You are considering the purchase of an apartment complex The

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. Show all work. (2 pts)

b.         Calculate the net sale proceeds from the sale of the property. Show all work. (2 pts)

c.         Calculate the net present value of this investment, assuming no mortgage debt. Should you purchase? Why? Show all work. (4 pts)

  d.         Calculate the internal rate of return of this investment, assuming no debt. Should you purchase? Why? Show all work. (1.5 pts)

e.         Calculate the monthly mortgage payment. What is the total per year? Show all work. (2 pts)

f.          Calculate the loan balance at the end of year 4.  Show all work. (2 pts)

g.         Calculate the levered required initial equity investment. Show all work. (2 pts)

h.         Calculate the before-tax cash flow (BTCF) for each of the four years. Show all work. (2 pts)

i.          Calculate the before-tax equity reversion (BTER) from the sale of the property.  Show all work. (2 pts)

j.          Calculate the levered net present value of this investment. Should you purchase? Why? Show all work. (4 pts)

k.         Calculate the levered internal rate of return of this investment (assuming no debt and no taxes). Should you purchase? Why? Show all work. (1.5 pts)

Solution

a.         Calculate net operating income (NOI) for each of the four years. Show all work.

b.         Calculate the net sale proceeds from the sale of the property. Show all work. (2 pts)

Growth in Market Value of the house is going to increase by 5.25% every year for four years.

Value at the end of four years = Purchase Price * (1+growth rate) = 1,050,000 * (1.0525)⁴ = $1,288,480.105

Selling expenses = 4.25% of $1,288,480.105 = $54,760.40

Net Sales Proceed = $1,288,480.105 - $54,760.40 = $1,233,720

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

As per the Net Present Value is negative, it cannot be the right option to purchase.

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

IRR is calculated as per the following formula:

IRR is the internal rate of return when NPV is zero

Hence,

We can calculate IRR with the help of financial calculator, by following the steps:

Step 1: Clear the existing memory by pressing CF->2nd->CE/C

Step 2: Enter the Initial Cash Flow (CF0) = -1050,000

Then enter the cash inflows for four years as:

CF1-> $66,500

CF2 - > $68,827.5

CF3 -> $71,236.46

CF4 -> $1,307,449

Now press IRR button and then press CPT

You will get the IRR.

Hence the IRR calculated is 10.39%

The required rate of return is 12.5%

IRR = 10.39%

Since IRR is less than required rate of return

Hence it should be rejected

Particulars	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