Question

You are considering the purchase of an apartment complex. The following assumptions are made: • The purchase price is $1,150,000. • Potential gross income (PGI) for the first year of operations is projected to be $195,000. • PGI is expected to increase at 4 percent per year. • 3% vacancies are expected. • Operating expenses are estimated at 30 percent of effective gross income. Capital expenditures are estimated at 10 percent of effective gross income. • The market value of the investment is expected to increase 4.25 percent per year. • Selling expenses will be 3 percent. • The holding period is 4 years. • The appropriate unlevered rate of return to discount projected NOIs and the projected NSP is 14.5 percent. • The required levered rate of return is 15.5 percent. • 75 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 percent. • Financing costs will equal 4.5 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.

Answer 1

a. Calculate net operating income (NOI) for each of the four years.
	1	2	3	4
Potential gross income (PGI) 4% increase each year after Ist Year.	$195,000.00	$202,800.00	$210,912.00	$219,348.48
Less: Annual vacancy rate = 3% x PGI	$5,850.00	$6,084.00	$6,327.36	$6,580.45
Effective gross income (EGI)	$189,150.00	$196,716.00	$204,584.64	$212,768.03
Less: Annual operating expense = 30% x EGI	$56,745.00	$59,014.80	$61,375.39	$63,830.41
Less: Capital expenditures (CAPX) = 10% x EGI	$18,915.00	$19,671.60	$20,458.46	$21,276.80
Net operating Income (NOI)	$113,490.00	$118,029.60	$122,750.78	$127,660.82
b. Calculate the net sale proceeds from the sale of the property.
Selling price = $1,150,000 x (1+ 4.25%)^4	$1,358,320.00
Less: Selling expenses (at 3% of SP)	$40,749.60
Net sale proceeds	$1,317,570.40
Net sale proceed will be added to year 4 NOI for calculating NPV.
c. Calculate the net present value of this investment, assuming no mortgage debt. Should you purchase? Why?
Year	Cash Flow	PV @ 14.5%	Present Value
0	-$1,150,000.00	1	-$1,150,000.00
1	$113,490.00	0.873362445	$99,117.90
2	$118,029.60	0.762761961	$90,028.49
3	$122,750.78	0.666167652	$81,772.60
4	$1,445,231.21	0.581805809	$840,843.92
		NPV	-$38,237.09
No, The property should not be purchased because NPV is negative..
d. Calculate the internal rate of return of this investment, assuming no debt. Should you purchase? Why?
Year	Cash Flow
0	-$1,150,000.00
1	$113,490.00
2	$118,029.60
3	$122,750.78
4	$1,445,231.21
IRR	13.40%
No, The property should not be purchased because IRR is less than unlevered required rate of return is 14.50 percent