smart person with a lot if experience, who's advices very valuable and has weight.

So I have fixed the returns including monthly payments in them! Thanx!

 

[HallsofIvy]

Heheh, look who's here! Hello there! Thanks for double check! Didn't mean no offense saying mastodon, sorry if that made you feel bad. I use it as a metaphor to someone wise and heavy-weight in some field. Same as bonza, shark or just keen smart person with a lot if experience, who's advices very valuable and has weight.

What did you mean by "not super bright", then?

So I have fixed the returns including monthly payments in them! Thanx!

 

[JeffM]

What did you mean by "not super bright", then?

That was me, Halls, correcting a misapprehension.