P$9.$ You are considering buying a small commercial property for $$1,250,000.$ Rental

income is estimated at $$200,000$ during the first year, and you expect rental income

to grow at $3$ percent per year thereafter. Vacancy and collection losses are expected

to be $10$ percent. Operating expenses should be $35\%$ of effective gross income. Your

lender agreed to a $30-$year, fully amortizing, $70$ percent loan at a fixed rate of $11$

Page $3$

percent, with monthly compounding and no prepayment penalties. You expect the

property to appreciate in value at $3$ percent per year, and that you will own the

property for $3$ years and then sell it$.$ You determine that the building represents $90\%$

of the acquisition price. The building should be depreciated using the straight line

method over $39$ years. Your marginal tax rate is $36$ percent, and you have enough

passive income from other activities that any passive losses here would not be subject

to any passive activity loss limitations$.$ Capital gains from price appreciation will

be taxed at $20$ percent and depreciation recapture will be taxed at $25\%.$

$($a$)$ What would be the after$-$tax internal rate of return on equity invested?

$($b$)$ You are also considering an alternative investment opportunity of similar risk

that would bring you an annualized after$-$tax return of $15\%.$ Should you invest

in this office building? Why or why not?

$($c$)$ What is the NPV of this investment, assuming a $15\%$ discount rate?

$($d$)$ What is the going$-$in cap rate? What is the terminal or going$-$out cap rate?

$($e$)$ Now assume the investment is financed with a $70\%$ loan$-$to$-$value, interest$-$only

mortgage with a fixed $11\%$ interest rate. What would be the after$-$tax IRR?