SHOW WORK ON EXCEL

You plan to purchase an office building for $3 million, selling it at the end of year 5 at a cap rate of 10%. Selling cost will be $60,000 at the end of year 5.

Over the next year, its 10 suites will rent for $4,000 per month per suite.

Assume vacancy and collection losses of 10%. Miscellaneous income is $5,000 per year, while operating expenses and capex together are 30% of EGI plus a fixed component of $30,000. The miscellaneous income, fixed costs, OE-ratio, and V&L-ratio will not change YoY.

A 20-year amortization, 5-year mortgage can be obtained for 6% at a wide range of LTVs, with no fees.

Your RE market analysis suggests the following outcomes for PGI growth over the next 6 years: -2% (10% probability), 0% (20%), 3% (40%), 5% (20%), and 8% (10%).

If the rf rate is 0.5%, what are the Sharpe ratios for an unlevered investment and an investment at 50% LTV? Which alternative is better assuming equity capital opportunity cost is not a concern?