An investor would like to purchase a new apartment property for $$2\mathrm{.}2$ million. However, she faces the decision of whether to use $70$ percent or $80$ percent financing. The $70$ percent loan can be obtained at $4$ percent interest for $20$ years. The $80$ percent loan can be obtained at $5$ percent interest for $20$ years.

NOI is expected to be $$150,000$ per year and increase at $2$ percent annually, the same rate at which the property is expected to increase in value. The building and improvements represent $80$ percent of value and will be depreciated over $39$ years $(1-$: $39$ per year$)$ with no mid$-$month convention for year $1.$ The project is expected to be sold after five years. Assume a $35$ percent tax bracket for ordinary income, a $25$ percent for depreciation recapture, and $20$ percent for capital gains taxes.

Required:

a$.$ What would the BTIRR and ATIRR be at each level of financing $($assume monthly mortgage amortization$)?$

b$.$ What is the break$-$even interest rate $($BEIR$)$ for this project?