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

A). in the first part we need to calculate net operating income (NOI) for 5 years from income approach.

year	1	2	3	4	5
Gross rental income (exp growth 5% per year)	540,000	567,000	593,350	625,117.5	656,373.37
other income (exp growth 3%per year)	18,000	18,540	19,096.2	19,669.08	20,259.158
potential gross income [1]	558,000	585,540	612,446.2	644,786.58	676,632.528
Vacancy and collection losses (5% of the potential gross income) [2]	(27,900)	(29,277)	(30,622.31)	(32,239.32)	(33,831.626)
Operating expenses (35% of the effective gross income) i.e( potential- vacancy) [3]	(185,535)	(194,692.05)	(203,638.36)	(214,391.53)	(224,980.31)
Net operating income [1] -[2] -[3]	344565	361,571(appx)	378,185.53	398,155.73	417,820.59

  

------> now we need to calculate net present value of the unlevered cash flow

So, value at time zero = NOI OF YEAR 1 / GOING in cap rate

= 344565/.065

= 5,301,000

So, NPV = -5,301,000 + 344,565/1.12 + 361,571/(1.12)^2+ 378,185.53/(1.12)^3 + 398155.73/(1.12)^4 + 417,820.59/(1.12)^5

= -3,945,807

B)