Question

Suppose that you are considering an investment in an apartment building. The specifics are: - The building is five years old, has a 80 percent occupancy rate, and has an expected useful life of 25 years. Assume that this occupancy rate is expected to continue for the life of the building. - There are 90 2-bedroom units, 100 1-bedroom units, and 70 studios. - The 2-bedroom units rent for $3000 per month, the 1-bedroom units for $2200 per month, and the studios for $1200 per month. - Current rent control laws will prevent the rents from ever being raised. - The estimated annual maintenance cost for the building is $1200000 per year (this is independent of the number of apartments rented). - There is an additional estimated maintenance cost at $175 per unit per month, when each unit is rented. - There will be no salvage value to the building in 25 years, but it is estimated that it will cost 5 million dollars at that time to demolish the building as will be required in the purchase contract. (You are not purchasing the land. You will have a 25-year lease of the land, which is paid for in the purchase of the building.) - The asking price of the building is $32 million. - The tax-rate is 30%, and assume the building will be fully depreciated over its useful life. - The WACC is 8%. Develop the pro-forma income statement, compute the Operating Cash-Flows and NPV. What is the OCF breakeven for the project (roundup nearest unit)?

Answer 1

Let us walk over the revenues and costs.

Revenues (per year): -

• One 2-bedroom units bring revenue of $3,000/month and hence, $36,000/year. Thus, maximum revenues from 2-bedroom units are $(36,000 X 90) = $3,240,000/year
• One 1-bedroom unit bring revenue of $2,200/month and hence, $26,400/year. Thus, maximum revenues from 2-bedroom units are $(26,400 X 100) = $2,640,000/year
• One studio unit bring revenue of $1,200/month and hence, $14,400/year. Thus, maximum revenues from 2-bedroom units are $(14,400 X 70) = $1,008,000/year
• Total maximum revenues is obtained by adding the above three: -

$(3,240,000+2,640,000+1,008,000)/year = $6,888,000/year

• Given 80% occupancy rate, total revenues obtained: - $(6,888,000 X 0.8)/year = $5,510,400/year

Expenses (per year): -

• Maintenance cost of $1,200,000/year
• Total units are 260. Additional maintenance costs of $175/month per unit or $2,100/year per unit. Hence, additional maintenance costs are $(2,100 X 260 X 0.8) = $436,800/year
• Depreciation cost can be calculated as asking price minus salvage value divided by the remaining useful life using the straight-line depreciation method. Given salvage value is 0, the expected useful life is 25 years and asking price is $32,000,000.

The depreciation cost is calculated as $(32,000,000/25) = $1,280,000/year

• There is no other recurring costs. Thus, the total costs are obtained by adding the above three: -

$(1,200,000+436,800+1,280,000)/year = $2,916,800/year

Net Income (per year): -

• Net income (before tax) can be calculated as: - $(5,510,400-2,916,800)/year = $2,593,600/year
• Net income (after tax) can be calculated as: - $2,593,600 X 0.7 = $1,815,520/year

Operating Cash Flows: -

• Operating Cash Flows are obtained using the formulae: -

• At year 0, there is a purchase cash outflow of $32,000,000.
• From years 1 to 24, Operating Cash Flow can be calculated as adding depreciation back to net income after tax. Hence, Operating Cash Flow is $(1,815,520 + 1,600,000)/year = $3,415,520/year
• In year 25, there is additional cash outflow of $5,000,000 for demolishing. Hence, operating cash flow in year 25 is $(3,415,520 - 5,000,000)/year = - $1,584,480/year

NPV calculations can be obtained by using NPV function in excel. Given WACC is 8%, write $32,000,000 in cell A1, $3,415,520/year in cells A2 to A25, and -$1,584,480/year in cell A26. Use formulae:- NPV(8%,A2:A26) - A1 to get NPV of $3,729,822.04.

Using trail and error to calculated NPV after different years, we can check that in terms of time value, NPV(8%,A2:A19) - A1 gives $9,687.95. Hence, the breakeven period in terms of time value is 18 years.