Question

Assume that you are an investment analyst preparing an analysis of an investment opportunity for a client. Your client is considering the acquisition of an apartment complex from a developer at the point in time when the apartments are ready for first occupancy. Your have developed the following information.

1) Number of units = 36

2) First year market rent per unit = $450 per month

3) Rent is projected to increase by 8% each year

4) Annual vacancy rate = 3% of PGI

5) Annual collection loss = 2% of PGI

6) Annual operating expense = 35% of EGI

7) Miscellaneous yearly income (parking and washers/dryers) = $800

8) Monthly miscellaneous income is expected to remain constant

9) Purchase price = $2,000,000

10) Estimated value of land = $500,000

11) Anticipated mortgage terms:

a) Loan to value ratio = .80

b) Interest rate = 6%

c) Years to maturity = 25

d) Points charged = 3

e) Prepayment penalty = 2% of outstanding balance

f) Level payment, fully amortized

g) Fixed interest rate, annual payments

12) Anticipated holding period = 4 years

13) Proportion by which property is expected to appreciate during the holding period -- 5% a year

14) Estimated selling expenses as proportion of future sales price = 5%

15) Marginal income tax rate for the client = 28%

16) It is assumed that the property is put into service on January 1 st and sold on December 31st

17) Assume the client is "active" in the property management

18) It is assumed that the client has an adjusted gross income of $95,000 and has no other passive income not offset by other passive losses (for each year of the anticipated holding period)

19) Client's minimum required after tax rate of return on equity = 11%

Calculate: a. The before-tax and after-tax cash flows for each year of the holding period and the before-tax and after-tax equity reversion.

b. For the first year of operation the: (1) Overall (cap) rate of return (2) Equity dividend rate (3) Gross income multiplier (4) Debt coverage ratio

c. The after-tax net present value and the after-tax internal rate of return.

d. Is this an investment that should be considered? Explain.

Answer 1

Rent per year is calculated as $450 per month for 12 months and for 36 apartments.

=$450*12*36

=$194,400

Annual increment in rent is 8%

	First year	second year	3 rd year	4th year
Anticipated rent growing @8%	$194,400.00	$209,952.00	$226,748.16	$244,888.01

Loan value =$2,000,000 * 0.8 =$1,600,000.

Down payment =$400,000

therefore, cash paid at the time of disbursal of the loan =$1,600,000 * 3%=$48,000

Loan schedule

Year	Principal outstanding @ beginning	Interest	EMI	Principal repayment	Principal @ end of the year
1	$1,600,000.00	$96,000.00	$125,162.75	$29,162.75	$1,570,837.25
2	$1,570,837.25	$94,250.24	$125,162.75	$30,912.52	$1,539,924.74
3	$1,539,924.74	$92,395.48	$125,162.75	$32,767.27	$1,507,157.47
4	$1,507,157.47	$90,429.45	$125,162.75	$34,733.30	$1,472,424.17

Prepayment fees =$1,472,424.17*2% =$29,448.48

Value of the property at the end of holding period:

	1st year	2nd year	3rd year	4th year
Value of the property@ end of the year	$2,100,000.00	$2,205,000.00	$2,315,250.00	$2,431,012.50

Selling expenses of the property in the year of sale =5% of$2,431,012.50

=$121,550.63

Overall (cap) rate of return

Capitalization Rate = Net OperatingIncome / Current Market Value

Calculation of Net operating Income
Total rent	$     184,797
Annual operating expense	$     (64,679)
Miscellaneous yearly income	$             800
Net Operating Income(NOI)	$     120,918
Market Value at T0	$ 2,000,000
Capitalization Rate	6.05%

Equity dividend rate

EDR = BTECF / Equity investment

Where,

BTECF = Before-Tax Equity Cash Flow

Equity Investment = Total InvestmentCost – Loan Amount

Calculation of Equity dividend rate
Net Operating Income(NOI)	$120,917.82
an annual debt service	($129,962.75)
Before-Tax Equity Cash Flow	($9,044.93)
Equity Investment	$400,000
Equity dividend rate	-2.26%

Gross income multiplier = PropertyValue/ Gross annual rental Income

Calculation of Gross incomemultiplier
Market Value	$    2,000,000
Gross Rental Income	$        194,400
Gross income multiplier	10.29x

DSCR = Net Operating Income /Total Debt Service

Calculation of Debt coverage ratio
Net Operating Income(NOI)	$        120,918
Total Debt Service	$        125,163
DSCR	0.97x