Question

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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 1st 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

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 :

Particulars	Year 1 $	Year2 $	Year 3 $	Year 4 $
Adjusted Gross Income	95,000.00	95,000.00	95,000.00	95,000.00
Less : Debt expense See note 1	-120000	-115200	-110400	-105600
Add : Rental Income See note 2	194400	209952	226748	244888
Less : Vacancy & Collection Loss ( 3% + 2% OF Rental Income)	- 9720	- 10498	- 11337	- 12244
Effective Gross Income	159680	179254	200011	222044
Less : ( Annual Operating Expenses - Miscellenious Yearly Income ) i.e. 35% of EGI - $ 800	-55088	- 61939	- 69204	- 77715
Before Tax Cash Flow	104592	117315	130807	144329
Less : Tax at 28%	29286	32848	36626	40412
After Tax Cash Flow	75306	84467	94181	103917

Note 1 : Debt Expense

Analysis of Given Data,

Purchase price = $2,000,000 ; Estimated value of land = $500,000 ;

Hence, Total Loan Amount = $2,500,000

Anticipated mortgage terms:

a) Loan to value ratio = .80 i.e. $ 2,000,000

b) Interest rate = 6%

c) Years to maturity = 25

Hence each year repayment of Principal = $(2000000/25) = $ 80000

Interest on Loan : for Year 1

$ 2000000 x 6% = $ 120000

Year 2: $ ( 2000000-80000) x 6% = $ 115200

Year 3 : $ ( 2000000-80000 - 80000) x 6% = $ 110400

Year 4 : $ 2000000-80000-80000-80000) x 6% = $ 105600

Note 2 : Rental Income

Year 1 : $ 450 x 36 units x 12 =$194400

Year 2 :$ 194400 x 1.08 = $209952

Year 3 :$ 209952 x 1.08 = $226748

before-tax and after-tax equity reversion

It is given that Proportion by which property is expected to appreciate during the holding period is 5% a year and Estimated selling expenses as proportion of future sales price is 5%. Also there is Prepayment penalty which is 2% of outstanding balance

Before Tax Equity Revision :

$ ( 2500000 x 1.05 x 1.05 x 1.05 x 1.05) - ( 2000000 - 400000) - (( 2000000 - 400000) x 2% = $ 1406766

After Tax Equity Revision : $  1406766 x (1- 0.28) = $ 1012871

b. For the first year of operation the:

(1) Overall (cap) rate of return = ($ 75306 + 84467 + 94181 +103917 / $ 1012871) x 100 = 35.33%

(2) Equity dividend rate = ($ 75306 / $ 1012871) x 100 = 7.43%

(3) Gross income multiplier =

$ ( 75306 + 84467 + 94181 +103917 ) / ( 159680 + 179254 + 200011 + 222044 ) = 0.3265  

(4) Debt coverage ratio = $ 2000000 / 1406766 = 1.42

Here, we taken before tax amounts.

c. The after-tax net present value =

$ ( 75306 / ( 1.11 ) + 84467/ (1.11)² + 94181 / (1.11 )³ +103917/ ( 1.11)⁴ ) - $ 1012871 x 11% = 162300

after-tax internal rate of return =

(($ 75306 + 84467 + 94181 +103917 / $ 1012871) x 100) / 4 = 35.33%/4 = 8.8325%

d. Is this an investment that should be considered?

Even if NPV is positive but Internal rate of retuen is less than cost of Equity project should not be considered.

Year 4 : $226748 x 1.08 = $ 244888