You are considering the purchase of an apartment complex. The following assumpti

Question

You are considering the purchase of an apartment complex. The following assumptions are made:

•           The purchase price is $1,050,000.

•           Potential gross income (PGI) for the first year of operations is projected to be $175,000.

•           PGI is expected to increase at 3.5 percent per year.

•           5% vacancies are expected.

•           Operating expenses are estimated at 45 percent of effective gross income. Capital expenditures are estimated at 15 percent of effective gross income.

•           The market value of the investment is expected to increase 5.25 percent per year.

•           Selling expenses will be 4.25 percent.

•           The holding period is 4 years.

•           The appropriate unlevered rate of return to discount projected NOIs and the projected NSP is 12.5 percent.

•           The required levered rate of return is 14 percent.

•           70 percent of the acquisition price can be borrowed with a 30-year, monthly payment mortgage.

•           The annual interest rate on the mortgage will be 7.5 percent.

•           Financing costs will equal 3.5 percent of the loan amount.

•           There are no prepayment penalties.

a.         Calculate net operating income (NOI) for each of the four years. (1 pts)

b.         Calculate the net sale proceeds from the sale of the property. (1 pts)

c.         Calculate the net present value of this investment, assuming no mortgage debt. Should you purchase? Why? (3 pts)

  d.         Calculate the internal rate of return of this investment, assuming no debt. Should you purchase? Why? (1 pts)

e.         Calculate the monthly mortgage payment. What is the total per year? (1 pts)

f.          Calculate the loan balance at the end of year 4.  (1 pts)

g.         Calculate the levered required initial equity investment. (1 pts)

h.         Calculate the before-tax cash flow (BTCF) for each of the four years. (1 pts)

i.          Calculate the before-tax equity reversion (BTER) from the sale of the property.  (1 pts)

j.          Calculate the levered net present value of this investment. Should you purchase? Why? (3 pts)

   k.         Calculate the levered internal rate of return of this investment (assuming no debt and no taxes). Should you purchase? Why? (1 pts)

Explanation / Answer

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Market value of house increses by 5.25% every year. So it's value at the end of four years will be = $1050000 * (1+5.25%)4 = $1288480.105

Selling Price at the end of holding period = $1288480.105

Selling Expenses = 4.25% of Selling price

Net Sales proceeds = $1288480.105 - 4.25% of $1288480.105 = $1233719.701

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Will not purchase as NPV is negative.

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IRR is the rate at which NPV is 0

66500/(1+IRR) + 68827.5/(1+IRR)2 + 71236.46252/(1+IRR)3 + 73729.73868 +1233719.701/(1+IRR)4

Using IRR function in excel, IRR is calculated as 10.3937%

This rate is again lower than required rate of return of 12.5%. Hence this project should not be accepted.

Year 1 year 2 Year 3 Year 4 PGI (increases by a factor of 1.035) 175000 181125 187464.375 194025.6281 Less Vacancies (@5%) 8750 9056.25 9373.21875 9701.281405 Effective Gross Income or EGI 166250 172068.75 178091.1563 184324.3467 Less Operating Expenses (@45% of EGI) 74812.5 77430.9375 80141.02034 82945.95602 Less Capital Expenses (@15% of EGI) 24937.5 25810.3125 26713.67345 27648.65201 Net Operating Income 66500 68827.5 71236.46252   73729.73868  

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