Parthenon Equities owns an $100,000$ RSF office building in suburban Atlanta. One of its tenants, Red Door Marketing leases $8,000$ SF with a lease that expires on March $31$ next year. Red Door is currently paying a base rent of $$21$ per RSF through lease expiration. An analyst for Parthenon is projecting rents for the next year and isn't sure what to assume for the $8,000$ SF leased by Red Door. He thinks there is a $75\%$ chance that Red Door will renew. If they renew, the analyst believes they will pay $$22/$RSF in base rent and will negotiate $2$ months of free rent at the beginning of their renewal period. If they do not renew, the space will likely sit vacant for $6$ months and a new tenant will negotiate a market lease. Current market terms are $$24/$RSF for base rent and $4$ months of free rent.

a$.$ What should the analyst assume for market rent $($$$/$RSF$)$ at rollover $($after lease expiration$)?$

b$.$ How many months of vacancy should the analyst assume at rollover?

c$.$ How many months of free rent should the analyst assume Parthenon will realize at rollover?

d$.$ How much income from base rents should the Parthenon analyst forecast for Red Door's $8,000$ RSF suite next year?

e$.$ Even though a landlord does not receive base rent both when a space is vacant and during the free rent period, why might a landlord prefer the free rent period to vacancy?