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  1. Mr. Davies owns an apartment building in Boston and has no other wealth. The building’s apartments generate a rental income, and Mr. Davies projects that next year’s free cash flow will be $250,000. Mr. Davies has lived in Boston all his life, and, thanks to his friendships with contractors and building inspectors as well as his willingness to do some repair work himself, he is able achieve low maintenance costs for the building.

Mr. Davies was recently approached by First Union Real Estate Corporation, a New York-based REIT, which owns rental properties nation-wide. First Union would like to acquire Mr. Davies’ building and continue to rent out the apartments. Mr. Davies estimates that First Union would have substantially higher maintenance costs and projects that under First Union’s management the building will generate a free cash flow of only $300,000 next year.

The volatility of free cash flows is 30% per year under either Mr. Davies’ or First Union’s management, and their market beta is 0.5. The expected market risk premium is 5%, and the volatility of market returns is 15% per year. The current yield on a 30-year treasury bond is 3%.

What is the maximum that First Union would pay for the building? (Hint: what discount rate should First Union use to value the building?) How much is the building worth to Mr. Davies? (Hint: what discount rate should Mr. Davis use for his valuation?) Would Mr. Davies ever agree to sell the building to First Union? Assume that free cash flows are projected to grow at the rate of inflation, or 3% a year, in perpetuity. Hint: use the Gordon Growth Model to value the building. (15 points)


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