Question

Suppose that you are contemplating an investment in an apartment building. Use the information provided below to answer the questions that follow:

Type of Property: Apartment Building

Number of Units: 30

Average Rent: $1,500 per unit per month

Expected Growth in Rents: 5% per year

Vacancy and Collection Losses: 5% of Potential Gross Income

Other Income: $50 per unit per month

Expected Growth in Other Income: 3% per year

Operating Expenses: 35% of Effective Gross Income

Capital Expenditures: 4% of Effective Gross Income

Selling Expenses: 5% of Future Selling Price

Going-Out Cap Rate: 6.5%

Expected Purchase Price: $5.25 million

Loan Terms:

Loan Amount: 85% of purchase price

Interest Rate: 4.5% per year with monthly payments and monthly

compounding

Amortization Term: 30 years

a. What is the net present value of the before-tax unlevered cash flows if you assume a

five-year holding period and a discount rate of 12%?

b. What is the internal rate of return of the before-tax levered cash flows if you still

assume a five-year holding period?

Answer 1

Solution:

Details given in the question:
Number of Apartment Units			30
Average Rent/month			$                1,500	per unit
Expect Growth of rent			5%	annual
Vacancy Loss			5%	of potential gross income
Other Income/month			$                50.00	per unit
Expect Growth of other income			3%
Operating Expenses			35%	of effective gross income
Cap Ex			4%	of effective gross income
Selling Expense			5%	of Future selling price
Going out cap rate			6.5%
Expected purchase price of property			$ 52,50,000.00
Loan			85%
Interest rate compounded monthly			4.5%
Amortization term			30 years
Terminal Cash Flow
		Last year NOI/Going out cap rate
Expected sale price of the property		$ 64,38,138.65
Selling Expense		$    3,21,906.93
Total expected realization		$ 61,16,231.72
Computation of expected income and cash flow
	Year 1	Year 2	Year 3	Year 4	Year 5
Income
Rent	$         5,40,000.00	$    5,67,000.00	$    5,95,350.00	$         6,25,117.50	$    6,56,373.38
Other Income	$             18,000.00	$       18,540.00	$       19,096.20	$            19,669.09	$       20,259.16
Total	$         5,58,000.00	$    5,85,540.00	$    6,14,446.20	$         6,44,786.59	$    6,76,632.53
Vacancy Loss	$             27,000.00	$       28,350.00	$       29,767.50	$            31,255.88	$       32,818.67
Effective Gross Income	$         5,31,000.00	$    5,57,190.00	$    5,84,678.70	$         6,13,530.71	$    6,43,813.86
Expenses
Operating Expense	$         1,85,850.00	$    1,95,016.50	$    2,04,637.55	$         2,14,735.75	$    2,25,334.85
Net Operating Income	$         3,45,150.00	$    3,62,173.50	$    3,80,041.16	$         3,98,794.96	$    4,18,479.01
Capital Expenditure	$             21,240.00	$       22,287.60	$       23,387.15	$            24,541.23	$       25,752.55
Net un-levered Cash flow	$         3,23,910.00	$    3,39,885.90	$    3,56,654.01	$         3,74,253.73	$    3,92,726.46
Terminal Cash Flow					$ 61,16,231.72
Unlevered Cash Flow	$         3,23,910.00	$    3,39,885.90	$    3,56,654.01	$         3,74,253.73	$ 65,08,958.17
Interest Expense	$         1,97,744.53	$    1,91,050.78	$    1,84,357.03	$         1,77,663.28	$    1,70,969.53
Net levered Cash Flow	$         1,26,165.47	$    1,48,835.12	$    1,72,296.98	$         1,96,590.45	$ 63,37,988.64
NPV of before tax unlevered cash flow		$ 47,45,222.28
IRR of before tax levered cash flow
Year	Cash Flow
0	$     -52,50,000.00
1	$         1,26,165.47
2	$         1,48,835.12
3	$         1,72,296.98
4	$         1,96,590.45
5	$       63,37,988.64
IRR	6.16%

Note: Interest schedule has not been presented here as it would have unnecessarily elongated the answer.