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

Step 1: Calculate the Effective Gross Income as given below. As these are straight forware calculation I am not giving the detailed formulas.

Items	Year 0	Year 1	Year 2	Year 3	Year 4	Year 5
Average Rent per month		$       1,500.00	$       1,575.00	$       1,653.75	$       1,736.44	$             1,823.26
Growth Rate of Rent	5%
Units	30
Rentals per Annum		$ 540,000.00	$ 567,000.00	$ 595,350.00	$ 625,117.50	$        656,373.38
Other Income per month		$             50.00	$             51.50	$             53.05	$             54.64	$                   56.28
Growth in Other Income	3.0%
Units	30
Other Income per annum		$    18,000.00	$    18,540.00	$    19,096.20	$    19,669.09	$           20,259.16
Total Gross Income before losses		$ 558,000.00	$ 585,540.00	$ 614,446.20	$ 644,786.59	$        676,632.54
Vacancy loss	5%	$    27,900.00	$    29,277.00	$    30,722.31	$    32,239.33	$           33,831.63
Effective Gross Income [A] Total Gross - Vacancy		$ 530,100.00	$ 556,263.00	$ 583,723.89	$ 612,547.26	$        642,800.91

Step 2: Calculate Expenses.

The loan amount is 85% of the Initial Investment. There is no information given regarding whether Principal is repaid or not. So assumption made is there is no principal repayment, only interest is paid monthly.

Expenditures		Year 1	Year 2	Year 3	Year 4	Year 5
Operating Expense [B]	35%	$ 185,535.00	$ 194,692.05	$ 204,303.36	$ 214,391.54	$        224,980.32
Capital Expenditure [C]	4%	$    21,204.00	$    22,250.52	$    23,348.96	$    24,501.89	$           25,712.04
Loan Amount - 85% of Purchase Price	$          4,462,500
Interest = 4.5% compounded Monthly		$    16,734.38	$    16,734.38	$    16,734.38	$    16,734.38	$           16,734.38
Annual Payout on Interest [D]		$ 200,812.50	$ 200,812.50	$ 200,812.50	$ 200,812.50	$        200,812.50

Step 3: Calculate NPV of Unlevered free cash flow. This is the cash flow before interest, capital expenditure.

Resale Value = Net Operating Income in Last year /Going Out cap rate = $417,820.59/6.5%

PV = cashflow/(1+r)^n

Unlevered Free Cash Flow	Year 0	Year 1	Year 2	Year 3	Year 4	Year 5
Operating Income [A-B]		$ 344,565.00	$ 361,570.95	$ 379,420.53	$ 398,155.72	$        417,820.59
Purchase Price	$ (5,250,000.00)
Resale Value - Going out cap - 6.5%						$     6,428,009.12
Selling Expense - 5%						$      (321,400.46)
TOTal Free cash flow [E]	$ (5,250,000.00)	$ 344,565.00	$ 361,570.95	$ 379,420.53	$ 398,155.72	$     6,524,429.25
Present value of Free cash flow	$ (5,250,000.00)	$ 307,647.32	$ 288,242.15	$ 270,064.04	$ 253,035.16	$     3,702,136.38
NPV	$     (428,874.96)

Step 4: Calculate IRR for levered cash flows

Levered cash flow can be calculated by subtracting the Interest and capex expenses from Unlevered cash flow shown in Step 3.

IRR is the interest rate that gives a NPV of zero.

In this cash if you sum up the Total Levered cash flow it comes to a Negative Value which is - $1,549,955, which means we have a negative IRR situation.

By calculating the approximate interest rate and calculating PV and NPV, the IRR comes to -6.97%.

A negative IRR would mean that the proposed project or investment is expected to cost more than it returns, or lose value for the company.

Timeline	Year 0	Year 1	Year 2	Year 3	Year 4	Year 5
Levered Cash Flow [E-C-D]	$       (5,250,000)	$          85,631	$          65,179	$          45,903	$          27,721	$           3,475,612
IRR	-6.970%
PV	$       (5,250,000)	$          92,046	$          75,312	$          57,012	$          37,009	$           4,987,882
NPV	$                   (738)