You've graduated from university and immediately begin to put your business education to good use by becoming a property developer. Having been gifted a large plot of vacant land as a graduation present, you decide to begin your career by constructing a warehouse on that land, which you know you can rent to Amazon.

 Your general contractor tells you that you can accomplish development and start renting
its space one month from when you start development and you know, beginning in month one, you can earn a certain monthly rent of $100,000.00. 1 After charming your banker and engaging in careful research, you also find that you can debt-finance the entire development with an interest only mortgage. 

This mortgage has an initial balance of $800,000.00, a monthly coupon rate of y = .10, and a maturity of one month. After assiduous reading of the Financial Post and a long conversation with your real estate finance professor one night in a dive bar, you learn that there is a future contingency that could affect your return to this development: its virtually certain that, like the economy as a whole, the market for warehouse space will either boom or bust two months from now. You know, as of today (t = 0), that one or the other outcome will occur, but as of today you don't know which one.

Based on the economic data currently available and the best available forecasts, however, you (correctly) believe that each alternative has an equal chance of occurring. Fortunately, you have a classmate working at Statistics Canada whom you can bribe into revealing new information about the economy next month (t = 1) which will be sufficient to reveal whether the market booms or busts in month two (t = 2).

 You carefully constructed a pro forma which incorporates the following alternative scenarios:

 If the market booms in month two, you will earn, with certainty, a monthly rent of $150,000.00 beginning in that month (t = 2) and in all future months thereafter.

• If the market busts in month two, you will earn, with certainty, a monthly rent of $50,000.00, also beginning in month two and in all future months.
• Your desired monthly yield on the project is also the same as the monthly mortgage coupon rate (10%), and so this is the value you will use in calculating the present value of the development.

Since you own the site for the development and have no rivals for renting warehouse space to Amazon at this location, you can choose to begin development immediately (t = 0) and start collecting rent from Amazon one month from now (t = 1), or you could wait and begin development a month from now, when you will know the state of the market beginning in month two and thereafter or you could simply abandon the development.

 This ability to delay your development and choose to proceed or abandon forces you to consider both the advantages and disadvantages of choosing to delay and of choosing to proceed with the development immediately 2 The pressure is on because you must decide what to do today. Suddenly, you remember your previous two courses in real estate finance and apply the skills and insights you learned in them to make the decision that maximizes the current discounted value of your equity. You must calculate the values needed to answer the following question

 

Questions:

 a. what is the current (date 0) market value of your equity if you start development today?

 b. what is the present discounted value of expected revenue to the development, as of today, if you start development a month from now, knowing the economy will boom?

 c. what is the expected revenue to the development, as of today, if you start development a month from now, knowing that the economy will bust?

 1 To be precise, if you begin development immediately (at t = 0) you begin receiving rent in month one (t = 1) but if you start development in month 1, you begin receiving rent in month two (t = 2.)

2 You should, at this point, think for a moment (before proceeding) about what these advantages and disadvantages are with respect to the maximization of your current equity value.

Simplified parameters

Monthly Rent = $100,000

 Mortgage = $800,000

Monthly Coupon Rate = .10 

Maturity = 1 Month

 Today (t=0)

Next Month (t=1) 

Two Months (t=2)

 Boom = $150,000 Monthly Rent in Month Two

Bust = $50,000 Monthly Rent in Month Two

 

Yield = 10% (used for the PV of development)