Worksheet $$ IRR, NPV and Equity Multiple $($Please show all work$)$

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. There is currently no vacancy, but vacancy is expected to increase to $3\mathrm{.}0\%$ as the new supply comes into the market. Notwithstanding that expectation, 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 $($from the base amount of expenses, not the percentage rate$)$ 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 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. They also want to see the NPV$,$ IRR and Equity Multiple on this potential investment.

$1.$ Katie reruns the DCF return. The market is assuming the discount rate to be $8\%$ and the reversion $($aka terminal or exit$)$ cap rate is estimated to be $7\%.$ What is the new DCF Katie calculates? Hint: the reversion value is based off of Year $6$ NOI.

$2.$ What is the estimate of value using the Direct Cap $($Income$)?$

$3.$ To arrive at the refined bid price, Katie weights the Cost Approach $10\%,$ the Market Approach $30\%,$ Direct Cap $20\%$ and the DCF $40\%.$ What is the bid price Katie presents to the client.

$4.$ Katie knows that the projected IRR is calculated from the bid price, estimated NOIs and Reversion Value less $4\%$ transaction costs. What is the IRR Katie calculates? What is the NPV$?$ We are looking for a net calculation, that is$,$ a comparison against the discount rate, not a standalone view of IRR and NPV because the client needs the information presented as a "make the investment or not" calculation.

$5.$ Katie$$s client also wants to know the equity multiple for the investment. What is the equity multiple Katie calculates?