What if there is no lease, Moe? What if it's month to month? If so, it's not a leased fee estate, and market rent would apply.
However, given the rent controls in place, and the fact that the tenant cannot be evicted so that the landlord can find someone to pay market rent, it's important to note that the owner's estate is like a leased fee estate because the tenant's interest is very much like a leasehold estate having positive value due to the spread between the lower contract rent and the higher market rent.
Technically, the operating income statement should consider market rents and not contract rents. However, without a doubt, that is misleading because the owner is not as of the date of the appraisal either receiving, or able to receive, market rent.
For this reason, I would use contract rents with an explanation such as I gave above. In addition, I would use a 0% vacancy rate. Further support for your unorthodox use of contract rent for income and the no-vacancy estimate may be adduced by noting the behavior of tenants of rent-controlled housing, who move out of such housing only when they have to, not really when they want to, and are entrenched due to a legal advantage conferring property rights essentially akin to leasehold.
By the way, I had no guidance in this analysis expect for my own knowledge of appraisal theory and procedure, so I may be wrong. I wouldn't offer these comments if I didn't think they could be useful, and I searched
The Appraisal Of Real Estate index for rent control but found nothing on the subject. There is very likely specialized literature on this topic but I don't know of, or have access to, it.
Most importantly, if you use market rent, then explain why you didn't use contract rent in light of the rent controls in effect, and if you use contract rent, explain why you didn't use market rent. Ideally, you would produce an operating income statement using both scenarios.
Lastly:
it is common to pay existing tenants relocation.
This is not a customary real estate expense. It becomes a real property expense only because of the distorting effect of rent controls. So while it is common in the affected market area, it is still not recognized as an operating expense proper.