In other words the $3k/month would not matter if you turn out to be making a 3% cap rate in a 9% cap market.Next, how is spending $135k going to improve your gross income from $5k to $9k and how long will that take?

A typical resident would see rents climb at a decent clip over a two year period as the apartment interior, exterior is renovated and improved property management increases desire and pride in staying.  

I have 750+ credit score and no debts.

The fact that you're investing from a distance doesn't improve the situation. 

L.I write about No Bank No Credit financing.If you want to play in the sandbox of no money no credit, you need:Private Lenders (knowledge of self directed IRAs)JV Partners (splitting profits w cash partners)Creative Financing (sub2, land contracts, installment sales, TIC contracts, using notes, etc)I used to live in Mt Kisco, Westchester.I get what you are trying to do.Good luck!

They charged $39 for the measure that was credited towards the install.

Or should I require him to pay the deposit and maybe give a discount on monthly rent equal to amount of work done (monthly discount applied until amount is credited).

Reverses can work with timing issues, needs for construction or improvement or if you're wanting to double dip appreciation and cash flow for a period of time.  

 $60,000 capital improvement for a conservative $1400 in additional rents.  

If you're credit is good it's likely a better option because there is no upfront mortgage insurance premium like there is for an FHA loan.