Katie Scarlett is analyzing the same $15-$unit apartment building for a client for possible purchase. She expanded her analysis from just the DCF $($Income$)$ to include the Direct Cap $($Income$),$ the Cost and the Market approaches to value. Remember she estimated the gross potential rents are $$250,000$ in Year $1$ and are expected to grow $5\%$ for through Year $3$ and then by $3\%$ starting in Year $4$ as new supply comes on line. Katie assumes a more typical vacancy and credit risk of $5\%$ for all periods. She refines her estimate for expenses since they run more inline with $45\%$ of Effective Gross Income at Year $1$ and will grow independently at the inflation rate $3\%$ per year.

She analyzed the replacement costs in the market and they are approximately $$155,000/$unit including cost of land. She identifies three sales comparables of similar apartment properties in the market that have sold within the last $6$ months. Based on these recent sales, the average cost is $$140,000/$unit$.$ The average cap rate is $6\mathrm{.}5\%$

Katie is going to analyze the investment on a $5-$year hold. The client wants Katie to refine the bid price to take into consideration both the cost and market approach to value.

What is the IRR Katie calculates? What is the NPV$?$