When people ask these questions, they're usually looking to justify renovations as "investments" as opposed to the expenses that they really are, and doing some mental gymnastics to justify the cost.
You will need to share more info for us to give you valid input l, but here's the basic run down on renos as an "investment".
Repairs: not an investment, this is basic maintenance of your asset. If you upgrade a system while doing maintenance, then that value will depreciate over time, but some will possibly be maintained in the sale value. So not an investment, just maintenance.
Additions: adding a bedroom, bathroom, square footage: like an addition or even finishing a basement. These can all add significant value to your home, but that value may or may not exceed the cost.These can be an investment, but aren't always, especially if done poorly, like adding a bathroom in the middle of a living room (yes, I have seen this).
Layout: This is major, costly work and can possibly add value beyond the cost, but often won't because you haven't added anything compared to what you spent, and layout trends can change.
Other renos: cosmetic, kitchen, bathroom, etc. Almost NONE of these will ever, ever pay off as any form of investment.
If you are flippers who can DIY at a professional level, know how to spot bargain houses, and know what sells, then you can make excellent money, but that's not what we're talking about.
If you are living in your home and planning renos for your own use and pleasure, then it's not an investment, it's run of the mill consumption. First, unless you can DIY to a professional level, it will look DIY. If you pay for professional results, you will pay too much to recoup the cost.
Regardless of whether you DIY or pay professionals, if you live in the space for 5+ years, the renos will rapidly become dated and damaged. It's hard enough to recoup the money on a brand new reno, it's a fantasy to recoup it on cabinets and tile work that has seen 5+ years of use and changes in style go by.
Now, if you buy an absolutely hideous, dated place with wood paneling everywhere, and a tiny galley kitchen, then if you renovate and bring it into the 21st century and open up the kitchen, then yeah, you will probably retain some of the value of the renos, but not likely the full value, so it's still not an investment.
So the smart way to perceive renovations of a house you aren't planning to sell right away is as maintenance or as standard lifestyle inflation spending. Then if you do retain any residual value of the renovation, it's a bonus. But you never know, by the time you sell, your house may only be valuable as a tear down for developers and no one will give a fuck that your backsplash is subway tiles oriented in a herringbone pattern.
Lastly, I don't understand ANY of your math of how your reno has anything to do with your loan. Can you or someone explain that to me? I'm really confused. How does the lifetime of the loan have anything to do with the cost and return of renos???
The math on whether or not you will get a return on your renos is the same whether or not you have a mortgage.