100k for home renovation: Cash or Heloc while cash earns interest

[Abby S.]

I'm trying to understand whether it's strategically wiser to use cash or a home equity loan to pay for that renovation. Hoping someone can check my thinking:

For the sake of keeping this example simple - $1M multi family building that after putting in 100k of renovation will benefit in an additional $1000 in rent increase per month. The cash on cash annual return is ($1000 x 12)/$100,000 = 12%

$1M loan @ 20% down @ 5.125% = $4355/month

$100k home equity loan @ 6% @ 20 years = $716/month for 20 years

1. 1. Combining the two into a single number I can compare gets me to a blended interest rate of 5.222% at $1.1M, is that correct?
2. 2. Separately, if $100k is earning 3.25% in a savings account (yes, I know that's high currently), is my effective rate of that loan actually (6% - 3.25% = 2.75%?)
3. 3. If I'm still gaining $284 ($1000-716) a month from the increase in rent, and getting $275/month from interest on the 100k that's still in the bank, my annual cash on cash return (($284+$275)*12)/$100,000 = 6.78% while still having 100k to access, correct?
4. 4. My gut tells me keeping cash on hand feels like the better option, but really wanting to remove "feeling" from this - something in my math "feels" off
5. 5. Or should I be looking at the CoC return for the entire monthly payment vs. total rent, not just the incremental return of the 100k?