@Dennis Guinto
Individual decisions should be based on the end goal/s. Are you looking to build cashflow, to have a place to move to later, etc.
With that said, here are some considerations:
1) Transferring title (you buying the house) will trigger a reassessment (higher property taxes), which will significantly affect any potential cashflow. The parent to child transfer of property tax base, was changed this year, due to Prop 19. Your situation does not seem to qualify for the tax base tfr. In order to qualify now, the property has to be your parents principal residence, and the property must become your principal residence within one year of the tfr.
The real world difference for you, is around $270/mth in additional property taxes. Right now, they are around $6,500/yr or $545/mth, that will go up to around $815/mth for a new assessed value of $850k
Also, don't make the mistake of thinking you can circumvent that, by having your Dad sell you the house at a discount, and therefore, think you will get a lower assessed value. While it might influence it somewhat, the assessed value should based on "value" not sale price. Therefore, an under market sale, may be assessed significantly higher than the sale price. Notice I am saying "should" and "may" since nothing is set in stone, but I wouldn't rely on the lower potential assessed value.
FYI - this is based on my past professional experience as an ex-Deputy Assessor for LA County. I was one of those people that used to assign some of the assessed values to tfr's, so I have some experience.
2) Market rents for similar properties in that neighborhood, are between $2850-$3,600, with the $3,600 being a "gorgeously updated craftsman," on a larger lot than yours. It also has a bonus room with the potential of a home office or 3rd bedroom. And 2 of the other higher rents are for 3 bedrooms homes ($3,350-$3,375).
Therefore, I wouldn't count on the higher range of rent for yours. The 2 bed/1 bath houses have rented in the range of $2,600-$2,900/mth, and they look like they are in average condition with average quality. So, renovated and having a 2nd bathroom, may help you get more rent. Also, they seem to be renting fast between 3-11 days on market, with one being 62 days (out of 7 total rentals).
3) So with those previous #'s, there would be a negative cashflow
SP - $850k
Down pmt - $100k
Loan- $750k
Pmt @ 3% = $3,162/mth
taxes = $815/mth (with new assessment)
insurance = $150/mth (guestimate)
PITI - $4,127/mth
Of course, those #'s are for a conventional purchase and new loan @ market rates. Those #'s can change drastically, if your Dad is carrying the paper (loan) and giving you favorable terms, or not charging interest, etc.
4) There is an option of converting the garage into an ADU, or adding an ADU over or adjacent to the garage. A 1 bed/1 bath 500sf guest house, in the neighborhood, recently rented for $1,700/mth after only 4 days on market.
So, let's say you can add/convert to an ADU for around $150k, that translates to around $630/mth additional loan pmt ($150k @ 3%), which would net you around $1,070 ($1,700-$630) in rent from the ADU, not taking into account additional property tax assessment or insurance.
Actually, I just noticed that previous $3,600/mth craftsman rental is the same property as the guest house ($1,700/mth) rental. So, all in all, it is very similar to what yours would be with an ADU, and that one is getting a total of $5,300/mth for both units (keep in mind that house's 3rd bedroom or office potential).
Looking at Pasadena's STR rules, it appears the property has to be a "primary residence" of the host, defined as where they reside at least 9 months per year. Seems to exclude your situation.
Also, be careful, if you are considering having your Dad transfer the property to you now, since that will affect the tax base value later, if you liquidate it and have to pay on the gain. That's referring to income tax rules, not property taxes. Talk to a CPA, if you are considering that.
Also, there are the new Senate Bills, SB9 and SB10, which are aimed at increasing density on R1 zoned lots. I am not going into those, since I haven't fully reviewed them yet, but those might provide more options to your situation.
That's some info and #'s for you to chew on. Do your own calculations, etc, and you can get a clearer picture of what might work for your situation. And as always, don't make any major decisions based on advice from this site (or anywhere else online), at face value, without consulting specific professionals regarding your specific situation, etc. (i.e. CPA's, attorney's, Brokers, etc.). P.S. my analysis was based on what I believe to be the actual property, which I was able to find, based on the little info in your original post.